{"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n_DHT_CONST := 2.5;\n\n#F TDHT(, ) - RDFT Nonterminal\nClass(TDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosInt(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> PkDHT1(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DHT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\n_DHTtoRDFT := N -> DirectSum(I(2), Tensor(I(N/2-1), F(2)));\n\n#F TXMatDHT() - X-matrix to translate a RC(DFT(N)) -> DHT(2*N)\nClass(TXMatDHT, TaggedNonTerminal, rec(\n abbrevs := [ (n) -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> _DHTtoRDFT(self.params[1]) * TConjEven(self.params[1]).terminate(),\n SmallRandom := () -> Random([2,4,6,8,10,12,16,18,24,30,32]),\n doNotMeasure := true\n));\n\n\n#F Translate DHT into RDFT\nNewRulesFor(TDHT, rec(\n DHT_DFT_tSPL := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]), # and t.hasTags(),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TXMatDHT(N).withTags(tags),\n TRC(DFT(N/2)).withTags(tags)\n ]]),\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\n\nNewRulesFor(TXMatDHT, rec(\n TXMatDHT_TConjEven := rec(\n switch := true,\n applicable := (self, t) >> IsEvenInt(t.params[1]),\n children := (self, t) >> let(N := t.params[1], tags := t.getTags(),\n [[\n TConjEven(N).withTags(tags),\n ]]),\n apply := (self, t, C, Nonterms) >> _DHTtoRDFT(t.params[1]) * C[1]\n )\n));\n", "meta": {"hexsha": "b626b4696baa437164bd9deee9c8d31510211121", "size": 1854, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dht.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/common/dht.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/common/dht.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 31.9655172414, "max_line_length": 110, "alphanum_fraction": 0.5469255663, "num_tokens": 619, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660687, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.44609739168276513}} {"text": "#\n# Read(\"~/Workspace/Chevalley.gap/init.gi\"); Read(Filename(home_dir,\"load.gi\")); Read(Filename(test_dir,\"chvadj.test.gi\"));\n#\n# Read(\"~/Workspace/Chevalley.gap/init.gi\"); Read(Filename(test_dir,\"chvadj.test.init.gi\")); Read(Filename(test_dir,\"chvadj.test.gi\"));\n#\n# Read(Filename(test_dir,\"chvadj.test.gi\"));\n#\n\nsys:=ChevalleyAdj(\"F\",4,GF(2));\nPrint(\"Created ChevalleyAdj \",sys,\"\\n\");\nPrint(\"\\t[\",IsChevalleyAdj(sys)=true,\"] IsChevalleyAdj(sys)=true\\n\");", "meta": {"hexsha": "4dab5417cf3d4028b594d097a175f75a9c253cac", "size": 456, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test/chvadj.test.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test/chvadj.test.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test/chvadj.test.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.4545454545, "max_line_length": 135, "alphanum_fraction": 0.6951754386, "num_tokens": 148, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6992544210587585, "lm_q2_score": 0.6370307806984444, "lm_q1q2_score": 0.44544658975389967}} {"text": "\nInstallMethod(NilpotentChv,\n \"NilpotentChv element in simple Lie type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n local object,\n B,admat,l;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then\n coeffs:=List(coeffs,i->[i[1],One(ring(sys))*i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then\n Error(\"NilpotentChv: The coefficients ar not in indicated ring.\");\n fi;\n\n object:=Objectify(NewType(NewFamily(\"NilpotentChvFamily\"),\n IsAttributeStoringRep and\n IsNilpotentChv and\n IsAdditiveElementWithInverse and\n IsAdditiveElementWithZero),\n rec());\n\n SetchevalleyAdj(object,sys);\n\n # Simplified form of the element (negative root vectors are also allowd \"2*Len..\")\n coeffs:=Filtered(List([1..2*Length(positiveRoots(sys))],\n i->[i,One(ring(sys))*Sum(List(Filtered(coeffs,\n j->j[1]=i),\n k->k[2]))]),\n l->l[2]<>Zero(ring(sys)));\n\n Setcoefficients(object,coeffs);\n\n B:=Basis(lieAlgebra(sys));\n if coeffs<>[] then SetLieAlgebraElement(object,Sum(coeffs,i->i[2]*B[i[1]]));\n else SetLieAlgebraElement(object,Zero(lieAlgebra(sys))); fi;\n SetLieAlgebraCoeffs(object,Coefficients(B,LieAlgebraElement(object)));\n\n# l:=Length(PRoots(R));\n# admat:=AdjointMatrix(B,LieAlgebraElement(e));\n# SetPositiveAde(object,List([1..l],i->admat[i]{[1..l]}));\n \n SetName(object,Concatenation(\"\"));\n return object;\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsPolynomialRing],\n function(e,inel)\n local sys,\n check;\n\n sys:=chevalleyAdj(e);\n\n if not IsPolynomialRing(inel) then\n Error(\"Ascend NilpotentChv: The new ring is not a polynomial ring to embed in!\\n\");\n elif CoefficientsRing(inel)<>ring(sys) then\n Error(\"Ascend NilpotentChv: CoefficientsRing and ring(sys) do not coincide!\\n\");\n fi;\n \n return NilpotentChv(ChevalleyAdj(sys,inel),List(coefficients(e),i->[i[1],One(inel)*i[2]]));\nend);\n\nInstallMethod(Ascend,\n \"If possible embed the parameters in a polynomial ring with coefficients ring the base ring\",\n [IsNilpotentChv,IsChevalleyAdj],\n function(e,sys)\n local syse,\n check;\n\n syse:=chevalleyAdj(e);\n\n if not IsPolynomialRing(ring(sys)) then\n Error(\"The new ring is not a polynomial ring to embed in.\");\n elif CoefficientsRing(ring(sys))<>ring(syse) then\n Error(\"CoefficientsRing and ring(syse) do not coincide.\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],One(ring(sys))*i[2]]));\nend);\n\nInstallMethod(\\*,\n \"multiplication by scalar for nilpotent elements s*e\",\n [IsRingElement,IsNilpotentChv],\n function(s,e)\n local sys;\n\n sys:=chevalleyAdj(e);\n if not s in ring(sys) then\n Error(\"Scalar*NilpotentChv: Scalar not in ring of nilpotent!\\n\");\n fi;\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],s*i[2]]));\nend);\n\nInstallMethod(\\+,\n \"addition for nilpotent elements e1+e2\",\n [IsNilpotentChv,IsNilpotentChv],\n function(e1,e2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(e1);\n sys2:=chevalleyAdj(e2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then\n Error(\"NilpotentChv+NilpotentChv: Not in the same family!\\n\");\n fi;\n \n return NilpotentChv(sys1,Concatenation(coefficients(e1),coefficients(e2)));\nend);\n\nInstallMethod(AdditiveInverseMutable,\n \"additive inverse for nilpotent elements -e1\",\n [IsNilpotentChv],\n function(e)\n local sys;\n\n sys:=chevalleyAdj(e);\n \n return NilpotentChv(sys,List(coefficients(e),i->[i[1],-i[2]]));\nend);\n\nInstallMethod(ZeroMutable,\n \"Zero vector of the Lie algebra\",\n [IsNilpotentChv],\n function(e)\n local sys;\n \n return NilpotentChv(chevalleyAdj(e),[]);\nend);\n", "meta": {"hexsha": "6d404a60c279bdce9dfef43290f6db8c8ea38821", "size": 5268, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/nilchv.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/nilchv.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/nilchv.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.3134328358, "max_line_length": 107, "alphanum_fraction": 0.5034168565, "num_tokens": 1199, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.445071066461832}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# ColDirectSum\n# ==========================================================================\nClass(ColDirectSum, BaseOverlap, rec(\n #-----------------------------------------------------------------------\n abbrevs := [ \n function(arg) \n arg:=Flat(arg); \n return [arg[1], arg{[2..Length(arg)]}];\n end ],\n #-----------------------------------------------------------------------\n new := meth(self, overlap, spls)\n return self._new(0, overlap, spls);\n end,\n #-----------------------------------------------------------------------\n dims := meth(self)\n local ovdim;\n\tovdim := self.ovDim(self.overlap,\n\t List(self._children, t -> t.dimensions[1]));\n\treturn [ ovdim[3] - ovdim[2] + 1, # max - min + 1\n\t Sum(self._children, t -> t.dimensions[2]) ];\n end,\n #-----------------------------------------------------------------------\n toAMat := meth(self) \n return \n\t AMatSPL(\n\t Sparse(\n\t\t self._coloverlap(\n\t\t List(self._children, t -> t.dimensions[1]),\n\t\t self.overlap\n\t\t )\n\t )\n\t ) *\n\t DirectSumAMat(List(self._children, AMatSPL));\n end,\n));\n\nColDirectSum._transpose_class := RowDirectSum;\nRowDirectSum._transpose_class := ColDirectSum;\n", "meta": {"hexsha": "9fc6e37d40ad33c6edf2e565ffdd544f9a729ec0", "size": 1432, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/ColDirectSum.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/ColDirectSum.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/ColDirectSum.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 31.8222222222, "max_line_length": 76, "alphanum_fraction": 0.3868715084, "num_tokens": 295, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754371026368, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.4450710592454823}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#P Permutations\n#P ------------\n#P\n#P Under different circumstances different objects are called permutations,\n#P even in the context of linear algrebra.\n#P\n#P Following list describes these objects and their representation in SPIRAL:\n#P\n#P 1. Regular permutations\n#P (a) in cycle notation : (1,2)(3,4)\n#P (b) as lists : [2,1,4,3]\n#P (c) as index space mapping function: i -> i+1 mod N\n#P\n#P 2. Parametrized permutation classes\n#P [For example stride permutations L(size,str) | size mod str = 0]\n#P Represented as a construction function, which returns an index mapping\n#P function - (c) above.\n#P\n#P Conversions: ListPerm (b) <- (a) [gap.perm]\n#P PermList (a) <- (b) [gap.perm]\n#P PermFunc (a) <- (c) [spiral.spl.perm]\n#P ListPermFunc (b) <- (c) [spiral.spl.perm]\n#P\n#P -------------------\n\n#F PermFunc(, ) . . . . . convert perm. function into explicit GAP perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F GAP permutation. Recall that GAP permutations are 1-based, and are in cycle\n#F representation.\n#F\nPermFunc := (func, size) ->\n PermList( List([0..size-1], func) + 1 );\n\n#F PermFunc(, ) . . . . . convert perm. function into explicit list perm.\n#F\n#F PermFunc converts a 0-based permutation function used in SPLs, into an explicit\n#F 1-based list permutation. List permutations can be converted to GAP permutations\n#F using PermList. Alternatively PermFunc can be used, wihch returns GAP permutation.\n#F\nListPermFunc := (func, size) ->\n List([0..size-1], func) + 1;\n\n# ==========================================================================\n# FuncClass\n#\n# Base class for symbolic functions\n# ==========================================================================\nClass(FuncClass, BaseMat, Function, rec(\n #-----------------------------------------------------------------------\n # Must be implemented in subclasses\n #-----------------------------------------------------------------------\n lambda := self >> Error(\"not implemented\"), \n domain := self >> Error(\"not implemented\"), \n range := self >> Error(\"not implemented\"), \n\n #-----------------------------------------------------------------------\n _perm := true,\n isReal := True,\n isPermutation := self >> false,\n perm := self >> Checked(self.isPermutation(), PermFunc(x->self.lambda().at(x), self.range())),\n\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(\n\tself.name, \"(\", PrintCS(self.params), \")\", When(self.transposed, \".transpose()\")),\n #-----------------------------------------------------------------------\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params,\n dims := self >> [self.range(), self.domain()],\n\n advdims := self >> [ [[ self.range() ]], [[ self.domain() ]] ],\n\n # size along each dimension, for a multidimensional range\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advrange := self >> [[ self.range() ]],\n\n # size along each dimension, for a multidimensional domain\n # for compatibility with ClassSPL, we wrap this into another list \n # (list of outputs, since ClassSPL can have >1 output)\n advdomain := self >> [[ self.domain() ]],\n\n # dimensionality of range (1-d, 2-d, etc)\n advrangeDim := self >> Length(self.advrange()[1]),\n # dimensionality of domain (1-d, 2-d, etc)\n advdomainDim := self >> Length(self.advdomain()[1]),\n #-----------------------------------------------------------------------\n toAMat := self >> Gath(self).toAMat(),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >> costMul(0) - costMul(0),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(transposed := not self.transposed )),\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(),\n #-----------------------------------------------------------------------\n normalizedArithCost := self >> 0,\n #-----------------------------------------------------------------------\n free := self >> Union(List(self.params, FreeVars)),\n #-----------------------------------------------------------------------\n # Rewrite rules support \n #\n from_rChildren := (self, rch) >> CopyFields(ApplyFunc(ObjId(self), rch), \n\trec(transposed:=self.transposed)),\n\n # NOTE: self.transposed not exposed\n rChildren := self >> self.params, \n\n rSetChild := meth(self, n, newChild)\n self.params[n] := newChild;\n # self.canonizeParams(); ??\n\tself.dimensions := self.dims();\n end,\n # ----------------------------------------------------------------------\n checkParams := meth(self, params)\n local nargs, nump;\n\tnargs := NumArgs(self.def);\n\tnump := Length(params);\n\tif nargs <> -1 and nargs <> nump then\n Error(self.name, \" needs \", NumArgs(self.def), \" parameters: \",\n\t\tParamsFunc(self.def), \"\\n\");\n\tfi;\n end,\n #-----------------------------------------------------------------------\n canonizeParams := meth(self, params)\n local A, nump;\n\tnump := Length(params);\n\tif IsBound(self.abbrevs) then\n for A in self.abbrevs do\n if NumArgs(A) = -1 or NumArgs(A) = nump then\n\t\t return ApplyFunc(A, params);\n\t\tfi;\n\t od;\n return params;\n\telse\n return params;\n\tfi;\n end,\n #-----------------------------------------------------------------------\n __call__ := meth(arg)\n local result, self, params, lkup, h;\n self := arg[1];\n params := arg{[2..Length(arg)]};\n params := self.canonizeParams(params);\n self.checkParams(params);\n\n h := self.hash;\n if h<>false then\n lkup := h.objLookup(self, params);\n if lkup[1] <> false then return lkup[1]; fi;\n fi;\n \n result := SPL(WithBases(self, rec(params := params, transposed := false)));\n result := Inherit(result, ApplyFunc(result.def, params));\n\tresult.dimensions := result.dims();\n \n if h<>false then return h.objAdd(result, lkup[2]);\n else return result;\n fi;\n end,\n\n# obsolete\n# checkInverse := self >> Checked(self.isPermutation(),\n# PermFunc(self.direct, self.range()) * PermFunc(self.inverse, self.domain())),\n));\n\nClass(PermClass, FuncClass, rec(\n isPermutation := self >> true,\n toAMat := self >> Gath(self).toAMat(),\n equals := (self, other) >> ObjId(other) = ObjId(self) and self.params=other.params\n));\n", "meta": {"hexsha": "5eeb94fc7b4ab3f15f8391facbe6595d572a87ba", "size": 6927, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/PermClass.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/PermClass.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/PermClass.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 39.5828571429, "max_line_length": 98, "alphanum_fraction": 0.5006496319, "num_tokens": 1589, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300698514777, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.4449897519246225}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F CondPat(, , , ..., , , [])\n#F\n#F CondPat is a conditional control-flow construct similar to Cond, but instead\n#F of normal boolean conditions it uses patterns that are matched against its\n#F first argument . CondPat returns the result that corresponds to the\n#F first matched pattern. If nothing matches is returned.\n#F\n#F Note: resultElse is optional\n#F \n#F CondPat is implemented as a function with delayed evaluation, and will\n#F only evaluate the result that corresponds to the matched patterns, all\n#F other results will not be evaluated, for example:\n#F\n#F CondPat(mul(X,2), [mul, @, 2], Print(\"yes\"), [add, @, 2], Print(\"no\"));\n#F\n#F will only execute Print(\"yes\") -- as expected.\n#F\n\nCondPat := UnevalArgs(function(arg)\n local usage, i, pat, obj;\n \n\tusage := \"CondPat(, , , ..., , , )\";\n \n\tif Length(arg) < 3 then \n\t\tError(usage); \n\tfi;\n\n obj := Eval(arg[1]);\n i := 2;\n while i <= Length(arg)-1 do\n pat := Eval(arg[i]);\n\t\tif PatternMatch(obj, pat, empty_cx()) then \n\t\t\treturn Eval(arg[i+1]); \n\t\tfi;\n\t\ti := i+2;\n od;\n if i=Length(arg) then\n\t\treturn Eval(Last(arg));\n else \n\t\tError(\"CondPat: No 'else' result, and no patterns match\");\n fi;\nend);\n", "meta": {"hexsha": "63b7ab21340ac871515f1582e3e29c4de071c4e5", "size": 1387, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/rewrite/condpat.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/rewrite/condpat.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/rewrite/condpat.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 28.8958333333, "max_line_length": 84, "alphanum_fraction": 0.6575342466, "num_tokens": 410, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.658417500561683, "lm_q2_score": 0.6757646075489392, "lm_q1q2_score": 0.44493524387041916}} {"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n\n# Radix n kernel for FFTE, targeting ARM SVE\n\nbuildSVEKernel_a := function(n, kk, conf, opts)\n local vlen, name, suffix, filesuffix, t, j, k, l, m, tmp1, tmp2, tmp3,\n gi, g, gc, si, ss, s, sc, dft, rts, rt, opcnts, dfts, dftc, i, twt, twf, twl, tws, twc,\n cl, cc, c, clp, useFMA, _FMA, lp;\n\n name := DFTnameStr(n, kk);\n suffix := \"a\";\n filesuffix := \"sve_\";\n# suffix := \"_j\";\n Print(\"\\n\\n// == Generating \\\"\", name, \"\\\" ==================================================\\n\\n\"); \n\n vlen := TInt;\n useFMA := When(IsBound(conf.useFMA), conf.useFMA, true);\n _FMA := When(useFMA, FMA, p -> p);\n\n # variables\n t := var.fresh_t(\"t\", TInt);\n j := var.fresh_t(\"j\", TInt);\n k := V(0);\n l := var.fresh_t(\"l\", TInt);\n m := V(1);\n lp := var.fresh_t(\"lp\", TPtr(TInt));\n# mp := var.fresh_t(\"mp\", TPtr(TInt));\n\n\n # temp arrays\n tmp1 := var.fresh_t(\"R\", TArray(TVectSVE, 2*n));\n tmp2 := var.fresh_t(\"S\", TArray(TVectSVE, 2*n));\n tmp3 := var.fresh_t(\"T\", TArray(TVectSVE, 2*n));\n\n # gather\n gi := _i -> VGath_L(1, vlen, 2*(k + j*m + _i*l*m));\n g := RulesSums(SumsSPL(VStack(List([0..n-1], gi)), opts));\n gc := Compile(opts.codegen(g, tmp1, X, opts), opts);\n \n # scatter\n si := _i -> ScatH(1, 1, 2*n*j+_i, 2*n);\n ss := SumsSPL(HStack(List([0..2*n-1], si)), opts);\n s := RulesSums(SubstTopDown(ss, @(1, ScatAcc), e->Scat(@(1).val.func)));\n sc := Compile(opts.codegen(s, Y, tmp3, opts), opts);\n\n # generate DFT kernel\n dft := RC(DFT(n, kk));\n rts := AllRuleTrees(dft, opts);\n opcnts := List(rts, r -> [ Length(Collect(CodeRuleTree(r, opts), @(1, [add, sub, mul], e->e.t=TReal))), r]);\n rt := Minimum(opcnts)[2];\n dfts := SumsRuleTree(rt, opts);\n dftc := BlockUnroll(opts.codegen(dfts, tmp2, tmp1, opts), opts);\n \n # twiddles as lookup table\n i := var.fresh_t(\"i\", 2*n);\n twt := var.fresh_t(\"TW\", TPtr(TReal)); \n twf := Lambda(i, cond(\n eq(i, 0), 1, \n eq(i, 1), 0, \n sve_gath(nth(twt, 2*((n-1)*j) + 2 * idiv(i, 2) + (imod(i, 2) - 2)).toPtr(TReal), TInt, opts.pg, 2*(n-1))\n ));\n \n # debug twiddles\n twl := Map(twf.tolist(), RulesStrengthReduce);\n DoForAll([0..Length(twl)-1], _i->Unparse(assign(nth(Y, _i), twl[_i+1]), CUnparser, 0, 1));\n tws := RCDiag(twf);\n twc :=BlockUnroll(unroll_cmd(opts.codegen(tws, tmp3, tmp2, opts)), opts);\n\n # stitch code fragments together\n cl := func(TVoid, \"transform\", [Y, X, twt, j, k, l, m, opts.pg], \n decl([tmp1, tmp2, tmp3], chain(gc, dftc, twc, sc)));\n cc := Compile(cl, opts);\n \n # fixup to push decls inside (?)\n c := func(TVoid, \"transform\", [Y, X, twt, j, l, opts.pg], \n decl(cc.vars, _FMA(cc.cmd.cmds[1].cmd)));\n \n # print Radix N FFTE kernel as function\n #PrintCode(name, c, opts);\n #PrintTo(name::\".c\", PrintCode(name, c, opts));\n \n ########################################################\n # version with j loop vectorized as m == 1, k == 0\n clp := func(TVoid, \"transform\", [Y, X, twt, lp], \n decl(c.cmd.vars::c.free()::[opts.pg, l], \n chain(\n assign(l, deref(lp)),\n sve_loopn(j, l, \n c.cmd.cmd\n )\n )\n )\n );\n\n # print Radix N FFTE kernel as function\n PrintCode(opts.FortranIze(name::suffix), clp, opts);\n PrintTo(name::filesuffix::suffix::\".c\", PrintCode(opts.FortranIze(name::suffix), clp, opts));\nend;\n\n\n\n\n", "meta": {"hexsha": "012d60ac9fe916cf3f0783131e46200063b8a9e6", "size": 3576, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "kernelgen/sve_a.gi", "max_stars_repo_name": "spiral-software/spiral-package-ffte", "max_stars_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "kernelgen/sve_a.gi", "max_issues_repo_name": "spiral-software/spiral-package-ffte", "max_issues_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "kernelgen/sve_a.gi", "max_forks_repo_name": "spiral-software/spiral-package-ffte", "max_forks_repo_head_hexsha": "19f751776c117e28bdbcc3d2530c895ad554d855", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-06-15T12:41:51.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:41:51.000Z", "avg_line_length": 34.3846153846, "max_line_length": 112, "alphanum_fraction": 0.5212527964, "num_tokens": 1246, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7549149868676283, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.44456123042008694}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nNewRulesFor(TICompose, rec(\n TICompose_DropTag := rec(\n applicable := t -> true,\n children := t -> [[ t.params[3] ]],\n apply := (t, C, Nonterms) -> ICompose(t.params[1], t.params[2], C[1])\n )\n));\n\n#F InitStreamSw()\n#F\n#F Example:\n#F opts := InitStreamSw(2);\n#F c := CodeRuleTree(opts.transforms.DFT(64), opts);\n#F me := CMatrix(c, opts);\n#F them := MatSPL(opts.transforms.DFT(64));\n#F InfinityNormMat(me-them);\n#F\nInitStreamSw := radix -> CopyFields(\n CplxSpiralDefaults, \n IntelC99Mixin, # uncomment this for C99 output (default = SSE2 intrinsics)\n rec(\n breakdownRules := rec(\n DFTDR := [CopyFields(DFTDR_tSPL_Pease, rec(precompute:=true)) ], \n DFT := [DFT_Base, DFT_CT ],\n TTensorI := [IxA_base, IxA_L_base, L_IxA_base, AxI_base],\n TCompose := [TCompose_tag],\n TICompose := [TICompose_DropTag],\n TDiag := [TDiag_base]\n ),\n\n transforms := rec(\n DFT := n -> DFTDR(n, radix, [AStream(radix)])\n ),\n\n# unparser := CMacroUnparserProg,\n\n globalUnrolling := radix\n));\n\n#F TestStreamSw(, , ) - software test of Pease DFT used for streaming hardware\n#F\n#F use_transpose = true: DRDFT\n#F use_transpose = false: DFTDR\n#F\nTestStreamSw := function(n, radix, use_transpose)\n local opts, t, rt, c, err, me, them;\n opts := InitStreamSw(radix);\n\n PrintErr(\"Compiling...\\n\");\n t := When(use_transpose, opts.transforms.DFT(n).transpose(), opts.transforms.DFT(n));\n rt := RandomRuleTree(t, opts);\n if rt = false \n then Error(\"No ruletrees.\"); fi;\n c := CodeRuleTree(rt, opts);\n\n PrintErr(\"Running and computing the code matrix...\\n\");\n me := CMatrix(c, opts);\n\n PrintErr(\"Comparing to the definition...\\n\");\n them := MatSPL(t);\n err := InfinityNormMat(me-them);\n\n if err < 1e-6 then PrintErr(t, \" -- \", GreenStr(\"OK\\n\")); \n else PrintErr(t, \" -- \", RedStr(\"FAIL\\n\")); fi;\nend;\n\nTestStreamSwPrint := function(n, radix, use_transpose)\n local opts, t, rt, c, err, me, them;\n opts := InitStreamSw(radix);\n\n t := When(use_transpose, opts.transforms.DFT(n).transpose(), opts.transforms.DFT(n));\n rt := RandomRuleTree(t, opts);\n if rt = false \n then Error(\"No ruletrees.\"); fi;\n c := CodeRuleTree(rt, opts);\n \n return PrintCode(\"function_name\", c, opts);\n# return rt;\nend;", "meta": {"hexsha": "13f2853897bb37c4520208b793119de6a021e3fe", "size": 2469, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/stream/sw.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/stream/sw.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/stream/sw.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 29.3928571429, "max_line_length": 104, "alphanum_fraction": 0.6148238153, "num_tokens": 747, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7310585786300049, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.444237373223837}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n_svctSizes := (N, p, v) -> Filtered([1..N], i->ForAll(Factors(i), j->j<=p) and IsInt(i/v^2));\n_defaultSizes := (func, default) -> ((arg) -> When(Length(arg) = 1, func(When(IsList(arg[1]), arg[1], [arg[1]])), func(default)));\n\n_parse := function(arglist)\n local isa, n, sizes, optrec;\n\n isa := \"f64re\";\n optrec := rec(interleavedComplex := true);\n\n if Length(arglist) = 0 then\n n := 1;\n elif Length(arglist) = 1 then\n if IsInt(arglist[1]) then\n n := arglist[1];\n elif IsList(arglist[1]) then\n n := arglist[1];\n else\n n := 0;\n isa := arglist[1];\n fi;\n elif Length(arglist) = 2 then\n n := arglist[1];\n isa := arglist[2];\n else\n n := arglist[1];\n isa := arglist[2];\n optrec := arglist[3];\n fi;\n\n sizes := When(IsList(n), n, List([1..n], i->2^i));\n\n return [sizes, isa, optrec];\nend;\n\n\ndoDft := function(arg)\n local sizes, opts, dpr, isa, trafos, t, optrec, dpbench, defaults;\n\n [sizes, isa, optrec] := _parse(arg);\n\n defaults := rec(\n breakdownRules := rec(\n DFT := [ DFT_Base, DFT_PD, DFT_CT, DFT_GoodThomas, DFT_Rader ],\n WHT := [ WHT_Base, WHT_BinSplit ],\n MDDFT := [ MDDFT_Base, MDDFT_RowCol ],\n TRC := [ TRC_tag ]\n ),\n unparser := CUnparserProg\n );\n opts := CopyFields(When(optrec.generateComplexCode, CplxSpiralDefaults, SpiralDefaults), defaults, optrec);\n opts := InitDataType(opts, isa);\n\n if opts.generateComplexCode then\n t := i -> RC(DFT(i));\n else\n t := When(IsBound(opts.tags), i -> ComplexT(DFT(i), opts).withTags(opts.tags), i ->ComplexT(DFT(i), opts));\n fi;\n opts.benchTransforms := List(sizes, k -> t(k));\n\n dpr := rec(verbosity := 0, timeBaseCases:=true);\n dpbench := spiral.libgen.DPBench(rec((Concat(isa, When(opts.interleavedComplex, \"_ic\", \"_sc\"))) := opts), dpr);\n if IsBound(optrec.verify) then dpbench.matrixVerify := optrec.verify; fi;\n\n return dpbench;\nend;\n\n# doDft auto-vectorization interface\n#b := doDft(10, \"f32re\", _autovect(IntelC, rec(interleavedComplex := true, language := \"c.icl.opt.core2\")));\n#b := doDft(16, \"f32c\", _autovect(IntelC, rec(interleavedComplex := true, language := \"c.icl.opt.core2\", generateComplexCode:=true)));\n\n_autovect := (cc, opts) -> CopyFields(opts, rec(\n useRestrict := true, \n looppragma := cc.looppragma,\n restrict := cc.restrict, \n postalign := cc.postalign,\n arrayBufModifier := Concat(\"static \", cc.alignmentSpecifier()), \n arrayDataModifier := Concat(\"static \", cc.alignmentSpecifier()),\n compileStrategy:=NoCSE\n));\n\nbenchScalar := () -> rec(\n float := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doDft(s, \"f32re\", rec(interleavedComplex := true)), 13)\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doDft(s, \"f32re\", rec(interleavedComplex := false)), 13)\n )\n ),\n double := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doDft(s, \"f64re\", rec(interleavedComplex := true)), 13)\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doDft(s, \"f64re\", rec(interleavedComplex := false)), 13)\n )\n )\n);\n\n", "meta": {"hexsha": "edf59e82c309d87f0be3fd35d1db4272533debab", "size": 3349, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/bench.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/bench.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/bench.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 31.8952380952, "max_line_length": 134, "alphanum_fraction": 0.5765900269, "num_tokens": 1005, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702761768249, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.4431726198312635}} {"text": "#############################################################################\n##\n#W listops.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n## AG_IsCorrectAutomatonList( , )\n##\nInstallGlobalFunction(AG_IsCorrectAutomatonList,\nfunction(list, invertible)\n local len, deg, i, j, sym, semi;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 1 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if not IsInt(list[i][j]) then\n return false;\n fi;\n if list[i][j] > len or list[i][j] < 1 then\n return false;\n fi;\n od;\n\n if not list[i][deg + 1] in sym then\n if not list[i][deg + 1] in semi then\n return false;\n fi;\n if invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n fi;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_IsCorrectRecurList( , )\n##\nInstallGlobalFunction(AG_IsCorrectRecurList,\nfunction(list, invertible)\n local len, deg, i, j, k, sym, semi, inv_states;\n\n if not IsDenseList(list) then\n return false;\n fi;\n\n len := Length(list);\n if len = 0 then\n return false;\n fi;\n\n for i in [1..len] do\n if not IsDenseList(list[i]) then\n return false;\n fi;\n if Length(list[i]) <> Length(list[1]) then\n return false;\n fi;\n od;\n\n deg := Length(list[1]) - 1;\n if deg < 2 then\n return false;\n fi;\n\n sym := SymmetricGroup(deg);\n semi := FullTransformationSemigroup(deg);\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j] > len or list[i][j] < -len or list[i][j] = 0 then\n return false;\n fi;\n elif IsList(list[i][j]) then\n if not IsDenseList(list[i][j]) then\n return false;\n fi;\n for k in list[i][j] do\n if (not IsInt(k)) or k > len or k < -len or k = 0 then\n return false;\n fi;\n od;\n else\n return false;\n fi;\n od;\n\n\n # Check that everything is correct here\n if (not IsPerm(list[i][deg + 1])) and (not IsTransformation(list[i][deg + 1])) then\n return false;\n elif LargestMovedPoint(list[i][deg + 1]) > deg then\n return false;\n elif IsTransformation(list[i][deg + 1]) and invertible and list[i][deg + 1]^-1=fail then\n return false;\n fi;\n od;\n\n\n# check if there is x^-1 in the list, while x is not invertible\n inv_states:=[];\n for i in [1..len] do\n if AG_IsInvertibleStateInList(i,list) then Add(inv_states,i); fi;\n od;\n\n for i in [1..len] do\n for j in [1..deg] do\n if IsInt(list[i][j]) then\n if list[i][j]<0 and not -list[i][j] in inv_states then\n return false;\n fi;\n else\n for k in list[i][j] do\n if k<0 and not -k in inv_states then\n return false;\n fi;\n od;\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ConnectedStatesInList(state, list)\n##\n## Returns list of states which are reachable from given state,\n## it does not check correctness of arguments\n##\nInstallGlobalFunction(AG_ConnectedStatesInList,\nfunction(state, list)\n local i, j, s, d, to_check, checked;\n\n d := Length(list[1]) - 1;\n\n to_check := [state];\n checked := [];\n\n while Length(to_check) <> 0 do\n for s in to_check do\n for i in [1..d] do\n if IsList(list[s][i]) then\n for j in AsSet(List(list[s][i],AbsInt)) do\n if (not j in checked) and (not j in to_check) then\n to_check := Union(to_check, [j]);\n fi;\n od;\n else\n if (not AbsInt(list[s][i]) in checked) and (not AbsInt(list[s][i]) in to_check) then\n to_check := Union(to_check, [AbsInt(list[s][i])]);\n fi;\n fi;\n od;\n checked := Union(checked, [s]);\n to_check := Difference(to_check, [s]);\n od;\n od;\n\n return checked;\nend);\n\n\n###############################################################################\n##\n## AG_IsTrivialStateInList( , )\n##\n## Checks whether given state is trivial.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsTrivialStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n # IsOne works for Transformation's\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> IsOne(list[s][deg+1]));\nend);\n\n\n###############################################################################\n##\n## AG_IsObviouslyTrivialStateInList( , )\n##\n## Checks whether given state is obviously trivial.\n## Works for lists generating self-similar groups.\n## Returns `true' if =(*,...,*)(), where\n## * could be either +- or [+-], or [].\n##\nInstallGlobalFunction(AG_IsObviouslyTrivialStateInList,\nfunction(state, list)\n local deg, check;\n\n check := function(s)\n if IsInt(s) then return state=AbsInt(s);\n else return s=[] or (Length(s)=1 and state=AbsInt(s[1]));\n fi;\n end;\n\n\n deg := Length(list[1]) - 1;\n if not IsOne(list[state][deg+1]) then return false; fi;\n # IsOne works for Transformation's\n return ForAll(list[state]{[1..deg]}, check);\nend);\n\n\n\n###############################################################################\n##\n## AG_IsInvertibleStateInList( , )\n##\n## Checks whether given state is invertible.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_IsInvertibleStateInList,\nfunction(state, list)\n local deg;\n deg := Length(list[1]) - 1;\n return ForAll(AG_ConnectedStatesInList(state, list),\n s -> (list[s][deg+1]^-1<>fail));\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInList( , , )\n##\n## Checks whether two given states are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInList,\nfunction(state1, state2, list)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list[s1][d+1] <> list[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list[s1][i], list[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_AreEquivalentStatesInLists( , , , )\n##\n## Checks whether two given states in different lists are equivalent.\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_AreEquivalentStatesInLists,\nfunction(state1, state2, list1, list2)\n local d, checked_pairs, pos, s1, s2, np, i;\n\n d := Length(list1[1]) - 1;\n checked_pairs := [[state1, state2]];\n pos := 0;\n\n while Length(checked_pairs) <> pos do\n pos := pos + 1;\n s1 := checked_pairs[pos][1];\n s2 := checked_pairs[pos][2];\n\n if list1[s1][d+1] <> list2[s2][d+1] then\n return false;\n fi;\n\n for i in [1..d] do\n np := [list1[s1][i], list2[s2][i]];\n if not np in checked_pairs then\n checked_pairs := Concatenation(checked_pairs, [np]);\n fi;\n od;\n od;\n\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_ReducedAutomatonInList( )\n##\n## Returns [new_list, list_of_states, old_states] where new_list is a new list\n## which represents reduced form of given automaton, i-th elmt of list_of_states\n## is the number of i-th state of new automaton in the old one.\n## old_states[i] is the number of state which corresponds to the i-th state\n## of the original automaton.\n##\n## First state of returned list is always first state of given one.\n## It does not remove trivial state, so it's not really \"reduced automaton\",\n## it just removes equivalent states.\n## TODO: write such function which removes trivial state\n##\n## Does not check correctness of list.\n##\n## WARNING: do *NOT* change it.\n##\nInstallGlobalFunction(AG_ReducedAutomatonInList,\nfunction(list)\n local i, n, triv_states, equiv_classes, checked_states, s, s1, s2,\n eq_cl, eq_cl_1, eq_cl_2, are_equiv, eq_cl_reprs,\n new_states, new_list, deg,\n reduced_automaton, state, states_reprs;\n\n n := Length(list);\n triv_states := [];\n equiv_classes := [];\n checked_states := [];\n deg := Length(list[1]) - 1;\n\n for s in [1..n] do\n if AG_IsTrivialStateInList(s, list) then\n triv_states := Union(triv_states, [s]);\n fi;\n od;\n\n equiv_classes:=[triv_states];\n for s1 in Difference([1..n], triv_states) do\n for s2 in Difference([s1+1..n], triv_states) do\n are_equiv := AG_AreEquivalentStatesInList(s1, s2, list);\n\n if s1 in checked_states then\n for eq_cl in equiv_classes do\n if s1 in eq_cl then\n eq_cl_1 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s1]]);\n eq_cl_1 := [s1];\n checked_states := Union(checked_states, [s1]);\n fi;\n if s2 in checked_states then\n for eq_cl in equiv_classes do\n if s2 in eq_cl then\n eq_cl_2 := StructuralCopy(eq_cl);\n break; fi; od;\n else\n equiv_classes := Union(equiv_classes, [[s2]]);\n eq_cl_2 := [s2];\n checked_states := Union(checked_states, [s2]);\n fi;\n\n if are_equiv then\n equiv_classes := Difference(equiv_classes, [eq_cl_1, eq_cl_2]);\n equiv_classes := Union(equiv_classes, [Union(eq_cl_1, eq_cl_2)]);\n fi;\n od;\n od;\n states_reprs := [1..n];\n for eq_cl in equiv_classes do\n for s in eq_cl do\n states_reprs[s] := Minimum(eq_cl);\n od;\n od;\n\n\n new_states := Set(states_reprs);\n new_list := [];\n\n for s in new_states do\n state := [];\n state[deg+1] := list[s][deg+1];\n for i in [1..deg] do\n state[i] := Position(new_states, states_reprs[list[s][i]]);\n od;\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states, List([1..n], i -> Position(new_states, states_reprs[i]))];\nend);\n\n\n###############################################################################\n##\n## AG_MinimalSubAutomatonInlist(, )\n##\n## Returns list representation of automaton given by which is minimal\n## subatomaton of automaton containing states .\n##\n## Does not check correctness of list.\n##\nInstallGlobalFunction(AG_MinimalSubAutomatonInlist,\nfunction(states, list)\n local s, new_states, state, new_list, i, deg;\n\n new_states := [];\n for s in states do\n new_states := Union(new_states, AG_ConnectedStatesInList(s, list));\n od;\n\n new_list := [];\n deg := Length(list[1]) - 1;\n\n for s in new_states do\n state := [];\n for i in [1..deg] do\n state[i] := Position(new_states, list[s][i]);\n od;\n state[deg+1] := list[s][deg+1];\n new_list := Concatenation(new_list, [state]);\n od;\n\n return [new_list, new_states];\nend);\n\n\n###############################################################################\n##\n## AG_PermuteStatesInList(, )\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_PermuteStatesInList,\nfunction(list, perm)\n local new_list, i, j, deg;\n\n deg := Length(list[1]) - 1;\n new_list := [];\n for i in [1..Length(list)] do\n new_list[i^perm] := [];\n for j in [1..deg] do\n new_list[i^perm][j] := list[i][j]^perm;\n od;\n new_list[i^perm][deg+1] := list[i][deg+1];\n od;\n\n return new_list;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateInList(, , , , )\n##\n## It's ProjectWord from selfs.g\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateInList,\nfunction(w, s, list, reduce, trivstate)\n local i, perm, d, proj, red, reduce_word;\n\n reduce_word := function(v)\n local len, red, x;\n len := 0;\n red := [];\n for x in v do\n if x <> trivstate then\n if len <> 0 and x = -red[len] then\n Remove(red, len);\n len := len - 1;\n else\n Add(red, x);\n len := len + 1;\n fi;\n fi;\n od;\n return red;\n end;\n\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n for i in [1..Length(w)] do\n Add(proj, list[w[i]][s^perm]);\n perm := perm * list[w[i]][d+1];\n od;\n if reduce then\n return reduce_word(proj);\n else\n return proj;\n fi;\nend);\n\n\n###############################################################################\n##\n## AG_WordStateAndPermInList(, , )\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_WordStateAndPermInList,\nfunction(w, s, list)\n local i, perm, perm_res, new_state, d, proj;\n d := Length(list[1])-1;\n proj := [];\n perm := ();\n perm_res := ();\n for i in [1..Length(w)] do\n new_state := list[w[i]][s^perm];\n Add(proj, new_state);\n perm := perm * list[w[i]][d+1];\n perm_res := perm_res * list[new_state][d+1];\n od;\n return [proj, perm_res];\nend);\n\n\n###############################################################################\n##\n## AG_ImageOfVertexInList(, , )\n##\n## Does not check correctness of arguments.\n##\nInstallGlobalFunction(AG_ImageOfVertexInList,\nfunction(list, s, seq)\n local deg, img, x;\n\n deg := Length(list[1]) - 1;\n img := [];\n for x in seq do\n Add(img, x^list[s][deg+1]);\n s := list[s][x];\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n## AG_DiagonalPowerInList(, )\n##\nInstallGlobalFunction(AG_DiagonalPowerInList,\nfunction(list, n, names)\n local d, nlist, nd, nalph, nstates, nperm,\n i, j, k, letter, n_letter, n_state, state,\n nnames;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nstates := Tuples([1..Length(list)], n);\n nlist := List([1..Length(nstates)], i -> []);\n nnames := List(nstates, s->List(s, i->names[i]));\n\n for i in [1..Length(nlist)] do\n nperm := [];\n state := nstates[i];\n for j in [1..nd] do\n letter := nalph[j];\n n_letter := [];\n n_state := [];\n for k in [1..n] do\n n_letter[k] := letter[k]^list[state[k]][d+1];\n n_state[k] := list[state[k]][letter[k]];\n od;\n nperm[j] := n_letter;\n nlist[i][j] := Position(nstates, n_state);\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n nnames := List(nnames, l->Concatenation(l));\n return [nlist, nnames];\nend);\n\n\n###############################################################################\n##\n## AG_MultAlphabetInList(, )\n##\nInstallGlobalFunction(AG_MultAlphabetInList,\nfunction(list, n)\n local d, nlist, nd, nalph, nperm,\n i, j, k, letter, n_letter, st;\n\n d := Length(list[1]) - 1;\n nd := d ^ n;\n nalph := Tuples([1..d], n);\n nlist := List(list, i -> []);\n\n for i in [1..Length(nlist)] do\n nperm := [];\n for j in [1..Length(nalph)] do\n letter := nalph[j];\n n_letter := [];\n st := i;\n for k in [1..n] do\n Add(n_letter, letter[k]^list[st][d+1]);\n st := list[st][letter[k]];\n od;\n nlist[i][j] := st;\n nperm[j] := n_letter;\n od;\n nlist[i][nd+1] := PermListList(nalph, nperm);\n od;\n\n return nlist;\nend);\n\n\n###############################################################################\n##\n## AG_HasDualInList()\n##\nInstallGlobalFunction(AG_HasDualInList,\nfunction(list)\n local i, j, p, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n for i in [1..d] do\n p := [];\n for j in [1..n] do\n p[j] := list[j][i];\n od;\n if PermListList([1..n], p) = fail then\n return false;\n fi;\n od;\n return true;\nend);\n\n\n###############################################################################\n##\n## AG_DualAutomatonList()\n##\nInstallGlobalFunction(AG_DualAutomatonList,\nfunction(list)\n local dual, d, n;\n d := Length(list[1]) - 1;\n n := Length(list);\n return List([1..d], i -> Concatenation(List([1..n], j -> i^list[j][d+1]),\n [PermList(List([1..n], j -> list[j][i]))]));\nend);\n\n\n###############################################################################\n##\n## AG_HasDualOfInverseInList()\n##\nInstallGlobalFunction(AG_HasDualOfInverseInList,\nfunction(list)\n return AG_HasDualInList(AG_InverseAutomatonList(list));\nend);\n\n\n###############################################################################\n##\n## AG_InverseAutomatonList()\n##\nInstallGlobalFunction(AG_InverseAutomatonList,\nfunction(list)\n local inv, d, i;\n d := Length(list[1]) - 1;\n inv := List(list, l -> Permuted(l, l[d+1]));\n for i in [1..Length(list)] do inv[i][d+1] := inv[i][d+1]^-1; od;\n return inv;\nend);\n\n\n#E\n", "meta": {"hexsha": "46feabccc68565e100d50b9c2a580f8cb234374a", "size": 17625, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/listops.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/listops.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/listops.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.9292786421, "max_line_length": 94, "alphanum_fraction": 0.5400283688, "num_tokens": 4920, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6688802735722128, "lm_q2_score": 0.6619228758499942, "lm_q1q2_score": 0.44274715428225}} {"text": "\nlocal reps,tori,labels,I,II,ords,blocks;\n\n\n#......Ross \nreps:=[[[1,1],[2,1],[3,1],[4,1],[5,1]], # D_5\n [[5,1],[4,1],[9,1],[7,1],[1,1]] # D_5(a_1)\n ];\n\nI:=[[],[]];\n\n#\n# The parabolic where the representative is distinguished\n#\nII:=[[],\n []];\n\nlabels:=[\"D_5\",\n \"D_5(a_1)\"\n ];\n\ntori:=[\n [],\n []\n ];\n\nblocks:=[];\n\nords:=[];\n\nreturn [reps,tori,labels,I,II,ords,blocks];\n", "meta": {"hexsha": "91dca283b9ba55be44d51d468228fb57d2b349e4", "size": 420, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/data/dataD5char2.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/data/dataD5char2.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/data/dataD5char2.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 13.125, "max_line_length": 57, "alphanum_fraction": 0.4357142857, "num_tokens": 160, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936430859597, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.44253102725349236}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(TDCT2, TDCT3, TDCT4);\n\n_DCT_CONST := 2.5;\n\n#######################################################################################\n# tSPL DCT rules\n\n\n# PDCT4_CT_SPL := rec(\n# isApplicable := P -> P > 2 and ForAny(DivisorPairs(2*P), d->IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# j := Ind(n/2),\n# T := Diag(Twid(2*N, m/2, 1, 1/2, 1/2, j)),\n#\n# Prm(Refl(N, 2*N-1, N, L(m*n, m))) *\n# IterDirectSum(j, j.range, Diag(BHN(m)) * C[1] * RC(T)) *\n# RC(L(m*n/4, n/2)) *\n# Tensor(I(m/2), C[2] * Diag(BHN(n))) *\n# Prm(Refl(N, 2*N-1, N, L(m*n, m)))\n# )\n# )\n#\n\n\n#F TDCT4(, tags) - Discrete Cosine Transform, Type IV, non-terminal\n#F Definition: (n x n)-matrix [ cos((k+1/2)*(l+1/2)*pi/n) | k,l = 0...n-1 ]\n#F Note: DCT4 is symmetric\n#F Example: DCT4(8)\nClass(TDCT4, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IVunscaled(self.params[1])),\n transpose := self >> Copy(self),\n SmallRandom := () -> Random([2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT4, rec(\n# DCT4_CT_tSPL := rec(\n# switch := false,\n#\n# applicable := (self, t) >> let(P:=t.params, P[1] > 2 and ForAny(DivisorPairs(2*P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])) and HasTags(t)),\n#\n# children := (self, t) >> let(tags := GetTags(t), N := t.params[1],\n# Map2(Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [\n# SetTag(TCompose([\n# TScat(Refl(N, 2*N-1, N, L(m*n, m))),\n# TTensorI(Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, APar, APar),\n# TRC(TDiag(fPrecompute(\n# fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n# ))),\n# TRC(TL(m*n/4, n/2, 1, 1)),\n# TTensorI(PRDFT3(n) * Diag(BHN(n)), m/2, APar, APar),\n# TGath(Refl(N, 2*N-1, N, L(m*n, m))) ]),\n# tags)\n# ])),\n#\n# apply := (self, t, C, Nonterms) >> C[1]\n# ),\n#\n# # Variant better suited for vectorization\n# PDCT4_CT_SPL_Vec := rec(\n# isApplicable := P -> P > 2 and (P mod 2) = 0,\n# forTransposition := false,\n#\n# allChildren := P -> let(N := P,\n# Map2(Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n# (m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n#\n# rule := (P,C) -> let(N := P, m := Rows(C[1]), n := Cols(C[2]),\n# TT := Diag(fPrecompute(fCompose(dOmega(8 * N, 1),\n# diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n#\n# IJ(N, n/2) *\n# L(N, m) *\n# Tensor(I(n/2),\n# M(m,m/2) * Diag(BHN(m)) * C[1]) *\n# RC(TT) *\n# L(N, n/2) *\n# Tensor(I(m/2),\n# L(n, 2) * C[2] * Diag(BHN(n)) * K(n, 2)) *\n# L(N, m/2) *\n# IJ(N, m/2)\n# )\n# )\n\n\n DCT4_CT_tSPL := rec(\n switch := false,\n\n applicable := (self, t) >> let(\n P:=t.params,\n P[1] > 2\n and ForAny(DivisorPairs(2*P[1]), d ->\n IsEvenInt(d[1]) and IsEvenInt(d[2])\n )\n and t.hasTags()\n ),\n\n children := (self, t) >> let(\n tags := t.getTags(),\n N := t.params[1],\n Map2(\n Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n (m,n) -> List([\n TPrm(IJ(N, n/2)),\n TTensorI(condM(m,m/2) * Diag(BHN(m)) * PRDFT3(m,-1).transpose(), n/2, AVec, AVec),\n TTensorI(L(n, 2) * PRDFT3(n) * Diag(BHN(n)) * condK(n, 2), m/2, APar, AVec),\n TPrm(IJ(N, m/2))\n ], i -> i.setTags(tags))\n )\n ),\n\n apply := (self, t, C, Nonterms) >> let(\n N:=t.params[1],\n n:=2*Rows(Nonterms[1].params[1].params[2]),\n m:=2*Rows(Nonterms[4].params[1].params[2]),\n Grp(\n C[1] * C[2]\n * ConjDiag(RC(Diag(fPrecompute(\n fCompose(dOmega(8 * N, 1), diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))\n ))), L(N, m), L(N, n/2))\n )\n * C[3] * C[4]\n )\n )\n));\n\n\n#F TDCT2() - Discrete Cosine Transform, Type II, non-terminal\n#F Definition: (n x n)-matrix [ cos(k*(l+1/2)*pi/n) | k,l = 0...n-1 ]\n#F Note: DCT2 is the transpose of DCT3\n#F Example: DCT2(8)\nClass(TDCT2, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIunscaled(self.params[1])),\n transpose := self >> TDCT3(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT2, rec(\n DCT2_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TS(t.params[1]).withTags(t.getTags()), TDCT4(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))) *\n C[1].transpose() * C[2] *\n Diag(List([0..P - 1], i -> 1/(2 * CosPi((2*i + 1)/(4*P))))))\n ))\n);\n\n\n\n#F TDCT3() - Discrete Cosine Transform, Type III, non-terminal (unscaled)\n#F Definition: (n x n)-matrix [ cos((k+1/2)*l*pi/n) | k,l = 0...n-1 ]\n#F [scaled] (n x n)-matrix [ a_l*cos((k+1/2)*l*pi/n) | k,l = 0...n-1 ]\n#F a_j = 1/sqrt(2) for j = 0 and = 1 else\n#F Note: DCT3 is the transpose of DCT2, scaled NOT supported yet\n#F Example: DCT3(8)\nClass(TDCT3, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n terminate := self >> Mat(DCT_IIIunscaled(self.params[1])),\n transpose := self >> TDCT2(self.params[1]),\n SmallRandom := () -> Random([2,3,4,5,6,8,9,10,12,15,16,18,24,27,30,32]),\n normalizedArithCost := (self) >> let(n := self.params[1], IntDouble(_DCT_CONST * n * d_log(n) / d_log(2)))\n));\n\n\nNewRulesFor(TDCT3, rec(\n DCT3_DCT2_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT2(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> C[1].transpose()\n ),\n DCT3_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TDCT4(t.params[1]).withTags(t.getTags()), TS(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> let(P := t.params[1],\n Diag(List([0..P - 1], i -> 1/(2 * CosPi((2*i + 1)/(4*P))))) *\n C[1] * C[2] *\n Diag(Concat([V(2.0)], List([1..P-1], i->V(1.0)))))\n )\n));\n", "meta": {"hexsha": "49dad3b65443d73e410b28749144292e1e9502fd", "size": 8093, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/dct.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/common/dct.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/common/dct.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 39.0966183575, "max_line_length": 151, "alphanum_fraction": 0.4470530088, "num_tokens": 2768, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943925708561, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.4393356577280819}} {"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt,IsPosInt],\n function(sys,coeffs,ordering,order,root)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))*i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n\n Setcoefficients(object,CanonicMod(sys,coeffs,ordering,root));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"\"));\n return object;\nend);\n\nInstallMethod(UnipotentMod,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,ordering,root)\n\n return UnipotentMod(sys,coeffs,ordering,-2,root);\nend);\n\n\n#\n# ---------- Canonic form of element modulo some roots ----------\n#\n\nInstallMethod(CanonicMod,\n \"Canonic form of coefficients of unipotent element in given ordering modulo some roots\",\n [IsChevalleyAdj,IsList,IsList,IsPosInt],\n function(sys,coeffs,Ordering,root)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k,pos;\n \n lista:=[];\n for i in coeffs do\n if Ordering[i[1]]<=Ordering[root] then\n Add(lista,ShallowCopy(i));\n fi;\n od;\n \n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and Ordering[lista[i][1]] < Ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]*pr[lista[i-1][1]]+cc[2]*pr[lista[i][1]];\n pos:=Position(pr,suma);\n if Ordering[pos]<=Ordering[root] then\n param:=cc[3]*((-1)^cc[1])*(lista[i-1][2]^cc[1])*(lista[i][2]^cc[2]);\n Add(lista,[pos,param],i+k);\n k:=k+1;\n fi;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n\n#\n# ---------- Arithmetic Operations modulo some roots ----------\n#\n\nInstallMethod(MMod,\n \"Multiplication for unipotent elements a*b modulo some roots and with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return UnipotentMod(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(CommMod,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return UnipotentMod(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\nInstallMethod(ConjMod,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent,IsPosInt],\n function(u1,u2,root)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2),\n root);\nend);\n\n", "meta": {"hexsha": "9af598ddff039e009eef1547af0c2410e4e2c03e", "size": 6478, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unimod.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/unimod.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/unimod.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 39.7423312883, "max_line_length": 126, "alphanum_fraction": 0.4487496141, "num_tokens": 1400, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506526772884, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4392722264466967}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# Conjugate(, )\n# perm^-1 * spl * perm\n# ==========================================================================\nClass(Conjugate, BaseOperation, rec(\n new := (self, spl, conj) >> Checked(IsSPL(spl), IsSPL(conj),\n\tWhen(Dimensions(conj) = [1,1], spl,\n\t SPL(WithBases( self, \n\t\t rec( _children := [spl, conj],\n\t\t\t dimensions := spl.dimensions ))))),\n #-----------------------------------------------------------------------\n isPermutation := False, \n #-----------------------------------------------------------------------\n dims := self >> self.dimensions,\n #-----------------------------------------------------------------------\n toAMat := self >> \n ConjugateAMat(AMatSPL(self._children[1]), AMatSPL(self._children[2])),\n #-----------------------------------------------------------------------\n print := (self, i, is) >>\n Print(\"(\", self.child(1).print(i, is), \") ^ (\", self.child(2).print(i+is, is), \")\", \n self.printA()),\n #-----------------------------------------------------------------------\n transpose := self >> \n Inherit(self, rec(_children := [ TransposedSPL(self._children[1]),\n\t\t\t\t\tself._children[2] ], \n\t dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n arithmeticCost := (self, costMul, costAddMul) >>\n self._children[1].arithmeticCost(costMul, costAddMul)\n));\n", "meta": {"hexsha": "0350773f7e3ad549679c03ccf10b7f35d834d6ff", "size": 1624, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Conjugate.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/Conjugate.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/Conjugate.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 45.1111111111, "max_line_length": 92, "alphanum_fraction": 0.368226601, "num_tokens": 330, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7905303186696748, "lm_q2_score": 0.5544704649604273, "lm_q1q2_score": 0.43832571335808934}} {"text": "ITER_POLY_WARN:=false;\nRead(Filename(home_dir,\"lib/io.gi\"));\nRead(Filename(home_dir,\"handle.gi\"));\n\n\nsys:=ChevalleyAdj(\"E\",8,GF(5));\nalg:=AlgebraicU(sys);\norbs:=UnipotentClasses(alg,\"Mix\");\n\nlabels:=List(AllClasses(orbs),x->Label(x));", "meta": {"hexsha": "4a90952d4fd293350c08957a6aa7227afee9d213", "size": 234, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/cases/e8/char5/init_char5.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/cases/e8/char5/init_char5.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/cases/e8/char5/init_char5.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.4, "max_line_length": 43, "alphanum_fraction": 0.7136752137, "num_tokens": 78, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7634837527911057, "lm_q2_score": 0.5736784074525096, "lm_q1q2_score": 0.4379941434170671}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nsetLeft := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := true;\n i.isRightChild := false;\n od;\n return(retval);\nend; \n\nsetRight := function(tags)\n local i, retval;\n retval := Copy(tags);\n for i in retval do\n i.isLeftChild := false;\n i.isRightChild := true;\n od;\n return(retval);\nend; \n\n\nNewRulesFor(WHT, rec(\n WHT_GT := rec(\n switch := false,\n maxSize := false,\n minSize := false,\n codeletSize := false,\n inplace := false,\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(WHT(LogInt(m, 2)), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(WHT(LogInt(n, 2)), XChain([1, 0]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> C[1] * C[2]\n )\n));\n\nNewRulesFor(DFT, rec(\n DFT_GT_CT := rec(\n switch := false,\n maxSize := false,\n minSize := 2,\n codeletSize := false,\n inplace := false,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(n := Rows(t),\n n > 2 and\n (self.maxSize=false or n <= self.maxSize) and\n (self.minSize=false or n >= self.minSize) and\n not IsPrime(n)),\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(a := t.getTags(), ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( t.getTags())\n\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags())\n\n children := (self, t) >> Map2(Filtered(DivisorPairs(Rows(t)), d->When(IsInt(self.codeletSize), d[1]<=self.codeletSize, true)),\n (m,n) -> [\n GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags(t.getTags()),\n GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags(t.getTags()),\n #GT(DFT(m, t.params[2] mod m), XChain([0, 1]), XChain([0, 1]), [n]).withTags( let(ts := t.getTags(), setLeft(ts)) ),\n #GT(DFT(n, t.params[2] mod n), XChain([0, 1]), XChain([1, 0]), [m]).withTags( let(ts := t.getTags(), setRight(ts)) ),\n ]),\n\n apply := (self, t, C, Nonterms) >> let(\n inplace := When(self.inplace, Inplace, Grp),\n n := Rows(Nonterms[2].params[1]),\n rot := t.params[2],\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n\n inplace(Buf(C[1] * Diag(compute(Tw1(Rows(t), n, rot))))) * C[2])\n )\n));\n\n# GT(DFT(), ...) rules\n#\nNewRulesFor(GT, rec(\n GT_DFT_Base2 := rec(\n applicable := (self, t) >> let(rank := Length(t.params[4]),\n rank = 0 and PatternMatch(t, [GT, DFT, @, @, @, @, @], empty_cx()) and Rows(t.params[1])=2),\n apply := (t, C, Nonterms) -> F(2)\n ),\n\n GT_DFT_CT := rec(\n maxSize := false,\n minSize := false,\n minRank := 0,\n maxRank := 1,\n codeletSize := 32,\n inplace := true,\n\n a := rec(\n precompute := true\n ),\n\n applicable := (self, t) >> let(\n rank := Length(t.params[4]), \n dft := t.params[1],\n\n rank >= self.minRank \n and rank <= self.maxRank \n and When(rank>0, t.getTags()=[], true) \n and (self.maxSize=false or Rows(dft) <= self.maxSize) \n and (self.minSize=false or Rows(dft) >= self.minSize) \n and PatternMatch(t, [GT, DFT, XChain, XChain, @, @, @], empty_cx()) \n and DFT_GT_CT.applicable(dft)\n ),\n \n children := (self, t) >> let(\n dft := t.params[1], \n g := t.params[2], s := t.params[3], \n rot := dft.params[2],\n loop_dims := t.params[4],\n nloops := Length(loop_dims),\n tags := t.getTags(),\n \n Map2( Filtered(DivisorPairs(Rows(dft)), d->d[1]<=self.codeletSize),\n (m,n) -> [\n GT(DFT(m, rot mod m),\n s.composeWith(XChain([0, 1])), s.composeWith(XChain([0, 1])),\n Concatenation([n], loop_dims)\n ).withTags(tags),\n \n GT(DFT(n, rot mod n),\n g.composeWith(XChain([0, 1])), s.composeWith(XChain([1, 0])),\n Concatenation([m], loop_dims)\n ).withTags(tags)\n ]\n )\n ),\n \n apply := (self, t, C, Nonterms) >> let(\n loop_dims := t.params[4], \n s := t.params[3],\n N := Rows(t.params[1]), \n k := t.params[1].params[2], \n n := Rows(Nonterms[2].params[1]),\n\n inplace := When(self.inplace, Inplace, Grp),\n compute := When(self.a.precompute, fPrecompute, fComputeOnline),\n \n inplace(Buf(C[1] * Diag(compute(s.toDiag(loop_dims, Tw1(N,n,k)))))) * C[2]\n )\n )\n));\n", "meta": {"hexsha": 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"max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 34.0542168675, "max_line_length": 134, "alphanum_fraction": 0.4900053069, "num_tokens": 1740, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702642896702, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.4377722279258806}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nIsIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t)) or IsInt(x);\nIsPosIntSym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v > 0) or (IsInt(x) and x > 0);\nIsPosInt0Sym := x -> (IsSymbolic(x) and IsOrdT(x.t)) or (IsValue(x) and IsOrdT(x.t) and x.v >= 0) or (IsInt(x) and x >= 0);\nIsRatSym := x -> (IsSymbolic(x) and (IsOrdT(x.t) or IsRealT(x.t) or x.t=TUnknown)) or IsRat(x) or (IsValue(x) and (IsOrdT(x.t) or IsRealT(x.t)));\nIsBoolSym := x -> x.t=TBool and (IsSymbolic(x) or IsValue(x));\n\nAnySyms := arg -> ForAny(arg, IsSymbolic);\n\n_ev := x->When(IsRec(x) and IsBound(x.ev), x.ev(), x);\n\n# in functions below\n# vec elements could be non-values (i.e. symbolic == expressions)\n\nisValueZero := e ->\n (e.v=0 or IsDouble(e.v) and AbsFloat(e.v)not IsSymbolic(x) and AbsFloat(_ev(x)) < TDouble.cutoff));\n\nisValueOne := e ->\n (e.v=1 or IsDouble(e.v) and AbsFloat(e.v-1)not IsSymbolic(x) and AbsFloat(_ev(x)-1) < TDouble.cutoff));\n\nisValueNegOne := e ->\n (e.v=-1 or IsDouble(e.v) and AbsFloat(e.v+1)not IsSymbolic(x) and AbsFloat(_ev(x)+1) < TReal.cutoff));\n\n_is0none := e -> Cond(IsValue(e), isValueZero(e), ObjId(e)=noneExp or e=0); \n_is1 := e -> Cond(IsValue(e), isValueOne(e), e=1);\n\n# in the patterns below 'e' could be a plan GAP integer or other non-class GAP object\n_0 := @(0).cond(e -> Cond(IsValue(e), isValueZero(e), e=0)); \n_0none:= @(0).cond(_is0none); \n_1 := @(0).cond(_is1);\n_2 := @(0).cond(x -> x=2);\n_neg1 := @(0).cond(e -> Cond(IsValue(e), isValueNegOne(e), e=-1)); \n\n_v0 := @(0, Value, isValueZero); \n_v0none:= @(0, [Value, noneExp], e -> Cond(ObjId(e)=noneExp, true, isValueZero(e))); \n_v1 := @(0, Value, isValueOne); \n_vneg1 := @(0, Value, isValueNegOne); \n\n_vtrivial := @(0, Value, e->isValueZero(e) or isValueOne(e) or isValueNegOne(e));\n\n\n_vtrue := @(0, Value, e -> e.v=true); \n_vfalse := @(0, Value, e -> e.v=false); \n\n\nDeclare(_divides_rec);\n\n_divides_rec := (d,n) -> Cond(\n ObjId(n) = add and ForAll( n.args, e -> _divides_rec(d, e) ), true,\n ObjId(n) = mul and ForAny( n.args, e -> _divides_rec(d, e) ), true,\n IsSymbolic(d) or IsSymbolic(n), d=n or n=0,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n_divides := (d,n) -> CondPat( d, \n [mul, param, param, ...], # product of distinct params\n ForAll( d.args, p -> IsParam(p) and _divides_rec(p,n) ) and Length(Set(d.args))=Length(d.args),\n [mul, Value, param],\n _divides_rec(d.args[1], n) and _divides_rec(d.args[2], n),\n # else\n _divides_rec(d,n));\n\n_isEven := x -> _divides(2, x);\n\n# We can't know for sure that d|n, because _dividesUnsafe returns true if either d or n is a variable\n_dividesUnsafe := (d,n) -> Cond(IsSymbolic(d) or IsSymbolic(n), true,\n (EvalScalar(n) mod EvalScalar(d)) = 0);\n\n\n_unwrap := n -> Cond(IsValue(n), n.v, n);\nDeclare(_stripval);\n_stripval := n -> Cond( IsValue(n), _stripval(n.v),\n IsList(n), List(n, _stripval),\n n );\n\n_unwrapV := (n) -> let(_n := EvalScalar(n), Cond(IsValue(_n), n.v, _n));\n", "meta": {"hexsha": "ff4735bdb74df7c5cf486bd25f7289a3742eadb5", "size": 3327, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/code/constraints.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/code/constraints.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/code/constraints.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 40.0843373494, "max_line_length": 149, "alphanum_fraction": 0.6086564472, "num_tokens": 1181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7577943712746406, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.4376227371750011}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# DSCirculant(,

, , , )\n# Downsampled circulant\n#\nClass(DSCirculant, Circulant, rec(\n abbrevs := [ (n, P, v, ds, ofs) -> \n\t [ Checked(IsPosInt(n), n),\n\t toFunc(P),\n\t Checked(IsInt(v), v),\n\t Checked(IsPosInt(ds), ds),\n\t Checked(IsPosInt0(ofs), ofs < ds, ofs) ]\n ],\n\n dims := self >> let(p:=self.params, n:=p[1], ds:=p[4], ofs:=p[5],\n\t[ FloorRat((n+ofs)/ds), n ]),\n\n terminate := self >> let(cterminate := Circulant.terminate,\n DownSample(self.params[1], self.params[4], self.params[5]) * \n cterminate(self)),\n\n transpose := NonTerminal.transpose,\n \n HashId := self >> let(p := self.params, [p[4], p[1], p[2].domain(), p[3]])\n));\n\n# since Circulant is already added, DSCirculant won't be added automatically\nAddNonTerminal(DSCirculant); \n\n## \n## Rules\n##\nRulesFor(DSCirculant, rec(\n ###################################################################\n ## Time domain methods\n ###################################################################\n\n #F RuleCirculant_Base: (base case)\n #F\n DSCirculant_Base := rec (\n\tinfo := \"DSCirculant -> Mat\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] <= d_sqrt(SPL_DEFAULTS.globalUnrolling),\n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> ApplyFunc(DSCirculant, P).terminate()\n ),\n\n DSCirculant_toFilt := rec (\n\tinfo := \"DSCirculant -> VStack(.., Filt, ...)\",\n\tforTransposition := false,\n\tisApplicable := P -> P[1] > 2 and (P[1]-P[2].domain()) > 2 and P[3] <= 0, \n\tallChildren := P -> [[ ]], \n\n\trule := function(P, C)\n\t local n,l,r,coeffs,nc,ds,ofs,ofs_l,ofs_r,ofs_filt,ds_l,ds_r,ds_filt,j,jj,k,kk,v,\n\t filtpoly,filtcoef,filtlen,f;\n\n\t n := P[1]; coeffs := P[2]; nc := coeffs.domain();\n\t l := -P[3]; r := -l + nc - 1; \n\n\t ds := P[4]; ofs := P[5];\n\n\t ofs_l := ofs;\n\t ofs_filt := (l - ofs_l) mod ds;\n\t ofs_r := (n-l-r - ofs_filt) mod ds; \n\n\t ds_l := CeilingRat((l - ofs_l) / ds);\n\t ds_filt := CeilingRat((n-l-r - ofs_filt) / ds);\n\t ds_r := CeilingRat((r - ofs_r) / ds);\n\n\t j := Ind( ds_l ); \n\t k := Ind( ds_r );\n\t f := Ind( ds_filt );\n\t v := Ind(nc);\n\t jj := Ind(l);\n\t kk := Ind(r);\n\n\t filtpoly := Poly(List(coeffs.tolist(),EvalScalar), -l);\n\t filtcoef := FillZeros(filtpoly)[1];\n\t filtlen := Length(filtcoef);\n\n\t return \n\t VStack(\n\t BB(ISum(j, j.range, \n\t\t Data(jj, ds*j+ofs_l,\n\t\t\t Scat(fBase(j)) * \n\t\t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,r+jj), v-jj+l, v-jj+l-nc)))) *\n\t\t\t Gath(n, nc, Lambda(v, cond(leq(v,r+jj), v, v+(n-l-r)-1)))))),\n\n\t\tISum(f, f.range,\n\t\t Scat(fBase(f)) *\n\t\t Blk([ filtcoef ]) *\n\t\t Gath(fAdd(n, filtlen, ds*f + ofs_filt))),\n\n\t\tBB(ISum(k, k.range, \n\t\t Data(kk, ds*k+ofs_r,\n\t\t\t Scat(fBase(k)) *\n\t\t\t RowVec(fCompose(coeffs, Lambda(v, cond(leq(v,kk), v-kk+(nc-1), v-kk-1)))) *\n\t\t\t Gath(n, nc, Lambda(v, cond(leq(v,kk), v, v+(n-l-r)-1))))))\n\t );\n\tend\n )\n));\n", "meta": {"hexsha": "ced829042d4114e2ea485155dc9dd7bc92fc82c2", "size": 3060, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/filtering/ds_circulant.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/filtering/ds_circulant.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/filtering/ds_circulant.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 28.5981308411, "max_line_length": 85, "alphanum_fraction": 0.5137254902, "num_tokens": 1002, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.757794360334681, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.43762273085722525}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(StreamGath);\nDeclare(StreamScat);\nDeclare(STensor);\nDeclare(SIterDirectSum);\n\nImport(compiler);\n\nClass(RootsOfUnity, Sym, rec(\n abbrevs := [ (n) -> [n]],\n\n def := (n) -> let(j := Ind(n),\n\tDiag(Lambda(j, omega(n, j)).setRange(Complexes))),\n\n tolist := self >> self.lambda().tolist(),\n lambda := self >> self.obj.element,\n sums := self >> Diag(self),\n isFunction := true,\n range := self >> TComplex,\n domain := self >> self.params[1],\n\n transpose := self >> self,\n\n isReal := self >> (self.params[1] <= 2),\n\n exportParams := self >> self.params\n\n));\n\nClass(streamDiagFunc, FuncClass, rec(\n def := (N, n, r) -> rec(\n N := N/2,\n n := N,\n\tr := r,\n ),\n\n\n tolist := self >> self.lambda().tolist(),\n lambda := self >> let(\n\ti := Ind(self.n),\n\tLambda(i, imod(i, self.params[2]) * idiv(i, self.params[2]))),\n domain := self >> self.n,\n range := self >> self.N\n));\n\n\n# ==========================================================================\n# StreamGath(, , ) - vector gather (read) matrix \n# ==========================================================================\nClass(StreamGath, BaseMat, SumsBase, rec(\n #-----------------------------------------------------------------------\n# rChildren := self >> [self.func],\n# rSetChild := rSetChildFields(\"func\"),\n rChildren := self >> [self.i],\n rSetChild := rSetChildFields(\"i\"),\n #-----------------------------------------------------------------------\n new := (self, i, range, bs) >> SPL(WithBases(self, \n rec(dimensions := [bs, bs*range], bs := bs, i := i, range := range))),\n #-----------------------------------------------------------------------\n sums := self >> self,\n area := self >> self.bs * self.range,\n isReal := self >> true,\n transpose := self >> StreamScat(self.i, self.range, self.bs),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.name, \"(\", self.i, \", \", self.range,\", \", self.bs,\")\"),\n #-----------------------------------------------------------------------\n toAMat := self >> Gath(fTensor(fBase(self.range, self.i), fId(self.bs))).toAMat()\n # make verilog\n));\n\n\n# ==========================================================================\n# StreamScat(, ) - vector scatter (write) matrix\n# ==========================================================================\nClass(StreamScat, BaseMat, SumsBase, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.i],\n rSetChild := rSetChildFields(\"i\"),\n #-----------------------------------------------------------------------\n new := (self, i, range, bs) >> SPL(WithBases(self, \n rec(dimensions := [bs*range, bs], bs := bs, i := i, range := range))),\n #-----------------------------------------------------------------------\n sums := self >> self,\n area := self >> self.func.domain() * self.v,\n isReal := self >> true,\n transpose := self >> StreamGath(self.i, self.range, self.bs),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.name, \"(\", self.i, \", \", self.range,\", \", self.bs,\")\"),\n #-----------------------------------------------------------------------\n toAMat := self >> TransposedAMat(StreamGath(self.i, self.range, self.bs).toAMat())\n# code := (self, y, x) >> VTensor(Scat(self.func), self.v).code(y,x) \n));\n\nRCExpandData := function(value)\n return ConcatList(value.v, x->[ReComplex(Complex(x.v)), ImComplex(Complex(x.v))]);\nend;\n\n#FixLocalize := (o) -> SubstBottomUpRules(o, [\n# [[Diag, @(1)], e -> Diag(GenerateData(ResolveMemos(e.element))), \"FixLocalize\" ]]);\n \n\nDeclare(BRAMPerm);\n\n# ===============================================\n# CodeBlock()\n# ==============================================\nClass(CodeBlock, BaseContainer, SumsBase, rec(\n isBlock:=true,\t\n\n sums := self >> CopyFields(self, rec(_children := [self.child(1).sums()])),\n\t\n code := false,\n\n\tcreateCode := meth(self) \n\t local i, s, res, d, dl;\n\t if (IsBound(self._children[1].isBlock)) then\n\t res := self._children[1].createCode();\n\t else \n\t s := self.child(1); \n\t res := CopyFields(self, rec(code := CodeSums(s, StreamDefaults)));\n\t fi;\t \t \n res.code := BinSplit(res.code);\n\t return res;\n\tend,\n\n rChildren := self >> [self._children[1], self.code],\n\n rSetChild := meth(self, n, what)\n if n=1 then\n self._children[1] := what;\n elif n=2 then\n self.code := what;\n else Error(\" must be in [1,2]\");\n fi;\n end,\n\n from_rChildren := (self, rch) >> CopyFields(ObjId(self)(rch[1]), rec(code:=rch[2])),\n\n print := (self,i,is) >> Print(self.name, \"(\", Cond(self.code<>false, self.code.print(i,is), self._children[1]), \")\")\n));\n\nClass(StreamSum, ISum, BaseIterative, SumsBase);\n\n# A streaming I tensor J primitive\nClass(StreamIxJ, BaseMat, SumsBase, rec(\n new := (self, k, p, bs) >> SPL(WithBases(self, rec(dimensions:=[k*p,k*p], element:=k, p:=p, bs:=bs))),\n print := (self,i,is) >> Print(self.name, \"(\", self.element, \", \", self.p, \", \", self.bs, \")\"),\n toAMat := self >> let(J := When(self.element = 2, I(2), Compose(Tensor(I(2), L(self.element/2, self.element/4)), L(self.element, 2))), Tensor(I(self.p), J).toAMat()),\n transpose := self >> self,\n area := self >> self.element,\n sums := self >> self,\n rChildren := self >> [],\n dimensions := self >> [self.element * self.p, self.element * self.p],\n dims := self >> self.dimensions,\n isReal := True\n));\n\n\n\n\n# parameters:\n# L[1]: SPL\n# L[2]: p: p in I_p x SPL\n# L[3]: bs: stream buffer size\nClass(STensor, Tensor, \n rec(\n new := (self, L) >> SPL(WithBases(self, rec(\n bs := L[3],\n dimensions := L[1].dimensions * Cond(IsValue(L[2]), L[2].ev(), L[2]), \n p := Cond(L[1].dims()[1] >= L[3], L[2], L[2]*L[1].dims()[1]/L[3]),\n _children := [Checked(L[1].dims()[1] = L[1].dims()[2], \n Cond(L[1].dims()[1] >= L[3], L[1], Tensor(I(L[3] / L[1].dims()[1]), L[1]))), Cond(L[1].dims()[1] >= L[3], L[2], L[2]*L[1].dims()[1]/L[3]), L[3]]\n# _children := [Checked(L[1].dims()[1] = L[1].dims()[2], \n# Cond(L[1].dims()[1] >= L[3], L[1], Tensor(I(L[3] / L[1].dims()[1]), L[1])))]\n ))),\n\n print := (self,i,is) >> Print(self.name, \"(\", self.child(1), \", \", self.p, \", \", self.bs, \")\"),\n createCode := self >> Cond(IsBound(self.child(1).createCode), STensor(self.child(1).createCode(), self.p, self.bs), self),\n isPermutation := False,\n toAMat := self >> Tensor(I(self.p), self.child(1)).toAMat(),\n sums := self >> self,\n dims := self >> Cond(IsValue(self.p), self.p.ev(), self.p) * self.child(1).dims()\n));\n\n\n# parameters: I_m x L^n_r x I_p\n# L[1]: n\n# L[2]: r\n# L[3]: p \n# L[4]: m \n# L[5]: stream buffer size\nClass(SIxLxI, Tensor, \n rec(\n new := (self, l) >> SPL(WithBases(self, rec(\n _children := [],\n dimensions := [l[1] * l[3] * l[4], l[1] * l[3] * l[4]],\n bs := l[5],\n p := l[3],\n m := l[4],\n\n createCode := self >> self,\n print := (self,i,is) >> Print(self.name, \"(\", l[1], \", \", l[2], \", \", self.p, \", \", self.m, \", \", self.bs, \")\"),\n isPermutation := False,\n toAMat := self >> Tensor(Tensor(I(self.m), L(l[1], l[2]), I(self.p))).toAMat(),\n transpose := self >> self,\n dims := self >> self.dimensions,\n# dimensions := l[1] * l[3] * l[4],\n sums := self >> self,\n)))));\n\n\n# ==========================================================================\n# Streaming iterative direct sum\n# SIterDirectSum(, , , )\n# Size of the must not depend on . \n# ==========================================================================\nClass(SIterDirectSum, BaseIterative, rec(\n abbrevs := [ (v,d,e, bs) -> [v,d,e,bs],\n\t (v,e,bs) -> [v, v.range, e, bs]],\n new := meth(self, var, domain, expr, bs) \n local res;\n var.isLoopIndex := true;\n res := SPL(WithBases(self, rec(\n#\t\t_children := [Checked(expr.dims()[1] <= bs and \n\t\t_children := [Checked(expr.dims()[1] = expr.dims()[2],\n\t\t\t\t Cond(expr.dims()[1] >= bs,\n\t\t\t\t\t expr,\n\t\t\t\t\t IterDirectSum(Ind(bs/expr.dims()[1]), expr)))],\t\t\n\t\tvar := var,\n\t\tbs := bs,\n\t\tdimensions := expr.dimensions * domain,\n\t\tdomain := domain)));\n return res;\n end,\n\n\n rChildren := self >> self._children,\n rSetChild := meth(self, n, what) self._children[n] := what; end,\n child := (self, n) >> self._children[n],\n children := self >> self._children,\n\n# Constraint(IsSPL(expr));\n# \tConstraint(not IsList(domain));\n# \t#domain := toRange(domain);\n# \tif domain = 1 then \n# \t return SubstBottomUp(expr, @.cond(e->Same(e,var)), e->V(0));\n# \tfi;\n# \tvar.range := domain;\n# return SPL(WithBases( self, \n# \t rec( expr := expr,\n# \t\t var := var,\n# \t\t domain := domain,\n# \t\t dimensions := domain * Dimensions(expr) )));\n# end,\n\n print := (self, i, is) >> Print(self.name, \"(\", self.var, \", \", self.domain, \", \", self.child(1).print(i+is, is), \", \", self.bs, \")\"),\n\n toAMat := self >> self.unroll().toAMat(),\n\n unroll := self >> DirectSum(\n\tList([ 0 .. self.domain - 1 ], \n\t index_value -> SubstBottomUp(\n\t\tCopy(self._children[1]), self.var, \n\t\te -> V(index_value)))),\n\n dims := self >> self.dimensions, \n #-----------------------------------------------------------------------\n isPermutation := False,\n #-----------------------------------------------------------------------\n createCode := self >> Cond(IsBound(self._children[1].createCode), \n\tSIterDirectSum(self.var, self.domain, self._children[1].createCode(), self.bs), self),\n\n transpose := # we use inherit to copy all fields of self\n self >> Inherit(self, rec(\n\t\t expr := TransposedSPL(self._children[1]), \n\t\t dimensions := Reversed(self.dimensions))),\n\n sums := self >> self\n));\n\nNoPull.createCode := meth ( self )\n local i, s, res, d, dl;\n if IsBound(self._children[1].isBlock) then\n res := self._children[1].createCode();\n else\n s := self.child(1);\n res := SPL(CopyFields(self, rec(\n code := CodeSums(self.dims()[1] * 2, s) )));\n fi;\n for i in [ 1 .. 10 ] do\n BinSplit(res.code);\n od;\n return res;\nend;\n\n\nClass(Omega, BaseIterative, rec(\n\t\n abbrevs := [ (N,n,i) ->[N, n, i] ],\n\n\n\n new := (self, N, n, i) >> let(j := Ind(n),\n Lambda(j, omega(N, i*j)).setRange(TComplex)),\n\n\n rChildren := self >> self._children,\n rSetChild := meth(self, n, what) self._children[n] := what; end,\n child := (self, n) >> self._children[1],\n children := self >> self._children,\n \n \n\n tolist := self >> self.lambda().tolist(),\n lambda := self >> self.obj.element,\n sums := self >> Diag(self),\n isFunction := true,\n range := self >> TComplex,\n domain := self >> self.params[1],\n\n transpose := self >> self,\n\n# isReal := self >> (self.params[1] = self.params[2] or self.params[2] = 1),\n\n exportParams := self >> self.params\n));\n\nPrm.createCode := (self) >> SPL(CopyFields(self, rec(code := CodeSums(self, StreamDefaults))));\nISum.createCode := (self) >> CodeBlock(self).createCode();\n\nTensor.createCode := self >>\n Tensor(\n List([1..Length(self.children())], i->\n Cond(IsBound(self.child(i).createCode),\n\t self.child(i).createCode(),\n\t self.child(i)\n )\n )\n );\n \nTw1Stride := (n,d,k,which,stride) -> Checked(IsPosIntSym(n), IsPosIntSym(d), IsPosIntSym(k),\n fCompose(dOmega(n,k), diagTensor(dLin(n/d, 1, 0, TInt), dLin(d/stride, 1, which, TInt))));\n\n# fReal := (f) -> fCompose(RCData(f), fTensor(fId(f.n), fBase(2, 0)));\nClass(fReal, FuncClass, rec(\n def := (f) -> rec(N := f.range(), n := f.domain(), f := f),\n tolist := self >> self.lambda().tolist(),\n lambda := self >> fCompose(RCData(self.f), fTensor(fId(self.n), fBase(2,0))).lambda(),\n domain := self >> self.n,\n range := self >> self.N\n));\n\n# fImag := (f) -> fCompose(RCData(f), fTensor(fId(f.n), fBase(2, 1)));\nClass(fImag, FuncClass, rec(\n def := (f) -> rec(N := f.range(), n := f.domain(), f := f),\n tolist := self >> self.lambda().tolist(),\n lambda := self >> fCompose(RCData(self.f), fTensor(fId(self.n), fBase(2,1))).lambda(),\n domain := self >> self.n,\n range := self >> self.N\n));\n\nClass(Stream1DFT2, BaseMat, SumsBase, rec(\n new := (self) >> SPL(WithBases(self, rec(dimensions:=[2,2]))),\n print := (self,i,is) >> Print(self.name),\n toAMat := self >> DFT(2,1).toAMat(),\n transpose := self >> self,\n sums := self >> self,\n rChildren := self >> [],\n dimensions := [2,2],\n dims := self >> self.dimensions,\n));\n\n\nClass(StreamPadDiscard, BaseMat, SumsBase, rec(\n abbrevs := [(n, m, w_in, w_out) -> [n, m, w_in, w_out]],\n\n new := (self, n, m, w_in, w_out) >> SPL(WithBases(self, rec(\n _children := [n,m, w_in, w_out],\n dimensions := [n, m],\n ))),\n\n rChildren := self >> self._children,\n\trSetChild := meth(self, n, what) self._children[n] := what; end,\n\tchild := (self, n) >> self._children[n],\n\tchildren := self >> self._children,\n\n toAMat := self >> RI(self.child(1), self.child(2)).toAMat(),\n dims := self >> [self.child(1), self.child(2)],\n\n));", "meta": {"hexsha": "a018827f78a52fa162b7c72a3e37af055a8dcf84", "size": 13564, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/stream/sums.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/stream/sums.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/stream/sums.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 34.4263959391, "max_line_length": 170, "alphanum_fraction": 0.4890150398, "num_tokens": 3835, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7853085909370422, "lm_q2_score": 0.5544704649604273, "lm_q1q2_score": 0.4354304195542798}} {"text": "# run this file with\n# gap -b -q < /dev/null group.gap | perl -pe 's/\\\\\\n//s' | indent -kr\n\nPrint(\"/* ----- data generated by group.gap begins ----- */\\n\\n\");\nPrint(\"struct group {\\n unsigned long autosize;\\n\");\nPrint(\" int order, ngens;\\n const char *gens;\\n};\\n\");\nPrint(\"struct groups {\\n int ngroups;\\n\");\nPrint(\" const struct group *groups;\\n};\\n\\n\");\nPrint(\"static const struct group groupdata[] = {\\n\");\noffsets := [0];\noffset := 0;\nfor n in [2..26] do\n Print(\" /* order \", n, \" */\\n\");\n for G in AllSmallGroups(n) do\n\n # Construct a representation of the group G as a subgroup\n # of a permutation group, and find its generators in that\n # group.\n\n # GAP has the 'IsomorphismPermGroup' function, but I don't want\n # to use it because it doesn't guarantee that the permutation\n # representation of the group forms a Cayley table. For example,\n # C_4 could be represented as a subgroup of S_4 in many ways,\n # and not all of them work: the group generated by (12) and (34)\n # is clearly isomorphic to C_4 but its four elements do not form\n # a Cayley table. The group generated by (12)(34) and (13)(24)\n # is OK, though.\n #\n # Hence I construct the permutation representation _as_ the\n # Cayley table, and then pick generators of that. This\n # guarantees that when we rebuild the full group by BFS in\n # group.c, we will end up with the right thing.\n\n ge := Elements(G);\n gi := [];\n for g in ge do\n gr := [];\n for h in ge do\n k := g*h;\n\tfor i in [1..n] do\n\t if k = ge[i] then\n\t Add(gr, i);\n\t fi;\n\tod;\n od;\n Add(gi, PermList(gr));\n od;\n\n # GAP has the 'GeneratorsOfGroup' function, but we don't want to\n # use it because it's bad at picking generators - it thinks the\n # generators of C_4 are [ (1,2)(3,4), (1,3,2,4) ] and that those\n # of C_6 are [ (1,2,3)(4,5,6), (1,4)(2,5)(3,6) ] !\n\n gl := ShallowCopy(Elements(gi));\n Sort(gl, function(v,w) return Order(v) > Order(w); end);\n\n gens := [];\n for x in gl do\n if gens = [] or not (x in gp) then\n Add(gens, x);\n\tgp := GroupWithGenerators(gens);\n fi;\n od;\n\n # Construct the C representation of the group generators.\n s := [];\n for x in gens do\n if Size(s) > 0 then\n Add(s, '\"');\n Add(s, ' ');\n Add(s, '\"');\n fi;\n sep := \"\\\\0\";\n for i in ListPerm(x) do\n chars := \"ABCDEFGHIJKLMNOPQRSTUVWXYZ\";\n Add(s, chars[i]);\n od;\n od;\n s := JoinStringsWithSeparator([\" {\", String(Size(AutomorphismGroup(G))),\n \"L, \", String(Size(G)),\n \", \", String(Size(gens)),\n \", \\\"\", s, \"\\\"},\\n\"],\"\");\n Print(s);\n offset := offset + 1;\n od;\n Add(offsets, offset);\nod;\nPrint(\"};\\n\\nstatic const struct groups groups[] = {\\n\");\nPrint(\" {0, NULL}, /* trivial case: 0 */\\n\");\nPrint(\" {0, NULL}, /* trivial case: 1 */\\n\");\nn := 2;\nfor i in [1..Size(offsets)-1] do\n Print(\" {\", offsets[i+1] - offsets[i], \", groupdata+\",\n offsets[i], \"}, /* \", i+1, \" */\\n\");\nod;\nPrint(\"};\\n\\n/* ----- data generated by group.gap ends ----- */\\n\");\nquit;\n", "meta": {"hexsha": "280adf4664e7218f46eb8bd74fdcc069596b6c84", "size": 3219, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "unfinished/group.gap", "max_stars_repo_name": "aardvark179/puzzles-1", "max_stars_repo_head_hexsha": "fb90f67aa09701eb41ec86ea9acc8d276e6f4b0c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 92, "max_stars_repo_stars_event_min_datetime": "2015-02-13T04:05:05.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-25T15:32:08.000Z", "max_issues_repo_path": "unfinished/group.gap", "max_issues_repo_name": "aardvark179/puzzles-1", "max_issues_repo_head_hexsha": "fb90f67aa09701eb41ec86ea9acc8d276e6f4b0c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2015-12-29T15:40:15.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-28T04:00:29.000Z", "max_forks_repo_path": "unfinished/group.gap", "max_forks_repo_name": "aardvark179/puzzles-1", "max_forks_repo_head_hexsha": "fb90f67aa09701eb41ec86ea9acc8d276e6f4b0c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 27, "max_forks_repo_forks_event_min_datetime": "2015-05-29T15:28:51.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-21T12:11:45.000Z", "avg_line_length": 32.8469387755, "max_line_length": 79, "alphanum_fraction": 0.5476856167, "num_tokens": 953, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.734119526900183, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.43508812396782176}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(PDTT_Base, TaggedNonTerminal, rec(\n abbrevs := [ n -> Checked(IsPosIntSym(n), [n]) ],\n dims := self >> [self.params[1], self.params[1]],\n isReal := True,\n print := (self,i,is) >> Print(self.__name__, \"(\", PrintCS(self.params), \")\", \n\tWhen(self.transposed, Print(\".transpose()\")),\n When(self.tags<>[], Print(\".withTags(\", self.tags, \")\"))),\n\n normalizedArithCost := self >> let(n := self.params[1],\n\tfloor(2.5 * n * log(n) / log(2.0)) )\n));\n\n#\n# Discrete Trigonometric Transforms (DTTs) via PRF\n# \nDeclare(PDST3, PDCT3);\n\nClass(PDST4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DST_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT4, PDTT_Base, rec(\n transpose := self >> Copy(self),\n terminate := self >> Mat(DCT_IVunscaled(EvalScalar(self.params[1]))),\n));\n\nClass(PDCT2, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT3(self.params[1])\n));\n\nClass(PDST2, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST3(self.params[1])\n));\n\nClass(PDCT3, PDTT_Base, rec(\n terminate := self >> Mat(DCT_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDCT2(self.params[1])\n));\n\nClass(PDST3, PDTT_Base, rec(\n terminate := self >> Mat(DST_IIIunscaled(EvalScalar(self.params[1]))), \n transpose := self >> PDST2(self.params[1])\n));\n\nRulesFor(PDST4, rec(\n PDST4_Base2 := DST4_Base, #BaseRule(PDST4, 2),\n PDST4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2*N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDST4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t # mult twid by -E(4) for RDFT, by 1/2 for DHT\n\t t := ScaledTwid(2*N, mf, 1, 1/2, 1/2, j, -E(4)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,-1],[-1,0]])),\n\t Ett := Tensor(I(mf),Mat([[0,-1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2*N-1, m, j, n)) * C[1] * #Ett *\n\t\t RC(T) * \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mc*nc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))*C[3]*Gath(H(2*mc*nc, m/2, 2*nf, 2*nc)))\n\t ) *\n\t SUM(\n\t\tISum(i, RC(Scat(H(mc*nc, nc, i*nc, 1))) * C[2] * Gath(BH(N, 2*N-1, n, i, m))),\n # output is imaginary, but we output into real slot, because subseq transform\n\t\t# is jIR2, which we implement as IR2 * (-j)\n\t\tWhen(IsEvenInt(m), [], Scat(H(2*mc*nc, nc, 2*mf*nc, 2))*C[3]*Gath(H(N,n/2,mf,m)))\n\t ))),\n\n PDST4_CT_SPL := rec(\n\tisApplicable := P -> P[1] > 2 and ForAny(DivisorPairs(2*P[1]), d->IsEvenInt(d[1]) and IsEvenInt(d[2])), \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(diagMul(fConst(N/2, -E(4)), \n fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n\t Prm(Refl(N, 2*N-1, N, L(m*n, m))) *\n\t Tensor(I(n/2), C[1]) * \n RC(TT) * \n RC(L(m*n/4, n/2)) *\n\t Tensor(I(m/2), C[2]) *\n\t Prm(Refl(N, 2*N-1, N, L(m*n, m)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n PDCT4_Base2 := rec(isApplicable:=P->P[1]=2, rule:=(P,C)->DCT4(2).terminate()),\n PDCT4_Base4 := rec(isApplicable:=P->P[1]=4, \n\t allChildren := P -> [[ DCT4(4) ]], \n\t\t rule:=(P,C)->C[1]),\n\n PDCT4_CT := rec(\n\tisApplicable := P -> P[1] > 2, #not IsPrime(P),\n\tforTransposition := false,\n\tallChildren := P -> let(N := P[1], Map2(DivisorPairs(2*N), (m,n) -> Cond(\n\t\tIsEvenInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n) ],\n\t\t#IsEvenInt(m) and IsEvenInt(n), [ PDHT3(m).transpose(), PDHT3(n) ],\n\t\tIsEvenInt(m) and IsOddInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(m/2) ],\n\t\tIsOddInt(m) and IsEvenInt(n), [ PRDFT3(m,-1).transpose(), PRDFT3(n), PDCT4(n/2) ],\n\t\tIsOddInt(m) and IsOddInt(n), Error(\"This can't happen\")))),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n\t nf:=Int(n/2), nc:=Int((n+1)/2), mf:=Int(m/2), mc:=Int((m+1)/2), j:=Ind(nf), i:=Ind(mf), \n\t t := fPrecompute(Twid(2*N, mf, 1, 1/2, 1/2, j)),\n\t T := When(IsOddInt(m), Diag(diagDirsum(t,fConst(1,1))), Diag(t)), \n\t Et := Tensor(I(mf),Mat([[0,1],[1,0]])),\n\t SUM(\n\t\tISum(j, \n\t\t Scat(BH(N, 2*N-1, m, j, n)) * Diag(BHN(m)) * C[1] *\n\t\t # mult twid by 1/2 for DHT\n\t\t RC(T) * \n\t\t #Et * # DHT only\n\t\t RC(Gath(H(mc*nc, mc, j, nc)))\n\t\t),\n\t\tWhen(IsEvenInt(n), [], Scat(H(N,m/2,nf,n))*C[3]*Gath(H(2*mc*nc, m/2, 2*nf, 2*nc)))\n\t ) *\n\t SUM(\n\t\tISum(i, RC(Scat(H(mc*nc, nc, i*nc, 1))) * C[2] * Diag(BHN(n)) * Gath(BH(N, 2*N-1, n, i, m))),\n\t\tWhen(IsEvenInt(m), [], Scat(H(2*mc*nc, nc, 2*mf*nc, 2))*C[3]*Gath(H(N,n/2,mf,m)))\n\t ))),\n));\n\nNewRulesFor(PDCT4, rec(\n PDCT4_CT_SPL := rec(\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n\tapplicable := t -> IsSymbolic(t.params[1]) or (t.params[1] > 2 and (t.params[1] mod 4) = 0), \n extraLeftTags := [],\n\tforTransposition := false,\n\n freedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n\tchild := (self, t, fr) >> let(N := t.params[1], f := fr[1], \n\t [ spiral.sym.ASP(-1).RDFT3(2*f).withTags(self.extraLeftTags).transpose(), \n\t spiral.sym.ASP.RDFT3(div(N,f)) ]),\n\n\tapply := (t,C,Nonterms) -> let(N := t.params[1], m := Rows(C[1]), n := Cols(C[2]),\n mh := Rows(C[1])/2, nh := Cols(C[2])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt)))))),\n\n Grp(Scat(Refl1(nh, m)) * \n Tensor(I(nh), Diag(BHN(m)) * C[1]) * \n D *\n Tensor(I(nh), Tr(2, mh))) * \n #RC(Tr(mh, nh)) *\n Grp(Tr(mh, n) *\n Tensor(I(mh), C[2] * Diag(BHN(n))) *\n Gath(Refl1(mh, n)))\n\t)\n )\n));\n\nRulesFor(PDCT4, rec(\n # Variant better suited for vectorization\n PDCT4_CT_SPL_Vec := rec(\n\tisApplicable := P -> P[1] > 2 and (P[1] mod 2) = 0, \n\tforTransposition := false,\n\n\tallChildren := P -> let(N := P[1], \n\t Map2(Filtered(DivisorPairs(2*N), d -> IsEvenInt(d[1]) and IsEvenInt(d[2])),\n\t\t(m,n) -> [ PRDFT3(m,-1).transpose(), PRDFT3(n) ])),\n\n\trule := (P,C) -> let(N := P[1], m := Rows(C[1]), n := Cols(C[2]),\n TT := Diag(fPrecompute(fCompose(dOmega(8 * N, 1), \n diagTensor(dLin(N/m, 2, 1, TInt), dLin(m/2, 2, 1, TInt))))),\n\n Prm(condIJ(N, n/2)) * \n Prm(L(N, m)) * \n\t Tensor(I(n/2), \n condM(m,m/2) * Diag(BHN(m)) * C[1]) * \n RC(TT) * \n Prm(L(N, n/2)) *\n\t Tensor(I(m/2), \n L(n, 2) * C[2] * Diag(BHN(n)) * condK(n, 2)) *\n Prm(L(N, m/2)) * \n Prm(condIJ(N, m/2))\n\t)\n )\n\n));\n\ntestPDCT4 := function(n)\n local opts, r, s;\n opts := CopyFields(SpiralDefaults, rec(\n breakdownRules := rec(\n PDCT4 := [PDCT4_Base2, PDCT4_CT_SPL_Vec],\n PRDFT1 := [PRDFT1_Base1, PRDFT1_Base2, PRDFT1_CT],\n PRDFT3 := [PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT],\n DFT := [DFT_Base, DFT_CT]\n )));\n r := RandomRuleTree(PDCT4(n), opts);\n s := SumsRuleTree(r, opts);\n return [opts,r,s];\nend;\n\n \nNewRulesFor(PDCT2, rec(\n PDCT2_Base2 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DCT2(2).terminate()\n ),\n\n PDCT2_Base4 := rec(\n\tforTransposition := true,\n applicable := t -> t.params[1] = 4, \n apply := (t, C, Nonterms) -> \n LIJ(4) * \n DirectSum(\n Diag(FList(TReal, [ 1, 0.70710678118654757 ])) * F(2),\n Rot(cospi(13/8), sinpi(13/8)) * J(2)) * \n (Tensor(I(2), F(2))) ^ LIJ(4)\n ),\n\n PDCT2_CT_SPL := rec(\n\tforTransposition := true,\n libApplicable := t -> eq(imod(t.params[1], 2), 0),\n extraLeftTags := [],\n\n\tapplicable := t -> let(N:=t.params[1], \n IsSymbolic(N) or \n (N > 2 and IsEvenInt(N) and (N mod 4) = 0)),\n\n\tfreedoms := t -> [ divisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = k*m\n child := (self, t, fr) >> let(N:=t.params[1], k:=fr[1], m:=N/2/k, \n [ PDCT2(2*k).withTags(self.extraLeftTags), \n spiral.sym.ASP(-1).RDFT3(2*k).transpose().withTags(self.extraLeftTags), \n spiral.sym.ASP(+1).URDFT(2*m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n D := RC(Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n diagTensor(dLin(m-1, 1, 1, TInt), dLin(k, 2, 1, TInt)))))),\n Grp(\n Scat(Refl0_u(m, 2*k)) * \n DirectSum(\n C[1] * KK(k, 2), \n Tensor(I(m-1), Diag(BHN(2*k)) * C[2]) * D\n )) *\n Grp(\n RC(Tr(k, m)) *\n Tensor(I(k), C[3]) *\n Gath(Refl1(k, 2*m))\n )\n\t)\n )\n));\n\nNewRulesFor(PDST2, rec(\n PDST2_Base2 := rec(\n applicable := t -> t.params[1] = 2, \n apply := (t, C, Nonterms) -> DST2(2).terminate()\n ),\n\n PDST2_CT_SPL := rec(\n\tforTransposition := true,\n\tapplicable := t -> let(N:=t.params[1], N > 2 and IsEvenInt(N) and (N mod 4) = 0),\n\tfreedoms := t -> [ DivisorsIntNonTriv(t.params[1]/2) ], \n\n # N/2 = k*m\n child := (t, fr) -> let(N:=t.params, k:=fr[1], m:=N/2/k, \n [ DST2(2*k), PRDFT3(2*k,-1).transpose(), URDFT(2*m) ]), \n\n\tapply := (t,C,Nonterms) -> let(N:=t.params[1], k:=Rows(C[1])/2, m:=Cols(C[3])/2,\n TT := Diag(fPrecompute(fCompose(dOmega(4 * N, 1), \n # ie multiply all twiddles by -E(4)\n diagAdd(diagDirsum(fConst(k, 0), fConst(k*(m-1), 3*N)), \n diagTensor(dLin(m, 1, 0, TInt), dLin(k, 2, 1, TInt)))))),\n\n J(N) * \n Kp(N, 2*k) * \n\t DirectSum(\n J(2*k) * C[1] * Diag(BHN(2*k)) * K(2*k, 2), \n Tensor(I(m-1), J(2*k) * M(2*k, k) * C[2])\n ) * \n RC(TT) * \n RC(L(N/2, m)) *\n\t Tensor(I(k), C[3] * Diag(BHN(2*m))) *\n\t Prm(Refl(N, 2*N-1, N, L(2*N, 2*k)))\n\t)\n )\n\n));\n\nRulesFor(DCT5, rec(\n DCT5_Rader := rec(\n\tforTransposition := false,\n\tisApplicable := P -> P > 2 and IsPrime(2*P-1),\n\tallChildren := P -> [[ IPRDFT(P-1,-1), PRDFT(P-1,-1) ]],\n\n\tdiag := N -> Sublist(\n\t DFT_Rader.raderDiag(2*N-1,1,PrimitiveRootMod(2*N-1)), \n\t [1..Int((N-1)/2)]*2),\n\n\t# 3rd col with 0's is for PRDFT, not necessary for (non-packed) RDFT\n\traderMid := (self, N) >> let(Fsize := 2*N-1, \n\t DirectSum(Mat([[1, 1, 0], [1, -1/(Fsize-1), 0], [0,0,0]]),\n\t\t\t RC(Diag(FData(self.diag(N)))))),\n\n\t# NOTE, special case for even P-1\n\trule := (self,P,C) >> let(N := P, \n\t #RealRR(N).transpose() * \n\t\t\n\t Gath(H(2*P-1, P, 0, 1)) *\n\t RR(2*P-1).transpose() *\n\t DirectSum(I(1), VStack(I(P-1), I(P-1))) *\n\n\t DirectSum(I(1), C[1]) *\n#\t\tC[1]*Diag(1,1, Replicate(2*Int((P-2)/2), 2), \n#\t\t When(IsEvenInt(P-1), [1,1],[]))) * \n\t self.raderMid(N) *\n\t DirectSum(I(1), C[2]) *\n\n # replace by RealRR\n\t Gath(H(2*P-1, P, 0, 1)) *\n\t RR(2*P-1) * DirectSum(I(1), VStack(I(P-1), J(P-1)))\n ))\n));\n\n#q:=ExpandSPL(DCT5(6))[1];\n#s:=SPLRuleTree(q);\n#me := MatSPL(s);\n#them := remat(MatSPL(q.node));\n\n#RDFT-11, DCT5(6) 15(6/9 rots) + 19(12/7 irdft) + 17(12/5 rdft) = 30/21 = 51\n# DST5(5)\n# 10(blk) \n# fftw 60/50\n\n# RDFT-13\n# DCT5(7) 18(8/10=4/8+0/1+2/1 rots) + 18(14/4 irdft) + 18(14/4 rdft) = 36/18=54\n# DST5(6) \n# 12(blk)\n# fftw 76/34=110\n\n# DFT-13\n# fftw 176+68=244\n# us = 54*2 (dct5) + 24(blk)*2 + dst5 \n", "meta": {"hexsha": "7dc3b1b35016bdd470a04dd8f5ad0ea1b9698020", "size": 12631, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/pdtt4.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/pdtt4.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/pdtt4.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 34.6054794521, "max_line_length": 109, "alphanum_fraction": 0.4979811575, "num_tokens": 4901, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837635542924, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.4350732469730729}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# input: imaginary, output: co1 (?)\n_j := N -> Tensor(I(approx.CeilingRat(N/2)),J(2)*Diag(-1,1));\n\nRealRR_Out := (N, root) -> let(\n rrind := RR(N, 1, root).tolist(),\n outind := List(rrind{[1..(N+1)/2]}, x->When(x.v >= (N+1)/2, N-x.v, x.v)),\n #same as Refl((N+1)/2, N, (N+1)/2, RR(N,1,root)).tolist(),\n\n # Reflective RR\n Scat(fTensor(FList((N+1)/2, outind), fId(2))) *\n # Conjugate complex elements that will be reflected\n Diag(ConcatList([0..(N-1)/2], x->When(rrind[x+1].v >= (N+1)/2, [1,-1], [1,1])))\n);\n\nRulesFor(PRDFT, rec(\n\n # PRDFT_PD : Projection of complex DFT partial diagonalization rule to real DFT \n # See also : PRDFT_Rader\n #\n PRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\t\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(RealRR_Out(N, root) *\n\t DirectSum(Mat([[1],[0]]), L(n, n/2)) * \n\t Mat(MatSPL(DFT_PD.core(N, k, root, true) * DFT_PD.A(N))) *\n\t DirectSum(I(1), Tensor(F(2), I(n/2))) * \n\t DirectSum(I(1), OS(n, -1)) *\n\t Gath(RR(N, 1, root)))\n\t)\n ),\n\n # PRDFT_Rader : Projection of complex DFT Rader rule to real DFT \n #\n # Note: PRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to PRDFT1,\n # which means that this rule enables implementation of a prime \n # size PRDFT of any type.\n PRDFT_Rader := rec(\n\tisApplicable := (self, P) >> P[1] > 3 and IsPrime(P[1]),\n\t\n\tdiag := (N, k, root) -> let(fulldiag := DFT_Rader.raderDiag(N,k,root),\n\t last := Int((N-1)/2),\n\t Concatenation(2*fulldiag{[1..last-1]}, [fulldiag[last]])),\n\n\t# 3rd col with 0's is for padding used by PRDFT\n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 1, 0], [1, -1/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FData(self.diag(N, k, root)))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2).transpose(), PRDFT3(n/2).transpose(), PRDFT(n, -1) ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t RealRR_Out(N, root) *\n\t DirectSum(Mat([[1],[0]]), ##\n\t\t L(n, n/2) *\n\t\t DirectSum(C[1], C[2] * _j(n/2)) *\n\t\t RC(L_or_OS(n/2+1, 2))) *\n\t self.raderMid(N, k, root) *\n\t DirectSum(I(1), C[3]) *\n\t Gath(RR(N, 1, root))\n\t)\n )\n));\n\nRulesFor(IPRDFT, rec(\n\n # IPRDFT_PD : Projection of complex DFT partial diagonalization rule to inverse real DFT \n # See also : IPRDFT_Rader\n #\n IPRDFT_PD := rec(\n\tforTransposition := true,\n\tmaxSize := 13,\n\tisApplicable := (self, P) >> P[1] > 2 and P[1] <= self.maxSize and IsPrime(P[1]),\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t BB(Scat(RR(N, 1, root)) *\n\t DirectSum(I(1), OS(n, -1)) *\n\t DirectSum(I(1), Tensor(F(2), I(n/2))) * \n\t Mat(MatSPL(TransposedSPL(DFT_PD.core(N, -k, root, true) * DFT_PD.A(N)) * DirectSum(I(1), 2*I(n)))) *\n\t DirectSum(Mat([[1,0]]), L(n, 2)) * \n\t RealRR_Out(N, root).transpose())\n\t)\n ),\n\n # IPRDFT_Rader : Projection of complex DFT Rader rule to inverse real DFT \n #\n # Note: IPRDFT of types 2--4 of odd size (which includes all primes > 2)\n # can be converted without arithmetic cost to IPRDFT1,\n # which means that this rule enables implementation of a prime \n # size IPRDFT of any type.\n IPRDFT_Rader := CopyFields(PRDFT_Rader, rec(\n\t# 3rd col with 0's is for padding, we also scale everything but 1st elt by 2,\n\t# as IPRDFT requires. \n\traderMid := (self, N, k, root) >> let(n:=N-1,\n\t DirectSum(Mat([[1, 2, 0], [1, -2/n, 0], [0,0,0]]),\n\t\t RCDiag(RCData(FConj(FData(2*self.diag(N, -k, root))))))),\n\n\tallChildren := P -> let(n:=P[1]-1,\n\t [[ PRDFT(n/2), PRDFT3(n/2), PRDFT(n,-1).transpose() ]]),\n\n\trule := (self,P,C) >> let(N:=P[1], n:=N-1, k:=P[2], root:=PrimitiveRootMod(N),\n\t Scat(RR(N, 1, root)) *\n\t DirectSum(I(1), C[3]) *\n\t self.raderMid(N, k, root) *\n\t DirectSum(Mat([[1,0]]), ##\n\t\t RC(L_or_OS(n/2+1, 2).transpose()) *\n\t\t DirectSum(C[1], _j(n/2).transpose() * C[2]) *\n\t\t L(n, 2)) *\n\t RealRR_Out(N, root).transpose()\n\t)\n ))\n));", "meta": {"hexsha": "d6ff32d471f83a5c606986e74dd4b8d89f2a0905", "size": 4303, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/realdft/rpd.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/realdft/rpd.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/realdft/rpd.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.8583333333, "max_line_length": 105, "alphanum_fraction": 0.5596095747, "num_tokens": 1623, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7520125737597972, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.43428377590773626}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n_vlist := (l,t)->List(Flat(l), x->t.value(x));\n\nClass(fNearestNeighbor, FuncClass, rec(\n# def := (N,n,base,stride) -> Checked(IntFloat(base + (n-1)*stride) < N, rec(N:=N, n:=n)),\n def := (N,n,base,stride) -> rec(N:=N, n:=n),\n domain := self >> self.params[2],\n range := self >> self.params[1],\n lambda := self >> let(h := var.fresh_t(\"h\", TInt), Lambda(h, floor(self.params[3]+h*self.params[4]+0.5))),\n # NOTE. FF: that is a temporary solution to make this function work inside Lambda. need to talk to YSV how to do it right.\n t := TFunc\n));\n\nClass(fZeroPadMiddle, FuncClass, rec(\n def := (N,n) -> Checked(IsEvenInt(n), rec(N:=N, n:=n)),\n domain := self >> self.params[2],\n range := self >> self.params[1],\n lambda := self >> let(N:=self.params[1], n:=self.params[2], fStack(fAdd(N, n/2, 0), fAdd(N, n/2, N-n/2)))\n));\n\nClass(Downsample, TaggedNonTerminal, rec(\n abbrevs := [ (dsfunc) -> [dsfunc] ],\n dims := self >> [self.params[1].domain(), self.params[1].range()],\n terminate := self >> Gath(self.params[1]),\n isReal := True,\n normalizedArithCost := self >> 0,\n TType := T_Complex(T_Real(64)),\n doNotMeasure := true,\n HashId := self >> let(h := [ ObjId(self.params[1]), self.params[1].range() ],\n When(IsBound(self.tags), Concatenation(h, self.tags), h)),\n\n));\n\nClass(Upsample, TaggedNonTerminal, rec(\n abbrevs := [ (usfunc) -> [usfunc] ],\n dims := self >> [self.params[1].range(), self.params[1].domain()],\n terminate := self >> Scat(self.params[1]),\n isReal := True,\n normalizedArithCost := self >> 0,\n TType := T_Complex(T_Real(64))\n));\n\nNewRulesFor(Upsample, rec(\n Upsample_base := rec(\n applicable := (self, nt) >> not nt.hasTags(),\n apply := (nt, C, cnt) -> Mat(MatSPL(Scat(nt.params[1])))\n )\n));\n\n\nNewRulesFor(Downsample, rec(\n Downsample_base := rec(\n applicable := (self, nt) >> not nt.hasTags(),\n apply := (nt, C, cnt) -> NeedInterleavedComplex(ScatGath(fId(nt.params[1].domain()), nt.params[1])) \n )\n));\n\n\n", "meta": {"hexsha": "4052a8de51e7d2be85523f14e46a73ec5c38ec60", "size": 2140, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/interpolate/sample.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/interpolate/sample.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/interpolate/sample.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.9682539683, "max_line_length": 126, "alphanum_fraction": 0.5873831776, "num_tokens": 662, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.43418868739439526}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# NOTE: MISSING (YV)\nClass(VScat_red);\n\nClass(BaseVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n sums := self >> self,\n dims := self >> self.dimensions,\n isReal := self >> true,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat()),\n conjTranspose := self >> self.transpose(), \n));\n\nClass(BaseSVScat, BaseMat, SumsBase, rec(\n isVScat := true,\n isSVScat := true,\n #-----------------------------------------------------------------------\n abbrevs := BaseSVGath.abbrevs, \n new := BaseSVGath.new, \n print := BaseSVGath.print,\n getConstantRem := BaseSVGath.getConstantRem,\n #-----------------------------------------------------------------------\n dims := self >> Error(ObjId(self), \".dims() is undefined\"),\n #-----------------------------------------------------------------------\n sums := self >> self,\n isReal := self >> true,\n needInterleavedLeft := True,\n needInterleavedRight := False,\n #-----------------------------------------------------------------------\n conjTranspose := self >> self.transpose(), \n area := self >> self.transpose().area(),\n toAMat := self >> TransposedAMat(self.transpose().toAMat())\n));\n\nIsVScat := x -> IsRec(x) and IsBound(x.isVScat) and x.isVScat;\nIsSVScat := x -> IsRec(x) and IsBound(x.isSVScat) and x.isSVScat;\n\n# ==========================================================================\n# VScat(, ) - vector scatter (write) matrix, assumes aligned output\n# ==========================================================================\nClass(VScat, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v),\n #-----------------------------------------------------------------------\n new := (self, func, v) >> SPL(WithBases(self, \n rec(func := func, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.func.range(), self.v * self.func.domain()],\n #-----------------------------------------------------------------------\n transpose := self >> VGath(self.func, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_u(, ) -- same as VScat but assumes that output is unaligned\n# ==========================================================================\nClass(VScat_u, VScat, rec(\n dims := self >> [ self.func.range(), self.v * self.func.domain()],\n transpose := self >> VGath_u(self.func, self.v)\n));\n\n# ==========================================================================\n# VScat_zero(N, n, ) - vector scatter (write) matrix\n# ==========================================================================\nClass(VScat_zero, BaseVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [],\n rSetChild := rSetChildFields(),\n from_rChildren := (self, rch) >> ObjId(self)(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n new := (self, N, n, v) >> SPL(WithBases(self,\n rec(n := n, N := N, v := v))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> [self.v * self.N, self.v * self.n],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_zero(self.N, self.n, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \",\n self.n, \", \", self.v,\")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_sv(, , ) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> [self.sv * self.func.range(),\n _roundup(self.sv * self.func.domain(), self.v)],\n #-----------------------------------------------------------------------\n transpose := self >> VGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# RCVScat_sv(, , ) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVScat_sv, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func], # self >> [self.func, self.v, self.sv],\n rSetChild := rSetChildFields(\"func\"), # rSetChildFields(\"func\", \"v\", \"sv\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v, self.sv, self.rem),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain() * self.sv, nv := _roundup(n, self.v), \n\tN := self.func.range() * self.sv, \n\t[2*N, 2*nv]),\n #-----------------------------------------------------------------------\n transpose := self >> RCVGath_sv(self.func, self.v, self.sv, self.rem),\n));\n\n# ==========================================================================\n# VStretchScat(, part, ) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(VStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v),\n [N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n\trec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n\n# ==========================================================================\n# vRCStretchScat(, part, ) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(vRCStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v/2),\n 2*[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, \n rec(func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> vRCStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n));\n\n# ==========================================================================\n# RCVStretchScat(, part, ) - vector scatter (write) matrix on subvectors\n# ==========================================================================\nClass(RCVStretchScat, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.part, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(\n\tn := self.func.domain(), N := self.func.range(), \n\tnv := self.part * _roundup(n / self.part, self.v),\n 2*[N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, func, part, v) >> SPL(WithBases(self, rec(\n func := func, part := part, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> RCVStretchGath(self.func, self.part, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.func, \", \",\n self.part, \", \", self.v, \")\", self.printA()),\n ));\n\n# ==========================================================================\n# VScat_pc(N, n, ofs, v) - vector scatter (write) matrix writing unaligned\n# partial contiguous vectors\n# ==========================================================================\nClass(VScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"N\", \"n\", \"ofs\", \"v\"),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.N, nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, N, n, ofs, v) >> SPL(WithBases(self, rec(\n N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> VGath_pc(self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.N, \", \", self.n, \", \",\n self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [self.k, self.N, self.n, self.ofs, self.v],\n rSetChild := rSetChildFields(\"k\", \"N\", \"n\", \"ofs\", \"v\"),\n\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), [self.k*self.N, self.k*nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n:= n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n toloop := (self, bksize) >> self.transpose().toloop(bksize).transpose(),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n# ==========================================================================\n# IxRCVScat_pc(k, N, n, ofs, v) - vector gather (read)\n# matrix reading unaligned\n# partial REAL contiguous vectors\n# ==========================================================================\nClass(IxRCVScat_pc, BaseSVScat, rec(\n #-----------------------------------------------------------------------\n rChildren := self >> [], # self >> [self.ofs], # SEEMS NOT TO WORK?!\n rSetChild := rSetChildFields(), # rSetChildFields(\"ofs\"),\n from_rChildren := (self, rch) >> ObjId(self)(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n dims := self >> let(nv := _roundup(self.n, self.v), 2 * [self.k*self.N, self.k*nv]),\n #-----------------------------------------------------------------------\n abbrevs := [],\n new := (self, k, N, n, ofs, v) >> SPL(WithBases(self, rec(\n k := k, N := N, n := n, ofs := ofs, v := v))).setDims(),\n #-----------------------------------------------------------------------\n transpose := self >> IxRCVGath_pc(self.k, self.N, self.n, self.ofs, self.v),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(self.__name__, \"(\", self.k, \", \", self.N, \", \",\n self.n, \", \", self.ofs, \", \", self.v,\")\", self.printA()),\n));\n\n\n# ==========================================================================\n# Accumulative scatter versions\n# NOTE: to be replaced by a Sigma-SPL lowering step, CodeSumsAcc, and \n# a specialized CodegenAcc\n#\n# NOTE(!!!): .transpose().transpose() on below classes will lead to non-accumulative\n# versions, and thus invalid code!\nClass(VScatAcc, VScat, rec());\nClass(VScatAcc_u, VScat_u, rec());\nClass(VScat_svAcc, VScat_sv, rec());\nClass(VScat_pcAcc, VScat_pc, rec());\n\n\n# ==========================================================================\n# Methods for vectorization of ScatGath constructs\n# NOTE: This is a hack\n\n# BB needed, as basic block size is not known due to varying function domain\nScatGath.toloopRCVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom), #ok := Error(\"caught\"),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [RCVScat_sv(sfunc, v, 1)]) ::\n\t\t [VScat(fTensor(fBase(i), fId(2*bksize/v)), v)]) *\n RCVGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n\nScatGath.toloopVec := (self, _bksize, v) >> let(\n bksize := When(_bksize = 1, v, _bksize),\n dom := RulesMergedStrengthReduce(_divideFunc(self.gfunc.domain(), bksize)), \n i := Ind(dom),\n sfunc := RulesFuncSimp(self.sfunc),\n ISum(i, dom,\n BB(\n Compose(When(ObjId(sfunc)=fId, [], [VScat_sv(sfunc, v, 1)]) :: \n\t\t [ VScat(fTensor(fBase(i), fId(bksize/v)), v)]) *\n VGath_sv(fCompose(self.gfunc, fTensor(fBase(i), fId(bksize))).setDomain(bksize), v, 1)\n )\n )\n);\n", "meta": {"hexsha": "729579d50f2a29c5d0dbf5e6a614725bcd7b7199", "size": 15944, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/scatter.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/scatter.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/scatter.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 50.9392971246, "max_line_length": 100, "alphanum_fraction": 0.3724912193, "num_tokens": 3484, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7310585669110202, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.43327399521844917}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nNewRulesFor(TRDiag, rec(\n # TRDiag is a tall matrix.\n # TRDiag.transpose() is a wide matrix\n #\n TRDiag_Vec := rec(\n forTransposition := true,\n\trequiredFirstTag := [AVecReg, AVecRegCx],\n applicable := t -> not AnySyms(t.params[1], t.params[2]), \n\n apply := (t, C, Nonterms) -> let(\n v := t.firstTag().v,\n N := t.params[1],\n n := t.params[2],\n nv := _roundup(n, v),\n\n VScat_zero(N/v, nv/v, v) *\n\t VDiag(fStretch(t.params[3], nv, n), v) *\n\t VGath_pc(n, n, 0, v) \n )\n ),\n\n TRDiag_VecN := rec(\n forTransposition := true,\n\trequiredFirstTag := [AVecReg, AVecRegCx],\n applicable := t -> true, #AnySyms(t.params[1], t.params[2]), \n\n apply := (t, C, Nonterms) -> let(\n v := t.firstTag().v,\n N := t.params[1],\n n := t.params[2],\n ndiv := idiv(n, v), \n\t nmod := imod(n, v),\n\t nmodrem := imod(v-nmod, v),\n\t j := Ind(ndiv),\n\n\t # * NOTE: redundant zero-padding operations when transposing the below\n\t # VGath_zero/VScat_zero type operations fix this\n\t # * Virtual pad seems to be a hack\n\t # * O.toloop() should be implemented, VO is missing\n\t # * Middle summand is super ugly, use ScatGath?\n\t #\n\t SUM(\n\t\tVirtualPad(N, n, \n\t\t ISum(j, j.range,\n\t\t\tVScat(HH(N/v, ndiv, 0, [1]), v) *\n\t\t\tVDiag(fCompose(t.params[3], fAdd(n, ndiv*v, j*v)), v) *\n\t\t\tVGath(HH(n/v, ndiv, 0, [1]), v))),\n\n\t\t# Below could be simplified, because the block completely disappears\n\t\t# when nmod==0\n\t\tScat(HH(N, nmod+nmodrem, ndiv*v, [1])) *\n\t\tVStack(\n\t\t Diag(fCompose(t.params[3], fAdd(n, nmod, ndiv*v))).toloop(1),\n\t\t O(nmodrem, nmod) # XXX NOTE: should have O.toloop() here \n\t\t) *\n\t\tGath(HH(n, nmod, ndiv*v, [1])),\n\t\t\n VirtualPad(N, n, \n\t\t VScat_zero(idiv(N,v), idiv(N,v)-ndiv, 0, v)) # XXX NOTE: VScat_zero needs to take 4th parameter (here it is 2nd) which is the scatter offset. This code won't work until VScat_zero is patched.\n\t )\n )\n )\n ));\n", "meta": {"hexsha": "8521ec9e94457f6ec8c66cf1ee9c65e3fddfc11c", "size": 2130, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tri.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tri.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tri.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 30.8695652174, "max_line_length": 197, "alphanum_fraction": 0.5507042254, "num_tokens": 701, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7217432062975979, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4331818707949549}} {"text": "# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(Function, rec(\n isFunction := true,\n\n range := self >> self._range,\n tolist := self >> self.lambda().tolist(),\n\n lambda := self >> Error(\"Not implemented\"),\n\n free := self >> self.lambda().free(),\n domain := self >> self.lambda().domain(),\n at := (self, pos) >> self.lambda().at(pos),\n\n from_rChildren := (self, rch) >> ApplyFunc(ObjId(self), rch),\n\n _domain := false,\n _range := false,\n setRange := meth(self, range)\n self._range := range;\n return self;\n end,\n setDomain := meth(self, domain)\n self._domain := spiral.code.RulesStrengthReduce(domain);\n return self;\n end,\n\n # NOTE: below is a hack that already causes problems if we compute w/ symbolic higher order functions\n # 2 methods below allow to use constant functions (ie domain=1) as expressions\n\n # NOTE: don't remember where the hack above is used, so I removed it, now need to test what happens\n eval := self >> self, #When(self.domain() = 1 and self.rank() = 0, self.at(0), self),\n ev := self >> self, #Checked(self.domain() = 1, self.at(0).ev()),\n));\n\nIsFunction := x -> IsRec(x) and IsBound(x.isFunction) and x.isFunction;\n\nDeclare(Lambda, LambdaOps, FList, FData);\n\n#F Lambda(, ) - symbolic representation of a function mapping vars -> expr\n#F\n#F must be a list of variables or a single variable\n#F is a symbolic expression using variables from \n#F\nClass(Lambda, Function, rec(\n rChildren := self >> [self.vars, self.expr, self._domain, self._range],\n rSetChild := rSetChildFields(\"vars\", \"expr\", \"_domain\", \"_range\"),\n isLambda := true,\n lambda := self >> self,\n\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], rch[2]).setDomain(rch[3]).setRange(rch[4]),\n\n domain := self >> When(self._domain <> false,\n self._domain,\n let(v := Last(self.vars), # ignore rank-associated vars\n When(IsBound(v.range) and not IsMeth(v.range), v.range, v.t))),\n\n # FF: need to be able to override range\n range := self >> When(self._range <> false, self._range, self.expr.t),\n\n tolist := self >> Checked(Length(self.vars)=1, let(dom := _unwrapV(self.domain()),\n Cond(IsType(dom), Error(\"Can't convert to a list, \",\n\t \"because its .domain() is not a bounded interval\"),\n\t IsSymbolic(dom), Error(\"Can't convert to a list, \",\n\t \"because its .domain() interval size is not known\"),\n\t List([0 .. dom-1], r -> self.at(r).eval())))),\n\n free := self >> Difference(self.expr.free(), self.vars),\n\n # FF: need to be able to override range\n print := self >> Print(self.name, \"(\", self.vars, \", \", self.expr, \")\",\n When(self._range <> false, Print(\".setRange(\", self._range, \")\"), \"\"),\n When(self._domain <> false, Print(\".setDomain(\", self._domain, \")\"), \"\")\n ),\n\n # at(args), strict version, must have Length(args) = Length(vars)\n at := meth(arg)\n local self, args, i, bind;\n self := arg[1];\n args := Drop(arg, 1);\n # support variable-length call through lists; required by OL\n if IsList(args[1]) then args := args[1]; fi;\n\n Constraint(Length(args) = Length(self.vars));\n bind := tab();\n for i in [1..Length(self.vars)] do\n if IsBound(args[i]) then\n bind.(self.vars[i].id) := toExpArg(args[i]);\n fi;\n od;\n return SubstVars(Copy(self.expr), bind);\n end,\n\n # relaxed_at(lvars, v), relaxed version of at() for multi-ranks, allows lvars to be of any length\n # equivalent to at(Concatenation(lvars, [v])), if Length(lvars)=Length(self.vars)-1\n # v is the \"standard\" variable, everything in lvars is a loop index\n relaxed_at := meth(self, lvars, v)\n local i, bind, la, lv, args, vars;\n args := Concatenation(lvars, [v]);\n\n # for multi-rank functions loop indices can stay unbound\n vars := self.vars;\n [la, lv] := [Length(args), Length(vars)];\n if la > lv then args := Drop(args, la - lv);\n elif lv > la then vars := Drop(vars, lv - la);\n fi;\n\n bind := tab();\n for i in [1..Length(vars)] do\n bind.(vars[i].id) := toExpArg(args[i]);\n od;\n return SubstVars(Copy(self.expr), bind);\n end,\n\n# computeType := self >> ApplyFunc(TFunc, Concatenation(\n# List(self.vars, x ->\n# When(IsBound(x.range) and not IsMeth(x.range), x.range, x.t)),\n# [self.expr.t])),\n\n computeType := self >> ApplyFunc(TFunc,\n List(self.vars, x ->\n Cond(IsBound(x.range) and not IsMeth(x.range), x.range,\n Collect(self.expr, x)=[], TDummy,\n x.t)\n ) :: [self.expr.t]),\n\n normalize := self >> let(\n\tt := self.computeType(),\n\tfirst_non_dummy := PositionProperty(DropLast(t.params,2), x->x<>TDummy),\n\tk := Cond(first_non_dummy=false, Length(self.vars), first_non_dummy),\n\tLambda(self.vars{ [k .. Length(self.vars)]}, \n\t self.expr)),\n\n forCmp := meth(self)\n local map, i, t;\n map := tab();\n for i in [1..Length(self.vars)] do\n t := self.vars[i].t;\n map.(self.vars[i].id) := param(When(IsType(t), t, InferType(t)), \"v\"::StringInt(i));\n od;\n return SubstParamsCustom([self.vars, self.expr], map, [var]);\n end, \n\n __call__ := meth(self, vars, expr)\n local usage, res, rank, loopvars;\n usage := Concatenation(\"Usage: Lambda(, )\\n\",\n \"Usage: Lambda(, )\");\n if not IsList(vars) then vars := [vars]; fi;\n if not ForAll(vars, x -> IsVar(x))\n then Error(\"all elements in must be variables\"); fi;\n if Length(vars) <> Length(Set(vars))\n then Error(\" should not contain any duplicates\"); fi;\n\n expr := toExpArg(expr);\n rank := _rank(expr);\n # if is ranked, add extra arguments to lambda\n if rank > 0 and Length(vars)=1 then\n loopvars := List([1..rank], i->var.fresh_t(\"q\", TInt));\n vars := Concatenation(loopvars, vars);\n expr := _downRankFull(expr, loopvars);\n fi;\n res := WithBases(self, rec(expr := expr, vars := vars, operations := LambdaOps));\n res.t := res.computeType();\n\t# NOTE: the below line should not be necessary, not sure what the purpose was\n # if IsExp(Last(res.vars).range) then res:=res.setDomain(Last(res.vars).range); fi;\n return res;\n end,\n\n downRank := meth(self, loopid, ind)\n local v, vars, exp;\n if Length(self.vars) <= loopid then\n return self;\n else\n v := self.vars[ Length(self.vars) - loopid ];\n vars := ListWithout(self.vars, Length(self.vars)-loopid);\n exp := SubstVars(Copy(self.expr), tab((v.id) := ind));\n return ObjId(self)(vars, exp);\n fi;\n end,\n));\n\nIsLambda := obj -> IsRec(obj) and IsBound(obj.isLambda) and obj.isLambda = true;\n\nCompatLambdas := (x, y) -> Length(x.vars) = Length(y.vars);\n\nLambdaCompose := function(l1, l2)\n if ObjId(l1)<>Lambda then l1 := l1.lambda(); fi;\n if ObjId(l2)<>Lambda then l2 := l2.lambda(); fi;\n Constraint(Length(l1.vars)=1); Constraint(Length(l2.vars)=1);\n return let(v:=l2.vars[1].clone(), Lambda(v, l1.at(l2.at(v))));\nend;\n\nClass(LambdaOps, rec(\n Print := x->x.print(),\n \\+ := (l1, l2) -> let(ll1:=l1.lambda(), ll2:=l2.lambda(), v:=l1.vars[1].clone(),\n Lambda(v, ll1.at(v) + ll2.at(v))),\n \\- := (l1, l2) -> let(ll1:=l1.lambda(), ll2:=l2.lambda(), v:=l1.vars[1].clone(),\n Lambda(v, ll1.at(v) - ll2.at(v))),\n \\* := (l1, l2) -> let(ll1:=l1.lambda(), ll2:=l2.lambda(), v:=l1.vars[1].clone(),\n Lambda(v, ll1.at(v) * ll2.at(v))),\n \\/ := (l1, l2) -> let(ll1:=l1.lambda(), ll2:=l2.lambda(), v:=l1.vars[1].clone(),\n Lambda(v, ll1.at(v) / ll2.at(v))),\n \\^ := (l1, l2) -> let(ll1:=l1.lambda(), ll2:=l2.lambda(), v:=l1.vars[1].clone(),\n Lambda(v, ll1.at(v) ^ ll2.at(v))),\n \\= := (l1, l2) -> IsLambda(l1) and IsLambda(l2) and l1.lambda().forCmp() = l2.lambda().forCmp(),\n \\< := (l1, l2) -> When( IsLambda(l1) and IsLambda(l2),\n l1.lambda().forCmp() < l2.lambda().forCmp(),\n BagAddr(l1) < BagAddr(l2) ),\n));\n\n\n#F FDataOfs(, , )\n#F\nClass(FDataOfs, Function, rec(\n __call__ := (self, datavar, len, ofs) >> WithBases(self, rec(\n var := datavar,\n operations := PrintOps,\n ofs := toExpArg(ofs),\n len := Checked(IsPosIntSym(len), len)\n )),\n\n# <-Daniele's changes\n# rChildren := self >> [ self.var, self.len, self.ofs],\n# rSetChild := rSetChildFields(\"var\", \"len\", \"ofs\"),\n\n rChildren := self >> [ self.var, self.len, self.ofs, self._domain, self._range],\n rSetChild := rSetChildFields(\"var\", \"len\", \"ofs\", \"_domain\", \"_range\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], rch[2], rch[3]).setDomain(rch[4]).setRange(rch[5]),\n# ->\n\n domain := self >> self.len,\n print := self >> Print(self.name,\"(\",self.var,\", \",self.len,\", \",self.ofs,\")\"),\n\n at := (self, n) >> When(IsInt(n) and IsValue(self.ofs) and IsBound(self.var.value),\n self.var.value.v[n + self.ofs.v + 1],\n nth(self.var, n + self.ofs)),\n\n tolist := self >> List([0..EvalScalar(self.len-1)], i -> nth(self.var, self.ofs+i)),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, nth(self.var, self.ofs+x))),\n\n domain := self >> self.len,\n range := self >> When(self._range=false, self.var.t.t, self._range),\n inline := true,\n free := self >> self.ofs.free()\n));\n\n#F FData() -- symbolic function i -> datavar[i],\n#F\n#F domain = datavar.range\n#F range = datavar.t\n#F\n#F\nClass(FData, Function, rec(\n __call__ := arg >> let(\n self := arg[1],\n _val := Cond(Length(arg)=2, When(IsList(arg[2]), arg[2], [arg[2]]),\n Drop(arg, 1)),\n val := When(Length(_val)=1 and IsLoc(_val[1]), _val[1], V(_val)),\n datavar := Cond(IsLoc(val), val,\n Dat(val.t).setValue(val)),\n WithBases(self, rec(var := datavar, operations := PrintOps))),\n\n print := self >> Print(self.name, \"(\", self.var, \")\"),\n rChildren := self >> [ self.var ],\n rSetChild := rSetChildFields(\"var\"),\n\n at := (self, n) >> When(IsInt(n), self.var.value.v[n+1], self.lambda().at(n)),\n tolist := self >> When(IsBound(self.var.value), self.var.value.v, self.lambda().tolist()),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, nth(self.var, x))),\n\n domain := self >> self.var.t.size,\n range := self >> self.var.t.t,\n\n inline := true,\n free := self >> Set([]),\n part := (self, len, ofs) >> FDataOfs(self.var, len, ofs),\n));\n\nClass(RCData, Function, rec(\n __call__ := (self, func) >> WithBases(self, rec(\n func := Checked(IsFunction(func) or IsFuncExp(func), func),\n operations := PrintOps)),\n\n print := self >> Print(self.name, \"(\", self.func, \")\"),\n rChildren := self >> [ self.func ],\n rSetChild := rSetChildFields(\"func\"),\n\n at := (self, n) >> cond(n mod 2, im(self.func.at(idiv(n,2))), re(self.func.at(idiv(n,2)))),\n tolist := self >> ConcatList(self.func.tolist(), x->[re(x), im(x)]),\n\n domain := self >> let(d:=self.func.domain(),\n Cond(not IsType(d), d * 2,\n d=TInt, TInt,\n Error(\"RCData: Invalid self.func.domain()\"))),\n\n range := self >> self.func.range().realType(),\n # this .lambda corrently handles the case of multirank self.func\n lambda := self >> let(\n x := Ind(self.domain()),\n f := self.func.lambda(),\n jv := DropLast(f.vars, 1),\n Lambda(Concatenation(jv, [x]),\n cond(neq(imod(x, 2),0), im(f.relaxed_at(jv, idiv(x,2))), re(f.relaxed_at(jv, idiv(x,2)))))),\n\n inline := true,\n free := self >> self.func.free()\n));\n\n#F\n#F CRData is the opposite of RCData: takes real function which assumed to be interleaved complex data\n#F and packs it into complex function: \n#F [re0, im0, re1, im1, ... ] -> [ (re0, im0), (re1, im1), ... ]\n#F\n\nClass(CRData, RCData, rec(\n \n at := (self, n) >> cxpack(self.func.at(2*n), self.func.at(2*n+1)),\n tolist := self >> let( l := self.func.tolist(), List([1..Length(l)/2], i->cxpack(l[2*i-1], l[2*i]))),\n \n lambda := self >> let(\n x := Ind(self.domain()),\n f := self.func.lambda(),\n jv := DropLast(f.vars, 1),\n Lambda(Concatenation(jv, [x]), cxpack(f.relaxed_at(jv, 2*x), f.relaxed_at(jv, 2*x+1)))),\n\n\n domain := self >> let(d:=self.func.domain(),\n Cond(not IsType(d), div(d, 2),\n d=TInt, TInt,\n Error(\"CRData: Invalid self.func.domain()\"))),\n\n range := self >> self.func.range().complexType(),\n));\n\nDeclare(FConj, FInv, FRConj);\n\nClass(FConj, Function, rec(\n __call__ := (self, func) >> When(ObjId(func)=FConj, func.func, WithBases(self, rec(\n func := Checked(IsFunction(func) or IsFuncExp(func), func),\n operations := PrintOps))),\n\n print := self >> Print(self.name, \"(\", self.func, \")\"),\n rChildren := self >> [ self.func ],\n rSetChild := rSetChildFields(\"func\"),\n\n at := (self, n) >> conj(self.func.at(n)),\n tolist := self >> List(self.func.tolist(), conj),\n\n domain := self >> self.func.domain(),\n range := self >> self.func.range(),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, self.at(x))),\n\n inline := true,\n free := self >> self.func.free()\n));\n\nClass(FInv, Function, rec(\n __call__ := (self, func) >> When(ObjId(func)=FInv, func.func, WithBases(self, rec(\n func := Checked(IsFunction(func) or IsFuncExp(func), func),\n operations := PrintOps))),\n\n print := self >> Print(self.name, \"(\", self.func, \")\"),\n rChildren := self >> [ self.func ],\n rSetChild := rSetChildFields(\"func\"),\n\n at := (self, n) >> 1/(self.func.at(n)),\n tolist := self >> List(self.func.tolist(), x -> 1/x),\n\n domain := self >> self.func.domain(),\n range := self >> self.func.range(),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, self.at(x))),\n\n inline := true,\n free := self >> self.func.free()\n));\n\n# conjugation of N complex entries stored as 2*N reals r,i,r,i,...\nClass(FRConj, Function, rec(\n __call__ := (self, func) >> When(ObjId(func)=FRConj, func.func, WithBases(self, rec(\n func := Checked(IsFunction(func) or IsFuncExp(func), func),\n operations := PrintOps))),\n\n print := self >> Print(self.name, \"(\", self.func, \")\"),\n rChildren := self >> [ self.func ],\n rSetChild := rSetChildFields(\"func\"),\n\n at := (self, n) >> cond(n mod 2, neg(self.func.at(n)), self.func.at(n)),\n tolist := self >> let(ll := self.func.tolist(),\n List([0..Length(ll)-1], i -> When(i mod 2 = 1, neg(ll[1+i]), ll[1+i]))),\n\n domain := self >> self.func.domain(),\n range := self >> self.func.range(),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, self.at(x))),\n\n inline := true,\n free := self >> self.func.free()\n));\n\n#F FList(, ) -- symbolic function i -> list[i],\n#F\n#F Example: FList(TInt, [1,2,3])\n#F See also: FData\nClass(FList, Function, rec(\n __call__ := (self, t, list) >> Checked(IsList(list), WithBases(self, rec(\n list := list,\n t := t, operations := PrintOps))),\n\n print := self >> Print(self.name, \"(\", self.t, \", \", self.list, \")\"),\n rChildren := self >> [self.t, self.list],\n rSetChild := rSetChildFields(\"t\", \"list\"),\n\n domain := self >> Length(self.list),\n range := self >> self.t,\n\n at := (self, n) >> When(IsInt(n), self.list[n+1], self.lambda().at(n)),\n\n _typ := self >> When(IsInt(self.t), TInt, self.t),\n tolist := self >> List(self.list, e->When(not IsSymbolic(e), Value(self._typ(), e), e)),\n tolistval := self >> Value(TArray(self._typ(), Length(self.list)), self.tolist()),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, nth(self.tolistval(), x))),\n\n todata := self >> FData(self.list),\n inline := false,\n free := self >> Union(List(self.list, FreeVars))\n));\n\n\n\nFF := x -> Cond(IsRec(x) and IsBound(x.isFunction), x,\n IsList(x), FList(x),\n Error(\" must be a function or a list\"));\n\n#F FPerm() -- function representing permutation\n#F\n#F Example: FPerm(Perm((1,2,3),4))\nClass(FPerm, Function, rec(\n __call__ := (self, perm) >> WithBases(self, rec(\n perm := perm,\n operations := PrintOps)),\n\n print := self >> Print(self.name, \"(\", self.perm, \")\"),\n rChildren := self >> [self.perm],\n rSetChild := rSetChildFields(\"perm\"),\n\n domain := self >> self.perm.dims()[1],\n range := self >> self.perm.dims()[1],\n\n at := (self, n) >> When(IsInt(n), self.list[n+1], self.lambda().at(n)),\n\n _typ := self >> TInt,\n tolist := self >> List(self.list, e->When(not IsSymbolic(e), Value(self._typ(), e), e)),\n tolistval := self >> Value(TArray(self._typ(), Length(self.list)), self.tolist()),\n lambda := self >> self.perm.sums().func.lambda(),\n\n inline := true,\n free := self >> FreeVars\n));", "meta": {"hexsha": "8e90d076fcda0af2955ffda42a7ef901859d007f", "size": 17093, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/code/lambda.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/code/lambda.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/code/lambda.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.2396514161, "max_line_length": 108, "alphanum_fraction": 0.5691218628, "num_tokens": 4931, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6757646140788307, "lm_q2_score": 0.6406358479787609, "lm_q1q2_score": 0.43291903657443187}} {"text": "\nlocal reps,tori,labels,I,II,ords,mizuno,blocks;\n\nmizuno:=[[ 1, 2, 3, 4, 5, 6, fail,\n 7, 8, 9, 10,\n 11, 6, 12, 13,\n 15, 14, 16, 11,\n 17, 18, 19, 21,\n 20, 16, 22, 23,\n 24, 25, 21, 20,\n 26, 27, 23, 28,\n 25, 29, 30, 27,\n 31, 28, 32, 33,\n 30, 31, 34, 32,\n 33, fail, 35, 34,\n fail, 36, 35, fail,\n 36, fail, fail, fail,\n fail, fail, fail, fail ],\n []];\n\nreps:=[[[1,1],[2,1],[3,1],[4,1],[5,1],[6,1]], # E_6\n [[2,1],[4,1],[5,1],[6,1],[8,1],[16,1]], # E_6(a_1)\n [[1,1],[2,1],[10,1],[11,1],[12,1]], # D_5\n [[8,1],[9,1],[12,1],[10,1],[11,1],[16,1]], # A_5+A_1\n [[8,1],[9,1],[16,1],[12,1],[18,1]], # D_5(a_1)\n [[1,1],[15,1],[16,1],[17,1],[6,1]], # A_5\n [[14,1],[15,1],[16,1],[17,1],[12,1]], # A_4+A_1\n [[2,1],[14,1],[16,1],[18,1]], # D_4\n [[14,1],[15,1],[17,1],[12,1]], # A_4\n [[14,1],[16,1],[22,1],[24,1]], # D_4(a_1)\n [[14,1],[22,1],[23,1],[24,1]], # A_3+A_1\n [[20,1],[21,1],[28,1],[23,1],[24,1]], # 2A_2+A_1\n [[14,1],[22,1],[24,1]], # A_3\n [[26,1],[27,1],[28,1],[29,1]], # A_2+2A_1\n [[20,1],[21,1],[23,1],[24,1]], # 2A_2\n [[26,1],[27,1],[35,1]], # A_2+A_1\n [[26,1],[35,1]], # A_2\n [[37,1],[38,1],[40,1]], # 3A_1\n [[42,1],[43,1]], # 2A_1\n [[53,1]] # A_1\n ];\n\nlabels:=[\"E_6\",\n \"E_6(a_1)\",\n \"D_5\",\n \"A_5+A_1\",\n \"D_5(a_1)\",\n \"A_5\",\n \"A_4+A_1\",\n \"D_4\",\n \"A_4\",\n \"D_4(a_1)\",\n \"A_3+A_1\",\n \"2A_2+A_1\",\n \"A_3\",\n \"A_2+2A_1\",\n \"2A_2\",\n \"A_2+A_1\",\n \"A_2\",\n \"3A_1\",\n \"2A_1\",\n \"A_1\",\n ];\n\nI:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\nII:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\ntori:=[ [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ], [ ] ];\n\n#blocks:=[];\nblocks:=[[[16, 4], [8, 1], [6, 1]], [[16, 2], [11, 2], [8, 2], [4, 2]], [[8, 9], [6, 1]], [[8, 8], [4, 2], [3, 2]], [[8, 5], [6, 1], [4, 8]], [[8, 8], [2, 6], [1, 2]], [[8, 4], [6, 2], [5, 2], [4, 4], [2, 4]], [[8, 1], [6, 9], [2, 8]], [[8, 2], [7, 4], [5, 2], [4, 2], [3, 4], [1, 4]], [[4, 18], [3, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 6], [1, 2]], [[4, 16], [2, 4], [1, 6]], [[4, 10], [3, 2], [2, 16]], [[4, 16], [1, 14]], [[4, 8], [3, 6], [2, 10], [1, 8]], [[4, 2], [3, 18], [1, 16]], [[2, 38], [1, 2]], [[2, 32], [1, 14]], [[2, 22], [1, 34]]];\n\n#ords:=[];\nords:=[ 16, 16, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2 ];\n\nreturn [reps,tori,labels,I,II,ords,blocks,mizuno];\n", "meta": {"hexsha": "0f3ef03ce49c351abd66d723ec48d4b317f2b95e", "size": 3243, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/data/dataE6char2Mizuno.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/data/dataE6char2Mizuno.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/data/dataE6char2Mizuno.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 41.5769230769, "max_line_length": 556, "alphanum_fraction": 0.2553191489, "num_tokens": 1555, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195152660688, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.4323150032247374}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F PolyDTT( )\n#F Parameters: \n#F Definition: Let be an (otionally skew) DCT or DST of type 1--8. Then\n#F Transform( \"PolyDTT\", ) represents the (n x n)-matrix\n#F obtained from dividing every row in by its first\n#F entry.\n#F This transform is called the polynomial version of\n#F the DCT or DST.\n#F Note: The transpose of PolyDTT() is\n#F TPolyDTT(^T).\n#F Example: PolyDTT(DCT2(8)).\n#F\nClass(PolyDTT, NonTerminal, rec(\n _short_print := true,\n abbrevs := [ nt -> Checked(IsNonTerminal(nt), \n\t ObjId(nt) in \n\t [ DCT1, DCT3, DCT5, DCT7, # PolyDTT(T)=T for these\n\t DCT2, DCT4, DCT6, DCT8, \n\t DST1, DST2, DST3, DST4,\n\t DST5, DST6, DST7, DST8,\n\t SkewDTT],\n\t [ Copy(nt) ]\n\t)],\n dims := self >> self.params[1].dimensions,\n terminate := self >> Mat(PolynomialDTT(MatSPL(TerminateSPL(self.params[1])))),\n isReal := True\n));\n\nClass(fr, Exp, rec(\n ev := self >> let(\n\tm := self.args[1].ev(),\n\ti := self.args[2].ev(),\n\tr := self.args[3].ev(),\n\tCond(i mod 2 = 0, (r + 2 * Int(i/2)) / m,\n\t i mod 2 = 1, (2 - r + 2 * Int(i/2)) / m))));\n\n#F Rules\n#F -----\nRulesFor(PolyDTT, rec(\n PolyDTT_ToNormal := rec(\n\tisApplicable := P -> ObjId(P[1]) in [DCT1, DCT3, DCT5, DCT7],\n\tallChildren := P -> [P[1]],\n\trule := P -> P[1]\n ),\n\n #F PolyDTT_Base2: (base case for non-skew DTTs of size 2)\n #F\n #F pDCT2_2 = F_2\n #F pDCT4_2 = F_2 * [[1, -1], [0, sqrt(2)]]\n #F pDCT6_2 = [ [ 1, 1 ], [ 1, -2 ] ]\n #F pDCT8_2 = [ [ 1, cos(2*pi/5) ], [ 1, cos(4*pi/5) ] ]\n #F pDST4_2 = F_2 * [[1, 1], [0, sqrt(2)]]\n #F\n #F Pueschel/Moura: Discrete Cosine and Sine Transforms, in preparation\n #F\n PolyDTT_Base2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) <> SkewDTT,\n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(nt := ObjId(P[1]), Cond(\n\t\tnt = DCT2, F(2),\n\t\tnt = DCT4, F(2) * Mat([[1, -1], [0,sqrt(2)]]),\n\t\tnt = DCT6, Mat([[1,1], [1,-2]]),\n\t\tnt = DCT8, Mat([[1,2*CosPi(2/5)], [1,2*CosPi(4/5)]]),\n\t\tnt = DST2, F(2),\n\t\tnt = DST3, F(2) * Diag([1, sqrt(2)]),\n\t\tnt = DST4, F(2) * Mat([[1, 1], [0, sqrt(2)]]),\n\t\tnt = DST5, Mat([[1,2*CosPi(2/5)], [1,2*CosPi(4/5)]]),\n\t\tnt = DST6, Mat([[1,2*CosPi(1/5)], [1,2*CosPi(3/5)]]),\n\t\tnt = DST7, Mat([[1,2*CosPi(1/5)], [1,2*CosPi(3/5)]]),\n\t\tnt = DST8, Mat([[1,2], [1,-1]]), \n\t\tError(\"unrecognized \"))\n\t)\n ),\n\n PolyDTT_SkewBase2 := rec (\n\tinfo := \"pDTT_2 -> F_2\",\n\tisApplicable := P -> Rows(P[1]) = 2 and ObjId(P[1]) = SkewDTT and\n\t ObjId(P[1].params[1]) = DST3, \n\tallChildren := P -> [[ ]],\n\trule := (P, C) -> let(skewnt := ObjId(P[1].params[1]), r := P[1].params[2], \n\t Cond(\n\t\tskewnt = DST3, F(2) * Diag(1, 2*CosPi(r/2)),\n\t\tError(\"unrecognized \"))\n\t)\n ),\n\n PolyDTT_SkewDST3_CT := rec(\n isApplicable := P -> ObjId(P[1]) = SkewDTT and\n ObjId(P[1].params[1]) = DST3 and\n Rows(P[1]) > 2 and not IsPrime(Rows(P[1])),\n\n allChildren := P -> let(\n\t N := Rows(P[1].params[1]), r := P[1].params[2],\n\t List(DivisorPairs(N), d->\n\t let(i := Ind(d[2]),\n\t\t ri := fr(d[2], i, r),\n\t\t [ PolyDTT(SkewDTT(DST3(d[1]), ri)), \n\t\t PolyDTT(SkewDTT(DST3(d[2]), r)) ]))), \n\t\t\n rule := (P,C) -> let(\n\t MN := Rows(P[1]), N := Rows(C[1]), M := Rows(C[2]), \n\t r := P[1].params[2],\n\t i := C[1].root.params.params[2].args[2],\n\n\t K(MN, N) * \n\t IterDirectSum(i, i.range, C[1]) *\n\t Tensor(C[2], I(N)) *\n\t B_DST3_U(MN, M)\n )\n )\n));\n", "meta": {"hexsha": "abe956f4b77ad55bde64beefd42b519dd57e23f6", "size": 3853, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dtt/polydtt.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dtt/polydtt.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dtt/polydtt.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.6525423729, "max_line_length": 82, "alphanum_fraction": 0.4949390086, "num_tokens": 1552, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837743174788, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.43214596758517027}} {"text": "#############################################################################\n##\n#W matgrp4.gi Karel Dekimpe\n#W Bettina Eick\n##\n## This file contains the 4-dimensional almost crystallographic groups\n## as integral matrix groups. There are 95 types of groups.\n##\nACDim4Nr001 := function ( k1, k2, k3)\nlocal a, b, c, d;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d] , IdentityMat(5) );\nend;\n \nACDim4Nr002 := function ( k1, k2, k3, k4, k5, k6, k7)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k3/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, k3/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k4, k5, k6, k7/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr003 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, - k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr004b := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 2*k3, k2/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr005 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr006 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 0, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2, k2, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr007b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k3, -k2/2, 2*k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr008 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, 0, k3/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009 := function ( k1, k2, k3)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, (3*k1)/4 - k2, 0, k3/2], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr009b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, -k2/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k2/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k2/2, -k2/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, k2/4 - k3, (3*k2)/4 - k3, 2*k4, 0], [0, 0, 1, 0, 0], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr010 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr011 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, 0, k3, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2, -2*k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr012 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k3, k4/2], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, 2*k2 - k5, k3, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr013 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 0, -2*k6, k3/2 + k6/2], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2, k4, -2*k6, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1, k1/2+ k2, 0, k3, -k3/4 + k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta:=[[1, k1 + k2, -k3 - 2*k6, k3, k5/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr014b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, -k2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k2/2 + 2*k3, k2/2, 0], [0, -1, 0, 0, 0], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k2 - 2*k3, k2 + 2*k3 - 2*k5 + 2*k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr015 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k1/4 + k2, -2*k6, k3/2 + k6/2], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k4, k1 + 2*k2 - k4, -2*k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr018 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2*k2 - 2*k3 + 2*k4, k1/2 - 2*k3, 0, \n k2/2 - (-k1 + 2*k2 - 2*k3 + 2*k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2*k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2*k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3*k1 + 2*k2 - 2*k3 + 2*k4, 0, -k1 - 2*k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019b := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 + 2*k2 - 2*k3 + 2*k4, k1/2 - 2*k3, 0, \n k2/2 - (-k1 + 2*k2 - 2*k3 + 2*k4)/4], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2*k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr019c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, 2*k2, -(- (3*k1)/2 - k4)/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, 2*k3, k1/2, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr026 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2*k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, k3, 0, k4/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr027 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, 0, 2*k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2*k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1/2, 2*k2 - 2*k3 + 2*k4, 0, k3/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2*k3 - 2*k4 + 2*k5, 0, k3/2 - (2*k3 - 2*k4 + 2*k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2*k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr029c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2*k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2*k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, -k1 + 2*(k1 + k2), -k1], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k3, -k1, 2*(k1 + k2), -k4/2], [0, 1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr030 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, 2*k3 + 2*k5, 0, k3/2 - (2*k3 + 2*k5)/4], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, 0, 2*k4, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr031 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2*k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -2*k3 + 2*k4, 0, k3/2], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr032 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2*k4, -3*k1 + 2*k2 - 2*k4 + 2*k5, 0, \n k2/2 - (-3*k1 + 2*k2 - 2*k4 + 2*k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2*k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, 2*k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 1/2], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 0, -k1 - 2*k3 + 2*k4, -k1/2, k3/2], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033b := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 - 2*k4, -3*k1 + 2*k2 + k3 - 2*k4 + 2*k5, 0, \n k2/2 - (-3*k1 + 2*k2 + k3 - 2*k4 + 2*k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2*k4, k1/2, -k3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr033c := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1/2, k1/2 + 2*k2, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2*k3, 0, k1 + 2*k2, -k4/2], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr034 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -2*k1 + k2 + 2*k3 + 2*k5, 0, \n k3/2 - (-2*k1 + k2 + 2*k3 + 2*k5)/4], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 - k2, k1/2, k1 + k2 + 2*k4, 0], [0, 1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr036 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, -k1/2, 2*k2, 0], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k3, -k3, 0, k4/2], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr037 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2 + 2*k4, 0, k3/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2*k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr041 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k2, k1 - 2*k5, -k2/2 + k3/2], [0, 0, -1, 0, 1/2], \n [0, -1, 0, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, k1/2 - k4, (-3*k1)/2 + k4, 2*k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr043 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2 + 2*k3 + 2*k5, k1/4 + k2, 2*k2 + 2*k3 + 2*k5, \n k3/2 - (2*k2 + 2*k3 + 2*k5)/4], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, -1, -1, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 + k2 + 2*k4, 2*k4, -k1/4 - k2, 0], [0, 0, 0, -1, 0], \n [0, 1, 1, 1, 1/2], [0, -1, 0, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr045 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na:=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:=[[1,k2, -k2, k2 - 2*k4 - 2*k5, k3/2], [0, 0, 1, -1, 0], [0, 1, 0, -1, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:=[[-1, -k4, k4 + 2*k5, k4, 0], [0, 0, 1, -1, 1/2], [0, 0, 1, 0, 1/2], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr055 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2*k2 + 2*k3 - 2*k4, -k1 - 2*k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2*k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2*k2 + 2*k3 - 2*k4, -k1 - 2*k3, k5, \n (2*k1 + k2 + k4 + k6)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr056 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + 2*k2 - 2*k3 + 2*(k1 - k2 + 2*k3 - k4), k1/2 - 2*k3, 0, \n k2/2 - (k1 - 2*k3)/4 - (-k1 + 2*k2 - 2*k3 + 2*(k1 - k2 + 2*k3 - k4))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2*k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2*k2 - 2*k3 + 2*(k1 - k2 + 2*k3 - k4), -2*k3, \n 2*k3 + 2*k5 - 2*k6, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr058 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1 - 2*k2 + 2*k3 - 2*k4, -k1 - 2*k3, 0, k2/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, k1/2 + 2*k3, 0, 0], [0, -1, 0, 0, 1/2], \n [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -k1 - 2*k2 + 2*k3 - 2*k4, -k1 - 2*k3, \n 4*k1 + 2*k2 + 2*k4 + 2*k5 - 2*k6, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr060 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2*k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2*k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2*(k1 - k2 + k3 - k4), k1 - 2*k3, 0, \n k2/2 + (k1 - k2 + k3 - k4)/2], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2*k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2*(k1 - k2 + k3 - k4), -2*k3, 2*k3 + 2*k5 - 2*k6, k6/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -2*k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 2*k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1, 0, k1 + 2*k2, 0], [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 7*k1 + 2*k2 - 2*k3 + 2*k4, 0, -2*k1 - 2*k2, \n -(-2*k1 - 2*k2)/4 + k3/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 8*k1 + 2*k2 - 2*k3 + 2*k4, 2*k1 + 2*k2 - 2*k6, -2*k1 - 2*k2, \n (-k1 + k3 - k4 + k5)/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061b := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, -2*k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 2*k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -2*k3 - 2*k5 - 2*k6 + 2*(-k1 + k2 + k4 + k5 + k6), k1 - 2*k3, 0, \n k2/2 - (-2*k3 - 2*k5 - 2*k6 + 2*(-k1 + k2 + k4 + k5 + k6))/4], \n [0, -1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1, 2*k3, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, -2*k3 - 2*k5 - 2*k6 + 2*(-k1 + k2 + k4 + k5 + k6), -2*k3, \n 2*k3 + 2*k6 - 2*(-k1 + k2 + k4 + k5 + k6), (-k1 + k2 + k4 + k5 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr061c := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, -2*k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 2*k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, 0, -k1, 2*k2, 2*k1 - k2/2], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 0, -3*k1 - 2*k2 - 2*k6 + 2*(k1 + k2 + k3 + k6), k1, -k4/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\ngamma :=[[1, 2*k2 + 2*k5 - 2*(k1 + k2 + k3 + k6), \n 4*k1 + 2*k2 + 2*k6 - 2*(k1 + k2 + k3 + k6), -2*k2, (k1 + k2 + k3 + k6)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr062 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta, gamma;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[-1, -k1/2, 0, k1/2 + 2*k2, 0], [0, -1, 0, 0, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 3*k1 + 2*k2 - 2*k3 + 2*k4, 0, -k1 - 2*k2, k3/2], \n [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\ngamma :=[[1, 3*k1 + 2*k2 - 2*k3 + 2*k4, -2*k6, -k1 - 2*k2, (k3 - k4 + k5)/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta, gamma] , IdentityMat(5) );\nend;\n \nACDim4Nr075 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr076 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/4], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr077 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr079 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr080 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/4 + k2, k1/4 - k2, k3, k1/16 - k2/4 + k3/4 + k4/4], \n [0, 0, 1, 0, 1/2], [0, 0, 1, -1, 0], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr081 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, 1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr082 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/4], [0, 0, -1, 0, 0], [0, 0, -1, 1, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr083 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, k5, k6/2], [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr084 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k2 + k3, -k2 + k3, -2*k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr085 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k2 - 2*k6, 0, \n -k1/8 + k2/4 + k3/4 - (-k1 + k2 - 2*k6)/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2*k2 - 2*k6, -2*k6, k4, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr086 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k1/2 + k3, 0, -k1/8 + k2/4 - k3/4 + k4/4], [0, 0, -1, 0, 0], \n [0, 1, 0, 0, 1/2], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 + k2 + k3, k1 - k2 + k3, -k1 + k2 - k3 - 2*k6, k5/2], \n [0, -1, 0, 0, 0], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr087 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, k3, k4/4], [0, 0, 1, 0, 0], [0, 0, 1, -1, 0], \n [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k5, -2*k2 + 2*k3 + k5, 2*k2 - k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr088 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1/2, -k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k2, -k1/4 + k3, -(-k1/4 + k2 + k3 - k4)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, 2*k2 + 2*k6, -k1 + 2*k3 + 2*k6, -2*k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr103 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, 0, k4/4], [0, 0, -1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2 - k3, 0, 2*k5, 0], [0, 1, 0, 0, 0], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr104 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 + k2 + 2*k3 + 2*k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 + k2 + 2*k3 + 2*k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -2*k2 - 2*k3 - 2*k5, k1/2, 2*k2 + 2*k3 + 2*k4 + 2*k5, 0], \n [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr106 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/2 + k2, -k1 - k2 - 2*k5, 0, \n -k1/8 - k2/4 + k3/4 - (-k1 - k2 - 2*k5)/4], [0, 0, -1, 0, 1/2], \n [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, 2*k5, k1/2, -2*k4, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr110 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, 0, -k1, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, 0, 0, k1, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, k1, -k1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, 4*k1 - 4*k2 + 2*k3 - 3*k4 + 2*k5, \n -4*k1 + 4*k2 - 2*k3 + 3*k4 - 2*k5, -k1/2 + k2, \n -(-k1/2 + k2 - k3 - (3*(-4*k1 + 4*k2 - 2*k3 + 3*k4 - 2*k5))/2 - \n (4*k1 - 4*k2 + 2*k3 - 3*k4 + 2*k5)/2)/4], [0, 0, 1, 0, 0], \n [0, 0, 1, -1, 0], [0, -1, 1, 0, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, 2*(k1 - k2 - k4) + k4, k4, 0], [0, 0, 1, -1, 1/2], \n [0, 0, 1, 0, 1/2], [0, -1, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr114 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, -k1/2 + k2, k1 - k2 - 2*k4, 2*k1 - 2*k2 + 2*k3 - 2*k4 + 2*k5, \n -(k1/2 + k3 + 2*k5)/4], [0, 0, 1, 0, 1/2], [0, -1, 0, 0, 0], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/2, 2*k4, 0, 0], [0, -1, 0, 0, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr143 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr144 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr146 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, -k2 - k3, k4/3], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr147 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr148 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, k3, k4, k5/6], [0, 0, 0, -1, 0], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr158 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/3], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k2, k2, 2*k5, 0], [0, 0, -1, 0, 0], [0, -1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr159 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1 - 2*k2 + 3*k4, -k1/2 + k2, 0, k3/3], [0, 0, -1, 0, 0], \n [0, 1, -1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k4, -k4, 2*k5, 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr161 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, k1/2, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, -k1/2, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nc :=[[1, -k1/2, k1/2, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k1/4 + k2, k3, -k1/4 - k2 - k3, \n -((5*k1)/8 + k2 + (-k2 - k3)/2 + (3*k3)/2 - k4)/3], [0, 0, 0, 1, 1/2], \n [0, 1, 0, 0, 1/2], [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1/4 - k2 - 2*k3 + 2*k5, (-3*k1)/4 - k2 - 2*k3 + 2*k5, 2*k5, \n 0], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr168 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr169 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 5/6], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr172 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/3], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr173 := function ( k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr174 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, k4, k5/6], [0, 0, -1, 0, 0], [0, 1, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4Nr175 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2*k3, -k1 + 2*k2 + 2*k3, k5, k6/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr176 := function ( k1, k2, k3, k4, k5, k6)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nbeta :=[[1, k1 - 2*k3, -k1 + 2*k2 + 2*k3, 2*k6, k5/2], [0, -1, 0, 0, 0], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4Nr184 := function ( k1, k2, k3, k4, k5)\nlocal a, b, c, d, alfa, beta;\na :=[[1, 0, -k1/2, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb :=[[1, k1/2, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nc :=[[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], \n [0, 0, 0, 0, 1]];\nd :=[[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa :=[[1, k2, -k1/2 + k3, 0, k4/6], [0, 0, 1, 0, 0], [0, -1, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nbeta :=[[-1, -k1 + k2 + 2*k3, k1 - k2 - 2*k3, 2*k5, 0], [0, 0, -1, 0, 0], \n [0, -1, 0, 0, 0], [0, 0, 0, 1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a, b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB1 := function ( k, k1, k2, k3)\nlocal a, b, c, d;\na:= [[1, (-2*k2)/3, 0, -k1/2 - (2*k*k3)/3 + (2*k*(k2 + k3))/3, 0], \n [0, 1, 0, -k/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2*k3)/3, k1/2 - (2*k*k3)/3, 0, 0], [0, 1, k/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k2/3, k3/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d] , IdentityMat(5) );\nend;\n \nACDim4NrB2 := function ( k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (-4*k1)/3, 0, (2*k*k1)/3 + (2*k*k2)/3 - 2*k*k3 + \n (-4*k*k1 - (16*k*k2)/3 - 2*k*k3 + 2*(2*k*k1 + 2*k*k2 + 2*k*k3))/2, 0], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4*k2)/3, (-4*k*k1 - (16*k*k2)/3 - 2*k*k3 + \n 2*(2*k*k1 + 2*k*k2 + 2*k*k3))/2, 0, 0], [0, 1, k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (2*k1)/3, (2*k2)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2*k3, -k1/3, -k2/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3c := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (k1*l)/3 + k3*l + ((-8*k1*l)/3 + k3*l + 2*(k1*l - k3*l))/2, \n 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2*k1)/3, ((-8*k1*l)/3 + k3*l + 2*(k1*l - k3*l))/2, -k2, 0], \n [0, 1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, k1 + (2*k1*l)/3 - 2*k2*l + ((2*k1)/3 - (16*k1*l)/3 - 2*k2*l + \n 2*(-k1 + 2*k1*l + 2*k2*l))/2, 0], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4*k1)/3, ((2*k1)/3 - (16*k1*l)/3 - 2*k2*l + \n 2*(-k1 + 2*k1*l + 2*k2*l))/2, -k3, 0], [0, 1, l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2*k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, -2*k2, -k2, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB3 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, 0, 0, (2*k1)/3 + (k1*l)/3 + (-k1 - (2*k1*l)/3)/2, 0], \n [0, 1, 0, (-1 - 2*l)/2, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nb:= [[1, (-2*k1)/3, (-k1 - (2*k1*l)/3)/2, -k3, 0], [0, 1, (1 + 2*l)/2, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 0, 0, 0, k4/2], [0, -1, -1, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (k*k1)/3 + k*k3 + ((-2*k*k1)/3 - k*k3)/2, -k4], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2*k1)/3, ((-2*k*k1)/3 - k*k3)/2, -(k*k1)/2 - k2 + (3*k*k3)/4, 0], \n [0, 1, k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB4b := function (k, k1, k2, k3)\nlocal a, b, c, d, alfa;\na:= [[1, (4*k1)/3, 0, (-5*k*k1)/3 + 2*k2 - 2*((-2*k*k1)/3 + k2), -k3], \n [0, 1, 0, -k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, -2*((-2*k*k1)/3 + k2), 0, 0], [0, 1, k, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2*k1)/3, 0, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, (-2*k1)/3, 0, 0, 0], [0, -1, 0, k/2, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2*k1)/3, 0, k3*l, k2], [0, 1, 0, -l, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2*k1)/3, 0, 0, 0], [0, 1, l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB5b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa;\na:= [[1, (-2*k1)/3, 0, k3*(1 + 2*l), k2], [0, 1, 0, (-1 - 2*l)/2, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (2*k1)/3, 0, 0, 0], [0, 1, (1 + 2*l)/2, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, k1/3, -k1/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[1, 2*k3, 0, 0, k4/2], [0, -1, 0, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa] , IdentityMat(5) );\nend;\n \nACDim4NrB7 := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4*k1*l)/3 - 4*k2*l + ((-8*k1*l)/3 + 4*k2*l)/2, 0], \n [0, 1, 0, -2*l, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-4*k1)/3, ((-8*k1*l)/3 + 4*k2*l)/2, 0, (5*k1)/6 - 2*k2 + \n ((-2*k1)/3 + 2*k2)/2 - k4], [0, 1, 2*l, 0, 0], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2*k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2*k2, 0, -k1/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (2*k1)/3 - 2*k2, -(((2*k1)/3 - 2*k2)*l)/2, 2*k3, 0], \n [0, -1, l, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB7b := function (l, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, (4*k1*(1 + 2*l))/3 - 2*k2*(1 + 2*l) + \n ((-8*k1*(1 + 2*l))/3 + 2*k2*(1 + 2*l))/2, 0], [0, 1, 0, -1 - 2*l, 0], \n [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-8*k1)/3, ((-8*k1*(1 + 2*l))/3 + 2*k2*(1 + 2*l))/2, 0, \n (5*k1)/3 - 2*k2 + ((-4*k1)/3 + 2*k2)/2 - k4], [0, 1, 1 + 2*l, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (4*k1)/3, 0], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2*k2, 0, (-2*k1)/3, 0], [0, 1, 0, 0, 1/2], [0, 0, -1, 0, 0], \n [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[1, (4*k1)/3 - 2*k2, -(((4*k1)/3 - 2*k2)*(1 + 2*l))/4, 2*k3, 0], \n [0, -1, (1 + 2*l)/2, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8 := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, 0, 0, -2*k*(k1 - 2*k2) - 8*k*k2 + (8*k*(2*(k1 - 2*k2) + 4*k2))/3 + \n (-4*k*k2 - (14*k*(2*(k1 - 2*k2) + 4*k2))/3 + \n 2*(2*k*(k1 - 2*k2) + 8*k*k2))/2, \n (k*(k1 + (-2*(k1 - 2*k2) - 4*k2)/6 - 2*k2))/4 - k3 + \n (k1 + (17*k*(k1 - 2*k2))/3 - 3*k2 + (34*k*k2)/3 + (-k1 + 2*k2)/2 + \n (-2*k*(k1 - 2*k2) - 8*k*k2)/2 + (k1 - 2*k*(k1 - 2*k2) - 6*k*k2)/2 + \n 2*k3 - 2*k4)/2], [0, 1, 0, -2*k, 0], [0, 0, 1, 0, 1], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, (-2*(2*(k1 - 2*k2) + 4*k2))/3, \n (-4*k*k2 - (14*k*(2*(k1 - 2*k2) + 4*k2))/3 + \n 2*(2*k*(k1 - 2*k2) + 8*k*k2))/2, k1 + (-2*(k1 - 2*k2) - 4*k2)/3 - \n 2*k*(k1 - 2*k2) - 2*k*k2 + (4*k*(2*(k1 - 2*k2) + 4*k2))/3 + \n ((-2*(k1 - 2*k2) - 4*k2)/3 - 4*k*k2)/2, 0], [0, 1, 2*k, 0, 0], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, 0, (2*(k1 - 2*k2) + 4*k2)/3, 0], [0, 1, 0, 0, 1], \n [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 2*k2, 2*k*k2, ((-2*(k1 - 2*k2) - 4*k2)/3 - 4*k*k2)/2, 0], \n [0, 1, 2*k, -2*k, 1/2], [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], \n [0, 0, 0, 0, 1]];\nbeta:= [[1, k1 + (-2*(k1 - 2*k2) - 4*k2)/6 - 2*k2, \n (k*(k1 + (-2*(k1 - 2*k2) - 4*k2)/6 - 2*k2))/2, \n k1 + (17*k*(k1 - 2*k2))/3 - 3*k2 + (34*k*k2)/3 + (-k1 + 2*k2)/2 + \n (-2*k*(k1 - 2*k2) - 8*k*k2)/2 + (k1 - 2*k*(k1 - 2*k2) - 6*k*k2)/2 + \n 2*k3 - 2*k4, 0], [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], \n [0, 0, 0, -1, 1/2], [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n \nACDim4NrB8b := function (k, k1, k2, k3, k4)\nlocal a, b, c, d, alfa, beta;\na:= [[1, (4*k1)/3, (-2*k1)/3 + (4*k*k1)/3 + \n ((-16*k*k1)/3 + 8*k*k2 - 2*(-2*k*k1 + 4*k*k2))/2 + \n 2*(k1/3 - (2*k*k1)/3 + ((16*k*k1)/3 - 8*k*k2 + \n 2*(-2*k*k1 + 4*k*k2))/ 2), (-10*k*k1)/3 + ((16*k*k1)/3 - 8*k*k2 + \n 2*(-2*k*k1 + 4*k*k2))/2, \n ((8*k*k1)/3 - 2*k*k2 + (-2*k*k1 + 4*k*k2)/2 + \n ((-16*k*k1)/3 + 8*k*k2 - 2*(-2*k*k1 + 4*k*k2))/2)/2 - k3], \n [0, 1, 0, -2*k, 0], [0, 0, 1, 0, 1], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nb:= [[1, 0, ((16*k*k1)/3 - 8*k*k2 + 2*(-2*k*k1 + 4*k*k2))/2, 0, \n (-2*k1)/3 - (2*k*k1)/3 + k2 + 4*k*k2 + (2*k*k1 - 4*k*k2)/2 + \n ((-16*k*k1)/3 + 8*k*k2 - 2*(-2*k*k1 + 4*k*k2))/4 + \n (k1/3 - (2*k*k1)/3 + ((16*k*k1)/3 - 8*k*k2 + 2*(-2*k*k1 + 4*k*k2))/2)/ 2 \n + ((-8*k*k1)/3 + 2*k*k2 + (2*k*k1 - 4*k*k2)/2 + \n ((16*k*k1)/3 - 8*k*k2 + 2*(-2*k*k1 + 4*k*k2))/2)/2 + k3 + k4], \n [0, 1, 2*k, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 1], [0, 0, 0, 0, 1]];\nc:= [[1, 0, (-2*k1)/3, 0, -k2], [0, 1, 0, 0, 1], [0, 0, 1, 0, 0], \n [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]];\nd:= [[1, 0, 0, 0, 1], [0, 1, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], \n [0, 0, 0, 0, 1]];\nalfa:= [[-1, 0, k1/3 - (2*k*k1)/3 + ((16*k*k1)/3 - 8*k*k2 + \n 2*(-2*k*k1 + 4*k*k2))/2, 0, 0], [0, 1, 2*k, -2*k, 1/2], \n [0, 0, -1, 0, 0], [0, 0, 0, -1, 0], [0, 0, 0, 0, 1]];\nbeta:= [[-1, (-2*k1)/3, 0, (8*k*k1)/3 - 2*k*k2 + (-2*k*k1 + 4*k*k2)/2 + \n ((-16*k*k1)/3 + 8*k*k2 - 2*(-2*k*k1 + 4*k*k2))/2, 0], \n [0, -1, -k, k, 0], [0, 0, 1, 0, 1/2], [0, 0, 0, -1, 1/2], \n [0, 0, 0, 0, 1]];\nreturn Group( [a , b, c, d, alfa, beta] , IdentityMat(5) );\nend;\n\n#############################################################################\n##\n#V ACDim4Funcs\n#V ACDim4Param\n#V ACDim4Types\n##\n\n#############################################################################\n##\n## some small helpers\n##\nACDim4Funcs := [ ACDim4Nr001, ACDim4Nr002, ACDim4Nr003, ACDim4Nr004,\nACDim4Nr004b, ACDim4Nr005, ACDim4Nr006, ACDim4Nr007, ACDim4Nr007b,\nACDim4Nr008, ACDim4Nr009, ACDim4Nr009b, ACDim4Nr010, ACDim4Nr011,\nACDim4Nr012, ACDim4Nr013, ACDim4Nr014,\nACDim4Nr014b, ACDim4Nr015, ACDim4Nr018, ACDim4Nr019, ACDim4Nr019b,\nACDim4Nr019c, ACDim4Nr026, ACDim4Nr027, ACDim4Nr029, ACDim4Nr029b,\nACDim4Nr029c, ACDim4Nr030, ACDim4Nr031, ACDim4Nr032, ACDim4Nr033,\nACDim4Nr033b, ACDim4Nr033c, ACDim4Nr034, ACDim4Nr036, ACDim4Nr037,\nACDim4Nr041, ACDim4Nr043, ACDim4Nr045, ACDim4Nr055, ACDim4Nr056,\nACDim4Nr058, ACDim4Nr060, ACDim4Nr061, ACDim4Nr061b, ACDim4Nr061c,\nACDim4Nr062, ACDim4Nr075, ACDim4Nr076, ACDim4Nr077, ACDim4Nr079,\nACDim4Nr080, ACDim4Nr081, ACDim4Nr082, ACDim4Nr083, ACDim4Nr084, ACDim4Nr085,\nACDim4Nr086, ACDim4Nr087, ACDim4Nr088, ACDim4Nr103, ACDim4Nr104, ACDim4Nr106,\nACDim4Nr110, ACDim4Nr114, ACDim4Nr143, ACDim4Nr144, ACDim4Nr146, ACDim4Nr147,\nACDim4Nr148, ACDim4Nr158, ACDim4Nr159, ACDim4Nr161, ACDim4Nr168, ACDim4Nr169,\nACDim4Nr172, ACDim4Nr173, ACDim4Nr174, ACDim4Nr175, ACDim4Nr176, ACDim4Nr184,\nACDim4NrB1, ACDim4NrB2, ACDim4NrB3c, ACDim4NrB3b, ACDim4NrB3, ACDim4NrB4,\nACDim4NrB4b, ACDim4NrB5, ACDim4NrB5b, ACDim4NrB7, ACDim4NrB7b, ACDim4NrB8,\nACDim4NrB8b ];\nMakeReadOnlyGlobal( \"ACDim4Funcs\" );\n\n#############################################################################\nACDim4Types := [\n\"001\", \"002\", \"003\", \"004\", \"004b\", \"005\", \"006\", \"007\", \"007b\", \"008\",\n\"009\", \"009b\", \"010\", \"011\", \"012\", \"013\", \"014\", \"014b\", \"015\", \"018\",\n\"019\", \"019b\", \"019c\", \"026\", \"027\", \"029\", \"029b\", \"029c\", \"030\", \"031\",\n\"032\", \"033\", \"033b\", \"033c\", \"034\", \"036\", \"037\", \"041\", \"043\", \"045\",\n\"055\", \"056\", \"058\", \"060\", \"061\", \"061b\", \"061c\", \"062\", \"075\", \"076\",\n\"077\", \"079\", \"080\", \"081\", \"082\", \"083\", \"084\", \"085\", \"086\", \"087\", \"088\",\n\"103\", \"104\", \"106\", \"110\", \"114\", \"143\", \"144\", \"146\", \"147\", \"148\", \"158\",\n\"159\", \"161\", \"168\", \"169\", \"172\", \"173\", \"174\", \"175\", \"176\", \"184\", \"B1\",\n\"B2\", \"B3c\", \"B3b\", \"B3\", \"B4\", \"B4b\", \"B5\", \"B5b\", \"B7\", \"B7b\", \"B8\", \"B8b\"\n];\nMakeReadOnlyGlobal( \"ACDim4Types\" );\n\n#############################################################################\nACDim4Param :=\n[ 3, 7, 4, 4, 3, 4, 3, 3, 4, 3, 3, 4, 6, 6, 6, 6, 6, 6, 6, 4, 4, 4, 4, 4, 5,\n 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 4, 4,\n 4, 4, 4, 5, 5, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 5, 5, 5, 5, 5, 4,\n 4, 4, 4, 5, 6, 6, 5, 4, 4, 5, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5 ];\nMakeReadOnlyGlobal( \"ACDim4Param\" );\n\n", "meta": {"hexsha": "eec6d2c6269174c6f6f8baa92d895223e01b0591", "size": 76488, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/matgrp4.gi", "max_stars_repo_name": "alex-konovalov/aclib", "max_stars_repo_head_hexsha": "d1afb020805bfd60a8bbb0a9a4adac77fe9b44f1", "max_stars_repo_licenses": ["Artistic-2.0"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "gap/matgrp4.gi", "max_issues_repo_name": "alex-konovalov/aclib", "max_issues_repo_head_hexsha": "d1afb020805bfd60a8bbb0a9a4adac77fe9b44f1", "max_issues_repo_licenses": ["Artistic-2.0"], "max_issues_count": 6, "max_issues_repo_issues_event_min_datetime": "2018-03-07T16:35:34.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:07.000Z", "max_forks_repo_path": "gap/matgrp4.gi", "max_forks_repo_name": "alex-konovalov/aclib", "max_forks_repo_head_hexsha": "d1afb020805bfd60a8bbb0a9a4adac77fe9b44f1", "max_forks_repo_licenses": ["Artistic-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-03-10T19:58:42.000Z", "max_forks_repo_forks_event_max_datetime": "2018-03-10T19:58:42.000Z", "avg_line_length": 45.6372315036, "max_line_length": 80, "alphanum_fraction": 0.3585268277, "num_tokens": 55040, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006919925839875, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.43155954894175685}} {"text": "Eval := function(f, x)\n return f(x);\nend;\n\nEval(x -> x^3, 7);\n# 343\n", "meta": {"hexsha": "d4b77ee6583d52723fee187daa208c249a005480", "size": 69, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Higher-order-functions/GAP/higher-order-functions.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Higher-order-functions/GAP/higher-order-functions.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Higher-order-functions/GAP/higher-order-functions.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 9.8571428571, "max_line_length": 22, "alphanum_fraction": 0.5217391304, "num_tokens": 28, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6187804337438502, "lm_q2_score": 0.6959583187272711, "lm_q1q2_score": 0.4306453903297015}} {"text": "# Copyright (c) 2018-2020, Carnegie Mellon University\n# See LICENSE for details\n#\n# Contains the rewrite rulesets for SPL-expression simplification\n# After the Breakdown Stage\n# Current Demo version focuses on CNOTs, and so we do not cancel single-qubit gates\n# Eventually we will convert all gates to generic rotations in Quantum_Format\n# Combine rotations in Quantum_Simplify, and convert back into non-generic rotations in Quantum_Terminate\n#\n# Additionally, Junction steps should be factored out in this stage versus in the unparser to enable a \n# few more optimizations. A SWE effort is underway.\n#\n\n##\n#F CheckIdentitySplit( , )\n##\n## return true if we can split an Identity transform into smaller matrices\nCheckIdentitySplit := function(a, b)\n if(ObjId(a) = I) then \n if a.params[1] > 2 then\n return true;\n fi;\n fi;\n if(ObjId(b) = I) then \n if b.params[1] > 2 then\n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CheckIdentity( , )\n##\n## are both objects identity\nCheckIdentity := function(a, b)\n if(ObjId(a) = I) then \n if(ObjId(b) = I) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F PullInTensor( , )\n##\n## compress two tensor expressions by pulling in symbols wherever sizes align\nPullInTensor := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) ) then \n ch1[pos1] := ch1[pos1] * ch2[pos2];\n ch2[pos2] := I(e2.dims()[1]);\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return [ch1, ch2];\nend;\n\n##\n#F CanPullIn( , )\n##\n## Similar to PullInTensor, but just checks to see if there is any simplification possible\nCanPullIn := function(ch1, ch2)\n local pos1, pos2, e1, e2, up1, up2, siz1, siz2;\n pos1 := 1;\n pos2 := 1;\n siz1 := 0;\n siz2 := 0;\n while pos1 <= Length(ch1) and pos2 <= Length(ch2) do\n e1 := ch1[pos1];\n e2 := ch2[pos2];\n if ( (e1.dims()[1] = e2.dims()[1]) and (pos1 = pos2) and ObjId(e2) <> I) then \n return true;\n fi;\n up1 := siz1 + log(e1.dims()[1], 2).v;\n up2 := siz2 + log(e2.dims()[1], 2).v;\n if (up1 <= up2) then \n pos1 := pos1 + 1;\n siz1 := siz1 + log(e1.dims()[1], 2).v;\n fi;\n if (up1 > up2) then \n pos2 := pos2 + 1;\n siz2 := siz2 + log(e2.dims()[1], 2).v;\n fi;\n od;\n return false;\nend;\n\n##\n#F ValidTensSimplifyMatch( , )\n##\n## SWrapper function to deterrmine if the tensor rewrite rule can be applied\nValidTensSimplifyMatch := function(e1, e2)\n if ObjId(e1)=Tensor and ObjId(e2)=Tensor then \n if CanPullIn(e1._children, e2._children) then \n return true;\n fi;\n fi;\n return false;\nend;\n\n##\n#F CombineReord( , , , , )\n##\n## Combine Reorder steps\nCombineReord := function(ord1, dir1, ord2, dir2, arch)\n local idx, adj1, adj2, adj3, start, n, t1, t2, a, b, new_list, o1, o2;\n adj1 := [];\n adj2 := [];\n if dir1 = -1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [idx, o1]);\n idx := idx + 1;\n od;\n fi;\n if dir1 = 1 then\n idx := 0;\n for o1 in ord1 do \n Add(adj1, [o1, idx]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = -1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [idx, o2]);\n idx := idx + 1;\n od;\n fi;\n if dir2 = 1 then\n idx := 0;\n for o2 in ord2 do \n Add(adj2, [o2, idx]);\n idx := idx + 1;\n od;\n fi;\n # now have adj1 and adj2\n adj3 := [];\n for a in adj1 do \n start := a[1];\n t1 := a[2];\n t2 := -1;\n for b in adj2 do\n if b[1] = t1 then \n t2 := b[2];\n fi;\n od;\n Add(adj3, [start, t2]);\n od;\n # full combine, and then check validity. If it isnt valid, then just dont simplify\n # TODO do a partial recombine if the entire reorder cannot be combined and be still implementable\n # not much harder, just a lot of code\n new_list := [0..Length(ord1)-1];\n idx := 1;\n for n in new_list do \n for a in adj3 do\n if n = a[1] then \n new_list[idx] := a[2];\n fi;\n od;\n idx := idx + 1;\n od;\n if VerifyPath(new_list, [0..Length(ord1)-1], arch) = true then \n return Reord(new_list, arch, 1);\n fi;\n return (Reord(ord1, arch, dir1) * Reord(ord2, arch, dir2));\nend;\n\n##\n#F Quantum_Format ruleset\n## \nClass(Quantum_Format, RuleSet);\nRewriteRules(Quantum_Format, rec(\n # Remove Grp structure \n remove_grp := ARule( Grp, [@(1)], x-> [(@(1).val)] ),\n\n # Flatten Tensors\n flatten_tensor_asoc := ARule(Tensor, [@(1), @(2).cond(e-> ObjId(@(1).val)=Tensor or ObjId(e)=Tensor)],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=Tensor, @(1).val._children, [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=Tensor, @(2).val._children, [@(2).val]),\n\t ch1::ch2\n\t )),\n\n #Split identities into I(2)\n split_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentitySplit(@(1).val, e)) )],\n\t e -> let(\n\t ch1 := Cond(ObjId(@(1).val)=I and @(1).val.params[1] > 2, Tensor(I(2), I(@(1).val.params[1]/2)), [@(1).val]),\n\t ch2 := Cond(ObjId(@(2).val)=I and @(2).val.params[1] > 2, Tensor(I(2), I(@(2).val.params[1]/2)), [@(2).val]),\n [ch1]::[ch2]\n\t )),\n));\n\n##\n#F Quantum_Simplify ruleset\n## \nClass(Quantum_Simplify, RuleSet);\nRewriteRules(Quantum_Simplify, rec(\n\n # Pull-In Tensors \n pull_in_tensor := ARule(Compose, [@(1), @(2).cond(e-> ValidTensSimplifyMatch(@(1).val, e))],\n\t e -> let(\n # both 1 ans 2 are tensors, can access a list of arguments via _children\n ch := PullInTensor(@(1).val._children, @(2).val._children),\n\t [Tensor(ch[1])]::[Tensor(ch[2])]\n\t )),\n\n # Remove Identity Multiplications\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n # Cancel Composition of CNOTS\n cancel_cnot := ARule(Compose, [[CNOT, @(1), @(2)], [CNOT, @(3).cond(x -> (x = @(1).val)), @(4).cond(x -> (x = @(2).val))]], x->[I(2^(@(1).val + 1))] ),\n\n # Combine Reorder Compositions\n cancel_reorder := ARule(Compose, [[Reord, @(1), @(2), @(3)], [Reord, @(4), @(5), @(6)]], x-> [CombineReord(@(1).val, @(3).val, @(4).val, @(6).val, @(5).val)]),\n));\n\n\n##\n#F Quantum_Terminate ruleset\n## \nClass(Quantum_Terminate, RuleSet);\nRewriteRules(Quantum_Terminate, rec(\n # Recombine Identities - Good\n recomb_identity := ARule(Tensor, [@(1), @(2).cond(e-> (CheckIdentity(@(1).val, e) ))],\n\t e -> [I(@(1).val.params[1] * @(2).val.params[1])]),\n\n # Remove Identity Multiplications - Good\n remove_identity_right := ARule( Compose, [@(1), @(2).cond(e -> ObjId(e)=I)], x-> [(@(1).val)]),\n remove_identity_left := ARule( Compose, [@(1).cond(e -> ObjId(e)=I), @(2)], x-> [(@(2).val)]),\n\n));\n\n\n##\n#F QuantumRewriteInternal( , )\n##\n## Rewrites a quantum SPL expression, for internal use\nQuantumRewriteInternal := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuitInternal( , )\n##\n## Finds the best circuit implementing transform t, for internal use\nBestCircuitInternal := function (t, opts)\n local dpopts, best, s;\n dpopts := rec(verbosity := 0, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewriteInternal(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n s := QuantumRewriteInternal(SPLRuleTree(best[1].ruletree), opts);\n return s;\nend;\n\n##\n#F TerminateReord( , ,

)\n##\n## Convert a reorder object to CNOTs\nTerminateReord := function (l, arch, dir)\n local mats, mat, dir, spl;\n mats := ShiftMat(l, [0..Length(arch)-1], arch, Length(arch));\n if dir = -1 then \n mat := mats[2];\n fi;\n if dir = 1 then\n mat := mats[1];\n fi;\n # now mat in an unreduced Non-terminal expression\n # we need the SPL expression\n spl := BestCircuitInternal(mat, SpiralDefaults);\n return spl;\nend;\n\n##\n#F Quantum_Reorder ruleset\n## \nClass(Quantum_Reorder, RuleSet);\nRewriteRules(Quantum_Reorder, rec(\n\n # Combine Reorder Compositions\n reorder_convert := Rule([Reord, @(1), @(2), @(3)], x-> TerminateReord(@(1).val, @(2).val, @(3).val)),\n));\n\n\n# ------------------------- For External Use ----------------------------------------\n\n##\n#F QuantumRewrite( , )\n##\n## Simplifies an SPL expression representing a quantum circuit (s)\nQuantumRewrite := function (s, opts)\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Reorder], BUA, opts);\n s := RulesSums(s);\n s := ApplyStrategy(s, [Quantum_Format], BUA, opts); \n s := ApplyStrategy(s, [Quantum_Simplify], BUA, opts);\n s := ApplyStrategy(s, [Quantum_Terminate], BUA, opts);\n return s;\nend;\n\n##\n#F BestCircuit( , )\n##\n## Finds the best circuit implementing transform t\n## Hardcoded to count number CNOT gates as the cost function\nBestCircuit := function (t, opts)\n local dpopts, best, s, cnot_list;\n dpopts := rec(verbosity := 1, hashTable := HashTableDP()); \n dpopts.measureFunction := (rt, opts) ->\n let(c := SPLRuleTree(rt), # generate SPL Ruletree and then run a collect on CNOTs \n c2 := QuantumRewrite(c, opts),\n Length(Collect(c2, @(1,CNOT)))\n ); \n best := DP(t, dpopts, opts);\n Print(\"\\n SPL \\n\");\n Print(SPLRuleTree(best[1].ruletree));\n Print(\"\\n\");\n s := QuantumRewrite(SPLRuleTree(best[1].ruletree), opts);\n Print(\"\\ncost :\");\n Print(Length(Collect(s, @(1,CNOT))));\n Print(\"\\n\");\n Print(\"---------------- BestCircuit: \\n\");\n return s;\nend;\n\n\n\n\n", "meta": {"hexsha": "a0a7e78606106d0c2dd9f5399597de1ad69942e3", "size": 10880, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "qrewrite.gi", "max_stars_repo_name": "spiral-software/spiral-package-quantum", "max_stars_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "qrewrite.gi", "max_issues_repo_name": "spiral-software/spiral-package-quantum", "max_issues_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "qrewrite.gi", "max_forks_repo_name": "spiral-software/spiral-package-quantum", "max_forks_repo_head_hexsha": "dd2323983495adbbc6261c0cdf840320d19d099d", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.4761904762, "max_line_length": 163, "alphanum_fraction": 0.5509191176, "num_tokens": 3439, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7217431943271999, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.43047156418765287}} {"text": "Enqueue := function(v, x)\n Add(v[1], x);\nend;\n\nDequeue := function(v)\n local n, x;\n n := Size(v[2]);\n if n = 0 then\n v[2] := Reversed(v[1]);\n v[1] := [ ];\n n := Size(v[2]);\n if n = 0 then\n return fail;\n fi;\n fi;\n return Remove(v[2], n);\nend;\n\n# a new queue\nv := [[], []];\n\nEnqueue(v, 3);\nEnqueue(v, 4);\nEnqueue(v, 5);\nDequeue(v);\n# 3\nEnqueue(v, 6);\nDequeue(v);\n# 4\nDequeue(v);\n# 5\nDequeue(v);\n# 6\nDequeue(v);\n# fail\n", "meta": {"hexsha": "59c46b3fa4a12e24b7b393c1051132ec4f08cc28", "size": 461, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Queue-Definition/GAP/queue-definition.gap", "max_stars_repo_name": "djgoku/RosettaCodeData", "max_stars_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "Task/Queue-Definition/GAP/queue-definition.gap", "max_issues_repo_name": "djgoku/RosettaCodeData", "max_issues_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Queue-Definition/GAP/queue-definition.gap", "max_forks_repo_name": "djgoku/RosettaCodeData", "max_forks_repo_head_hexsha": "91df62d46142e921b3eacdb52b0316c39ee236bc", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 12.8055555556, "max_line_length": 29, "alphanum_fraction": 0.4750542299, "num_tokens": 181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.5926665855647395, "lm_q2_score": 0.7248702761768248, "lm_q1q2_score": 0.4296063915590885}} {"text": "################################################################################\n##\n#W pointed_data.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for pointed_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n\n################################################################################\n##\n#F pointed_data(,,). . . . compute the data of C(G,q,chi)\n##\nInstallGlobalFunction(pointed_data, function(G,q,chi)\n local S, T, FPdim, FPdimC, GSet, N, g,h,r,g_idx,h_idx,CC,g_cc,h_cc;\n GSet := AsSet(G);\n r:=Size(GSet);\n CC:=ConjugacyClasses(G);\n T:=List(GSet,g->0);\n S:=NullMat(r,r);\n for g_idx in [1..r] do\n g:=GSet[g_idx];\n g_cc:=Position(CC,ConjugacyClass(G,g));\n T[g_idx]:=chi[g_cc]*q(g);\n for h_idx in [g_idx..r] do\n h:=GSet[h_idx];\n h_cc:=Position(CC,ConjugacyClass(G,h));\n S[g_idx][h_idx]:=chi[g_cc]*chi[h_cc]*q(g*h)/(q(g)*q(h));\n S[h_idx][g_idx]:=S[g_idx][h_idx];\n od;\n od;\n FPdimC:=Order(G);\n FPdim:=List(GSet,g->1);\n if S[1] <> FPdim then\n Error(\"First row of S is not FPdimension\\n\");\n fi;\n\n N:=compute_fusion_rules(S,FPdimC);\n return [GSet,S,T,N,FPdim,FPdimC];\nend);\n#E pointed_data.gi . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "ffa6c3b76b6d0f28e93aa84a3cc2809230afeb4c", "size": 1480, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/pointed_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/pointed_data.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/pointed_data.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 31.4893617021, "max_line_length": 84, "alphanum_fraction": 0.5141891892, "num_tokens": 437, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195385342971, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.42953418931956067}} {"text": "\n\nNewRulesFor(PrunedMDPRDFT, rec(\n PrunedMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)),\n PrunedPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])) ]],\n\n apply := (nt, C, cnt) -> RC(Tensor(C[1], I(C[2].dims()[1]/2))) * Tensor(I(Product(List(cnt[1].params[4], i->Length(i)))), C[2])\n )\n));\n\n\nNewRulesFor(PrunedIMDPRDFT, rec(\n PrunedIMDPRDFT_Base := rec(\n applicable := nt -> Length(nt.params[1]) = 1,\n\n children := nt -> [[ PrunedIPRDFT(nt.params[1][1], nt.params[2]).withTags(nt.getTags()) ]],\n\n apply := (nt, C, Nonterms) -> C[1]\n ),\n\n PrunedIMDPRDFT_RowCol1 := rec(\n applicable := nt -> Length(nt.params[1]) > 1 and not nt.hasTags(),\n\n children := nt -> [[ PrunedIPRDFT(Last(nt.params[1]), nt.params[3], 1, Last(nt.params[2])),\n PrunedIMDDFT(DropLast(nt.params[1], 1), nt.params[3], 1, DropLast(nt.params[2], 1)) ]],\n\n apply := (nt, C, cnt) -> Tensor(I(Product(List(cnt[2].params[4], i->Length(i)))), C[1]) * RC(Tensor(C[2], I(C[1].dims()[2]/2)))\n )\n));\n\n\n\n", "meta": {"hexsha": "28cb1fb3701aae461f9dd15e62e5f680d19b5373", "size": 1538, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "breakdown/prune.gi", "max_stars_repo_name": "mikefranusich/spiral-package-fftx", "max_stars_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "breakdown/prune.gi", "max_issues_repo_name": "mikefranusich/spiral-package-fftx", "max_issues_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "breakdown/prune.gi", "max_forks_repo_name": "mikefranusich/spiral-package-fftx", "max_forks_repo_head_hexsha": "a1a355f3764aade9665145aa63c2318201421543", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.9545454545, "max_line_length": 136, "alphanum_fraction": 0.5253576073, "num_tokens": 502, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583124210896, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.4280755059156686}} {"text": "# Built-in\nUnorderedTuples([\"iced\", \"jam\", \"plain\"], 2);\n", "meta": {"hexsha": "94fac30a0d2ee6e606394d8a33a3d5ab3bc5fd93", "size": 57, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Combinations-with-repetitions/GAP/combinations-with-repetitions.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Combinations-with-repetitions/GAP/combinations-with-repetitions.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Combinations-with-repetitions/GAP/combinations-with-repetitions.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 19.0, "max_line_length": 45, "alphanum_fraction": 0.6140350877, "num_tokens": 20, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6757646010190476, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.428036229439233}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# Don't forget to Import(platforms.sse)\n\n#NOTE:\n# Bluestein breaks for SSE_2x64f -- disabled for small for now\n\n# doParSimdDft seems broken\nbenchSSE := function()\n if LocalConfig.cpuinfo.SIMD().hasSSE2() then\n return rec(\n 2x32f := rec(\n wht := rec(\n small := _defaultSizes(s->doSimdWht(s, SSE_2x32f, rec(propagateNth := true, useDeref := true, verify := true, oddSizes := true, svct := true, stdTTensor := true, tsplPFA := false)), [4]),\n medium := _defaultSizes(s->doSimdWht(s, SSE_2x32f, rec(propagateNth := true, useDeref := true, oddSizes := false, svct := true, stdTTensor := true, tsplPFA := false)), List([2..10], i->2^i))\n ),\n 1d := rec(\n dft_sc := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_2x32f, rec(propagateNth := true, useDeref := true, verify:=true, tsplBluestein:=false, interleavedComplex := true, PRDFT:=true, URDFT:= true, cplxVect := true, stdTTensor := false, globalUnrolling:=10000)), [ 2..32 ]),\n\n ),\n dft_ic := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_2x32f, rec(propagateNth := true, useDeref := true, verify:=true, tsplBluestein:=false, interleavedComplex := true, PRDFT:=true, URDFT:= true, cplxVect := true, stdTTensor := false, globalUnrolling:=10000)), [2..32])\n )\n )\n ),\n 2x64f := rec(\n wht := rec(\n small := _defaultSizes(s->doSimdWht(s, SSE_2x64f, rec(verify := true, oddSizes := true, svct := true, stdTTensor := true, tsplPFA := false)), [4]),\n medium := _defaultSizes(s->doSimdWht(s, SSE_2x64f, rec(oddSizes := false, svct := true, stdTTensor := true, tsplPFA := false)), List([2..10], i->2^i))\n ),\n 1d := rec(\n dft_sc := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_2x64f, rec(verify:=true, tsplBluestein:=false, interleavedComplex := false, PRDFT:=true, URDFT:= true, cplxVect := true, stdTTensor := false, globalUnrolling:=10000)),\n [ 2..32 ]),\n medium := _defaultSizes(s->doSimdDft(s, SSE_2x64f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false)),\n _svctSizes(1024, 16, 2)),\n # medium := spiral.libgen.doParSimdDft(SSE_2x64f, 1, _svctSizes(1024, 16, 4), false, true, false, false),\n # large := spiral.libgen.doParSimdDft(SSE_2x64f, 1, List([4..20], i->2^i), false, true, false, false)\n\n ),\n dft_ic := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_2x64f, rec(verify:=true, tsplBluestein:=false, interleavedComplex := true, PRDFT:=true, URDFT:= true, cplxVect := true, stdTTensor := false, globalUnrolling:=10000)),\n [2..32]),\n medium := _defaultSizes(s->doSimdDft(s, SSE_2x64f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := true)),\n _svctSizes(1024, 16, 2)),\n medium_cx := _defaultSizes(s->doSimdDft(s, SSE_2x64f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := true, cplxVect := true, realVect := false)),\n _svctSizes(1024, 16, 2)),\n # medium := spiral.libgen.doParSimdDft(SSE_2x64f, 1, _svctSizes(1024, 16, 4), false, true, false, true),\n # large := spiral.libgen.doParSimdDft(SSE_2x64f, 1, List([4..20], i->2^i), false, true, false, true)\n ),\n trdft := _defaultSizes(s->doSimdSymDFT(TRDFT, s, SSE_2x64f, rec( verify:=true, \n interleavedComplex := true, PRDFT:=true, URDFT:= true, tsplBluestein := false, cplxVect := true,\n realVect := true, propagateNth := true, useDeref := true, \n globalUnrolling:=10000)), 4*[1..32]),\n\n dht := _defaultSizes(s->doSimdSymDFT(TDHT, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dct2 := _defaultSizes(s->doSimdSymDFT(TDCT2, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dct3 := _defaultSizes(s->doSimdSymDFT(TDCT3, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dct4 := _defaultSizes(s->doSimdSymDFT(TDCT4, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dst2 := _defaultSizes(s->doSimdSymDFT(TDST2, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dst3 := _defaultSizes(s->doSimdSymDFT(TDST3, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n dst4 := _defaultSizes(s->doSimdSymDFT(TDST4, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n mdct := _defaultSizes(s->doSimdSymDFT(TMDCT, s, SSE_2x64f, rec(verify :=true)), 8*[1..12]),\n imdct := _defaultSizes(s->doSimdSymDFT(TIMDCT, s, SSE_2x64f, rec(verify :=true)), 8*[1..12])\n ),\n 2d := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_2x64f, rec(interleavedComplex := true,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 4*List([1..16], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_2x64f, rec(verify:=true, interleavedComplex := true, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_2x64f, rec(interleavedComplex := false,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 4*List([1..16], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_2x64f, rec(verify:=true, interleavedComplex := false, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dct2 := _defaultSizes(s->doSimdSymMDDFT(DCT2, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16]),\n dct3 := _defaultSizes(s->doSimdSymMDDFT(DCT3, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16]),\n dct4 := _defaultSizes(s->doSimdSymMDDFT(DCT4, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16]),\n dst2 := _defaultSizes(s->doSimdSymMDDFT(DST2, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16]),\n dst3 := _defaultSizes(s->doSimdSymMDDFT(DST3, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16]),\n dst4 := _defaultSizes(s->doSimdSymMDDFT(DST4, s, SSE_2x64f, rec(verify := true)), [4, 8, 12, 16])\n )\n ),\n 4x32i := rec(\n wht := rec(\n small := _defaultSizes(s->doSimdWht(s, SSE_4x32i, rec(verify := true, oddSizes := true, svct := true, stdTTensor := true, tsplPFA := false)), List([], i->2^i)),\n medium := _defaultSizes(s->doSimdWht(s, SSE_4x32i, rec(oddSizes := false, svct := true, stdTTensor := true, tsplPFA := false)), List([4..10], i->2^i))\n )\n ),\n 4x32f := rec(\n wht := rec(\n small := _defaultSizes(s->doSimdWht(s, SSE_4x32f, rec(verify := true, oddSizes := true, svct := true, stdTTensor := true, tsplPFA := false)), List([1..3], i->2^i)),\n medium := _defaultSizes(s->doSimdWht(s, SSE_4x32f, rec(oddSizes := false, svct := true, stdTTensor := true, tsplPFA := false)), List([4..10], i->2^i))\n ),\n 1d := rec(\n dft_sc := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_4x32f, rec(verify:=true, interleavedComplex := false, stdTTensor := false, globalUnrolling:=10000)),\n [ 2..64 ]),\n medium := _defaultSizes(s->doSimdDft(s, SSE_4x32f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false)),\n _svctSizes(1024, 16, 4)),\n # medium := spiral.libgen.doParSimdDft(SSE_4x32f, 1, _svctSizes(1024, 16, 4), false, true, false, false),\n # large := spiral.libgen.doParSimdDft(SSE_4x32f, 1, List([4..20], i->2^i), false, true, false, false)\n\n ),\n dft_ic := rec(\n small := _defaultSizes(s->doSimdDft(s, SSE_4x32f, rec(verify:=true, interleavedComplex := true, PRDFT:=true, URDFT:= true, cplxVect := true, stdTTensor := false, globalUnrolling:=10000)),\n [ 2..64 ]),\n medium := _defaultSizes(s->doSimdDft(s, SSE_4x32f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := true)),\n _svctSizes(1024, 16, 4)),\n medium_cx := _defaultSizes(s->doSimdDft(s, SSE_4x32f, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := true,\n cplxVect := true, realVect := false, PRDFT := false, URDFT := true)),\n _svctSizes(1024, 16, 4))\n # medium := spiral.libgen.doParSimdDft(SSE_4x32f, 1, _svctSizes(1024, 16, 4), false, true, false, true),\n # large := spiral.libgen.doParSimdDft(SSE_4x32f, 1, List([4..20], i->2^i), false, true, false, true)\n ),\n rdft := _defaultSizes(s->doSimdSymDFT(TRDFT, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n trdft := _defaultSizes(s->doSimdSymDFT(TRDFT, s, SSE_4x32f, rec( verify:=true, \n interleavedComplex := true, PRDFT:=true, URDFT:= true, tsplBluestein := false, cplxVect := true,\n stdTTensor := false, realVect := true, propagateNth := true, useDeref := true, \n globalUnrolling:=10000)), 8*[1..32]),\n dht := _defaultSizes(s->doSimdSymDFT(TDHT, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dct2 := _defaultSizes(s->doSimdSymDFT(TDCT2, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dct3 := _defaultSizes(s->doSimdSymDFT(TDCT3, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dct4 := _defaultSizes(s->doSimdSymDFT(TDCT4, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dst2 := _defaultSizes(s->doSimdSymDFT(TDST2, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dst3 := _defaultSizes(s->doSimdSymDFT(TDST3, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n dst4 := _defaultSizes(s->doSimdSymDFT(TDST4, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n mdct := _defaultSizes(s->doSimdSymDFT(TMDCT, s, SSE_4x32f, rec(verify :=true)), 32*[1..12]),\n imdct := _defaultSizes(s->doSimdSymDFT(TIMDCT, s, SSE_4x32f, rec(verify :=true)), 32*[1..12])\n ),\n 2d := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_4x32f, rec(interleavedComplex := true,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 16*List([1..8], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_4x32f, rec(verify:=true, interleavedComplex := true, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_4x32f, rec(interleavedComplex := false,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 16*List([1..8], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_4x32f, rec(verify:=true, interleavedComplex := false, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dct2 := _defaultSizes(s->doSimdSymMDDFT(DCT2, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n dct3 := _defaultSizes(s->doSimdSymMDDFT(DCT3, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n dct4 := _defaultSizes(s->doSimdSymMDDFT(DCT4, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n dst2 := _defaultSizes(s->doSimdSymMDDFT(DST2, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n dst3 := _defaultSizes(s->doSimdSymMDDFT(DST3, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n dst4 := _defaultSizes(s->doSimdSymMDDFT(DST4, s, SSE_4x32f, rec(verify := true)), [4, 8, 12, 16]),\n\t\t\t\t# DO NOT USE BECAUSE IT GENERATES A NON_COMPATIBLE INIT() FUNCTION FOR USE WITH STANDARD TIMER\n # conv := _defaultSizes(s->doSimdMdConv(s, SSE_4x32f, rec(svct := true, oddSizes := false, \n\t\t\t\t#\t\t\t\t\tsplitComplexTPrm := true, TRCDiag_VRCLR := true, globalUnrolling := 150, measureFinal := false)),\n\t\t\t\t#\t\t\t\t\t16*[1..32])\n )\n ),\n 8x16i := rec(\n wht := rec(\n small := _defaultSizes(s->doSimdWht(s, SSE_8x16i, rec(verify := true, oddSizes := true, svct := true, stdTTensor := true, tsplPFA := false)), List([1..5], i->2^i)),\n medium := _defaultSizes(s->doSimdWht(s, SSE_8x16i, rec(oddSizes := false, svct := true, stdTTensor := true, tsplPFA := false)), List([6..10], i->2^i))\n ),\n 1d := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doSimdDft(s, SSE_8x16i, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := true, verify := true)), 64*[1..4]),\n small := _defaultSizes(s->doSimdDft(s, SSE_8x16i, rec(verify:=true, interleavedComplex := true, stdTTensor := false, globalUnrolling:=10000)), [2..16])\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doSimdDft(s, SSE_8x16i, rec(tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false, verify := true)), 64*[1..4]),\n small := _defaultSizes(s->doSimdDft(s, SSE_8x16i, rec(verify:=true, interleavedComplex := false, stdTTensor := false, globalUnrolling:=10000)), [2..16])\n ),\n rdft := _defaultSizes(s->doSimdSymDFT(TRDFT, s, SSE_8x16i, rec(verify := true)), 128*[1..4]),\n dht := _defaultSizes(s->doSimdSymDFT(TDHT, s, SSE_8x16i, rec(verify :=true)), 128*[1..4]),\n dct2 := _defaultSizes(s->doSimdSymDFT(TDCT2, s, SSE_8x16i, rec(verify := true, fracbits := 8)), [128]),\n dct3 := _defaultSizes(s->doSimdSymDFT(TDCT3, s, SSE_8x16i, rec(verify := true, fracbits := 8)), [128]),\n dct4 := _defaultSizes(s->doSimdSymDFT(TDCT4, s, SSE_8x16i, rec(verify := true)), 128*[1..4]),\n dst2 := _defaultSizes(s->doSimdSymDFT(TDST2, s, SSE_8x16i, rec(verify := true)), 128*[1..4]),\n dst3 := _defaultSizes(s->doSimdSymDFT(TDST3, s, SSE_8x16i, rec(verify := true)), 128*[1..4]),\n dst4 := _defaultSizes(s->doSimdSymDFT(TDST4, s, SSE_8x16i, rec(verify := true)), 128*[1..4]),\n mdct := _defaultSizes(s->doSimdSymDFT(TMDCT, s, SSE_8x16i, rec(verify :=true)), 128*[1..4]),\n imdct := _defaultSizes(s->doSimdSymDFT(TMDCT, s, SSE_8x16i, rec(verify :=true)), 128*[1..4])\n ),\n 2d := rec(\n dft_ic := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_8x16i, rec(interleavedComplex := true,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 64*List([1..2], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_8x16i, rec(verify:=true, interleavedComplex := true, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dft_sc := rec(\n medium := _defaultSizes(s->doSimdMddft(s, SSE_8x16i, rec(interleavedComplex := false,\n oddSizes := false, svct := true, splitL := false, pushTag := true, flipIxA := false, stdTTensor := true, tsplPFA := false)),\n 64*List([1..2], i->[i,i])),\n small := _defaultSizes(s->doSimdMddft(s, SSE_8x16i, rec(verify:=true, interleavedComplex := false, globalUnrolling:=10000,\n tsplPFA := false, pushTag:= false, oddSizes := true, svct := true, splitL := false)),\n List([2..16], i->[i,i]))\n ),\n dct2 := _defaultSizes(s->doSimdSymMDDFT(DCT2, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16]),\n dct3 := _defaultSizes(s->doSimdSymMDDFT(DCT3, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16]),\n dct4 := _defaultSizes(s->doSimdSymMDDFT(DCT4, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16]),\n dst2 := _defaultSizes(s->doSimdSymMDDFT(DST2, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16]),\n dst3 := _defaultSizes(s->doSimdSymMDDFT(DST3, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16]),\n dst4 := _defaultSizes(s->doSimdSymMDDFT(DST4, s, SSE_8x16i, rec(verify := true, fracbits := 10)), [8, 16])\n )\n )\n );\n else\n return false;\n fi;\nend;\n", "meta": {"hexsha": "c64354ad3521bc4ee1c4a86c54886aac124b262c", "size": 19335, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/sse/bench.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/sse/bench.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/platforms/sse/bench.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 85.5530973451, "max_line_length": 285, "alphanum_fraction": 0.5189552625, "num_tokens": 5929, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.78793120560257, "lm_q2_score": 0.5428632831725052, "lm_q1q2_score": 0.4277389211874814}} {"text": "\n#\n# ---------- Constructors ----------\n#\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList,IsInt],\n function(sys,coeffs,ordering,order)\n local object;\n \n if Filtered(coeffs,i->not i[2] in Integers)=[] then coeffs:=List(coeffs,i->[i[1],One(ring(sys))*i[2]]);\n elif Filtered(coeffs,i->not i[2] in ring(sys))<>[] then Error(\"The coefficients ar not in indicated ring.\"); fi;\n\n object:=Objectify(NewType(NewFamily(\"UnipotentFamily\"),\n IsAttributeStoringRep and\n IsUnipotent and\n IsMultiplicativeElementWithInverse and\n IsMultiplicativeElementWithOne),\n rec());\n\n SetchevalleyAdj(object,sys);\n SetOrdering(object,ordering);\n \n Setcoefficients(object,Canonic(sys,coeffs,ordering));\n# SetInverse(object,InverseOp(object)); This is set at the first call Inverse(obj);\n\n if order = -1 and Characteristic(sys)>0 then\n SetOrder(object,OrderOp(object));\n elif order > -1 then\n SetOrder(object,order);\n fi;\n \n SetName(object,Concatenation(\"\"));\n return object;\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n\n return Unipotent(sys,coeffs,ordering,-2);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList,IsInt],\n function(sys,coeffs,order)\n local ordering,tmp,i,slot;\n \n tmp:=ShallowCopy(coeffs);\n Sort(tmp,function(a,b) return a[1]ordering[i[1]]);\n\n for i in [1..Length(coeffs)] do\n ordering[coeffs[i][1]]:=tmp[i];\n od; \n\n return Unipotent(sys,Filtered(coeffs,i->i[2]<>Zero(ring(sys))),ordering,order);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsChevalleyAdj,IsList],\n function(sys,coeffs)\n\n return Unipotent(sys,coeffs,-2);#-1);\nend);\n\nInstallMethod(Unipotent,\n \"Unipotent element in simple adjoint type\",\n [IsNilpotentChv],\n function(e)\n\n return Unipotent(chevalleyAdj(e),coefficients(e));\nend);\n\n\n#\n# ---------- Canonic form of element ----------\n#\n\nInstallMethod(Canonic,\n \"Canonic form of coefficients of unipotent element in given ordering\",\n [IsChevalleyAdj,IsList,IsList],\n function(sys,coeffs,ordering)\n local lista,\n pr,Cijrs,\n flag,i,temp,suma,param,cc,k;\n \n lista:=List(coeffs,i->ShallowCopy(i));\n pr:=positiveRoots(sys);\n\n Cijrs:=C(sys);\n flag:=true;\n while flag do\n flag:=false;\n i:=Length(lista);\n while 0 < i do\n if lista[i][2] = Zero(ring(sys)) then \n Remove(lista,i);\n flag:=true;\n elif 1 < i and lista[i][1] = lista[i-1][1] then\n lista[i-1][2]:=lista[i-1][2]+lista[i][2];\n Remove(lista,i);\n flag:=true;\n elif 1 < i and ordering[lista[i][1]] < ordering[lista[i-1][1]] then\n temp:=lista[i]; lista[i]:=lista[i-1]; lista[i-1]:=temp;\n \n #aici r si s sunt pe pozitia i-1 si repsectiv i\n k:=1;\n for cc in Cijrs[lista[i-1][1]][lista[i][1]] do\n suma:=cc[1]*pr[lista[i-1][1]]+cc[2]*pr[lista[i][1]];\n param:=cc[3]*((-1)^cc[1])*(lista[i-1][2]^cc[1])*(lista[i][2]^cc[2]);\n Add(lista,[Position(pr,suma),param],i+k);\n k:=k+1;\n od;\n flag:=true;\n fi;\n i:=i-1;\n od;\n od;\n\n return Immutable(lista);\nend);\n\n#\n# ---------- Arithmetic Operations ----------\n#\n\nInstallMethod(InverseMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n local i,lista,len,reverse_order;\n \n lista:=List(coefficients(u),i->StructuralCopy(i));\n len:=Length(lista);\n for i in [1..len] do\n Add(lista,[lista[len-i+1][1],-lista[len-i+1][2]]);\n Remove(lista,len-i+1);\n od;\n\n reverse_order:=function(o)\n local maxim;\n maxim:=Maximum(o);\n return List(o,i->maxim-i+1);\n end;\n \n return Unipotent(chevalleyAdj(u),lista,reverse_order(Ordering(u)),-2);#0);\nend);\n\nInstallMethod(OneMutable,\n \"Inverse of unipotent element\",\n [IsUnipotent],\n function(u)\n\n return One(chevalleyAdj(u),[],0);\nend);\n\nInstallMethod(\\*,\n \"Multiplication for unipotent elements a*b with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2,\n generic,result,coeffs1,coeffs2,\n APR,avars,pr_len,\n i;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n \n return Unipotent(sys2,Concatenation(coefficients(u1),coefficients(u2)),Ordering(u2));\nend);\n\nInstallMethod(\\*,\n \"Action of unipotent element u on nilpotent e: u*e\",\n [IsUnipotent,IsNilpotentChv],\n function(u,e)\n local result,\n sys1,sys2,Mrsi,pr,\n uas,r,s,i,pos;\n \n sys1:=chevalleyAdj(u);\n sys2:=chevalleyAdj(e);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\");\n fi;\n \n pr:=positiveRoots(sys1);\n Mrsi:=M(sys1);\n\n uas:=Reversed(coefficients(u));\n result:=List(coefficients(e),i->ShallowCopy(i));\n\n # for this see Carter pg.64\n for r in uas do\n for s in result do\n for i in [1..Length(Mrsi[r[1]][s[1]])] do\n pos:=Position(pr,i*pr[r[1]]+pr[s[1]]);\n result:=Concatenation(result,[[pos,Mrsi[r[1]][s[1]][i]*r[2]^i*s[2]]]);\n od;\n od;\n od;\n\n return NilpotentChv(sys2,result);\nend);\n\nInstallMethod(OrderOp,\n \"Order of unipotent element\",\n [IsUnipotent],\n function(u)\n local result,\n p,u_to_p,putere,i;\n\n if coefficients(u)=[] then return 1; fi;\n\n p:=Characteristic(chevalleyAdj(u));\n\n u_to_p:=u;\n for i in [1..p-1] do u_to_p:=u_to_p*u; od;\n\n result:=1;\n putere:=u_to_p;\n while coefficients(putere)<>[] do\n putere:=putere*u_to_p;\n result:=result+1;\n od;\n \n return p*result;\nend);\n\nInstallMethod(Comm,\n \"Commutator for unipotent elements a^-1b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u1^-1),coefficients(u2^-1),\n coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Conj,\n \"Conjugation for unipotent elements b^-1ab with the ordering of b\",\n [IsUnipotent,IsUnipotent],\n function(u1,u2)\n local sys1,sys2;\n\n sys1:=chevalleyAdj(u1);\n sys2:=chevalleyAdj(u2);\n if type(sys1)<>type(sys2) or\n rank(sys1)<>rank(sys2) or\n ring(sys1)<>ring(sys2) then Error(\"Not in the same family.\"); fi;\n return Unipotent(sys2,\n Concatenation(coefficients(u2^-1),coefficients(u1),coefficients(u2)),\n Ordering(u2));\nend);\n\nInstallMethod(Subword,\n \"Subword of a unipotent element by list of roots\",\n [IsUnipotent,IsList],\n function(u,l)\n local coeffs;\n coeffs:=Filtered(coefficients(u),i->i[1] in l);\n \n return Unipotent(chevalleyAdj(u),coeffs,Ordering(u));\nend);\n\nInstallMethod(InsertWord,\n \"Shuffles a word into a unipotent element u according to the ordering of u\",\n [IsUnipotent,IsList],\n function(u,word)\n local coeffs,\n sys,check,ord;\n\n sys:=chevalleyAdj(u);\n check:=ForAll(word,i-> i[2] in ring(sys));\n if not check then\n Error(\"The word cannot be shuffled into u: not over the same ring!\\n\");\n fi;\n\n coeffs:=coefficients(u);\n coeffs:=Concatenation(coeffs,word);\n ord:=Ordering(u);\n Sort(coeffs,function(a,b) return ord[a[1]]Coefficients(B,i));\n \n zero:=Zero(ring(sys));\n unu:=One(ring(sys));\n\n A_rs:=A(sys);\n M_rsi:=M(sys);\n\n result:=[];\n # s in positive roots\n for s in [1..pr_len] do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root then\n tmp[s]:=unu;\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,i*roots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]*param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # s in negative roots\n for s in [1..pr_len]+pr_len do\n tmp:=List([1..Dimension(L)],i->zero);\n \n if s = root+pr_len then\n # e_{-r}\n tmp[s]:=unu;\n # -t^2*e_{r}\n tmp[root]:=-param^2;\n # t*h_{r}\n tmp:=tmp+param*cochars[root];\n else\n tmp[s]:=unu;\n for i in [1..Length(M_rsi[root][s])] do\n poz:=Position(roots,i*roots[root]+roots[s]);\n tmp[poz]:=M_rsi[root][s][i]*param^i;\n od;\n fi;\n Add(result,tmp);\n od;\n\n # h_s\n for s in [1..Rank] do\n tmp:=List([1..Dimension(L)],i->zero);\n # h_s\n tmp:=tmp+cochars[s];\n # -A_{sr}*t*e_r\n tmp[root]:=-A_rs[s][root]*param;\n Add(result,tmp);\n od;\n\n return result;#TransposedMat(result);\nend);\n\nInstallMethod(Adu,\n \"Adu on the whole Lie algebra\",\n [IsUnipotent],\n function(u)\n return Product(coefficients(u),i->AduAlphat(chevalleyAdj(u),i[1],i[2]));\nend);\n\nInstallMethod(AduJordanBlocksOp,\n \"Computes Jordan Blocks of Adu using SageMath\",\n [IsUnipotent],\n function(u)\n local sage_script,current_dir,tmp_file,result,\n ad,dim,i,j;\n\n sage_script:=Concatenation(\"~/sage/sage-4.7.2-linux-32bit-ubuntu_10.04_lts-i686-Linux/sage \",\n \"~/workspace/ChevalleyAdj/sage/tmp/jordan.sage\");\n current_dir:=Directory(\"~/workspace/ChevalleyAdj/sage/tmp/\");\n tmp_file:=Filename(current_dir,\"matrix.sage\");\n result:=Filename(current_dir,\"blocks.gap\");\n\n #while IsPolynomialRing(ring(chevalleyAdj(u))) do u:=Descend(u,CoefficientsRing(ring(chevalleyAdj(u)))); od;\n if IsAlgebraicU(chevalleyAdj(u)) then u:=Descend(u,chevalleyAdj(chevalleyAdj(u))); fi;\n ad:=Adu(u);\n ad:=List(ad,i->List(i,j->Int(j)));\n PrintTo(tmp_file,\"p=\",String(Characteristic(chevalleyAdj(u))),\"\\nmat=\");\n AppendTo(tmp_file,\"[\");\n dim:=Length(ad);\n for i in [1..dim] do\n AppendTo(tmp_file,\"[\");\n for j in [1..dim] do\n AppendTo(tmp_file,String(ad[i][j]));\n if j<>dim then AppendTo(tmp_file,\",\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n if i<>dim then AppendTo(tmp_file,\",\\n\"); fi;\n od;\n AppendTo(tmp_file,\"]\");\n\n Exec(sage_script);\n\n result:=ReadAsFunction(result);\n result:=result();\n\n return result;\nend);\n\nInstallMethod(PositiveAdu,\n \"Ad(u) restricted to Lie(U) where U is spanned by positive root groups\",\n [IsUnipotent],\n function(u)\n local result,\n sys,\n baza,b,pr,pr_len;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n baza:=List([1..pr_len],i->NilpotentChv(sys,[[i,1]]));\n\n result:=[];\n for b in baza do\n result:=Concatenation(result,[u*b]);\n od;\n\n return List(result,i->LieAlgebraCoeffs(i){[1..pr_len]});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n function(u,roots)\n local sys,adu,pr,\n croots,check;\n\n if not IsInt(roots[1]) then TryNextMethod(); fi;\n\n sys:=chevalleyAdj(u);\n adu:=PositiveAdu(u);\n pr:=positiveRoots(sys);\n croots:=Filtered([1..Length(pr)],i->not i in roots);\n\n check:=Filtered(Concatenation(List(croots,i->adu[i]{roots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n check:=Filtered(Concatenation(List(roots,i->adu[i]{croots})),j->j<>Zero(ring(sys)));\n if check<>[] then Error(\"Ade cannot be restricted like this.\"); fi;\n \n return List(roots,i->adu[i]{roots});\nend);\n\nInstallMethod(RestrictedAdu,\n \"Ad(u) restricted to a subspace of Lie(U) spanned given (positive) roots\",\n [IsUnipotent,IsList],\n 1,\n function(u,vectors)\n local result,vectors_len,\n adu,img,\n CPR,cvar_names,cvars,cvectors,sysCPR,uu,\n tmp,generic,relations,relations_len,sol,i;\n\n vectors_len:=Length(vectors);\n\n cvar_names:=List([1..vectors_len],i->Concatenation(\"c_\",String(i)));\n CPR:=PolynomialRing(ring(chevalleyAdj(u)),cvar_names);\n cvars:=IndeterminatesOfPolynomialRing(CPR);\n sysCPR:=ChevalleyAdj(chevalleyAdj(u),CPR);\n\n cvectors:=List(vectors,i->Ascend(i,sysCPR));\n uu:=Ascend(u,sysCPR);\n img:=List(cvectors,i->uu*i);\n\n result:=[];\n for i in [1..vectors_len] do\n tmp:=ShallowCopy(cvars);\n generic:=Sum(List([1..vectors_len],i->tmp[i]*cvectors[i]));\n relations:=List(coefficients(img[i]-generic),i->i[2]);\n relations:=Filtered(relations,i->i<>Zero(CPR));\n #Error(\"!\");\n tmp:=SolveRelations(relations,cvars,tmp,CPR);\n if tmp[2]<>[] then\n #Error(\"!\");\n Print(\"RestrictedAdu: did not solve all relations! \",relations,\"\\n\");\n fi;\n tmp:=List(tmp[1],i->Value(i,cvars,cvars));\n #tmp:=Sum(List([1..vectors_len],i->tmp[i]*vectors[i])); # I want the matrix\n Add(result,tmp);\n od;\n\n return result; \nend);\n\nInstallMethod(PositiveFixedspace,\n \"Ker of PositiveAdu\",\n [IsUnipotent],\n function(u)\n local result,\n adu,sys,unu,pr,pr_len,ns;\n\n sys:=chevalleyAdj(u);\n pr:=positiveRoots(sys);\n pr_len:=Length(pr);\n\n adu:=PositiveAdu(u);\n unu:=DiagonalMat(List([1..pr_len],i->One(ring(sys))));\n ns:=NullspaceMat(adu-unu);\n\n result:=List(ns,v->List([1..pr_len],j->[j,v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\nInstallMethod(RestrictedFixedspace,\n \"Ker of RestrictedAdu\",\n [IsUnipotent,IsList],\n function(u,roots)\n local result,\n radu,sys,unu,roots_len,ns;\n\n sys:=chevalleyAdj(u);\n roots_len:=Length(roots);\n\n radu:=RestrictedAdu(u,roots);\n unu:=DiagonalMat(List([1..roots_len],i->One(ring(sys))));\n ns:=NullspaceMat(radu-unu);\n\n result:=List(ns,v->List([1..roots_len],j->[roots[j],v[j]]));\n result:=List(result,i->NilpotentChv(sys,i));\n \n return result;\nend);\n\n\n", "meta": {"hexsha": "a1d3fc619e8b254502d90afd9af6b356c5182013", "size": 19936, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/unichv.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/unichv.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "lib/unichv.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 35.4103019538, "max_line_length": 126, "alphanum_fraction": 0.4629313804, "num_tokens": 4607, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6992544210587585, "lm_q2_score": 0.611381973294151, "lm_q1q2_score": 0.42751154778156286}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(JoinDirectSums, RuleSet);\nRewriteRules(JoinDirectSums, rec(\n combine := ARule(Compose, [@(1, DelayedDirectSum), @(2, DelayedDirectSum,\n e -> let(c1:=@(1).val.children(), c2:=e.children(), Length(c1) = Length(c2) and ForAll([1..Length(c1)], i->c1[i].dims()[2] = c2[i].dims()[1]))) ],\n e -> let(c1:=@(1).val.children(), c2:=@(2).val.children(), [ DelayedDirectSum(List([1..Length(c1)], i -> c1[i] * c2[i])) ])\n )\n));\n\nClass(TerminateDirectSums, RuleSet);\nRewriteRules(TerminateDirectSums, rec(\n terminate := Rule(@(1, DelayedDirectSum), e-> DirectSum(@(1).val.children()).sums())\n));\n", "meta": {"hexsha": "964158d586ae0f472c596ce652b5faf1735eff5b", "size": 694, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/directsum.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/sigma/directsum.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/sigma/directsum.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.5555555556, "max_line_length": 154, "alphanum_fraction": 0.6325648415, "num_tokens": 226, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191337850932, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554503059056686}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# Sparse\n# ==========================================================================\nClass(Sparse, BaseMat, rec(\n new := meth(self, L)\n Constraint(IsList(L));\n\tif not ForAll(L, t -> IsList(t) and Length(t)=3 and \n\t\t IsInt(t[1]) and IsInt(t[2])) then\n\t Error(\" must be a list of triples [i, j, a_(i,j)]\");\n\tfi;\t\n return SPL(WithBases( self, rec( element := L,\n\t\t\t\t dimensions := [ Maximum(List(L, t->t[1])),\n\t\t\t\t Maximum(List(L, t->t[2])) ]\n )));\n end,\n #-----------------------------------------------------------------------\n dims := self >> [ Maximum(List(self.element, t->t[1])), \n\t Maximum(List(self.element, t->t[2])) ],\n #-----------------------------------------------------------------------\n isPermutation := False, \n #-----------------------------------------------------------------------\n isReal := self >> ForAll(self.element, t -> IsRealNumber(t[3])),\n #-----------------------------------------------------------------------\n toAMat := self >> AMatMat(List(MatSparseSPL(self), r -> List(r, EvalScalar))),\n #-----------------------------------------------------------------------\n transpose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], t[3]]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n conjTranspose := meth(self) # we use CopyFields to copy all fields of self\n local L, t;\n\tL := [ ];\n\tfor t in self.element do\n\t Add(L, [t[2], t[1], Global.Conjugate(t[3])]);\n\tod;\n\treturn CopyFields(self, rec(element := L, \n\t\t dimensions := Reversed(self.dims())));\n end,\n #-----------------------------------------------------------------------\n arithmeticCost := meth(self, costMul, costAddMul)\n local cost, row, elms;\n\tcost := costMul(0) - costMul(0); # will work even when costMul(0) <> 0\n\tfor row in [1..self.dimensions[1]] do\n\t elms := Filtered(self.element, e -> e[1]=row);\n\t if Length(elms) > 0 then\n\t\tcost := cost + costMul(elms[1][3]) \n\t\t + Sum(elms{[2..Length(elms)]}, e -> costAddMul(e[3]));\n\t fi;\n\tod;\n\treturn cost;\n end\n));\n\n", "meta": {"hexsha": "98600b50d9d7c68e417c1239c5f00dd26879f3ca", "size": 2474, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Sparse.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/Sparse.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/Sparse.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.65625, "max_line_length": 82, "alphanum_fraction": 0.4114793856, "num_tokens": 583, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7090191214879992, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.42554502320999416}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n\n#F RuleTreeOps.\\=( , )\n#F returns true if and are equal, i.e., they\n#F represent the same breakdown strategy. Otherwise, false is returned.\n#F\n\nRuleTreeOps := CantCopy(OperationsRecord(\"RuleTreeOps\"));\n\n\nIsRuleTree := T -> IsRec(T) and IsBound(T.isRuleTree) and T.isRuleTree;\n\n\n#F Ruletrees\n#F =========\n#F\n#F A ruletree is a record with the following mandatory fields:\n#F\n#F isRuleTree = \"true\" # identifies ruletrees\n#F operations = RuleTreeOps # operations record\n#F node = # the spl expanded\n#F transposed = false/true # indicates whether or\n#F transpose - - transpose\n#F rule = # the rule chosen\n#F children = # the children, a list of\n#F ruletrees/non-terminal spls\n#F\n#F Note that children can be a list of ruletrees as well as non-terminal spls.\n#F The field children is empty iff the ruletree is a leaf.\n#F In general, the .node is a non-terminal spl that is expanded by .rule.\n#F\n#F The following fields are optional:\n#F splOptions = [ , , .. ]\n#F valid : \"unrolled\", \"pcl\"\n#F\n\nClass(RuleTreeClass, rec(\n spl := self >> SPLRuleTree(self),\n measure := self >> SPLRuleTree(self).measure(),\n shortPrint := false,\n dims := self >> self.node.dims(),\n dmn := self >> self.node.dmn(),\n rng := self >> self.node.rng(),\n\n print := meth(self, i, is)\n local ch;\n\n if Length(self.children) = 0 then\n # print leaves in one line\n Print(self.rule, \"( \");\n When (self.transposed, Print(\"\\\"T\\\",\"));\n self.node.print(i+is, is);\n When (IsBound(self.splOptions),\n Print(\", \", self.splOptions, \" )\"),\n Print(\" )\"));\n else\n # print children on separate lines\n Print(self.rule, \"( \",\n When(self.transposed, \"\\\"T\\\", \", \"\"),\n When(not self.shortPrint, self.node.print(i+is, is), \"\"), \",\\n\", Blanks(i+is)\n );\n self.children[1].print(i+is, is);\n for ch in Drop(self.children, 1) do\n Print(\",\\n\", Blanks(i+is));\n ch.print(i+is, is);\n od;\n\n When (IsBound(self.splOptions),\n Print(\"\\n\", Blanks(i), \", \", self.splOptions, \" )\"),\n Print(\" )\"));\n fi;\n end,\n\n # new with tSPL and opts.baseHash:\n # we cannot blindly transpose everything, as vector\n # permutations that are automatically generated\n # may not support transposition\n transpose := self >>\n When((not self.node.transposeSymmetric()) and self.node.isSymmetric(),\n self,\n RuleTree(\n self.rule,\n When(self.transposed, \"\", \"T\"),\n self.node.transpose(),\n List(self.children, x->x.transpose())\n )\n ),\n # RuleTreeRewriting enabled by default\n # one can disable it with \"EnableRuleTreeRewriting(false)\"\n rChildren := (self) >> [ self.node, self.children ],\n rSetChild := rSetChildFields(\"node\", \"children\"),\n from_rChildren := (self, rch) >>\n RuleTree(self.rule, When(self.transposed, \"T\", \"\"), rch[1], rch[2])\n));\n\nRuleTreeOps.\\= := function( T1, T2 )\n return\n IsRuleTree(T1) and IsRuleTree(T2) and\n T1.rule = T2.rule and\n T1.transposed = T2.transposed and\n IsIdenticalSPL(T1.node, T2.node) and\n T1.children = T2.children and\n ( ( IsBound(T1.splOptions) and \n\t\t IsBound(T2.splOptions) and\n T1.splOptions = T2.splOptions\n\t\t\t) or\n ( not IsBound(T1.splOptions) and \n\t\t\t not IsBound(T2.splOptions)\n\t\t\t)\n );\nend;\n\n#F RuleTreeNC( , , )\n#F returns the corresponding ruletree without any checking.\n\nRuleTreeNC := function ( R, S, C )\n return WithBases(RuleTreeClass,\n rec(\n isRuleTree := true,\n operations := RuleTreeOps,\n node := S,\n transposed := false,\n rule := R,\n children := C\n\t\t)\n );\nend;\n\n\n#F RuleTree(\n#F ,\n#F [ \"T\" ,]\n#F \n#F [, ]\n#F [, ]\n#F )\n#F\n#F Creates a ruletree for \n#F using with . The can be non-terminal spls\n#F or ruletrees. It is checked whether can be derived\n#F from using .\n#F If the string \"T\" is supplied, then instead of , the\n#F sequence transpose - - transpose is denoted. In this case\n#F and are also transposed. This construction\n#F avoids unnecessary recoding of rules that are just transposes of\n#F other rules. In this case, must have the field\n#F .forTransposition set to true.\n#F\n#F The argument provides options used for spl compilation.\n#F See top of this file for valid options; examples are \"unrolled\" and \"pcl\".\n#F might be empty (default) in which case the ruletree\n#F returned is a leaf.\n#F\nRuleTree := function ( arg )\n local a, R, t, S, C, u, S1, C1, RT;\n S := false;\n t := false;\n u := [ ];\n C := [ ];\n R := false;\n\n for a in arg do\n if IsString(a) and a = \"T\" then \n\t t := true;\n elif IsList(a) and ForAll(a, IsString) then \n\t u := a;\n elif IsSPL(a) then\n\t\t\tif S=false then \n\t\t\t\tS := a;\n\t\t\telse \n\t\t\t\tAdd(C, a); \n\t\t\tfi;\n\t\telif IsRuleTree(a) then \n\t\t\tAdd(C, a);\n\t\telif IsList(a) then \n\t\t\tAppend(C, a);\n\t\telif IsRule(a) and R=false then \n\t\t\tR := a;\n\t\telse Error(\n\t\t\t\"usage: \\n\",\n\t\t\t\" RuleTree( \\n\",\n\t\t\t\" , [ \\\"T\\\" ,] \\n\",\n\t\t\t\" [, ] [, ] )\");\n\n\t\tfi;\n od;\n\n Constraint(IsRule(R));\n Constraint(IsSPL(S));\n\n if not IsList(u) and ForAll(u, IsString) then\n Error(\" must be a list of spl options\");\n elif not (IsList(C) and ForAll(C, c -> IsSPL(c) or IsRuleTree(c))) then\n Error(\" must be a list of ruletrees or non-terminal spls\");\n fi;\n\n RT := RuleTreeNC(R, S, C);\n if u <> [ ]\n\t then RT.splOptions := u;\n\tfi;\n return RT;\nend;\n\n\n#F ExtractChildrenSPL ( )\n#F returns the list of non-terminal spls contained in .\n#F The order is left first - depth first (non-terminals are\n#F always leaves.\n#F\nExtractChildrenSPL := S -> Collect(S, @.cond(IsNonTerminal));\n\n\n#F CopyRuleTree( )\n#F returns a copy of . All fields apart from .children\n#F are copied by reference.\n#F\nCopyRuleTree := function( orig )\n local new;\n new := ShallowCopy(orig);\n if IsRuleTree(new) then \n\t new.children := List(orig.children, CopyRuleTree);\n\tfi;\n return new;\nend;\n\n_matchChildren := (C1, C2) ->\n Length(C1)=Length(C2) and\n ForAll([1..Length(C1)],\n j -> IsHashIdenticalSPL(HashAsSPL(C1[j]), HashAsSPL(C2[j])) or\n (ObjId(C1[j])=InfoNt and ObjId(C2[j])=InfoNt));\n\n#F ApplyRuleTreeSPL( , , )\n#F creates a ruletree for using rules from the \n#F (if possible)\n#F Uses: opts.breakdownRules (for backwards compatibility of R.switch only)\nApplyRuleTreeSPL := function ( rtree, spl, opts )\n local i, R, C, C1, CC, children, L;\n Constraint(IsRuleTree(rtree));\n Constraint(IsSPL(spl));\n\n if rtree.transposed then\n return ApplyRuleTreeSPL(rtree.transpose(), spl.transpose(), opts).transpose();\n fi;\n\n R := rtree.rule;\n children:=[];\n\n # if was not compatible with .node to start with\n # then at some point there will be a split in that is not\n # applicable to the generated ruletree.\n if not IsApplicableRule( R, spl, opts.breakdownRules ) then\n Error(\" can not be expanded from \");\n fi;\n\n # determine the right set of children from allChildren to be used\n # in expansion\n C1 := _allChildren(R, rtree.node, opts);\n C := List([1..Length(rtree.children)], c -> rtree.children[c].node);\n i := PositionProperty([1..Length(C1)], j -> _matchChildren(C1[j], C));\n\n # DEBUG HACK: AppendTo(\"applytree\", R, \"\\n\", C, \"\\n\", C1, \"\\n---------\\n\");\n if i = false then\n Error(\" can not be expanded from , could not find matching children\"); \n\tfi;\n\n # determine all children for and pick the right set\n L := _allChildren(R, spl, opts);\n if i > Length(L) then\n Error(\" can not be expanded from \");\n else\n C1 := L[i];\n fi;\n\n # recurse and return\n children := List([1..Length(rtree.children)], i -> ApplyRuleTreeSPL(rtree.children[i], C1[i], opts));\n\n return RuleTreeNC(R, spl, children);\nend;\n\n\n#F Printing RuleTrees\n#F ------------------\n#F\n\n#F RuleTreeOps.Print( [, , ] )\n#F prints with . Further indenting is done\n#F in steps of size . The default is\n#F indent = 0, indentStep = 2.\n#F\nRuleTreeOps.Print := function ( arg )\n local T, indent, indentStep; \n\tif Length(arg) = 1 then\n T := arg[1];\n indent := 0;\n indentStep := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n indent := arg[2];\n indentStep := arg[3];\n else\n Error(\"usage: RuleTreeOps.Print( [, , ] )\");\n fi;\n Constraint(IsRuleTree(T));\n Constraint(IsPosInt0(indent));\n Constraint(IsPosInt0(indentStep));\n T.print(indent, indentStep);\nend;\n\nPrintRuleTreeCustom := function (T, i, is, spl_print, ruletree_print)\n local ch;\n Constraint(IsRuleTree(T) or IsSPL(T));\n Constraint(IsPosInt0(i));\n Constraint(IsPosInt0(is));\n\n if IsSPL(T) then \n spl_print(T);\n else # T is a ruletree\n Print(Blanks(i), ruletree_print(T), \"\\n\");\n for ch in T.children do\n PrintRuleTreeCustom(ch, i+is, is, spl_print, ruletree_print);\n od;\n fi;\nend;\n\n#F PrintNodesRuleTree(\n#F [, , ]\n#F )\n#F pretty prints by displaying only the nodes (non-terminals)\n#F and its parameters. The tree structure is expressed by indentation.\n#F Non-terminals are being marked by (nt).\n#F\n\nPrintNodesRuleTree := function ( arg )\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; \n\t\ti := 0; \n\t\tis := 2;\n elif Length(arg) = 3 then\n T := arg[1];\n\t\ti := arg[2];\n\t\tis := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( [, , ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(T, \" (nt)\"),\n T -> Print(T.node));\nend;\n\n\n#F PrintRulesRuleTree(\n#F [, , ]\n#F )\n#F pretty prints by displaying only the rules and\n#F the node sizes in parentheses. Transposed rules are marked\n#F by ^T. The tree structure is expressed by indentation.\n#F Non-terminals are denoted by nt.\n#F\nPrintRulesRuleTree := function(arg)\n local T, i, is;\n if Length(arg) = 1 then\n T := arg[1]; i := 0; is := 2;\n elif Length(arg) = 3 then\n T := arg[1]; i := arg[2]; is := arg[3];\n else\n Error(\"usage: PrintRulesRuleTree( [, , ] )\");\n fi;\n PrintRuleTreeCustom(T, i, is,\n T -> Print(\"nt (\", T.dimensions[1], \")\"),\n T -> Print(T.rule, When(T.transposed,\" ^ T\",\"\"), \"(\", T.node.dimensions[1], \")\"));\nend;\n\n\n\n#F PrettyPrintRuleTree(\n#F [, [, ] ]\n#F )\n#F pretty prints by displaying only the nodes (non-terminals),\n#F their parameters, and the rules. The tree structure is expressed by\n#F indentation. Non-terminals are being marked by (nt).\n#F\n\nPrettyPrintRuleTree := function ( arg )\n local T, chIndent, whiteIndent, linedIndent, oldLinedIndent, newline, params, i;\n\n # new line plus indents\n newline := function ( )\n local i;\n\n Print(\"\\n\");\n for i in [1..whiteIndent] do\n Print(\" \");\n od;\n if not linedIndent = \"\" then\n Print( linedIndent, \"--\" );\n fi;\n end;\n\n # decode arg\n if Length(arg) = 1 then\n T := arg[1];\n whiteIndent := 0;\n linedIndent := \"\";\n elif Length(arg) = 2 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := \"\";\n elif Length(arg) = 3 then\n T := arg[1];\n whiteIndent := arg[2];\n linedIndent := arg[3];\n else\n Error(\"usage: PrintNodesRuleTree( [, , ] )\");\n fi;\n\n # check arguments\n if not ( IsRuleTree(T) or IsSPL(T) and T.type = \"nonTerminal\" ) then\n Error(\" must be a ruletree or a non-terminal spl\");\n fi;\n if not IsInt(whiteIndent) and whiteIndent >= 0 then\n Error(\" must be pos-int\");\n fi;\n if not IsString(linedIndent) then\n Error(\" must be a string\");\n fi;\n\n chIndent := whiteIndent+Length(linedIndent)+4;\n # spl case\n if IsSPL(T) then\n T.print(chIndent, 2); Print(\" (nt)\");\n return;\n fi;\n \n T.node.print(chIndent, 2);\n Print(\" {\" );\n Print(T.rule);\n if T.transposed then\n Print(\" ^ T\");\n fi;\n if IsBound(T.splOptions) then\n Print(\", \", T.splOptions);\n fi;\n Print( \"}\" );\n\n if Length(T.children) > 0 then\n if linedIndent = \"\" then\n oldLinedIndent := linedIndent;\n else\n oldLinedIndent := Concatenation( linedIndent, \" \" );\n fi;\n linedIndent := Concatenation( oldLinedIndent, \" |\" );\n for i in [1..Length(T.children)-1] do\n newline();\n PrettyPrintRuleTree(T.children[i], whiteIndent, linedIndent);\n od;\n linedIndent := Concatenation( oldLinedIndent, \" \\`\" );\n newline();\n linedIndent := Concatenation( oldLinedIndent, \" \" );\n PrettyPrintRuleTree(T.children[Length(T.children)],\n whiteIndent, linedIndent);\n linedIndent := oldLinedIndent;\n fi;\n if whiteIndent = 0 and linedIndent = \"\" then\n newline();\n fi;\nend;\n\n\n#F Converting RuleTrees\n#F --------------------\n#F\n\n#F AMatRuleTree( ) - returns an amat corresponding to ruletree.\n#F\nAMatRuleTree := T -> AMatSPL(SPLRuleTree(T));\n\n#F MatRuleTree( ) - returns the matrix corresponding to ruletree.\n#F\nMatRuleTree := T -> MatSPL(SPLRuleTree(T));\n\n\n#F Creating Random RuleTrees\n#F -------------------------\n#F\n\nDeclare(SemiRandomRuleTree, _SemiRandomRuleTree);\n\n#F RandomRuleTree( , )\n#F returns a random rule tree for \n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nRandomRuleTree := (spl, opts) -> _SemiRandomRuleTree(spl, false, s->false, opts);\n\nRandomRuleTreeCutoff := (spl, cutoff_func, opts) -> _SemiRandomRuleTree(spl, false, cutoff_func, opts);\n\nRandomRuleTreeDP := (t, opts) -> let(res := spiral.search.DP(t, rec(measureFunction := (R,O)->Random([1..10000]), verbosity := 0), opts), When(res = [], false, res[1].ruletree));\n\n#F SemiRandomRuleTree( , , opts )\n#F returns a random rule tree for with fixed top-level rule\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nSemiRandomRuleTree := (spl, top_rule, opts) -> _SemiRandomRuleTree(spl, top_rule, s->false, opts);\n\n\n_SemiRandomRuleTree := function(spl, top_rule, cutoff_func, opts)\n local ch, i, R, rules, rule, rand, candidates, ch, children, ch_candidates;\n\n if not (IsSPL(spl)) then\n Error(\"usage: SemiRandomRuleTree( , , , )\");\n elif cutoff_func(spl) then\n\t return spl;\n elif MultiHashLookup(opts.baseHashes, spl) <> false then\n return MultiHashLookup(opts.baseHashes, spl)[1].ruletree;\n else\n if top_rule <> false then\n rules := [top_rule];\n else\n rules := AllApplicableRulesDirect(spl, opts.breakdownRules);\n if rules = [ ] then\n return false;\n fi;\n fi;\n\n candidates := Set([1..(Length(rules))]);\n while candidates <> [] do\n rand := RandomList(candidates);\n RemoveSet(candidates, rand);\n\n if rand <= Length(rules) then\n rule := rules[rand];\n ch_candidates := _allChildren(rule, spl,opts);\n ch_candidates := Permuted(ch_candidates, Random(SymmetricGroup(Length(ch_candidates))));\n for children in ch_candidates do\n children := List( children, s -> _SemiRandomRuleTree(s, false, cutoff_func, opts) );\n if not ForAny(children, c -> IsBool(c) and c=false) then\n return RuleTreeNC( rule, spl, children );\n fi;\n od;\n fi;\n od;\n return false;\n fi;\nend;\n\n\n#F Creating all RuleTrees\n#F ----------------------\n#F\n#ExpandSPLRules := function( S, ruleset )\nExpandSPLRules := function( arg )\n local i, L, R, S, ruleset, opts;\n S := arg[1];\n ruleset := arg[2];\n Constraint(IsSPL(S));\n\n if IsBound(arg[3]) then\n\t opts := arg[3];\n else \n\t opts := rec();\n\tfi;\n\n L := [ ];\n for R in AllApplicableRulesDirect(S, ruleset) do\n Append(L, List(_allChildren(R,S,opts), c -> RuleTreeNC(R, S, c)));\n od;\n\n return L;\nend;\n\n#F ExpandSPL( , )\n#F performs one expansion of in all possible ways,\n#F and returns the list of the derived ruletrees.\n#F If there are no breakdown rules for (i.e., not a non-terminal)\n#F then the default base cases rule @_Base is used, which means that\n#F the recursion will continue on its children\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nExpandSPL := (S, opts) -> ExpandSPLRules(S, opts.breakdownRules, opts);\n\n\n_AllRuleTrees := function ( S, cutoff, memohash, opts )\n local L, L1, T, Lc, i, cs, T1, lkup;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n\t\treturn [S];\n\tfi;\n lkup := MultiHashLookup(opts.baseHashes, S);\n if lkup <> false then\n\t\treturn [lkup[1].ruletree];\n\tfi;\n\n lkup := HashLookup(memohash, S);\n if lkup <> false\n\t\tthen return lkup;\n\tfi;\n\n L := ExpandSPL(S, opts);\n if ForAll(L, r -> r.children = [ ]) then\n\t\tHashAdd(memohash, S, L);\n\t\treturn L;\n fi;\n\n L1 := [ ];\n for T in L do\n Lc := [ ];\n\t\tfor i in [1..Length(T.children)] do\n Lc[i] := _AllRuleTrees(T.children[i], cutoff, memohash, opts);\n\t\tod;\n\t\tfor cs in Cartesian(Lc) do\n T1 := ShallowCopy(T);\n\t\t\tT1.children := cs;\n\t\t\tAdd(L1, T1);\n\t\tod;\n od;\n\n HashAdd(memohash, S, L1);\n return L1;\nend;\n\n#F AllRuleTrees( , )\n#F expands in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\nAllRuleTrees := (S, opts) -> _AllRuleTrees(S, x->false, HashTableSPL(), opts);\n\n#F AllRuleTreesCutoff( , , )\n#F expands in all possible ways and returns the obtained list\n#F of fully expanded ruletrees (ruletrees containing no non-terminals).\n#F Note that subtrees are \"by reference\", i.e., modifying one subtree\n#F alters the same subtree in some other expansions.\n#F is of the form e -> e = \n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F\nAllRuleTreesCutoff := (S, cutoff_func, opts) -> _AllRuleTrees(S, cutoff_func, HashTableSPL(), opts);\n\n\n\n_NofRuleTrees := function ( S, cutoff, memohash, opts, level, trace )\n local p, Cs, n, lkup, indentstr, i;\n Constraint(IsSPL(S));\n Constraint(IsRec(opts));\n\n if trace then\n indentstr := \"\";\n for i in [2..level] do\n indentstr := Concat(indentstr, \". \");\n od;\n indentstr := Concat(indentstr, String(level), \" \");\n Print(indentstr, \">> _NofRuleTrees(\", S, \")\\n\");\n fi;\n\n # check cutoff, baseHashes, and our memoization hash\n if cutoff(S) then\n if trace then\n Print(indentstr, \"<< (cutoff) 1\\n\");\n fi;\n return 1; \n fi;\n if MultiHashLookup(opts.baseHashes, S) <> false then\n if trace then\n Print(indentstr, \"<< (MultiHashLookup) 1\\n\");\n fi;\n return 1; \n fi;\n lkup := HashLookup(memohash, S);\n if lkup <> false then\n if trace then\n Print(indentstr, \"<< hashed: \", lkup, \"\\n\");\n fi;\n return lkup; \n fi;\n\n # first apply rules as they are\n Cs := List(AllApplicableRulesDirect(S, opts.breakdownRules), r -> _allChildren(r,S, opts));\n\tif trace then\n Print(indentstr, \" Cs: \", Cs, \"\\n\");\n fi;\n\n if Cs = [ [ ] ] then\n n := 1;\n else\n n := Sum(Cs, c -> Sum(c, l -> Product(l, x -> _NofRuleTrees(x, cutoff, memohash, opts, level+1, trace))));\n fi;\n\n HashAdd(memohash, S, n);\n \n if trace then\n Print(indentstr, \"<< (\", S, \") \", n, \"\\n\");\n fi;\n \n return n;\nend;\n\n#F NofRuleTrees ( , )\n#F returns the number of ruletrees for .\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F opts.restrictSplit\n#F opts.restrictSplitSize\n#F\n#F if opts.verbosity > 3 prints trace info\n\nNofRuleTrees := (spl, opts) -> _NofRuleTrees(spl, x->false, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\nNofRuleTreesCutoff := (spl, cutoff_func, opts) -> _NofRuleTrees(spl, cutoff_func, HashTableSPL(), opts, 1, IsBound(opts.verbosity) and (opts.verbosity > 3));\n\n\n#F RulesInRuleTree( )\n#F return the set of rules contained in .\n#F\nRulesInRuleTree := function ( T )\n local C;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([T.rule]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Set(Concatenation(List(C, RulesInRuleTree)));\n AddSet(C, T.rule);\n return C;\nend;\n\n\n#F RulesInRuleTreeAll( )\n#F return the histogram of all rules contained in as set\n#F of pairs [rule, number].\n#F\nRulesInRuleTreeAll := function ( T )\n local C, C1, c, i;\n Constraint(IsRuleTree(T));\n\n # base case\n if T.children = [ ] then\n\t return Set([ [T.rule, 1] ]);\n\tfi;\n\n # recurse with ruletree children\n C := Filtered(T.children, IsRuleTree);\n C := Concatenation(List(C, RulesInRuleTreeAll));\n\n # merge\n C1 := [ ];\n for c in C do\n i := PositionProperty(C1, p -> c[1] = p[1]);\n if i = false then\n AddSet(C1, c);\n else\n C1[i][2] := C1[i][2] + c[2];\n fi;\n od;\n\n i := PositionProperty(C1, p -> p[1] = T.rule);\n if i = false then\n AddSet(C1, [T.rule, 1]);\n else\n C1[i][2] := C1[i][2] + 1;\n fi;\n return C1;\nend;\n\n\nApplyRuleTreeStep := function ( rt, recurse )\n local nt, C, Nonterms, S, c;\n if IsNonTerminal(rt) or IsSPL(rt) then \n\t return rt;\n\tfi;\n\n Constraint(IsRuleTree(rt));\n\n C := List(rt.children, recurse);\n nt := rt.node;\n Nonterms := List(rt.children, c -> When(IsRuleTree(c), c.node, c));\n\n if rt.transposed then\n nt := TransposedSPL(nt);\n C := List(C, TransposedSPL);\n Nonterms := List(Nonterms, TransposedSPL);\n fi;\n\n S := _apply(rt.rule, nt, C, Nonterms);\n if rt.transposed then \n\t S := TransposedSPL(S); \n\tfi;\n\n trace_log.addTreeExpansion(rt.rule,nt,S,rt.children,CopyFields(rt.node, rec(params := C)), var);\n\n S.root := rt.node;\n return S;\nend;\n\nSPLRuleTreeStep := rt -> ApplyRuleTreeStep(rt, c -> RecursStep(\n When(IsRuleTree(c), RTWrap(c), c)));\n\n_SPLRuleTree := rt -> ApplyRuleTreeStep(rt, _SPLRuleTree);\n\nSPLRuleTree := function(rt)\n local spl, t, tag;\n trace_log.beginStage(\"tSPL\",\"SPL\", rt.node); \n spl := ApplyRuleTreeStep(rt, _SPLRuleTree);\n\n # tags may inject container objects\n t := rt.node;\n if IsBound(t.getTags) then\n for tag in Reversed(t.getTags()) do\n if IsBound(tag.container)\n\t\t\t then spl := tag.container(spl);\n\t\t\tfi;\n od;\n fi;\n trace_log.endStage(\"tSPL\",\"SPL\", spl); \n return spl;\nend;\n\n# forward declaration for function that does all the work.\nDeclare(_ruleTreeN);\n\n#F RandomRuleTrees( , , )\n#F returns random rule trees for \n#F uniformly distributed amongst the potential trees\n#F or 'false' if no breakdown rule combination leads to a\n#F fully expanded ruletree.\n#F\n#F Uses: opts.baseHashes\n#F opts.breakdownRules\n#F Optional: (see Doc(_allChildren) ) for usage\n#F\nRandomRuleTrees := function(spl, num, opts)\n local n, rand, memohash;\n\n memohash := HashTableSPL();\n\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num >= n then\n rand := [1..n];\n else\n rand := [];\n while Length(rand) <> num do\n rand := Set(Concat(rand, [RandomList([1..n])]));\n od;\n fi;\n\n return List(rand, e -> _ruleTreeN(spl, e-1, memohash, opts));\nend;\n\n# helper functions/arrays for _ruleTreeN and _ruleTree1\n\n_getNumTrees := (s, memohash, opts) -> let(\n n := HashLookup(memohash, s), \n When(n = false,\n _NofRuleTrees(s, e -> false, memohash, opts, 1, false),\n n\n )\n);\n#F RuleTreeN(, , )\n#F returns ruletree of index \n#F\n#F Uses: opts.basHashes, opts.breakdownRules.\n#F\nRuleTreeN := function(spl, num, opts)\n local memohash, n, r;\n\n memohash := HashTableSPL();\n n := _NofRuleTrees(spl, s -> false, memohash, opts, 1, false);\n\n if num in [1..n] then\n r := _ruleTreeN(spl, num-1, memohash, opts);\n\n else\n r := false;\n fi;\n\n return r;\nend;\n\n\n# fold list inside out, favoring the right hand side\n\n_foldedMidFirst := function(origlist)\n\tlocal len, midpt, front, back, newlist;\n\t\n\tlen := Length(origlist);\n\tif len < 2 then\n\t\treturn origlist;\n\tfi;\n\tmidpt := Int(len/2);\n\tfront := Reversed(Sublist(origlist, [1..midpt]));\n\tback := Sublist(origlist, [midpt+1..len]);\n\t\n\tnewlist := [];\n\t\n\tif IsOddInt(len) then\n\t\tAppend(newlist, [back[1]]);\n\t\tback := Drop(back,1);\n\tfi;\n\t\n\twhile (front <> []) or (back <> []) do\n\t\tif back <> [] then\n\t\t\tAppend(newlist, [back[1]]);\n\t\t\tback := Drop(back,1);\n\t\tfi;\n\t\tif front <> [] then\n\t\t\tAppend(newlist, [front[1]]);\n\t\t\tfront := Drop(front, 1);\n\t\tfi;\t\n\tod;\n\t\n\treturn newlist;\nend;\n\n\nDeclare(_ruleTreeMid);\n\n#F RuleTreeMid(spl, opts)\n#F\n#F Similar to RuleTree1, but tries to grab the middle of each range of choices\n#F \n\nRuleTreeMid := (spl, opts) -> _ruleTreeMid(spl, HashTableSPL(), opts);\n\n_ruleTreeMid := function(spl, memohash, opts)\n local h, R, r, C, c, ch, npc, idx, idxlist, ridx, ridxlist;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n\tridxlist := [1..Length(R)];\n\tif Length(ridxlist) > 1 then\n\t\tif Length(_allChildren(R[1], spl, opts)) < 2 then\n\t\t\tridxlist := _foldedMidFirst(ridxlist);\n\t\tfi;\n\tfi;\n for ridx in ridxlist do\n\t\tr := R[ridx];\n\t\tC := _allChildren(r, spl, opts);\n\t\tidxlist := _foldedMidFirst([1..Length(C)]);\n\t\tfor idx in idxlist do \n\t\t\tc := C[idx];\n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTreeMid(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n\n\nDeclare(_ruleTree1);\n\n#F RuleTree1(spl, opts)\n#F\n#F returns the first ruletree. this is often useful for\n#F testing whether a particular rule is firing, and you\n#F want to avoid the randomness of RandomRuleTree\n#F\n#F NOTE: this function does not check if a tree can\n#F actually just be created, it just tries to return\n#F the first one. RuleTreeN(spl, 1, opts) does the\n#F same thing but first checks.\n#F \n\nRuleTree1 := (spl, opts) -> _ruleTree1(spl, HashTableSPL(), opts);\n\n_ruleTree1 := function(spl, memohash, opts)\n local h, R, r, i, c, ch, npc;\n\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n for r in R do\n\t\tfor c in _allChildren(r, spl, opts) do \n\t\t\tnpc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\t\t\tif npc > 0 then\n\t\t\t\tch := List(c, e -> _ruleTree1(e, memohash, opts));\n\t\t\t\tif not ForAny(ch, e -> IsBool(e) and e=false) then\n\t\t\t\t\treturn RuleTreeNC(r, spl, ch);\n\t\t\t\tfi;\n\t\t\tfi;\n od;\n od;\n\t# no tree, return original spl\n return spl;\nend;\n \n\n#F _ruleTreeN(, , , )\n#F internal function which returns a ruletree for \n#F with index given by . This is a recursive\n#F routine. Note that is 0-based, unlike everything\n#F else in SPIRAL, which is 1-based.\n#F \n_ruleTreeN := function(spl, num, memohash, opts)\n local R, rtNC, h, r, c, npc, off, ch, i, n, p, offset;\n\n # lookup stuff like SSE base cases.\n h := MultiHashLookup(opts.baseHashes, spl);\n\n if h <> false then\n return h[1].ruletree;\n fi;\n\n # get list of normal rules\n R := AllApplicableRulesDirect(spl, opts.breakdownRules);\n offset := 0;\n\n for r in R do\n for c in _allChildren(r, spl, opts) do \n # figure out which group of children we should be looking at.\n npc := Product(c, e -> _getNumTrees(e, memohash, opts));\n\n # is this the correct group?\n if num < offset + npc then\n off := npc;\n ch := [];\n\n # step through the kids, and push down the ruletree number\n for i in [1..Length(c)] do\n n := _getNumTrees(c[i], memohash, opts);\n\n off := When(n > 0, off / n, off);\n\n p := When(n <= 0 or num <= offset, \n 0, \n RemInt(QuoInt(num - offset, off), n)\n );\n\n # all the kids get evaluated\n Add(ch, _ruleTreeN(c[i], p, memohash, opts));\n od;\n\n # no kids should be false, but just in case.\n if not ForAny(ch, e -> IsBool(e) and e=false) then\n return RuleTreeNC(r, spl, ch);\n fi;\n fi;\n\n # fixup offset\n offset := offset + npc;\n od;\n od;\n\n\t# no tree, return original spl\n return spl;\nend;\n\nDeclare(_ruleTreeGetN);\n\n#F RuleTreeGetN(, )\n#F given a ruletree, determine the index\n#F\n#F uses:\n#F opts.breakdownRules\n#F opts.baseHashes\n#F\n\nRuleTreeGetN := function(ruletree, opts)\n local memohash, r;\n \n memohash := HashTableSPL();\n\n # prime the memohash.\n _NofRuleTrees(ruletree.node, s -> false, memohash, opts, 1, false);\n\n r := _ruleTreeGetN(ruletree, memohash, opts, 0);\n\n # ruleTreeGetN may return false if we couldn't match the tree in the passed\n # in breakdownRules/baseHashes.\n return When(IsInt(r), r + 1, false);\nend;\n\n_ruleTreeGetN := function(rt, memohash, opts, offset)\n local h, R, r, c, ch, off, n;\n\n # is the ruletree something from the baseHashes?\n h := MultiHashLookup(opts.baseHashes, rt.node);\n if IsList(h) and rt = h[1].ruletree then\n return offset;\n fi;\n\n R := AllApplicableRulesDirect(rt.node, opts.breakdownRules);\n\n for r in R do\n # does rule match?\n if r = rt.rule then\n for c in _allChildren(r, rt.node, opts) do\n # does child match?\n if c = List(rt.children, e -> e.node) then\n off := Product(rt.children, e -> _getNumTrees(e.node, memohash, opts));\n for ch in rt.children do\n n := _getNumTrees(ch.node, memohash, opts);\n off := When(n > 0, off / n, off);\n offset := offset + (off * _ruleTreeGetN(ch, memohash, opts, 0));\n od;\n return offset;\n # child doesn't match, increase offset\n else\n offset := offset + Product(c, e -> _getNumTrees(e, memohash, opts));\n fi; \n od;\n # rule doesn't match, so increase offset by all possible expansions we didn't use\n else\n offset := offset \n + Sum(_allChildren(r, rt.node, opts), C -> \n Product(C, c -> _getNumTrees(c, memohash, opts))\n );\n fi;\n od;\n\n return offset;\nend;\n", "meta": {"hexsha": "1d0009a09272fd41a4782af754b83ad098ad272d", "size": 33659, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/formgen/ruletree.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/formgen/ruletree.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/formgen/ruletree.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 28.9415305245, "max_line_length": 178, "alphanum_fraction": 0.5857868624, "num_tokens": 9761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6513548646660543, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.42426315972413386}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nbenchMACRO := function()\n return rec(\n 2xf := rec(\n wht := _defaultSizes(s->doSimdWht(s, MACRO_2xf, rec(verify := true, oddSizes := false, svct := true)), List([3..8], i->2^i)),\n 1d := rec(\n dft_ic := rec(\n small := rec(\n real := _defaultSizes(s->doSimdDft(s, MACRO_2xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := true, cplxVect := false, stdTTensor := false, interleavedComplex := true)), [2..64]),\n cmplx := _defaultSizes(s->doSimdDft(s, MACRO_2xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := false, cplxVect := true, stdTTensor := false, interleavedComplex := true)), [2..64])\n ),\n medium := _defaultSizes(s->doSimdDft(s, MACRO_2xf, rec(verify := true, globalUnrolling := 128, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := false, realVect := true)),\n List([2..16], i->2^i)),\n medium_cx := _defaultSizes(s->doSimdDft(s, MACRO_2xf, rec(globalUnrolling := 64, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := true, realVect := false)),\n List([1..16], i->2^i))\n ),\n dft_sc := _defaultSizes(s->doSimdDft(s, MACRO_2xf, rec(verify := true, globalUnrolling := 10000, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false)), 8*[1..16])\n )\n ),\n\n 4xf := rec(\n wht := _defaultSizes(s->doSimdWht(s, MACRO_4xf, rec(verify := true, oddSizes := false, svct := true)), List([4..8], i->2^i)),\n 1d := rec(\n dft_ic := rec(\n small := rec(\n real := _defaultSizes(s->doSimdDft(s, MACRO_4xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := true, cplxVect := false, stdTTensor := false, interleavedComplex := true)), [2..64]),\n cmplx := _defaultSizes(s->doSimdDft(s, MACRO_4xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := false, cplxVect := true, stdTTensor := false, interleavedComplex := true)), [2..64])\n ),\n medium := _defaultSizes(s->doSimdDft(s, MACRO_4xf, rec(verify := true, globalUnrolling := 128, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := false, realVect := true)),\n List([4..16], i->2^i)),\n medium_cx := _defaultSizes(s->doSimdDft(s, MACRO_4xf, rec(globalUnrolling := 64, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := true, realVect := false)),\n List([2..16], i->2^i))\n ),\n dft_sc := _defaultSizes(s->doSimdDft(s, MACRO_4xf, rec(verify := true, globalUnrolling := 10000, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false)), 16*[1..8])\n )\n ),\n 8xf := rec(\n wht := _defaultSizes(s->doSimdWht(s, MACRO_8xf, rec(verify := true, oddSizes := false, svct := true)), List([6..8], i->2^i)),\n 1d := rec(\n dft_ic := rec(\n small := rec(\n real := _defaultSizes(s->doSimdDft(s, MACRO_8xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := true, cplxVect := false, stdTTensor := false, interleavedComplex := true)), [2..64]),\n cmplx := _defaultSizes(s->doSimdDft(s, MACRO_8xf, rec(verify := true, globalUnrolling := 10000, tsplBluestein:=true,\n PRDFT:=true, URDFT:= true, CT := true, minCost := true, tsplPFA := true, tsplCT := true, oddSizes := true, PD := true, PFA := true,\n RealRader := true, Rader := true, realVect := false, cplxVect := true, stdTTensor := false, interleavedComplex := true)), [2..64])\n ),\n medium := _defaultSizes(s->doSimdDft(s, MACRO_8xf, rec(verify := true, globalUnrolling := 128, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := false, realVect := true)),\n List([6..16], i->2^i)),\n medium_cx := _defaultSizes(s->doSimdDft(s, MACRO_8xf, rec(globalUnrolling := 128, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false,\n interleavedComplex := true, cplxVect := true, realVect := false)),\n List([4..16], i->2^i))\n ),\n dft_sc := _defaultSizes(s->doSimdDft(s, MACRO_8xf, rec(verify := true, globalUnrolling := 10000, tsplRader:=false, tsplBluestein:=false, tsplPFA:=false, oddSizes:=false, interleavedComplex := false)), 64*[1..4])\n )\n )\n );\nend;\n", "meta": {"hexsha": "be33787be7c6b72df5058269de6d7b31970d7997", "size": 6449, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/platforms/macro/bench.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/platforms/macro/bench.gi", 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YES\n2. YES", "lm_q1_score": 0.82893881677331, "lm_q2_score": 0.5117166047041654, "lm_q1q2_score": 0.42418175682672643}} {"text": "#\n# usage:\n# Read(\"~/Workspace/Chevalley.gap/init.gap\"); Read(Filename(home_dir,\"load.gap\")); Read(Filename(home_dir,\"main.gap\"));\n#\n# Read(Filename(home_dir,\"main.gap\"));\n#\n\nITER_POLY_WARN:=false;\nRead(Filename(home_dir,\"lib/io.gi\"));\nRead(Filename(home_dir,\"handle.gap\"));\n\n\n\nalg:=AlgebraicU(\"G\",2,GF(2));\n#alg:=AlgebraicU(sys);\n\norbs:=UnipotentClasses(alg,\"\");\n\ninfos:=List(AllClasses(orbs),orb->handleClassShort(orb));", "meta": {"hexsha": "a7dae0c26e5ea5922f0feb4420d58f3b1823b105", "size": 422, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "main.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "main.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "main.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.2105263158, "max_line_length": 119, "alphanum_fraction": 0.6990521327, "num_tokens": 132, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.743168019989179, "lm_q2_score": 0.5698526514141572, "lm_q1q2_score": 0.42349626663704304}} {"text": "\n## Copyright (c) 2018-2021, Carnegie Mellon University\n## See LICENSE for details\n\n#F FDataNT(, )\n#F\nClass(FDataNT, Function, rec(\n __call__ := (self, datavar, nt) >> WithBases(self, rec(\n var := datavar,\n operations := PrintOps,\n nt := nt,\n domain := self >> Rows(self.nt)\n )),\n\n rChildren := self >> [ self.var, self.nt, self._domain, self._range],\n rSetChild := rSetChildFields(\"var\", \"nt\", \"_domain\", \"_range\"),\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], rch[2]).setDomain(rch[4]).setRange(rch[5]),\n\n domain := self >> self.len,\n print := self >> Print(self.name,\"(\",self.var,\", \",self.nt,\")\"),\n\n# these are not yet right\n at := (self, n) >> When(IsInt(n) and IsValue(self.ofs) and IsBound(self.var.value),\n self.var.value.v[n + self.ofs.v + 1],\n nth(self.var, n + self.ofs)),\n\n tolist := self >> List([0..EvalScalar(self.len-1)], i -> nth(self.var, self.ofs+i)),\n lambda := self >> let(x := Ind(self.domain()), Lambda(x, nth(self.var, self.ofs+x))),\n# up to here\n\n domain := self >> Rows(self.nt),\n range := self >> When(self._range=false, self.var.t.t, self._range),\n inline := true,\n free := self >> self.ofs.free()\n));\n\n\n# These need to be implemented properly -- for now they are just markers in TDAG\nClass(TColMaj, TPtr); \n", "meta": {"hexsha": "d66c05356ed66f55cac7c77016bea14e78515dc9", "size": 1372, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "sigma/func.gi", "max_stars_repo_name": "franzfranchetti/spiral-package-fftx", "max_stars_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-15T12:40:19.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-15T12:40:19.000Z", "max_issues_repo_path": "sigma/func.gi", "max_issues_repo_name": "franzfranchetti/spiral-package-fftx", "max_issues_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2021-01-05T20:58:29.000Z", "max_issues_repo_issues_event_max_datetime": "2021-08-18T20:10:45.000Z", "max_forks_repo_path": "sigma/func.gi", "max_forks_repo_name": "franzfranchetti/spiral-package-fftx", "max_forks_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2020-12-14T18:24:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:40:20.000Z", "avg_line_length": 34.3, "max_line_length": 100, "alphanum_fraction": 0.5816326531, "num_tokens": 400, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952052, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4216503624790059}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n# ================================================================\n# Simplification of Intervals\n# ================================================================\n\nfull_II := (int, size) -> \n [int.target(II), size, 0, @.cond(e->e=size.val)];\n\nempty_II := (int, size) -> \n [int.target(II).cond(e->e.params[2]=e.params[3]), size, @, @];\n\nleft_II := (int, size, endd) -> \n [int.target(II), size, 0, endd];\n\nright_II := (int, size,start) -> \n [int.target(II), size, start, @.cond(e->e=size.val)];\n\nClass(RulesII, RuleSet);\n\nRewriteRules(RulesII, rec(\n # full II o index mapping func @(3) = II with domain of @(3)\n # II(n, 0, n) o f = II(domain(f), 0, domain(f))\n FullII_f := ARule(fCompose, [ full_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain()) ]),\n EmptyII_f := ARule(fCompose, [ empty_II(@, @(1)), @(2) ], e -> [ II(@(2).val.domain(),0,0) ]),\n\n # partial II o dirsum of perms\n # II(n, 0, k) o fDirsum(perm_k, perm_?) -> II(n,0,k)\n LeftII_fDirsum := ARule(fCompose, \n [ left_II(@(0), @(1), @(2)), [fDirsum, @(3).cond(e -> is_perm(e) and e.range()=@(2).val), ...]],\n e -> [ @(0).val ]),\n\n # partial II o dirsum of perms\n # II(n, n-k, n) o fDirsum(perm_?, perm_k) -> II(n,n-k,n)\n RightII_fDirsum := ARule( fCompose, \n [ right_II(@(0), @(1), @(2)), [fDirsum, ..., @(4).cond(e -> is_perm(e) and e.range() = @(1).val-@(2).val)]],\n e -> [ @(0).val ]),\n\n # fTensor(IIn, IIk) -> II(n*k)\n fullII_tensor_fullII := ARule(diagTensor, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val * @(2).val) ]),\n\n # fDirsum(IIn, IIk) -> II(n+k)\n fullII_dirsum_fullII := ARule(diagDirsum, [full_II(@(0), @(1)), full_II(@(0), @(2))], \n e -> [ II(@(1).val + @(2).val) ]),\n\n diagTensor_emptyII := Rule([diagTensor, ..., empty_II(@(1), @(2)), ...], e -> II(e.domain(),0,0)),\n diagTensor_fullII_Id1 := ARule(diagTensor, [@(0), full_II(@(1), @(2).cond(e->e=1))], e -> [ @(0).val ]),\n diagTensor_fullII_Id2 := ARule(diagTensor, [full_II(@(1), @(2).cond(e->e=1)), @(0)], e -> [ @(0).val ]),\n\n\n II_dirsum_emptyII := ARule(diagDirsum, [[II, @(1), @(2), @(3)], empty_II(@(4), @(5))], \n e -> [ II(@(1).val + @(5).val), @(2).val, @(3).val ]),\n\n emptyII_dirsum_II := ARule(diagDirsum, [empty_II(@(4), @(5)), [II, @(1), @(2), @(3)]], \n e -> [ II(@(1).val + @(5).val), @(5).val + @(2).val, @(5).val + @(3).val ]),\n\n # II Shifting, we support shift left (shift <= start), and right (shift >= end)\n # II o Z = shifted II# \n II_Z := ARule(fCompose, [[II, @(1), @(2), @(3)], [Z, @(4), @(5).cond(e -> (e<=@(2).val) or (e >= @(3).val))]],\n e -> [II(@(1).val, (@(2).val-@(5).val) mod @(1).val, \n # this makes 0->size, because size mod size = 0\n let(last:=(@(3).val-@(5).val) mod @(1).val, \n When(last=0, @(1).val, last))) ]),\n\n DiagFullII_toId := Rule([Diag, full_II(@(1), @(2))], e -> I(@(2).val)),\n Diag_fConst_toId := Rule([Diag, [fConst, @(2), @(1), 1]], e -> I(@(1).val)),\n Diag_fConstV_toId := Rule([Diag, [fConst, @(2), @(1), _1]], e -> I(@(1).val)),\n\n COND_fullII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(3).val),\n COND_emptyII := Rule([COND, full_II(@(1), @(2)), @(3), @(4)], e -> @(4).val)\n));\n", "meta": {"hexsha": "1ffde4fb9b8a73ad175686815d1f2bb4d2458ed4", "size": 3376, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/ii_rules.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/sigma/ii_rules.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/sigma/ii_rules.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 45.0133333333, "max_line_length": 116, "alphanum_fraction": 0.4721563981, "num_tokens": 1235, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6992544210587585, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4196843636807008}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\nClass(VDirectSum, DirectSum, rec(\n abbrevs := [(L, v) -> [L, v]],\n new := meth(self, L, v)\n if ForAll(L, IsIdentitySPL)\n then return I(Sum(L, Rows));\n else\n return SPL(WithBases( self,\n rec( _children := L,\n v := v,\n dimensions := [ Sum(L, t -> t.dimensions[1]),\n Sum(L, t -> t.dimensions[2]) ] )));\n fi;\n end,\n# sums := meth(self)\n# nblocks, c, cols, rows, bkcols, bkrows, gcd;\n# nblocks := self.numChildren();\n# c := self.children();\n# cols := EvalScalar(Cols(self));\n# rows := EvalScalar(Rows(self));\n# bkcols := List(c, i->EvalScalar(Cols(i)));\n# bkrows := List(c, i->EvalScalar(Rows(i)));\n# gcd := self.v;\n# bkrows_by_gcd := List(bkrows, i->i/gcd);\n# psr_by_gcd := List(DropLast(_partSum(bkrows), 1), i ->idiv(i,gcd));\n# fi;\n# psc := DropLast(Concat([0], List(Drop(_partSum(bkcols), 1), i->i-overlap)), 1);\n# return SUM( Map([1..nblocks],\n# i -> Compose(\n# Scat(fTensor(fAdd(rows/gcd, bkrows_by_gcd[i], Cond(i=1, 0, i=2, bkrows_by_gcd[i-1], psr_by_gcd[i])), fId(gcd))),\n# self.child(i).sums(),\n# Gath(fTensor(fAdd(cols/gcd, bkcols[i]/gcd, psc[i]/gcd), fId(gcd))))\n# ));\n));\n\n", "meta": {"hexsha": "4a0190e483110e194c35c559dab9e98ed93fe3af", "size": 1435, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vdirsum.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vdirsum.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vdirsum.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 36.7948717949, "max_line_length": 133, "alphanum_fraction": 0.5010452962, "num_tokens": 444, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.746138993030751, "lm_q2_score": 0.5621765008857981, "lm_q1q2_score": 0.4194618082764805}} {"text": "\nInstallGlobalFunction(IsCommutator,\nfunction(f, w)\n\tlocal fp, hom, res;\n\tfp := CommutatorFactorGroup(f);\n\thom := GroupHomomorphismByImages(f, fp, [f.1, f.2], [fp.1, fp.2]);\n\tres := IsOne(Image(hom, w));\n\treturn res;\nend);\n\n\n", "meta": {"hexsha": "02659954b52618b3a0844b38d0c386a8d761a469", "size": 226, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/Utils.gi", "max_stars_repo_name": "db213/GreenMachine", "max_stars_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "gap/Utils.gi", "max_issues_repo_name": "db213/GreenMachine", "max_issues_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2018-01-14T00:50:08.000Z", "max_issues_repo_issues_event_max_datetime": "2018-01-14T00:50:08.000Z", "max_forks_repo_path": "gap/Utils.gi", "max_forks_repo_name": "db213/GreenMachine", "max_forks_repo_head_hexsha": "fbed716dbd4332ba0deb5110eb7f5a00335b12c8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 18.8333333333, "max_line_length": 67, "alphanum_fraction": 0.6637168142, "num_tokens": 77, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7310585669110203, "lm_q2_score": 0.5736784074525096, "lm_q1q2_score": 0.4193925144200281}} {"text": "{\n \"geometry\":{\n \"num_positions\":9,\n \"vertices\":\n [0, 1, 2, 3, 4, 5, 7, 8, 6],\n \"triangles\":\n [[5, 6, 7], [7, 8, 5]],\n \"edges\":\n [[1, 2], [2, 3], [3, 4], [5, 6], [6, 7], [7, 8], [8, 5]],\n \"wires\":\n [[0, 1, 2], [3, 4, 5, 6]],\n \"faces\":\n [[[1], [0, 1]]],\n \"points\":\n [0],\n \"polylines\":\n [0],\n \"polygons\":\n [0],\n \"collections\":\n [[-1, [0], [0], [0]], [-1, [0], [0], []], [-1, [], [], [0]]]\n },\n \"attributes\":{\n \"positions\":[\n {\n \"name\":\"xyz\", \"data_type\":\"Float\", \"data_size\":3,\n \"data\":\n [[[4], [4.106176853179932, -0.4043693542480469, 0.0]], [[2], [-2.0990729331970215, -0.49967002868652344, 0.0]], [[6], [2.5, 9.5, 0.0]], [[8], [2.5, 14.5, 0.0]], [[7], [-2.5, 14.5, 0.0]], [[5], [-2.5, 9.5, 0.0]], [[3], [1.3960471153259277, 3.6317100524902344, 0.0]], [[0], [0.1866779327392578, -6.794528007507324, 0.0]], [[1], [-5.964423179626465, 4.619009971618652, 0.0]]]\n }\n ],\n \"vertices\":[\n {\n \"name\":\"Cd\", \"data_type\":\"Float\", \"data_size\":3,\n \"data\":[[[0, 1, 2, 3, 4, 5, 6, 7, 8], [1.0, 0.7283259034156799, 0.3436123728752136]]]\n },\n {\n \"name\":\"N\", \"data_type\":\"Float\", \"data_size\":3,\n \"data\":[[[0, 1, 2, 3, 4], [0.0, 0.0, 0.0]], [[5, 6, 7, 8], [-0.0, -0.0, 1.0]]]\n }\n ],\n \"edges\":[\n {\n \"name\":\"position\", \"data_type\":\"String\", \"data_size\":1,\n \"data\":[[[5], \"pos_8\"], [[1], \"pos_2\"], [[2], \"pos_3\"], [[0], \"pos_1\"], [[6], \"pos_6\"], [[4], \"pos_7\"], [[3], \"pos_5\"]]\n }\n ],\n \"wires\":[\n {\n \"name\":\"length\", \"data_type\":\"Float\", \"data_size\":1,\n \"data\":[[[0], 16.687231063842773], [[1], 20.0]]\n }\n ],\n \"faces\":[\n {\n \"name\":\"area\", \"data_type\":\"Float\", \"data_size\":1,\n \"data\":[[[0], 25.0]]\n }\n ],\n \"collections\":[\n {\n \"name\":\"name\", \"data_type\":\"String\", \"data_size\":1,\n \"data\":[[[0], \"everything\"], [[1], \"not_polygons\"], [[2], \"polygons\"]]\n }\n ]\n }\n}\n", "meta": {"hexsha": "fca392502bf5f78eec9803b45e29765860f79a3c", "size": 2385, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "assets/gi-json/point_line_polygon_with_attribs.gi", "max_stars_repo_name": "design-automation/mobius-parametric-modeller-0-4-30", "max_stars_repo_head_hexsha": "e3d048f68dfc6b32978d95543d06a2b5122367b3", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2018-11-19T02:30:15.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-15T03:38:39.000Z", "max_issues_repo_path": "assets/gi-json/point_line_polygon_with_attribs.gi", "max_issues_repo_name": "design-automation/mobius-parametric-modeller-0-4-30", "max_issues_repo_head_hexsha": "e3d048f68dfc6b32978d95543d06a2b5122367b3", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 654, "max_issues_repo_issues_event_min_datetime": "2018-12-10T04:06:51.000Z", "max_issues_repo_issues_event_max_datetime": "2020-10-07T14:47:20.000Z", "max_forks_repo_path": "assets/gi-json/point_line_polygon_with_attribs.gi", "max_forks_repo_name": "design-automation/mobius-parametric-modeller-0-4-30", "max_forks_repo_head_hexsha": "e3d048f68dfc6b32978d95543d06a2b5122367b3", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 7, "max_forks_repo_forks_event_min_datetime": "2018-12-20T02:12:13.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-25T23:15:11.000Z", "avg_line_length": 35.5970149254, "max_line_length": 392, "alphanum_fraction": 0.3459119497, "num_tokens": 882, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7826624789529375, "lm_q2_score": 0.5350984286266116, "lm_q1q2_score": 0.41880146263272533}} {"text": "#############################################################################\n##\n## ExternalPolymakePolytope.gi JConvex package\n## Martin Bies\n##\n## Copyright 2021 University of Pennsylvania\n##\n## A Gap package to do convex geometry by Polymake, Cdd and Normaliz\n##\n## Chapter Polytopes in Polymake\n##\n#############################################################################\n\n\n##############################################################################################\n##\n## Section GAP category of PolymakePolytopes\n##\n##############################################################################################\n\nDeclareRepresentation( \"IsPolymakePolytopeRep\", IsPolymakePolytope and IsAttributeStoringRep, [ ] );\n\nBindGlobal( \"TheFamilyOfPolymakePolytopes\", NewFamily( \"TheFamilyOfPolymakePolytopes\" ) );\n\nBindGlobal( \"TheTypeOfPolymakePolytope\", NewType( TheFamilyOfPolymakePolytopes, IsPolymakePolytopeRep ) );\n\nBindGlobal( \"MakePolymakePolytopeVRep\", function( vertices, lineality )\n local poly, kwargs, new_vertices, new_lin, v;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( vertices := Immutable( vertices ),\n lineality := Immutable( lineality ),\n number_type := \"rational\",\n rep_type := \"V-rep\" ) );\n\n # add 1s at the beginning, since Polymake always considers polytopes as intersections with the hyperplane x0 = 1\n new_vertices := [];\n for v in vertices do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_vertices, v );\n od;\n new_lin := [];\n for v in lineality do\n v := ShallowCopy( v );\n Add( v, 1, 1 );\n Add( new_lin, v );\n od;\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( new_vertices ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_vertices );\n\n # if we also have lineality, add them\n if Length( new_lin ) > 0 then\n kwargs.INPUT_LINEALITY := JuliaMatrixInt( new_lin );\n fi;\n elif Length( new_lin ) > 0 then\n kwargs.POINTS := JuliaMatrixInt( new_lin );\n kwargs.INPUT_LINEALITY := kwargs.POINTS;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\nBindGlobal( \"MakePolymakePolytopeHRep\", function( inequalities, equalities )\n local poly, kwargs;\n poly := Objectify( TheTypeOfPolymakePolytope,\n rec( inequalities := Immutable( inequalities ),\n equalities := Immutable( equalities ),\n number_type := \"rational\",\n rep_type := \"H-rep\" ) );\n\n kwargs := rec();\n\n # TODO: verify that kwargs is set correctly, also if one or both lists are empty\n\n # check for degenerate case\n if Length( inequalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( inequalities );\n\n # check if we also need equalities\n if Length( equalities ) > 0 then\n kwargs.EQUATIONS := JuliaMatrixInt( equalities );\n fi;\n elif Length( equalities ) > 0 then\n kwargs.INEQUALITIES := JuliaMatrixInt( equalities );\n kwargs.EQUATIONS := kwargs.INEQUALITIES;\n fi;\n\n poly!.pmobj := CallJuliaFunctionWithKeywordArguments( _Polymake_jl.polytope.Polytope, [], kwargs );\n return poly;\nend);\n\n\n##############################################################################################\n##\n## Constructors for PolymakePolytopes\n##\n##############################################################################################\n\n\nInstallGlobalFunction( Polymake_PolytopeByGenerators,\n function( arg )\n local poly, i, matrix, temp, dim;\n \n if Length( arg )= 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[1] ) then\n \n return Polymake_PolytopeByGenerators( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeVRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeByGenerators( poly );\n \n fi;\n \nend );\n\n\nInstallGlobalFunction( Polymake_PolytopeFromInequalities,\n function( arg )\n local poly, i, temp, matrix, dim;\n \n if Length( arg ) = 0 or ForAll( arg, IsEmpty ) then\n \n Error( \"Wrong input: Please provide some input!\" );\n \n elif Length( arg ) = 1 and IsList( arg[ 1 ] ) then\n \n return Polymake_PolytopeFromInequalities( arg[ 1 ], [ ] );\n \n elif Length( arg ) = 2 and IsList( arg[ 1 ] ) and IsList( arg[ 2 ] ) then\n \n if ( not IsEmpty( arg[ 1 ] ) ) and not ( IsMatrix( arg[ 1 ] ) ) then\n Error( \"Wrong input: The first argument should be a Gap matrix!\" );\n fi;\n \n if ( not IsEmpty( arg[ 2 ] ) ) and not ( IsMatrix( arg[ 2 ] ) ) then\n Error( \"Wrong input: The second argument should be a Gap matrix!\" );\n fi;\n \n poly := MakePolymakePolytopeHRep( arg[ 1 ], arg[ 2 ] );\n return Polymake_CanonicalPolytopeFromInequalities( poly );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Canonicalize polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_CanonicalPolytopeByGenerators,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, scale, lineality, scaled_lineality;\n \n if poly!.rep_type = \"H-rep\" then\n \n return fail;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n # also, Polymake requires x0 = 1 in affine coordinates - we remove this 1\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # extract lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\nInstallMethod( Polymake_CanonicalPolytopeFromInequalities,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"V-rep\" then\n \n return fail;\n \n else\n \n # compute facets\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute affine hull\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Conversion of polytopes\n##\n##############################################################################################\n\nInstallMethod( Polymake_V_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local vertices, v_copy, scaled_vertices, i, lineality, scaled_lineality;\n \n if poly!.rep_type = \"V-rep\" then\n \n return poly;\n \n else\n \n # compute vertices\n vertices := PolymakeMatrixToGAP( poly!.pmobj.VERTICES );\n \n # sometimes, Polymake returns rational vertices - we turn them into integral vectors\n scaled_vertices := [];\n for i in [ 1 .. Length( vertices ) ] do\n v_copy := ShallowCopy( vertices[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_vertices, v_copy );\n od;\n \n # compute lineality\n lineality := PolymakeMatrixToGAP( poly!.pmobj.LINEALITY_SPACE );\n \n # sometimes, Polymake returns rational lineality - we turn them into integral vectors\n scaled_lineality := [];\n for i in [ 1 .. Length( lineality ) ] do\n v_copy := ShallowCopy( lineality[ i ] );\n Remove( v_copy, 1 );\n Add( scaled_lineality, v_copy );\n od;\n \n # construct the new poly\n return MakePolymakePolytopeVRep( scaled_vertices, scaled_lineality );\n \n fi;\n \nend );\n\n\nInstallMethod( Polymake_H_Rep,\n [ IsPolymakePolytope ],\n function( poly )\n local ineqs, eqs;\n \n if poly!.rep_type = \"H-rep\" then\n \n return poly;\n \n else\n \n if poly!.rep_type = \"V-rep\" and poly!.vertices = [] then\n return Polymake_PolytopeFromInequalities( [ [ 0, 1 ], [ -1, -1 ] ] );\n fi;\n \n # compute inequalities\n ineqs := PolymakeMatrixToGAP( poly!.pmobj.FACETS );\n \n # compute equalities\n eqs := PolymakeMatrixToGAP( poly!.pmobj.AFFINE_HULL );\n \n # construct the new poly\n return MakePolymakePolytopeHRep( ineqs, eqs );\n \n fi;\n \nend );\n\n\n##############################################################################################\n##\n## Attributes of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_AmbientSpaceDimension,\n \"finding the dimension of the ambient space of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices[0] );\n \nend );\n\n\nInstallMethod( Polymake_Dimension,\n \" returns the dimension of the poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n if Polymake_IsEmpty( poly ) then\n return -1;\n fi;\n \n return poly!.pmobj.CONE_DIM - 1;\n \nend );\n\n\nInstallMethod( Polymake_Vertices,\n \" return the list of generating vertices\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.vertices );\n \nend );\n\n\nInstallMethod( Polymake_Linealities,\n \" return the list of linealities\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( Polymake_V_Rep( poly )!.linealities );\n \nend );\n\n\nInstallMethod( Polymake_Equalities,\n \" return the list of equalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.equalities );\n \nend );\n\n\nInstallMethod( Polymake_Inequalities,\n \" return the list of inequalities of a poly\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Set( ( Polymake_H_Rep( poly ) )!.inequalities );\n \nend );\n\n\nInstallMethod( Polymake_LatticePoints,\n \" return the list of the lattice points of poly\",\n [ IsPolymakePolytope ],\n function( poly )\n local point_list, lattice_points, i, copy;\n \n point_list := JuliaToGAP( IsList, JuliaMatrixInt( poly!.pmobj.LATTICE_POINTS_GENERATORS[1] ), true );\n\n # the point list is in affine coordinate, that is we have a 1 at position one, which should be removed\n lattice_points := [];\n for i in [ 1 .. Length( point_list ) ] do\n copy := ShallowCopy( point_list[ i ] );\n Remove( copy, 1 );\n Add( lattice_points, copy );\n od;\n \n # return result\n return lattice_points;\n \nend );\n\n\nInstallMethod( Polymake_Intersection,\n [ IsPolymakePolytope, IsPolymakePolytope ],\n function( poly1, poly2 )\n local poly1_h, poly2_h, new_ineqs, new_equ;\n \n # compute H-reps\n poly1_h := Polymake_H_Rep( poly1 );\n poly2_h := Polymake_H_Rep( poly2 );\n \n # add the inequalities and equalities\n new_ineqs := Concatenation( poly1_h!.inequalities, poly2_h!.inequalities );\n new_equ := Concatenation( poly1_h!.equalities, poly2_h!.equalities );\n \n # return result\n return Polymake_PolytopeFromInequalities( new_ineqs, new_equ );\n \nend );\n\n\n##############################################################################################\n##\n## Properties of PolymakeCones\n##\n##############################################################################################\n\nInstallMethod( Polymake_IsEmpty,\n \"finding if the poly empty is or not\",\n [ IsPolymakePolytope ],\n function( poly )\n \n return Length( Polymake_V_Rep( poly )!.vertices ) = 0;\n \nend );\n\n\nInstallMethod( Polymake_IsPointed,\n \"finding if the poly is pointed or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.POINTED;\n \nend );\n\n\nInstallMethod( Polymake_IsBounded,\n \" returns if the polytope is bounded or not\",\n [ IsPolymakePolytope ],\n function( poly )\n return poly!.pmobj.BOUNDED;\n \nend );\n", "meta": {"hexsha": "c969f54a2ca86be189c7a4ab0d0f99f4f58edd28", "size": 13778, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_stars_repo_name": "HereAround/JToric.jl", "max_stars_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_issues_repo_name": "HereAround/JToric.jl", "max_issues_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 44, "max_issues_repo_issues_event_min_datetime": "2021-09-17T01:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-11-25T00:15:13.000Z", "max_forks_repo_path": "pkg/JConvex/gap/ExternalPolymakePolytope.gi", "max_forks_repo_name": "HereAround/JToric.jl", "max_forks_repo_head_hexsha": "e8907f1ccd10a637254808916f859e354e479296", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-20T12:56:11.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-20T12:56:11.000Z", "avg_line_length": 30.0829694323, "max_line_length": 116, "alphanum_fraction": 0.5379590652, "num_tokens": 3364, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7217432062975979, "lm_q2_score": 0.5774953651858117, "lm_q1q2_score": 0.4168033564912099}} {"text": "\n## Copyright (c) 2018-2021, Carnegie Mellon University\n## See LICENSE for details\n\nClass(WarpXOpts, FFTXConvOpts, rec(\n tags := [],\n operations := rec(Print := s -> Print(\"\")) \n));\n\nwarpxOpts := function(arg) # specific to WarpX size 100...\n local opts, rfs;\n \n rfs := Copy(RulesFuncSimp);\n Unbind(rfs.rules.TensorIdId);\n \n opts := Copy(WarpXOpts);\n opts.breakdownRules.Circulant := [Circulant_PRDFT_FDataNT];\n opts.breakdownRules.PRDFT := List([PRDFT1_Base1, PRDFT1_Base2, CopyFields(PRDFT1_CT, \n rec(allChildren := P ->Filtered(PRDFT1_CT.allChildren(P), i->When(P[1] = 100, Cols(i[1]) = 4, true)))), \n PRDFT_PD], _noT);\n opts.breakdownRules.IPRDFT := List([ IPRDFT1_Base1, IPRDFT1_Base2, IPRDFT1_CT, IPRDFT_PD ], _noT);\n opts.breakdownRules.PRDFT3 := List([ PRDFT3_Base1, PRDFT3_Base2, PRDFT3_CT ], _noT);\n opts.breakdownRules.IPRDFT2 := List([ IPRDFT2_Base1, IPRDFT2_Base2, IPRDFT2_CT ], _noT);\n opts.breakdownRules.DFT := [ DFT_Base, \n CopyFields(DFT_CT, rec(children := nt ->Filtered(DFT_CT.children(nt), i->When(nt.params[1] = 100, Cols(i[1]) = 4, true)))), \n DFT_PD ];\n opts.breakdownRules.TTensorInd := [dsA_base, L_dsA_L_base, dsA_L_base, L_dsA_base]; \n opts.breakdownRules.MDDFT := [ MDDFT_Base, MDDFT_RowCol ];\n opts.breakdownRules.TL := [L_base];\n opts.breakdownRules.TSparseMat := [ TSparseMat_base ];\n \n opts.globalUnrolling := 23;\n opts.codegen := CopyFields( MultiPtrCodegenMixin, spiral.libgen.VecRecCodegen);\n opts.sumsgen.IterHStack := MultiPtrSumsgenMixin.IterHStack;\n opts.preProcess := t -> ApplyStrategy(t, \n [ RulesFFTXPromoteWarpX1, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX2), \n RulesFFTXPromoteNT, \n MergedRuleSet(rfs, RulesSums, RulesFFTXPromoteWarpX3) ],\n BUA, opts);\n opts.useDeref := false;\n # for debugging...\n opts.generateInitFunc := false;\n# opts.codegen := DefaultCodegen;\n opts.arrayBufModifier := \"\";\n opts.arrayDataModifier := \"static\";\n \n return opts;\nend;\n\n\nwarpxConf := rec(\n defaultName := \"defaultWarpXConf\",\n defaultOpts := (arg) >> rec(useWarpX := true),\n confHandler := warpxOpts \n);\n\nfftx.FFTXGlobals.registerConf(warpxConf);\n\n\n\n", "meta": {"hexsha": "0568b507b3b64208089c740a99feb5c2e144ddda", "size": 2348, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "knowledgebase/warpx.gi", "max_stars_repo_name": "franzfranchetti/spiral-package-fftx", "max_stars_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-15T12:40:19.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-15T12:40:19.000Z", "max_issues_repo_path": "knowledgebase/warpx.gi", "max_issues_repo_name": "franzfranchetti/spiral-package-fftx", "max_issues_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2021-01-05T20:58:29.000Z", "max_issues_repo_issues_event_max_datetime": "2021-08-18T20:10:45.000Z", "max_forks_repo_path": "knowledgebase/warpx.gi", "max_forks_repo_name": "franzfranchetti/spiral-package-fftx", "max_forks_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 5, "max_forks_repo_forks_event_min_datetime": "2020-12-14T18:24:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-06-15T12:40:20.000Z", "avg_line_length": 37.8709677419, "max_line_length": 132, "alphanum_fraction": 0.6528960818, "num_tokens": 732, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956580903722561, "lm_q2_score": 0.523420348936324, "lm_q1q2_score": 0.41646363529665553}} {"text": "#############################################################################\n##\n#W autom.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n#R IsAutomRep\n##\n## This is how IsAutom object is stored in GAP:\n## IsAutom object is a thing of kind \"w = (w_1, w_2, ..., w_d)\\pi\", where\n## deg = d - arity of tree;\n## perm = \\pi - permutation on first level;\n## w, w_1, ..., w_d - elements of free group representing elements of\n## automata group;\n## word = w;\n## states = [w_1, ..., w_d].\n##\nDeclareRepresentation(\"IsAutomRep\",\n IsComponentObjectRep and IsAttributeStoringRep,\n [\"word\", \"states\", \"perm\", \"deg\"]);\n\n\nInstallGlobalFunction(__AG_CreateAutom,\nfunction(family, word, states, perm, invertible)\n local a, cat;\n\n if invertible then\n cat := IsInvertibleAutom and IsAutomRep;\n\n if perm^-1=fail then\n Error(perm, \" is not invertible\");\n else\n perm := AG_PermFromTransformation(perm);\n fi;\n else\n cat := IsAutom and IsAutomRep;\n fi;\n\n a := Objectify(NewType(family, cat),\n rec(word := word,\n states := states,\n perm := perm,\n deg := family!.deg));\n\n SetIsActingOnBinaryTree(a, a!.deg = 2);\n\n return a;\nend);\n\n###############################################################################\n##\n#M Autom(, )\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutomFamily]\",\n [IsAssocWord, IsAutomFamily],\nfunction(w, fam)\n local exp, wstates, curstate, newstate, curletter, newletter,\n nperm, i, j, perm, a, wtmp, reduced, invertible;\n\n if fam!.use_rws then\n w := AG_ReducedForm(fam!.rws, w);\n fi;\n\n if Length(w) = 0 then\n return One(fam);\n elif Length(w) = 1 then\n if ExponentSyllable(w, 1) = 1 then\n return fam!.automgens[GeneratorSyllable(w, 1)];\n else\n return fam!.automgens[GeneratorSyllable(w, 1) + fam!.numstates];\n fi;\n fi;\n\n # TODO\n exp := LetterRepAssocWord(w);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then exp[i] := -exp[i] + fam!.numstates; fi;\n od;\n wstates := [];\n nperm := ();\n for i in [1..Length(exp)] do\n nperm := nperm * fam!.automatonlist[exp[i]][fam!.deg+1];\n od;\n\n for i in [1..fam!.deg] do\n wstates[i] := [];\n perm := ();\n\n for j in [1..Length(exp)] do\n newstate := fam!.automatonlist[exp[j]][i^perm];\n if newstate <> fam!.trivstate then\n if newstate > fam!.numstates then\n newstate := -(newstate - fam!.numstates);\n fi;\n if Length(wstates[i]) > 0 and wstates[i][Length(wstates[i])] = -newstate then\n Remove(wstates[i], Length(wstates[i]));\n else\n Add(wstates[i], newstate);\n fi;\n fi;\n perm := perm * fam!.automatonlist[exp[j]][fam!.deg+1];\n od;\n if Length(wstates[i]) > 0 then\n wstates[i] := AssocWordByLetterRep(FamilyObj(w), wstates[i]);\n else\n wstates[i] := One(fam!.freegroup);\n fi;\n if fam!.use_rws and not IsOne(wstates[i]) then\n wstates[i] := AG_ReducedForm(fam!.rws, wstates[i]);\n fi;\n od;\n\n invertible := true;\n if not fam!.isgroup then\n for i in exp do\n if i <= fam!.numstates and not IsInvertibleAutom(fam!.automgens[i]) then\n invertible := false;\n break;\n fi;\n od;\n fi;\n\n return __AG_CreateAutom(fam, w, wstates, nperm, invertible);\nend);\n\n\n###############################################################################\n##\n#M Autom(, )\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsAutom]\", [IsAssocWord, IsAutom],\nfunction(w, a)\n return Autom(w, FamilyObj(a));\nend);\n\n\nInstallMethod(MappedWord, [IsAssocWord,\n IsList and IsAssocWordCollection,\n IsList and IsAutomCollection],\nfunction(w, fgens, agens)\n local img;\n img := MappedWord(w, fgens, List(agens, a -> a!.word));\n return Autom(img, FamilyObj(agens[1]));\nend);\n\n\n###############################################################################\n##\n#M Autom(, )\n##\nInstallMethod(Autom, \"for [IsAssocWord, IsList]\",\n [IsAssocWord, IsList],\nfunction(w, list)\n local fam;\n fam := AutomFamily(list);\n if fam = fail then\n return fail;\n fi;\n return Autom(w, fam);\nend);\n\n\n###############################################################################\n##\n#M PrintObj()\n##\nInstallMethod(PrintObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n local deg, printword, i;\n\n printword := function(w)\n if IsOne(w) then Print(AG_Globals.identity_symbol);\n else Print(w); fi;\n end;\n\n if true then\n View(a);\n return;\n fi;\n\n deg := a!.deg;\n printword(a!.word);\n Print(\" = (\");\n for i in [1..deg] do\n printword(a!.states[i]);\n if i <> deg then Print(\", \"); fi;\n od;\n Print(\")\");\n if not IsOne(a!.perm) then AG_PrintTransformation(a!.perm); fi;\nend);\n\n\n###############################################################################\n##\n#M ViewObj()\n##\nInstallMethod(ViewObj, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then Print(AG_Globals.identity_symbol);\n else Print(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M String()\n##\nInstallMethod(String, \"for [IsAutom]\",\n [IsAutom],\nfunction (a)\n if IsOne(a!.word) then return AG_Globals.identity_symbol;\n else return String(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M Perm()\n##\nInstallMethod(Perm, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.perm;\nend);\n\n\n###############################################################################\n##\n#M Word()\n##\nInstallMethod(Word, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.word;\nend);\n\n\n###############################################################################\n##\n#M * \n##\nInstallMethod(\\*, \"for [IsAutom, IsAutom]\", [IsAutom, IsAutom],\nfunction(a1, a2)\n local a, i, fam, word, states;\n\n fam := FamilyObj(a1);\n word := a1!.word * a2!.word;\n\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n fi;\n\n if IsOne(word) then\n return One(a1);\n fi;\n\n states := List([1..a1!.deg], i -> a1!.states[i] * a2!.states[i^(a1!.perm)]);\n\n if fam!.use_rws then\n for i in [1..a1!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a1), word, states, a1!.perm * a2!.perm,\n IsInvertibleAutom(a1) and IsInvertibleAutom(a2));\nend);\n\n\nAG_IsOne_Autom := function(a)\n local deg, w, aw, checked, to_check;\n\n if IsOne(a!.word) then\n return true;\n fi;\n\n if not IsOne(a!.perm) then\n return false;\n fi;\n\n deg := a!.deg;\n checked := [];\n to_check := Filtered(a!.states, w -> not IsOne(w) and w <> a!.word);\n\n while not IsEmpty(to_check) do\n w := Remove(to_check, Length(to_check));\n # TODO Use AddSet() here?\n Add(checked, w);\n aw := Autom(w, a);\n if not IsOne(aw!.perm) then\n return false;\n fi;\n for w in aw!.states do\n if not IsOne(w) and not w in checked and not w in to_check then\n # TODO Use AddSet() here?\n Add(to_check, w);\n fi;\n od;\n od;\n\n return true;\nend;\n\n###############################################################################\n##\n#M IsOne(a)\n##\nInstallMethod(IsOne, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n local i, w, nw, d, to_check, checked, deb_i, perm, autlist, pos, istrivstate, exp, G, trivstate;\n\n if IsOne(a!.word) then return true; fi;\n\n G := GroupOfAutomFamily(FamilyObj(a));\n if G <>fail and HasIsContracting(G) and IsContracting(G) and FamilyObj(a)!.use_contraction = true then\n return IsOneContr(a);\n fi;\n\n # this seems working well enough\n return AG_IsOne_Autom(a);\n\n d := a!.deg;\n autlist := FamilyObj(a)!.automatonlist;\n trivstate := FamilyObj(a)!.trivstate;\n checked := [];\n\n istrivstate := function(v)\n local i, j, perm;\n\n if IsEmpty(v) then\n return true;\n fi;\n\n if v in checked then\n return true;\n else\n perm := ();\n for i in [1..Length(v)] do perm := perm * autlist[v[i]][d+1]; od;\n if perm <> () then return false; fi;\n Add(checked, v);\n for j in [1..d] do\n if not istrivstate(AG_WordStateInList(v, j, autlist, true, trivstate)) then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := LetterRepAssocWord(a!.word);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then\n exp[i] := -exp[i] + FamilyObj(a)!.numstates;\n fi;\n od;\n\n return istrivstate(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 = a2\n##\nInstallMethod(\\=, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local areequalstates, exp, i, d, checked, autlist, G, trivstate;\n\n G := GroupOfAutomFamily(FamilyObj(a1));\n if G <> fail and HasIsContracting(G) and IsContracting(G) and UseContraction(G) then\n return IsOneContr(a1*a2^-1);\n fi;\n\n # TODO can there be a problem if we do this?\n if G <> fail then\n return AG_IsOne_Autom(a1*a2^-1);\n fi;\n\n d := a1!.deg;\n checked := [];\n autlist := FamilyObj(a1)!.automatonlist;\n trivstate := FamilyObj(a1)!.trivstate;\n\n areequalstates := function(p)\n local i, j, perm1, perm2;\n\n if p[1] = p[2] then\n return true;\n fi;\n\n if p in checked then\n return true;\n else\n perm1 := ();\n perm2 := ();\n\n for i in [1..Length(p[1])] do\n perm1 := perm1 * autlist[p[1][i]][d+1];\n od;\n for i in [1..Length(p[2])] do\n perm2 := perm2 * autlist[p[2][i]][d+1];\n od;\n\n if perm1 <> perm2 then\n return false;\n fi;\n\n AddSet(checked, p);\n for j in [1..d] do\n if not areequalstates([AG_WordStateInList(p[1], j, autlist, true, trivstate),\n AG_WordStateInList(p[2], j, autlist, true, trivstate)])\n then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n return areequalstates(exp);\nend);\n\n\n###############################################################################\n##\n#M a1 < a2\n##\nInstallMethod(\\<, \"for [IsAutom, IsAutom]\", IsIdenticalObj, [IsAutom, IsAutom],\nfunction(a1, a2)\n local d, checked, pos, aw1, aw2, p, np, i, exp, perm1, perm2, autlist, cmp;\n\n d := a1!.deg;\n autlist := FamilyObj(a1)!.automatonlist;\n exp := [LetterRepAssocWord(a1!.word), LetterRepAssocWord(a2!.word)];\n for i in [1..Length(exp[1])] do\n if exp[1][i] < 0 then exp[1][i] := -exp[1][i] + FamilyObj(a1)!.numstates; fi;\n od;\n for i in [1..Length(exp[2])] do\n if exp[2][i] < 0 then exp[2][i] := -exp[2][i] + FamilyObj(a2)!.numstates; fi;\n od;\n checked := [exp];\n pos := 0;\n\n while Length(checked) <> pos do\n pos := pos + 1;\n p := checked[pos];\n perm1 := ();\n perm2 := ();\n for i in [1..Length(p[1])] do perm1 := perm1 * autlist[p[1][i]][d+1]; od;\n for i in [1..Length(p[2])] do perm2 := perm2 * autlist[p[2][i]][d+1]; od;\n cmp := AG_TrCmp(perm1, perm2, d);\n if cmp < 0 then\n return true;\n elif cmp > 0 then\n return false;\n fi;\n for i in [1..d] do\n np := [AG_WordStateInList(p[1], i, autlist, false, 0),\n AG_WordStateInList(p[2], i, autlist, false, 0)];\n if not np in checked then\n Add(checked, np);\n fi;\n od;\n od;\n\n return false;\nend);\n\n\n###############################################################################\n##\n#M InverseOp()\n##\nInstallMethod(InverseOp, \"for [IsInvertibleAutom]\", [IsInvertibleAutom],\nfunction(a)\n local i, inv, fam, word, states;\n\n fam := FamilyObj(a);\n word := a!.word ^ -1;\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n if IsOne(word) then\n return One(a);\n fi;\n fi;\n\n states := List([1..a!.deg], i -> a!.states[i^(a!.perm^-1)]^-1);\n\n if fam!.use_rws then\n for i in [1..a!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateAutom(FamilyObj(a), word, states, a!.perm^-1, true);\nend);\n\n\n###############################################################################\n##\n#M OneOp()\n##\nInstallMethod(OneOp, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return One(FamilyObj(a));\nend);\n\n\n###############################################################################\n##\n#M StatesWords()\n##\nInstallMethod(StatesWords, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.states;\nend);\n\n\n###############################################################################\n##\n#M Sections(a)\n##\nInstallMethod(Sections, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return List(a!.states, s -> Autom(s, a));\nend);\n\n\n###############################################################################\n##\n#M Section(a, k)\n##\nInstallMethod(Section, \"for [IsAutom, IsPosInt]\", [IsAutom, IsPosInt],\nfunction(a, k)\n if k > a!.deg then\n Error(\"in Section(IsAutom, IsPosInt): invalid vertex \", k);\n fi;\n return Autom(a!.states[k], a);\nend);\n\n\n###############################################################################\n##\n#M Section(a, seq)\n##\n## TODO\nInstallMethod(Section, \"for [IsAutom, IsList]\", [IsAutom, IsList],\nfunction(a, v)\n if Length(v) = 0 then\n return a;\n fi;\n\n if Length(v) = 1 then\n return Section(a, v[1]);\n fi;\n\n return Section(Section(a, v[1]), v{[2..Length(v)]});\nend);\n\n\n###############################################################################\n##\n#M k ^ a\n##\nInstallMethod(\\^, \"for [IsPosInt, IsAutom]\", [IsPosInt, IsAutom],\nfunction(k, a)\n return k ^ Perm(a);\nend);\n\n\n###############################################################################\n##\n#M seq ^ a\n##\nInstallMethod(\\^, \"for [IsList, IsAutom]\", [IsList, IsAutom],\nfunction(seq, a)\n local i, deg, img, cur;\n\n deg := DegreeOfTree(a);\n for i in seq do\n if not IsInt(i) or i < 1 or i > deg then\n Error(\"\\^(IsList, IsAutom): \",\n i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# Print(\"\\^(IsList, IsAutom): \",\n# i, \" is out of range 1..\", deg, \" and is not a letter of the alphabet\\n\");\n# return seq;\n fi;\n od;\n\n if Length(seq) = 0 then return []; fi;\n if Length(seq) = 1 then return [seq[1]^Perm(a)]; fi;\n\n cur := LetterRepAssocWord(Word(a));\n for i in [1..Length(cur)] do\n if cur[i] < 0 then cur[i] := -cur[i]+FamilyObj(a)!.numstates; fi;\n od;\n cur := [cur, Perm(a)];\n\n img := [];\n for i in [1..Length(seq)] do\n img[i] := seq[i]^cur[2];\n cur := AG_WordStateAndPermInList(cur[1], seq[i],\n FamilyObj(a)!.automatonlist);\n od;\n\n return img;\nend);\n\n\n###############################################################################\n##\n#M PermOnLevelOp(a, k)\n##\n## TODO\nInstallMethod(PermOnLevelOp, \"for [IsIsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, k)\n local dom, perm;\n\n if k = 1 then\n return a!.perm;\n fi;\n\n dom := AsList(Tuples([1.. a!.deg], k));\n perm := List(dom, s -> s ^ a);\n perm := PermListList(dom, perm);\n\n return perm;\nend);\n\nInstallMethod(TransformationOnFirstLevel, [IsAutom],\nfunction(a)\n return AsTransformation(a!.perm);\nend);\n\n\n###############################################################################\n##\n#M IsActingOnBinaryTree()\n##\nInstallMethod(IsActingOnBinaryTree, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n return a!.deg = 2;\nend);\n\n\nInstallMethod(SphericalIndex, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n # XXX check uses of SphericalIndex everywhere\n return rec(start := [], period := [a!.deg]);\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(DegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(TopDegreeOfTree, \"for [IsAutom]\", [IsAutom],\nfunction(a)\n return a!.deg;\nend);\n\n\n###############################################################################\n##\n#M CanEasilyTestSphericalTransitivity()\n##\nInstallTrueMethod(CanEasilyTestSphericalTransitivity,\n IsActingOnBinaryTree and IsAutom);\n\n\n###############################################################################\n##\n#M IsSphericallyTransitive()\n##\nInstallMethod(IsSphericallyTransitive, \"for [IsAutom]\",\n [IsInvertibleAutom],\nfunction(a)\n local w, i, ab, abs;\n\n if IsOne(Word(a)) then\n Info(InfoAutomGrp, 3, \"IsSphericallyTransitive(a): false\");\n Info(InfoAutomGrp, 3, \" IsOne(Word(a)): a = \", a);\n return false;\n fi;\n\n TryNextMethod();\nend);\n\n\n#########################################################################\n##\n#M Order()\n##\nInstallMethod(Order, \"for [IsInvertibleAutom]\", true,\n [IsInvertibleAutom],\nfunction(a)\n local ord_loc;\n if IsGeneratedByBoundedAutomaton(GroupOfAutomFamily(FamilyObj(a))) then\n return OrderUsingSections(a, infinity);\n fi;\n if IsActingOnBinaryTree(a) and IsSphericallyTransitive(a) then\n return infinity;\n fi;\n ord_loc := OrderUsingSections(a, 10);\n if ord_loc <> fail then\n return ord_loc;\n fi;\n return OrderUsingSections(a, infinity);\nend);\n\n\n#########################################################################\n##\n#M IsTransitiveOnLevel( , )\n##\nInstallMethod(IsTransitiveOnLevel, \"for [IsInvertibleAutom, IsPosInt]\",\n [IsInvertibleAutom, IsPosInt],\nfunction(a, lev)\n return Length(OrbitPerms([PermOnLevel(a, lev)], 1)) = a!.deg^lev;\nend);\n\n\n\n#########################################################################\n##\n#M AllSections( )\n##\nInstallMethod(AllSections, \"for [IsAutom]\",\n [IsAutom],\nfunction(a)\n local states, find_all_sections;\n\n find_all_sections := function(s)\n local i;\n if not s in states then\n Add(states, s);\n for i in [1..s!.deg] do find_all_sections(Section(s, i)); od;\n fi;\n end;\n\n states := [];\n find_all_sections(a);\n return states;\nend);\n\n\n#E\n", "meta": {"hexsha": "1a258a4efd57dc34d94a2cc904edf914da996765", "size": 18607, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/autom.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/autom.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/autom.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 24.3547120419, "max_line_length": 105, "alphanum_fraction": 0.5134626753, "num_tokens": 5207, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6959583376458152, "lm_q2_score": 0.5964331462646254, "lm_q1q2_score": 0.41509262099119204}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F ==========================================================================\n#F AParSMP(, ) - SMP parallelization tag\n#F .params[1] becomes num_threads\n#F .params[2] becomes tid\n#F \nClass(AParSMP, AGenericTag, rec(\n isSMP := true,\n updateParams := meth(self)\n if Length(self.params)=1 then self.params := [self.params[1], threadId()];\n elif Length(self.params)=2 then ;\n else Error(\"Usage: AParSMP(, [])\");\n fi;\n end\n));\n\n#F ==========================================================================\n#F SMPBarrier(, , ) \n#F\n#F ==========================================================================\nClass(SMPBarrier, Buf, BaseContainer, rec( \n # inheriting from Buf helps to get extra methods from Buf, for example \n # .cannotChangeDataFormat (from paradigms/vector). Buf is considered a general wrapper. \n doNotMarkBB := true,\n new := (self, nthreads, tid, spl) >> Checked(IsPosInt0Sym(tid), IsPosIntSym(nthreads), IsSPL(spl),\n SPL(WithBases(self, rec(_children:=[spl], tid := tid, nthreads := nthreads, dimensions := spl.dims())))),\n\n dims := self >> self._children[1].dims(),\n\n rChildren := self >> [self.nthreads, self.tid, self._children[1]],\n rSetChild := meth(self, n, newC)\n if n=1 then self.nthreads := newC;\n elif n=2 then self.tid := newC;\n elif n=3 then self._children[1] := newC;\n else Error(\" must be in [1..3]\");\n fi;\n end\n));\n\n#F ==========================================================================\n#F SMPSum(, , , , ) - parallel loop with threads \n#F\n#F As a matrix SMPSum(p, var, domain, spl) == ISum(var, domain, spl)\n#F ==========================================================================\nClass(SMPSum, ISum, rec(\n doNotMarkBB := true,\n abbrevs := [ (p, var, domain, spl) -> Checked(\n IsInt(p) or IsScalar(p), IsVar(var), IsInt(p) or IsScalar(domain), IsSPL(spl), \n [p, threadId(), var, domain, spl]) ],\n\n new := meth(self, nthreads, tid, var, domain, spl)\n local res;\n Constraint(IsSPL(spl)); \n\t# if domain is an integer (not symbolic) it must be non-zero\n\tConstraint(IsPosIntSym(domain));\n var.isLoopIndex := true;\n var.range := domain;\n\tres := SPL(WithBases(self, rec(nthreads:=nthreads, tid:=tid, _children := [spl], var := var, domain := domain)));\n\tres.dimensions := res.dims();\n\treturn res;\n end,\n \n rChildren := self >> [self.nthreads, self.tid, self.var, self.domain, self._children[1]],\n\n from_rChildren := (self, rch) >> ApplyFunc(ObjId(self), rch),\n\n rSetChild := meth(self, n, newChild) \n\tif n=1 then self.nthreads := newChild;\n\telif n=2 then self.tid := newChild;\n\telif n=3 then self.var := newChild;\n\telif n=4 then self.var.range := newChild; self.var.isLoopIndex := true;\n\telif n=5 then self._children[1] := newChild;\n else Error(\" must be in [1..5]\");\n\tfi;\n end, \n\n print := (self, i, is) >> Print(self.__name__, \"(\", self.nthreads, \", \", self.tid, \", \", \n self.var, \", \", self.domain, \",\\n\", Blanks(i+is), self.child(1).print(i+is, is), \"\\n\",\n\tBlanks(i), \")\", self.printA())\n));\n\n#F ==========================================================================\n#F SMP(, , ) - parallel container for rewriting\n#F\n#F SMP(ISum(...)) -- becomes --> SMPSum(...)\n#F ==========================================================================\nClass(SMP, BaseContainer, rec(\n doNotMarkBB := true,\n\n abbrevs := [ (nthreads, spl) -> Checked(IsInt(nthreads) or IsScalar(nthreads), IsSPL(spl), \n [nthreads, threadId(), spl]) ],\n\n new := (self, nthreads, tid, spl) >>\n\tSPL(WithBases(self, rec(nthreads:=nthreads, tid:=tid, dimensions := spl.dimensions, _children := [spl]))),\n\t\n rChildren := self >> [self.nthreads, self.tid, self._children[1]],\n\n rSetChild := meth(self, n, newChild)\n if n = 1 then self.nthreads := newChild;\n elif n = 2 then self.tid := newChild;\n\telif n = 3 then self._children[1] := newChild;\n\telse Error(\" must be in [1..3]\"); fi;\n\treturn self;\n end,\n\n sums := self >> ObjId(self)(self.nthreads, self.tid, self.child(1).sums()),\n\n normalizedArithCost := self >> self.child(1).normalizedArithCost()\n));\n\n", "meta": {"hexsha": "cc259cce298aeaaacbd37323df1668a13d56147c", "size": 4481, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/smp/sigmaspl.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/smp/sigmaspl.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/smp/sigmaspl.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.9652173913, "max_line_length": 114, "alphanum_fraction": 0.5338094175, "num_tokens": 1209, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6477982315512488, "lm_q2_score": 0.6406358685621719, "lm_q1q2_score": 0.4150027827228733}} {"text": "#############################################################################\n##\n#W selfs.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n\nInstallGlobalFunction(ReduceWord,\nfunction(v)\n local i, b;\n b := [];\n for i in [1..Length(v)] do\n if v[i] <> 1 then\n Add(b, v[i]);\n fi;\n od;\n return b;\nend);\n\n\nInstallGlobalFunction(ProjectWord, function(w, s, G)\n local i, perm, d, proj;\n d := Length(G[1])-1;\n if s > d or s < 1 then\n Error(\"Incorrect index of a subtree\");\n fi;\n proj := [];\n perm := ();\n for i in [1..Length(w)] do\n Add(proj, G[w[i]][s^perm]);\n perm := perm*G[w[i]][d+1];\n od;\n return proj;\nend);\n\n\nInstallGlobalFunction(WordActionOnFirstLevel, function(w, G)\n local i, perm, d;\n d := Length(G[1])-1;\n perm := ();\n for i in [1..Length(w)] do perm := perm*G[w[i]][d+1]; od;\n return perm;\nend);\n\n\nInstallGlobalFunction(WordActionOnVertex, function(w, ver, G)\n local i, cur_w, new_ver, perm;\n new_ver := [];\n cur_w := ShallowCopy(w);\n for i in [1..Length(ver)] do\n perm := WordActionOnFirstLevel(cur_w, G);\n new_ver[i] := ver[i]^perm;\n cur_w := ProjectWord(cur_w, ver[i], G);\n od;\n return new_ver;\nend);\n\n\nInstallMethod(OrbitOfVertex, \"for [IsList, IsTreeHomomorphism, IsCyclotomic]\", true, [IsList, IsTreeHomomorphism, IsCyclotomic],\nfunction(ver, g, n)\n local i, ver_tmp, orb;\n i := 0; orb := [];\n ver_tmp := ver;\n while i < n and (ver <> ver_tmp or i = 0) do\n Add(orb, ver_tmp);\n ver_tmp := ver_tmp^g;\n i := i+1;\n od;\n return orb;\nend);\n\n\nInstallMethod(OrbitOfVertex, \"for [IsList, IsTreeHomomorphism]\", [IsList, IsTreeHomomorphism],\nfunction(ver, g)\n return OrbitOfVertex(ver, g, infinity);\nend);\n\n\nInstallMethod(OrbitOfVertex, \"for [IsString, IsTreeHomomorphism, IsCyclotomic]\", true, [IsString, IsTreeHomomorphism, IsCyclotomic],\nfunction(ver, g, n)\n local i, ver_tmp, orb, ch;\n\n ver_tmp := [];\n for i in [1..Length(ver)] do\n ch := Int(String([ver[i]]));\n if ch < 1 or ch > g!.deg then\n Error(\"received string \", ver, \" does not represent a valid vertex\");\n fi;\n Add(ver_tmp, ch);\n od;\n ver := ver_tmp;\n\n i := 0; orb := [];\n ver_tmp := ver;\n while i < n and (ver <> ver_tmp or i = 0) do\n Add(orb, ver_tmp);\n ver_tmp := ver_tmp^g;\n i := i+1;\n od;\n return orb;\nend);\n\n\nInstallMethod(OrbitOfVertex, \"for [IsString, IsTreeHomomorphism]\",\n [IsString, IsTreeHomomorphism],\nfunction(ver, g)\n return OrbitOfVertex(ver, g, infinity);\nend);\n\n\nInstallMethod(PrintOrbitOfVertex, \"for [IsList, IsTreeHomomorphism, IsCyclotomic]\",\n [IsList, IsTreeHomomorphism, IsCyclotomic],\nfunction(ver, w, n)\n local orb, i, j;\n orb := OrbitOfVertex(ver, w, n);\n if w!.deg = 2 then\n for i in [1..Length(orb)] do\n for j in [1..Length(orb[1])] do\n # Print(orb[i][j]);\n if orb[i][j] = 1 then Print(\" \"); else Print(\"x\"); fi;\n od;\n Print(\"\\n\");\n od;\n else\n for i in [1..Length(orb)] do\n for j in [1..Length(orb[1])] do\n Print(orb[i][j]);\n od;\n Print(\"\\n\");\n od;\n fi;\nend);\n\nInstallMethod(PrintOrbitOfVertex, \"for [IsString, IsTreeHomomorphism]\", [IsList, IsTreeHomomorphism],\nfunction(ver, g)\n PrintOrbitOfVertex(ver, g, infinity);\nend);\n\n\nInstallGlobalFunction(IsOneWordSelfSim, function(w, G)\n local i, IsOneWordIter, ReachedWords, d;\n\n IsOneWordIter := function(v)\n local i, j, perm;\n if v in ReachedWords then return true;\n else\n perm := ();\n for i in [1..Length(v)] do perm := perm*G[v[i]][d+1]; od;\n if perm <> () then return false; fi;\n Add(ReachedWords, v);\n for j in [1..d] do\n if not IsOneWordIter(ProjectWord(v, j, G)) then return false; fi;\n od;\n return true;\n fi;\n end;\n\n d := Length(G[1])-1;\n if Length(w) = 0 then return true; fi;\n ReachedWords := [];\n return IsOneWordIter(w);\nend);\n\n\nInstallGlobalFunction(IsOneWordContr, function(word, G)\n local IsOneWordContrLocal;\n\n IsOneWordContrLocal:=function(word)\n local i, b, l, v, c, k, res, t, w;\n w := ShallowCopy(word);\n# Print(\"w=\",w,\"\\n\");\n if Length(w) = 0 then return true; fi;\n if Length(w) = 1 then\n if w = [1] then return true;\n else return false;\n fi;\n fi;\n if Length(w) mod 2 = 1 then Add(w, 1); fi;\n l := [];\n for i in [1..Length(w)/2] do\n Add(l, StructuralCopy(G[w[2*i-1]][w[2*i]]));\n od;\n # Print(\"l = \", l);\n # list c contains permutations c[i+1] = pi[1]*pi[2]*...*pi[i]\n c := [(), l[1][Length(l[1])]];\n t := Length(l);\n for i in [2..t] do\n # Print(\"c[\", i, \"] = \", c[i], \", l[\", i, \"] = \", l[i][Length(l[i])], \";\");\n Add(c, c[i]*l[i][Length(l[i])]);\n l[i][Length(l[i])] := c[i];\n od;\n if c[Length(c)] <> () then\n return false;\n fi;\n l[1][Length(l[1])] := ();\n b := [];\n for i in [1..Length(l)] do\n b[i] := Permuted(l[i],(l[i][Length(l[i])])^(-1));\n od;\n i := 1;\n res := true;\n while res and (i <= Length(b[1])-1) do\n v := [];\n for k in [1..Length(b)] do\n Add(v, b[k][i]);\n od;\n v := ReduceWord(v);\n res := IsOneWordContrLocal(v);\n i := i+1;\n od;\n return res;\n end;\n\n return IsOneWordContrLocal(word);\nend);\n\n\nInstallGlobalFunction(AG_IsOneList, function(w, G)\n if IsList(G[1][1]) then return IsOneWordContr(w, G);\n else return IsOneWordSelfSim(w, G);\n fi;\nend);\n\n\nInstallMethod(AG_MinimizedAutomatonList, \"for [IsAutomGroup]\", [IsAutomGroup],\nfunction(H)\n return AG_AddInversesListTrack(List(AutomatonList(H), x -> List(x)));\nend);\n\n\nInstallGlobalFunction(CONVERT_ASSOCW_TO_LIST, function(w)\n local w_list, w_ext, i, j, numstates, cur_gen;\n numstates := FamilyObj(w)!.numstates;\n w_list := [];\n w_ext := ExtRepOfObj(w!.word);\n for i in [1..Length(w_ext)/2] do\n if w_ext[2*i] > 0 then\n cur_gen := w_ext[2*i-1];\n else\n cur_gen := w_ext[2*i-1]+numstates;\n fi;\n for j in [1..AbsInt(w_ext[2*i])] do Add(w_list, cur_gen); od;\n od;\n return w_list;\nend);\n\n\nInstallGlobalFunction(IsOneContr,\nfunction(a)\n local a_list, a_list_orig, track_l, Gi, i;\n\n a_list_orig := CONVERT_ASSOCW_TO_LIST(a);\n\n\n Gi := AG_MinimizedAutomatonList(GroupOfAutomFamily(FamilyObj(a)));\n track_l := Gi[3];\n\n #a_list := [];\n #for i in [1..Length(a_list_orig)] do Add(a_list, track_l[a_list_orig[i]]); od;\n\n a_list := List(a_list_orig, i -> track_l[i]);\n\n return IsOneWordContr(a_list, AG_ContractingTable(GroupOfAutomFamily(FamilyObj(a))));\nend);\n\n\n###############################################################################\n##\n#M AG_IsOneList(w, G) (IsList, IsAutomGroup)\n##\n#InstallGlobalFunction(AG_IsOneList,\n#function(w, G)\n# if HasIsContracting(G) and IsContracting(G) and UseContraction(G) then\n# return IsOneWordContr(w, AG_ContractingTable(G));\n# else\n# return IsOneWordSelfSim(w, AG_MinimizedAutomatonList(G)[1]);\n# fi;\n#end);\n\n\n\nInstallGlobalFunction(AG_ChooseAutomatonList,\nfunction(G)\n if HasIsContracting(G) and IsContracting(G) and UnderlyingAutomFamily(G)!.use_contraction then\n return AG_ContractingTable(G);\n else\n return AG_MinimizedAutomatonList(G)[1];\n fi;\nend);\n\n\nInstallMethod(AG_OrderOfElement, \"for [IsList, IsList, IsCyclotomic]\", true,\n [IsList, IsList, IsCyclotomic],\nfunction(v, G, size)\n local w, k;\n v := ReduceWord(v);\n w := StructuralCopy(v); k := 1;\n if Length(G[1]) = 3 then\n while (not AG_IsOneList(w, G)) and k < size do\n Append(w, w);\n# Print(w, \";\");\n k := 2*k;\n od;\n else\n while (not AG_IsOneList(w, G)) and k < size do\n Append(w, v);\n# Print(w, \";\");\n k := k+1;\n od;\n fi;\n if AG_IsOneList(w, G) then return k; else return fail; fi;\nend);\n\n\nInstallMethod(AG_OrderOfElement, \"for [IsList, IsList, IsPosInt]\",\n [IsList, IsList],\nfunction(v, G)\n return AG_OrderOfElement(v, G, infinity);\nend);\n\n\nInstallGlobalFunction(GeneratorActionOnVertex, function(G, g, w)\n local i, v, gen, d;\n d := Length(G[1])-1;\n gen := g; v := [];\n for i in [1..Length(w)] do\n Add(v, (w[i]+1)^G[gen][d+1]-1);\n gen := G[gen][w[i]+1];\n od;\n return v;\nend);\n\n\nInstallGlobalFunction(AG_NumberOfVertex, function(w, d)\n local i, s;\n s := 0;\n for i in [1..Length(w)] do\n s := s+w[i]*d^(Length(w)-i);\n od;\n return s;\nend);\n\n\nInstallGlobalFunction(NumberOfVertex, function(w, d)\n local i, s, w_loc;\n s := 0;\n if IsString(w) then\n w_loc := List(w, x -> Int(String([x]))-1);\n else\n w_loc := List(w, x -> x-1);\n fi;\n for i in w_loc do\n if i < 0 or i >= d then\n Error(\"received string \", w, \" does not represent a valid vertex\");\n fi;\n od;\n for i in [1..Length(w)] do\n s := s+w_loc[i]*d^(Length(w)-i);\n od;\n return s+1;\nend);\n\n\nInstallGlobalFunction(AG_VertexNumber, function(k, n, d)\n local i, l, l1, t;\n t := k; l := [];\n while t > 0 do\n Add(l, t mod d);\n t := (t-(t mod d))/d;\n od;\n for i in [Length(l)+1..n] do Add(l, 0); od;\n l1 := [];\n for i in [1..n] do l1[i] := l[n-i+1]; od;\n return l1;\nend);\n\n\nInstallGlobalFunction(VertexNumber, function(k, n, d)\n local i, l, l1, t;\n t := k-1; l := [];\n while t > 0 do\n Add(l, t mod d);\n t := (t-(t mod d))/d;\n od;\n for i in [Length(l)+1..n] do Add(l, 0); od;\n l1 := [];\n for i in [1..n] do l1[i] := l[n-i+1]; od;\n return List(l1, x -> x+1);\nend);\n\n\nInstallGlobalFunction(GeneratorActionOnLevel, function(G, g, n)\n local l, d, i, s, v, w, k;\n s := (); d := Length(G[1])-1;\n l := [];\n for i in [1..d^n] do Add(l, 0); od;\n i := 0;\n while i < d^n do\n k := 0;\n while l[k+1] > 0 do\n k := k+1;\n od;\n w := AG_VertexNumber(k, n, d);\n v := StructuralCopy(w);\n i := i+1;\n repeat\n l[AG_NumberOfVertex(v, d)+1] := 1;\n v := GeneratorActionOnVertex(G, g, v);\n if v <> w then\n s := s*(k+1, AG_NumberOfVertex(v, d)+1);\n i := i+1;\n fi;\n until v = w;\n od;\n return s;\nend);\n\n\nInstallGlobalFunction(PermActionOnLevel, function(perm, big_lev, sm_lev, deg)\n local l, i;\n l := [];\n for i in [0..deg^sm_lev-1] do\n Add(l, Int(((1+i*deg^(big_lev-sm_lev))^perm-1)/(deg^(big_lev-sm_lev)))+1);\n od;\n return PermList(l);\nend);\n\n\nInstallGlobalFunction(WordActionOnLevel, function(G, w, n)\n local gen, perm;\n perm := ();\n for gen in w do\n perm := perm*GeneratorActionOnLevel(G, gen, n);\n od;\n return perm;\nend);\n\n\nInstallGlobalFunction(AG_IsWordTransitiveOnLevel, function(G, w, lev)\n return Length(OrbitPerms([WordActionOnLevel(G, w, lev)], 1)) = (Length(G[1])-1)^lev;\nend);\n\n\nInstallGlobalFunction(AG_GeneratorActionOnLevelAsMatrix, function(G, g, n)\n local perm, i, j, m, d;\n perm := GeneratorActionOnLevel(G, g, n);\n d := Length(G[1])-1;\n m := List([1..d^n], x -> List([1..d^n], x -> 0));\n for i in [1..d^n] do\n m[i][i^perm] := 1;\n od;\n return m;\nend);\n\n\nInstallGlobalFunction(PermOnLevelAsMatrix, function(g, lev)\n local perm, i, j, m, d;\n perm := PermOnLevel(g, lev);\n d := g!.deg;\n m := List([1..d^lev], x -> List([1..d^lev], x -> 0));\n for i in [1..d^lev] do\n m[i][i^perm] := 1;\n od;\n return m;\nend);\n\n\nInstallGlobalFunction(TransformationOnLevelAsMatrix, function(g, lev)\n local trans, i, j, m, d;\n trans := TransformationOnLevel(g, lev);\n d := DegreeOfTransformation(trans);\n m := List([1..d], x -> List([1..d], x -> 0));\n for i in [1..d] do\n m[i][i^trans] := 1;\n od;\n return m;\nend);\n\n\nInstallGlobalFunction(InvestigatePairs, function(G)\n local i, j, k, i1, j1, k1, Pairs, Trip, n, IsPairEq, d, res, tmp;\n\n IsPairEq := function(i, j, k) # ij = k?\n local t, res;\n if (not IsList(Pairs[i][j])) or (IsList(Pairs[i][j])\n and (Pairs[i][j][1] <> k)) then\n if (not IsList(Pairs[i][j])) and (Pairs[i][j] <> -1) then\n if Pairs[i][j] = k then return true;\n else return false;\n fi;\n fi;\n if IsList(Pairs[i][j]) then\n if Length(Pairs[i][j]) = 1 then\n Trip[i][j][Pairs[i][j][1]] := 0;\n else\n Trip[i1][j1][k1] := 0;\n return true;\n fi;\n fi;\n if Trip[i][j][k] = 0 then return false;\n else\n if G[i][d+1]*G[j][d+1] <> G[k][d+1] then\n Trip[i][j][k] := 0;\n return false;\n fi;\n Pairs[i][j] := [k];\n t := 1; res := true;\n while res and (t <= d) do\n# Print(\"i = \", i, \", j = \", j, \", k = \", k, \", t = \", t, \"; \");\n res := IsPairEq(G[i][t], G[j][t^G[i][d+1]], G[k][t]);\n t := t+1;\n od;\n if res then\n if Trip[i][j][k] <> 0 then\n Pairs[i][j] := [k, 1];\n return true;\n else\n Pairs[i][j] := -1;\n return false;\n fi;\n else\n Trip[i][j][k] := 0;\n Pairs[i][j] := -1;\n return false;\n fi;\n fi;\n else\n return true;\n fi;\n end;\n\n Pairs := [[]]; Trip := [];\n n := Length(G);\n d := Length(G[1])-1;\n for j in [1..n] do Add(Pairs[1], j); od;\n for i in [2..n] do\n Add(Pairs, [i]);\n Trip[i] := [];\n for j in [2..n] do\n Pairs[i][j] := -1;\n Trip[i][j] := [];\n for k in [1..n] do Trip[i][j][k] := -1; od;\n od;\n od;\n# Print(Pairs);\n# Print(Trip);\n for i1 in [2..n] do for j1 in [2..n] do\n if Pairs[i1][j1] = -1 then\n k1 := 1; res := false;\n while (not res) and (k1 <= n) do\n res := IsPairEq(i1, j1, k1);\n# Print(Pairs, \"\\n\");\n for i in [2..n] do for j in [2..n] do\n if IsList(Pairs[i][j]) then\n if res then Pairs[i][j] := Pairs[i][j][1];\n else Pairs[i][j] := -1;\n fi;\n fi;\n od; od;\n k1 := k1+1;\n od;\n if Pairs[i1][j1] = -1 then Pairs[i1][j1] := 0; fi;\n fi;\n od; od;\n return Pairs;\nend);\n\n\nInstallMethod(ContractingLevel, \"for [IsAutomGroup]\", [IsAutomGroup],\nfunction(H)\n if not HasIsContracting(H) then\n Info(InfoAutomGrp, 1, \"If < H > is not contracting, the algorithm will never stop\");\n fi;\n FindNucleus(H,false);\n return ContractingLevel(H);\nend);\n\n\n\n\nInstallMethod(AG_ContractingTable, \"for [IsAutomGroup]\", [IsAutomGroup],\nfunction(H)\n local AG_ContractingTableLocal;\n AG_ContractingTableLocal := function(G)\n local lev, n, d, i, j, ContractingPair, Pairs, ContTable;\n ContractingPair := function(i, j)\n local l, k, t, PairAct, TmpList, g1, g2;\n if Pairs[i][j] <> 0 then PairAct := [Pairs[i][j]];\n else PairAct := [[i, j]];\n fi;\n for l in [1..lev] do\n TmpList := [];\n for t in [1..Length(PairAct)] do\n if not IsList(PairAct[t]) then\n for k in [1..d] do Add(TmpList, G[PairAct[t]][k]); od;\n else\n for k in [1..d] do\n g1 := G[PairAct[t][1]][k];\n g2 := G[PairAct[t][2]][k^G[PairAct[t][1]][d+1]];\n if Pairs[g1][g2] <> 0 then Add(TmpList, Pairs[g1][g2]);\n else Add(TmpList, [g1, g2]);\n fi;\n od;\n fi;\n od;\n PairAct := StructuralCopy(TmpList);\n od;\n Add(PairAct, GeneratorActionOnLevel(G, i, lev)*GeneratorActionOnLevel(G, j, lev));\n return PairAct;\n end;\n\n lev := ContractingLevel(H);\n Pairs := InvestigatePairs(G);\n n := Length(G);\n d := Length(G[1])-1;\n ContTable := [];\n for i in [1..n] do\n Add(ContTable, []);\n for j in [1..n] do Add(ContTable[i], ContractingPair(i, j)); od;\n od;\n return ContTable;\n end;\n################ AG_ContractingTable itself #################################\n\n if not HasIsContracting(H) then\n Info(InfoAutomGrp, 1, \"If < H > is not contracting, the algorithm will never stop\");\n fi;\n return AG_ContractingTableLocal(AG_GeneratingSetWithNucleusAutom(H));\nend);\n\n\nInstallMethod(ContractingTable, \"for [IsAutomGroup]\", [IsAutomGroup],\nfunction(H)\n local T, i, j, k, deg, numstates;\n T := StructuralCopy(AG_ContractingTable(H));\n deg := Length(T[1][1])-1;\n numstates := Length(T);\n for i in [1..numstates] do\n for j in [1..numstates] do\n for k in [1..deg] do\n T[i][j][k] := GeneratingSetWithNucleus(H)[T[i][j][k]];\n od;\n T[i][j] := TreeAutomorphism(T[i][j]{[1..deg]} , T[i][j][deg+1]);\n od;\n od;\n return T;\nend);\n\n\n# The base of the code of the function below below was written by Andriy Russev\nInstallGlobalFunction(AG_MinimizationOfAutomatonListTrack, function(A)\n local n, perms, m, classes, states, list, i, j, ids, temp, s, d, new_as_old, old_as_new, aut_list, perm, state;\n n := Length(A);\n d:=Length(A[1])-1;\n perms := SSortedList(List(A,x->x[d+1]));\n # In the minimization process the set of states is partitioned into classes\n m := Length(perms); # number of states of automaton A\n\n # \"classes\" contains classes of states. To each state of automaton A we assign an number from 1 to m\n # (the first element in the list; if the class is not \"finished\", we add n)\n classes := List([1..n], x -> [Position(perms, A[x][d+1])]);\n # Canonical representatives of classes of states\n states := [];\n\n # The list of states of A that have not been classified yet\n list := [1..n];\n\n # At this moment all the states that belong to the same class act identically\n # on words of length 1. During each iteration, classes consist of states that\n # act identically on the words of length k will be partitioned into smalled\n # subclasses of states that act identically on words of length k+1.\n # If no class was partitioned during an iteration, then all the states in\n # each class are equivalent and act identically on words of arbitrary length.\n # This is the end of minimization procedure\n while true do\n # states from each class act identically on all words of length k.\n for i in list do\n # Define classes for the states of the first level\n classes[i][2] := List(A[i]{[1..d]}, x -> classes[x][1]);\n od;\n\n # the extended identifier of a class contains information about the action\n # of this state, and of its first level states on words of length k.\n # I.e., it describes the action of the state on words of the length k+1.\n # If extended identifiers of states coincide, then these states act\n # identically on words of length k+1.\n # Update the identifiers of classes; save to \"temp\" the list of classes\n # that contain one state\n ids := [];\n temp := [];\n s := Length(states);\n for i in list do\n j := Position(ids, classes[i]);\n if j = fail then\n Add(ids, ShallowCopy(classes[i]));\n j := Length(ids);\n temp[j] := i;\n else\n Unbind(temp[j]);\n fi;\n classes[i][1] := s + j + n;\n od;\n # Check if new classes created during the iteration\n if s + Length(ids) = m then break; fi;\n m := s + Length(ids);\n # Find canonical representatives of classes that contain only a single state of A\n temp := Compacted(temp);\n for i in temp do\n s := s + 1;\n classes[i][1] := s;\n states[s] := i;\n od;\n # remove all classes with one state from future iterations.\n SubtractSet(list, temp);\n od;\n # Find canonical representatives of the remaining classes\n\n\n ids := [];\n for i in list do\n classes[i][1] := classes[i][1] - n;\n j := Position(ids, classes[i]);\n if j = fail then\n Add(ids, classes[i]);\n states[classes[i][1]] := i;\n fi;\n od;\n\n aut_list:=List(states,\n x -> Flat([List(A[x]{[1..d]}, y -> classes[y][1]),\n A[x][d+1]]));\n old_as_new:=List(classes,c->c[1]);\n new_as_old:=List([1..Length(states)],x->Position(old_as_new,x));\n\n #Now sort the new list in the same order as the old states\n perm:=Sortex(new_as_old);\n\n aut_list:=Permuted(aut_list,perm);\n for state in aut_list do\n for i in [1..d] do\n state[i]:=state[i]^perm;\n od;\n od;\n\n Apply(old_as_new, x->x^perm);\n\n return [aut_list,\n new_as_old,\n old_as_new];\nend);\n\n\nInstallGlobalFunction(AG_MinimizationOfAutomatonList, function(G)\n return AG_MinimizationOfAutomatonListTrack(G)[1];\nend);\n\n\nInstallGlobalFunction(AG_AddInversesListTrack, function(H)\n local d, n, G, idEl, st, i, perm, inv, minimized_autlist;\n\n## track_s - new generators in terms of old ones\n## track_l - old generators in terms of new ones\n\n d := Length(H[1])-1;\n n := Length(H);\n if n < 1 or d < 1 then return fail; fi;\n idEl := Flat([List([1..d],x->1),()]);\n G := [idEl];\n for i in [1..n] do Add(G, StructuralCopy(H[i])); od;\n\n for st in [2..n+1] do\n for i in [1..d] do G[st][i] := G[st][i]+1; od;\n od;\n\n for st in [2..n+1] do\n inv := [];\n perm := G[st][d+1]^(-1);\n for i in [1..d] do Add(inv, G[st][i^perm]+n); od;\n Add(inv, perm);\n Add(G, inv);\n od;\n# return AG_MinimizationOfAutomatonListTrack(G, [0..Length(G)-1], [2..Length(G)]);\n minimized_autlist := AG_MinimizationOfAutomatonListTrack(G);\n return [minimized_autlist[1], List(minimized_autlist[2],x->x-1), minimized_autlist[3]{[2..Length(minimized_autlist[3])]}];\nend);\n\n\nInstallGlobalFunction(AG_AddInversesList, function(H)\n return AG_AddInversesListTrack(H)[1];\nend);\n\n\n\nInstallMethod(UseContraction, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n local H;\n H := GroupOfAutomFamily(UnderlyingAutomFamily(G));\n\n if not HasIsContracting(H) then\n Print(\"Error in UseContraction(): It is not known whether the group of family is contracting\\n\");\n return fail;\n elif not IsContracting(H) then\n Print(\"Error in UseContraction(): The group of family is not contracting\");\n return fail;\n fi;\n\n # IsContracting returns either true or false or an error (it can not return fail)\n UnderlyingAutomFamily(G)!.use_contraction := true;\n return true;\nend);\n\n\nInstallMethod(DoNotUseContraction, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n UnderlyingAutomFamily(G)!.use_contraction := false;\n return true;\nend);\n\n\n\nInstallMethod(FindNucleus, \"for [IsAutomatonGroup, IsCyclotomic, IsBool]\", true,\n [IsAutomatonGroup, IsCyclotomic, IsBool],\nfunction(H, max_nucl, print_info)\n local G, g, Pairs, i, j, PairsToAdd, AssocWPairsToAdd, res, ContPairs, n, d, found, num, DoesPairContract, AddPairs, lev, maxlev, tmp, Nucl, IsElemInNucleus,\n nucl_final, cur_nucl, cur_nucl_tmp, Hi, track_s, track_l, G_track, automgens, cur_nucl_length, info;\n\n# DoesPairContract := function(i, j, lev)\n# local t, res;\n# if lev > maxlev then maxlev := lev; fi;\n#\n# # ContPairs[i][j] may take the following values:\n# # -1 - [i, j] was not met before\n# # 1 - [i, j] contracts\n# # 2 - [i, j] was met above in the tree\n#\n# if (ContPairs[i][j] = 1) then return true; fi;\n# if Pairs[i][j] <> 0 then\n# ContPairs[i][j] := 1;\n# return true;\n# fi;\n# # if we've seen this pair before it needs to be in the nucleus\n# if ContPairs[i][j] = 2 then return [i, j]; fi;\n# t := 1; res := true;\n# ContPairs[i][j] := 2;\n# while res = true and (t <= d) do\n# res := DoesPairContract(G[i][t], G[j][t^G[i][d+1]], lev+1);\n# t := t+1;\n# od;\n# if res = true then\n# ContPairs[i][j] := 1;\n# return true;\n# else return res;\n# fi;\n# end;\n\n\n DoesPairContract := function(i, j, lev)\n local t, res, localmaxlev;\n if lev > maxlev then maxlev := lev; fi;\n\n# ContPairs[i][j] may take the following values:\n# -1 - [i, j] was not met before\n# [k] - [i, j] contracts on level k\n# 2 - [i, j] was met above in the tree\n\n if IsList(ContPairs[i][j]) then\n if lev+ContPairs[i][j][1] > maxlev then maxlev := lev+ContPairs[i][j][1]; fi;\n return true;\n fi;\n if Pairs[i][j] <> 0 then\n ContPairs[i][j] := [0];\n return true;\n fi;\n if ContPairs[i][j] = 2 then return [i,j]; fi;\n t := 1; res := true;\n ContPairs[i][j] := 2;\n localmaxlev := 0;\n while res = true and (t <= d) do\n res := DoesPairContract(G[i][t], G[j][t^G[i][d+1]], lev+1);\n if res = true then\n if ContPairs[G[i][t]][G[j][t^G[i][d+1]]][1]+1 > localmaxlev then\n localmaxlev := ContPairs[G[i][t]][G[j][t^G[i][d+1]]][1]+1;\n fi;\n fi;\n t := t+1;\n od;\n if res = true then\n ContPairs[i][j] := [localmaxlev];\n return true;\n else return res;\n fi;\n end;\n\n AddPairs := function(i, j)\n local tmp, l, CurNum;\n if Pairs[i][j] > 0 then return Pairs[i][j]; fi;\n Pairs[i][j] := num;\n CurNum := num;\n Add(PairsToAdd, []);\n num := num+1;\n tmp := [];\n for l in [1..d] do\n Add(tmp, AddPairs(G[i][l], G[j][l^G[i][d+1]]));\n od;\n Add(tmp, G[i][d+1]*G[j][d+1]);\n Append(PairsToAdd[CurNum-n], tmp);\n AssocWPairsToAdd[CurNum-n] := cur_nucl[i]*cur_nucl[j];\n return CurNum;\n end;\n\n IsElemInNucleus := function(g)\n local i, res;\n if g in tmp then\n for i in [Position(tmp, g)..Length(tmp)] do\n if not (tmp[i] in Nucl) then Add(Nucl, tmp[i]); fi;\n od;\n return g = tmp[1];\n fi;\n Add(tmp, g);\n res := false; i := 1;\n while (not res) and i <= d do\n res := IsElemInNucleus(G[g][i]);\n i := i+1;\n od;\n Remove(tmp);\n return res;\n end;\n\n# ****************** FindNucleus itself *******************************\n\n if HasIsContracting(H) and not IsContracting(H) then\n return fail;\n fi;\n\n automgens := UnderlyingAutomFamily(H)!.automgens;\n d := UnderlyingAutomFamily(H)!.deg;\n cur_nucl := [One(UnderlyingAutomFamily(H))];\n\n Hi := StructuralCopy(AG_MinimizedAutomatonList(H));\n# Print(\"Gi = \", Gi, \"\\n\");\n G := Hi[1];\n\n track_s := Hi[2];\n track_l := Hi[3];\n\n for i in [2..Length(track_s)] do Add(cur_nucl, automgens[track_s[i]]); od;\n\n found := false;\n\n while (not found) and Length(G) < max_nucl do\n res := true; maxlev := 0; ContPairs := [];\n Pairs := InvestigatePairs(G);\n n := Length(G);\n# Print(\"n = \", n, \"\\n\");\n if print_info = true then\n Print(\"Trying generating set with \", n, \" elements\\n\");\n else\n Info(InfoAutomGrp, 3, \"Trying generating set with \", n, \" elements\");\n fi;\n# for i in [1..n] do\n# Add(ContPairs, [1]);\n# for j in [1..n-1] do\n# if i = 1 then Add(ContPairs[i], 1);\n# else Add(ContPairs[i], -1);\n# fi;\n# od;\n# od;\n\n for i in [1..n] do\n Add(ContPairs, [[0]]);\n for j in [1..n-1] do\n if i = 1 then Add(ContPairs[i], [0]);\n else Add(ContPairs[i], -1);\n fi;\n od;\n od;\n\n\n i := 1;\n\n while res = true and (i <= n) do\n j := 1;\n while res = true and (j <= n) do\n #Print(\"i = \", i, \", j = \", j, \"\\n\");\n if ContPairs[i][j] = -1 then res := DoesPairContract(i, j, 0); fi;\n if res <> true then\n PairsToAdd := [];\n AssocWPairsToAdd := [];\n# num represents current number of generators\n num := n+1;\n AssocWPairsToAdd := [];\n AddPairs(res[1], res[2]);\n if print_info = true then\n Print(\"Elements added:\", List(AssocWPairsToAdd, x -> x!.word), \"\\n\");\n else\n Info(InfoAutomGrp, 3, \"Elements added:\", List(AssocWPairsToAdd, x -> x!.word));\n fi;\n Append(G, PairsToAdd);\n# Print(\"G = \", G, \"\\n\");\n Append(cur_nucl, AssocWPairsToAdd);\n G_track := AG_AddInversesListTrack(G);\n# Print(\"G_track = \", G_track, \"\\n\");\n G := G_track[1];\n cur_nucl_tmp := [];\n cur_nucl_tmp := [One(UnderlyingAutomFamily(H))];\n cur_nucl_length := Length(cur_nucl);\n for i in [2..Length(G_track[2])] do\n if G_track[2][i] <= cur_nucl_length then\n Add(cur_nucl_tmp, cur_nucl[G_track[2][i]]);\n else\n Add(cur_nucl_tmp, cur_nucl[G_track[2][i]-cur_nucl_length]^-1);\n fi;\n od;\n cur_nucl := StructuralCopy(cur_nucl_tmp);\n fi;\n j := j+1;\n od;\n i := i+1;\n od;\n if res = true then\n found := true;\n fi;\n od;\n\n if not found then return fail; fi;\n Nucl := [];\n# first add elements of cycles\n for i in [1..Length(G)] do\n tmp := [];\n if not (i in Nucl) then IsElemInNucleus(i); fi;\n od;\n\n# now add sections of elements\n for g in Nucl do\n for i in [1..d] do\n if not (G[g][i] in Nucl) then\n Add(Nucl, G[g][i]);\n fi;\n od;\n od;\n# Print(\"Nucleus:\", Nucl, \"\\n\");\n\n nucl_final := [];\n for i in Nucl do Add(nucl_final, cur_nucl[i]); od;\n\n SetIsContracting(H, true);\n SetGroupNucleus(H, nucl_final);\n SetGeneratingSetWithNucleus(H, cur_nucl);\n SetAG_GeneratingSetWithNucleusAutom(H, G);\n SetGeneratingSetWithNucleusAutom(H, MealyAutomaton(G));\n SetContractingLevel(H, maxlev);\n UseContraction(H);\n\n return [nucl_final, cur_nucl, GeneratingSetWithNucleusAutom(H)];\nend);\n\n\nInstallMethod(FindNucleus, \"for [IsAutomatonGroup, IsBool]\", true,\n [IsAutomatonGroup, IsBool],\nfunction(H, print_info)\n return FindNucleus(H, infinity, print_info);\nend);\n\nInstallMethod(FindNucleus, \"for [IsAutomatonGroup, IsCyclotomic]\", true,\n [IsAutomatonGroup, IsCyclotomic],\nfunction(H, max_nucl)\n return FindNucleus(H, max_nucl, true);\nend);\n\nInstallMethod(FindNucleus, \"for [IsAutomatonGroup]\", true,\n [IsAutomatonGroup],\nfunction(H)\n return FindNucleus(H, infinity, true);\nend);\n\n\n\n\n\nInstallMethod(IsContracting, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n local res;\n if IsSelfSimilar(G) = false then\n Info(InfoAutomGrp, 3, \"The group is not self-similar, so it is not contracting\");\n return false;\n elif not IsAutomatonGroup(G) then\n Print(\"Represent as a group generated by finite automaton\\n\");\n return fail;\n fi;\n if FindNucleus(G, 50, false) <> fail then return true; fi;\n if IsNoncontracting(G, 10, 10) = true then return false; fi;\n Info(InfoAutomGrp, 3, \"You can try FindNucleus( , ) or\");\n Info(InfoAutomGrp, 3, \" IsNoncontracting( , , ) with bigger bounds\");\n TryNextMethod();\nend);\n\n\nInstallMethod(GroupNucleus, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n FindNucleus(G, false);\n return GroupNucleus(G);\nend);\n\n\nInstallMethod(GeneratingSetWithNucleus, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n FindNucleus(G, false);\n return GeneratingSetWithNucleus(G);\nend);\n\n\nInstallMethod(GeneratingSetWithNucleusAutom, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n FindNucleus(G, false);\n return GeneratingSetWithNucleusAutom(G);\nend);\n\n\n\nInstallMethod(AG_GeneratingSetWithNucleusAutom, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n FindNucleus(G, false);\n return AG_GeneratingSetWithNucleusAutom(G);\nend);\n\n\n\nInstallGlobalFunction(InversePerm, function(G)\n local i, j, viewed, inv, found;\n viewed := []; inv := ();\n for i in [1..Length(G)] do\n if not (i in viewed) then\n j := 1; found := false;\n while j <= Length(G) and not found do\n #Print(\"[\", i, \", \", j, \"]\\n\");\n if AG_IsOneList([i, j], G) then\n found := true;\n if i <> j then\n inv := inv*(i, j);\n Append(viewed, [i, j]);\n else\n Add(viewed, i);\n fi;\n fi;\n j := j+1;\n od;\n fi;\n od;\n return inv;\nend);\n\n\n\nInstallGlobalFunction(AG_AutomPortraitMain, function(w)\n local PortraitIter, bndry, inv, d, Perm_List, max_lev, G, w_list, w_list_orig, Gi, track_l, nucl;\n\n PortraitIter := function(v, lev, plist)\n local i, j, tmpv, sigma;\n for i in [1..Length(G)] do\n tmpv := StructuralCopy(v);\n Add(tmpv, i);\n if AG_IsOneList(tmpv, G) then\n Add(bndry, [lev, nucl[i^inv]]);\n Add(plist, nucl[i^inv]);\n return;\n fi;\n od;\n\n for i in [1..d] do\n tmpv := []; sigma := ();\n for j in v do\n Add(tmpv, G[j][i^sigma]);\n sigma := sigma*G[j][d+1];\n od;\n if i = 1 then Add(plist, sigma);fi;\n Add(plist, []);\n PortraitIter(tmpv, lev+1, plist[i+1]);\n od;\n end;\n\n d := w!.deg;\n G := AG_GeneratingSetWithNucleusAutom(GroupOfAutomFamily(FamilyObj(w)));\n nucl := GeneratingSetWithNucleus(GroupOfAutomFamily(FamilyObj(w)));\n\n Gi := AG_MinimizedAutomatonList(GroupOfAutomFamily(FamilyObj(w)));\n track_l := Gi[3];\n w_list_orig := CONVERT_ASSOCW_TO_LIST(w);\n w_list := List(w_list_orig, i -> track_l[i]);\n\n\n bndry := [];\n Perm_List := [];\n inv := InversePerm(G);\n max_lev := 0;\n PortraitIter(w_list, 0, Perm_List);\n return [d, bndry, Perm_List];\nend);\n\nInstallGlobalFunction(AutomPortrait, function(w)\n return AG_AutomPortraitMain(w)[3];\nend);\n\nInstallGlobalFunction(AutomPortraitBoundary, function(w)\n return AG_AutomPortraitMain(w)[2];\nend);\n\nInstallGlobalFunction(AutomPortraitDepth, function(w)\n local bndry;\n return Maximum(List(AG_AutomPortraitMain(w)[2], x -> x[1]));\nend);\n\n\n\n################################################################################\n##\n#F WritePortraitToFile. . . . . . . . . . .Writes portrait in a file in the form\n## understandable by Maple\n\n# InstallGlobalFunction(WritePortraitToFile, function(p, file, add)\n# local WritePerm, l;\n#\n# WritePerm := function(perm)\n# local j;\n# AppendTo(file, \"[ \");\n# if Length(perm) > 0 then\n# AppendTo(file, \"`\", perm[1], \"`\");\n# for j in [2..Length(perm)] do\n# AppendTo(file, \", \");\n# WritePerm(perm[j]);\n# od;\n# fi;\n# AppendTo(file, \" ]\");\n# end;\n#\n#\n# l := [p[1], List(p[2], x -> [x[1], x[2]!.word])];\n# if add then AppendTo(file, \"[ \", l[1], \", \");\n# else PrintTo(file, \"[ \", l[2], \", \");\n# fi;\n# WritePerm(p[3]);\n# AppendTo(file, \" ]\");\n# end);\n\n\n################################################################################\n##\n#F WritePortraitsToFile. . . . . . . . . . . . .Writes portraitso of elements of\n## a list in a file in the form understandable by Maple\n\n# InstallGlobalFunction(WritePortraitsToFile, function(lst, G, file, add)\n# local WritePerm, i, p;\n#\n# if add then AppendTo(file, \"[ \");\n# else PrintTo(file, \"[ \");\n# fi;\n#\n# for i in [1..Length(lst)] do\n# if i = 1 then\n# AppendTo(file, \"[ \", lst[i], \", \");\n# else\n# AppendTo(file, \", [ \", lst[i], \", \");\n# fi;\n# p := AutomPortrait(lst[i], G);\n# WritePortraitToFile(p, file, true);\n# AppendTo(file, \"]\");\n#\n# od;\n# end);\n\n\nInstallMethod(Growth, \"for [IsAutomGroup, IsCyclotomic]\", true,\n [IsGroup, IsCyclotomic],\nfunction(G, max_len)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, viewed, oldgr, New, k, cur_els;\n\n# produce a symmetric generating set\n orig_gens := ShallowCopy(GeneratorsOfGroup(G));\n Append(orig_gens, List(orig_gens, x -> x^-1));\n\n gens := [];\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do if orig_gens[i] = orig_gens[j] then new_gen := false; fi; od;\n if new_gen then Add(gens, orig_gens[i]); fi;\n fi;\n od;\n\n ElList := [One(G)]; Append(ElList, ShallowCopy(gens));\n GrList := [1, Length(gens)+1];\n len := 1;\n\n while len < max_len and GrList[len] <> GrList[len+1] do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for gen in gens do\n g := ElList[i]*gen;\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n if g = ElList[k] then New := false; fi;\n k := k+1;\n od;\n if New then Add(ElList, g); fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Print(\"There are \", Length(ElList), \" elements of length up to \", len+1, \"\\n\");\n len := len+1;\n od;\n if GrList[len] = GrList[len+1] then\n SetSize(G, GrList[len]);\n fi;\n return GrList;\nend);\n\n\nInstallMethod(Growth, \"for [IsTreeHomomorphismSemigroup, IsCyclotomic]\", true,\n [IsTreeHomomorphismSemigroup, IsCyclotomic],\nfunction(G, max_len)\n local iter, g, i;\n iter := Iterator(G, max_len);\n for g in iter do od;\n return List(iter!.levels, x -> x[Length(x)]);\nend);\n\n\nInstallMethod(ListOfElements, \"for [IsTreeHomomorphismSemigroup, IsCyclotomic]\", true,\n [IsGroup, IsCyclotomic],\nfunction(G, max_len)\n return FindElements(G, ReturnTrue, true, max_len);\nend);\n\n\nInstallMethod(AG_FiniteGroupId, \"for [IsAutomatonGroup, IsPosInt]\", true,\n [IsAutomatonGroup, IsCyclotomic],\nfunction(H, size)\n local gr, len, ElList, GrList, inv, i, j, k, oldgr, v, tmpv, New, IsNewRel, inverse, G, FinG, tmpl, push, ProductEls, act, rels, LongCycle;\n\n inverse := function(w)\n local i, iw;\n iw := [];\n for i in [1..Length(w)] do\n iw[i] := w[Length(w)-i+1]^inv;\n od;\n return iw;\n end;\n\n ProductEls := function(i, j)\n local t, v, tmpv;\n v := StructuralCopy(ElList[i]);\n Append(v, ElList[j]);\n for t in [1..Length(ElList)] do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverse(ElList[t]));\n if AG_IsOneList(tmpv, G) then return t; fi;\n od;\n end;\n\n LongCycle := function(n)\n local l, i;\n l := [];\n for i in [2..n] do Add(l, i); od;\n Add(l, 1);\n return PermList(l);\n end;\n\n IsNewRel := function(v)\n local tmp, i, j, cyc, cycr, v_cyc, r_cyc, r, r_cyc_inv;\n cyc := LongCycle(Length(v));\n for i in [0..Length(v)-1] do\n v_cyc := Permuted(v, cyc^i);\n if v_cyc[1] = v_cyc[Length(v)]^inv then return false; fi;\n for r in rels do\n cycr := LongCycle(Length(r));\n for j in [0..Length(r)-1] do\n r_cyc := Permuted(r, cycr^j);\n r_cyc_inv := inverse(Permuted(r, cycr^j));\n if PositionSublist(v_cyc, r_cyc) <> fail or PositionSublist(v_cyc, r_cyc_inv) <> fail then\n return false;\n fi;\n od;\n od;\n od;\n return true;\n end;\n \n\n\n####################### _FiniteGroupId itself #########################################\n gr := 1; len := 1;\n\n G := AG_ChooseAutomatonList(H);\n\n inv := InversePerm(G);\n if not HasIsFinite(H) then\n Info(InfoAutomGrp, 2, \"warning, if < H > is infinite the algorithm will never stop\");\n fi;\n GrList := [1, Length(G)];\n ElList := []; rels := [];\n for i in [1..Length(G)] do\n Add(ElList, [i]);\n od;\n while GrList[len+1] > GrList[len] and GrList[len+1] < size do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for j in [2..Length(G)] do\n v := StructuralCopy(ElList[i]);\n if j <> v[Length(v)]^inv then\n Add(v, j);\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]+1; fi;\n while New and k <= oldgr do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverse(ElList[k]));\n if AG_IsOneList(tmpv, G) then\n New := false;\n## show relations\n if IsNewRel(tmpv) then\n Add(rels, tmpv);\n# Info(InfoAutomGrp, 3, v, \"*\", ElList[k], \"^(-1) = 1\");\n# Print(tmpv, \"\\n\");\n fi;\n fi;\n k := k+1;\n od;\n if New then Add(ElList, v); fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n\n if GrList[len+1] > GrList[len] then return fail; fi;\n\n SetSize(H, GrList[len]);\n\n# in case of finite group construct Cayley table\n\n\n FinG := [];\n for i in [2..UnderlyingAutomFamily(H)!.numstates+1] do\n act := ();\n tmpl := [];\n while Length(tmpl) < Length(ElList) do\n j := 1;\n while j in tmpl do j := j+1; od;\n Add(tmpl, j);\n push := ProductEls(j, i);\n while push <> j do\n Add(tmpl, push);\n act := act*(j, push);\n push := ProductEls(push, i);\n od;\n od;\n Add(FinG, act);\n od;\n\n return GroupWithGenerators(FinG);\nend);\n\n\nInstallMethod(AG_FiniteGroupId, \"for [IsAutomGroup]\",\n [IsAutomGroup],\nfunction(G)\n return AG_FiniteGroupId(G, infinity);\nend);\n\n\nInstallMethod(AG_FiniteGroupId, \"for [IsAutomGroup, IsCyclotomic]\",\n [IsAutomGroup, IsCyclotomic],\nfunction(G, n)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, viewed, oldgr, New, k, ProductEls, FinG, tmpl, push, act, track_l,\n num_diff_gens, num_orig_gens, old_gens;\n\n ProductEls := function(i, j)\n local t;\n for t in [1..Length(ElList)] do\n if IsOne(ElList[i]*ElList[j]*ElList[t]^-1) then return t; fi;\n od;\n return fail;\n end;\n\n orig_gens := ShallowCopy(GeneratorsOfGroup(G));\n num_orig_gens := Length(orig_gens);\n Append(orig_gens, List(orig_gens, x -> x^-1));\n\n gens := [];\n\n# select pairwise different generators and track the original ones.\n# examlpe: assume b^2 = 1\n# orig_gens = [a, e, a, b, b, c, a^-1, e^-1, a^-1, b^-1, b^-1, c^-1]\n# track_l = [1, 0, 1, 2, 2, 3, 4, 0, 4, 2, 2, 5 ]\n# gens = [a, b, c, a^-1, c^-1]\n# num_orig_gens = 6\n# num_diff_gens = 3\n track_l := [];\n for i in [1..Length(orig_gens)] do\n if IsOne(orig_gens[i]) then\n track_l[i] := 0;\n else\n new_gen := true;\n j := 1;\n while j < i and new_gen do\n if orig_gens[i] = orig_gens[j] then\n new_gen := false;\n track_l[i] := track_l[j];\n fi;\n j := j+1;\n od;\n if new_gen then\n Add(gens, orig_gens[i]);\n track_l[i] := Length(gens);\n fi;\n if i = num_orig_gens then num_diff_gens := Length(gens); fi;\n fi;\n od;\n\n ElList := [One(G)]; Append(ElList, ShallowCopy(gens));\n GrList := [1, Length(gens)+1];\n len := 1;\n\n while len < n and GrList[len] <> GrList[len+1] do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for gen in gens do\n g := ElList[i]*gen;\n# Print(\"g = \", g, \"\\n\\n\");\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n# Print(g*ElList[k]^-1, \"\\n\");\n if IsOne(g*ElList[k]^-1) then New := false; fi;\n k := k+1;\n od;\n if New then Add(ElList, g); fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n\n if GrList[len] <> GrList[len+1] then return fail; fi;\n\n SetSize(G, GrList[len]);\n\n# in case of finite group construct Cayley table\n FinG := [];\n for i in [2..num_diff_gens+1] do\n act := ();\n tmpl := [];\n while Length(tmpl) < Length(ElList) do\n j := 1;\n while j in tmpl do j := j+1; od;\n Add(tmpl, j);\n push := ProductEls(j, i);\n while push <> j do\n Add(tmpl, push);\n act := act*(j, push);\n push := ProductEls(push, i);\n od;\n od;\n Add(FinG, act);\n od;\n\n# switch to the original generating set\n old_gens := [];\n for i in [1..num_orig_gens] do\n if track_l[i] = 0 then\n old_gens[i] := ();\n else\n old_gens[i] := FinG[track_l[i]];\n fi;\n od;\n\n return GroupWithGenerators(old_gens);\nend);\n\n\nInstallGlobalFunction(AG_IsOneWordSubs, function(w, subs, G)\n local i, v;\n v := [];\n for i in w do Append(v, subs[i]); od;\n return AG_IsOneList(v, G);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection, IsList, IsCyclotomic, IsCyclotomic]\", true,\n [IsList and IsAutomCollection, IsList, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, names, max_len, num_of_rels)\n local G, gens, Gi, H, rel, rels, rels0, k, track_s, track_l, AssocW, FindGroupRelationsLocal, gens_autom, i, j, subs, subs1, w_list, FindGroupRelationsSubsLocal, w_ext, w, automgens, numstates, F, cur_gen;\n\n AssocW := function(w)\n return Product(List(w, i -> gens[i]));\n end;\n\n FindGroupRelationsSubsLocal := function(subs, G)\n local gr, len, ElList, GrList, inv, i, j, k, oldgr, v, tmpv, New, IsNewRelS, inverse, inverseS, H, FinG, tmpl, push, ProductEls, act, rels, LongCycle, invslist, invs, origlength, w, invadded, AssocWrels;\n\n inverse := function(w)\n local i, iw;\n iw := [];\n for i in [1..Length(w)] do\n iw[i] := w[Length(w)-i+1]^inv;\n od;\n return iw;\n end;\n\n inverseS := function(w)\n local i, iw;\n iw := [];\n for i in [1..Length(w)] do\n iw[i] := w[Length(w)-i+1]^invs;\n od;\n return iw;\n end;\n\n ProductEls := function(i, j)\n local t, v, tmpv;\n v := StructuralCopy(ElList[i]);\n Append(v, ElList[j]);\n for t in [1..Length(ElList)] do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverse(ElList[t]));\n if AG_IsOneList(tmpv, G) then return t; fi;\n od;\n end;\n\n LongCycle := function(n)\n local l, i;\n l := [];\n for i in [2..n] do Add(l, i); od;\n Add(l, 1);\n return PermList(l);\n end;\n\n IsNewRelS := function(v)\n local tmp, i, j, cyc, cycr, v_cyc, r_cyc, r, r_cyc_inv;\n cyc := LongCycle(Length(v));\n for i in [0..Length(v)-1] do\n v_cyc := Permuted(v, cyc^i);\n if v_cyc[1] = v_cyc[Length(v)]^invs then return false; fi;\n for r in rels do\n cycr := LongCycle(Length(r));\n for j in [0..Length(r)-1] do\n r_cyc := Permuted(r, cycr^j){[1..Int(Length(r)/2)+1]};\n r_cyc_inv := inverseS(Permuted(r, cycr^j)){[1..Int(Length(r)/2)+1]};\n if PositionSublist(v_cyc, r_cyc) <> fail or PositionSublist(v_cyc, r_cyc_inv) <> fail then\n return false;\n fi;\n od;\n od;\n od;\n return true;\n end;\n#************************ FindGroupRelationsSubsLocal itself ****************************************************\n\n rels := [];\n# G := GroupOfAutomFamily(FamilyObj(subs_words[1]));\n inv := InversePerm(G);\n #check if there are any identity elements in subs list\n for i in [1..Length(subs)] do\n if AG_IsOneList(subs[i], G) then\n Error(AssocW([i]), \" = id, remove this element from a list and try again\");\n fi;\n od;\n\n AssocWrels := [];\n\n #check if there are any equal elements in subs list\n invslist := [];\n for i in [1..Length(subs)] do\n for j in [i..Length(subs)] do\n if i <> j and AG_IsOneList(Concatenation(subs[i], inverse(subs[j])), G) then\n Error(AssocW([i]), \" = \", AssocW([j]), \", remove one of these elements from a list and try again\");\n fi;\n\n # Print(AG_IsOneList(Append(StructuralCopy(subs[i]), subs[j]), G), \"\\n\");\n # Print(Concatenation(subs[i], subs[j]), \"\\n\");\n\n if AG_IsOneList(Concatenation(subs[i], subs[j]), G) then\n invslist[i] := j; invslist[j] := i;\n Add(rels, [i, j]);\n Add(AssocWrels, AssocW([i, j]));\n Print(AssocW([i, j]), \"\\n\");\n fi;\n od;\n od;\n\n # add inverses to subs list\n origlength := Length(subs);\n invadded := false;\n for i in [1..origlength] do\n if not IsBound(invslist[i]) then\n invadded := true;\n Add(subs, inverse(subs[i]));\n Add(gens, gens[i]^-1);\n invslist[i] := Length(subs);\n invslist[Length(subs)] := i;\n fi;\n od;\n\n invs := PermList(invslist);\n\n GrList := [1, Length(subs)+1];\n ElList := [];\n\n gr := 1; len := 1;\n\n for i in [1..Length(subs)] do\n Add(ElList, [i]);\n od;\n while GrList[len+1] > GrList[len] and len < max_len and Length(rels) < num_of_rels do\n for i in [GrList[len]..GrList[len+1]-1] do\n oldgr := Length(ElList);\n for j in [1..Length(subs)] do\n v := StructuralCopy(ElList[i]);\n if j <> v[Length(v)]^invs then\n Add(v, j);\n New := true;\n # k := 1;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverseS(ElList[k]));\n if AG_IsOneWordSubs(tmpv, subs, G) then\n New := false;\n ## show relations\n if IsNewRelS(tmpv) then\n Add(rels, tmpv);\n if Length(AssocW(tmpv)) > 0 then\n Add(AssocWrels, AssocW(tmpv));\n Print(AssocW(tmpv), \"\\n\");\n fi;\n fi;\n fi;\n k := k+1;\n od;\n if New then Add(ElList, v); fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList)+1);\n # Print(\"ElList[\", len, \"] = \", ElList, \"\\n\");\n Info(InfoAutomGrp,3,\"There are \", Length(ElList) + 1, \" elements of length up to \", len+1);\n len := len+1;\n od;\n return AssocWrels;\n end;\n\n\n#************************ FindGroupRelationsSubs itself ****************************************************\n\n if Length(subs_words) <> Length(names) then\n Error(\"The number of names must coincide with the number of generators\");\n fi;\n F := FreeGroup(names);\n G := GroupOfAutomFamily(FamilyObj(subs_words[1]));\n\n# gens is a mutable list of generators\n gens := ShallowCopy(GeneratorsOfGroup(F));\n\n automgens := UnderlyingAutomFamily(G)!.automgens;\n numstates := UnderlyingAutomFamily(G)!.numstates;\n\n#convert associative words into lists\n subs1 := List(subs_words, CONVERT_ASSOCW_TO_LIST);\n\n Gi := StructuralCopy(AG_MinimizedAutomatonList(G));\n# Print(\"Gi = \", Gi, \"\\n\");\n H := Gi[1];\n\n track_s := Gi[2];\n track_l := Gi[3];\n\n subs := [];\n\n for w in subs1 do\n w_list := [];\n for i in [1..Length(w)] do Add(w_list, track_l[w[i]]); od;\n Add(subs, ShallowCopy(w_list));\n od;\n rels0 := [];\n\n# for k in [1..Length(AutomatonList(G))] do\n# Print(\"Beam\\n\");\n# if track_l[k] = 1 then Add(rels0, AssocW([k]));\n# elif track_s[track_l[k]] <> k then Add(rels0, AssocW([k, track_s[track_l[k]]+Length(AutomatonList(G))]));\n# fi;\n# od;\n\n\n rels := FindGroupRelationsSubsLocal(subs, AG_ChooseAutomatonList(G));\n if rels = fail then return fail; fi;\n Append(rels0, rels);\n# Print(rels0);\n return rels0;\nend);\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection, IsList, IsCyclotomic]\", true,\n [IsList and IsAutomCollection, IsList, IsCyclotomic],\nfunction(subs_words, names, max_len)\n return FindGroupRelations(subs_words, names, max_len, infinity);\nend);\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection, IsList]\",\n [IsList and IsAutomCollection, IsList],\nfunction(subs_words, names)\n return FindGroupRelations(subs_words, names, infinity, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsAutomGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsAutomatonGroup, IsCyclotomic, IsCyclotomic],\nfunction(G, max_len, num_of_rels)\n local gens, Gi, H, rel, rels, rels0, k, track_s, track_l, AssocW, FindGroupRelationsLocal;\n\n AssocW := function(w)\n #Print(w);\n return Product(List(w, i -> gens[i]));\n end;\n\n\n FindGroupRelationsLocal := function(subs, G)\n local gr, len, ElList, GrList, inv, i, j, k, oldgr, v, tmpv, New, IsNewRelS, inverse, inverseS, H, FinG, tmpl, push, ProductEls, act, rels, LongCycle, invslist, invs, origlength, w, invadded, tmpv_orig, AssocWrels;\n\n inverse := function(w)\n local i, iw;\n iw := [];\n for i in [1..Length(w)] do\n iw[i] := w[Length(w)-i+1]^inv;\n od;\n return iw;\n end;\n\n inverseS := function(w)\n local i, iw;\n iw := [];\n for i in [1..Length(w)] do\n iw[i] := w[Length(w)-i+1]^invs;\n od;\n return iw;\n end;\n\n ProductEls := function(i, j)\n local t, v, tmpv;\n v := StructuralCopy(ElList[i]);\n Append(v, ElList[j]);\n for t in [1..Length(ElList)] do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverse(ElList[t]));\n if AG_IsOneList(tmpv, G) then return t; fi;\n od;\n end;\n\n LongCycle := function(n)\n local l, i;\n l := [2..n];\n Add(l, 1);\n return PermList(l);\n end;\n\n IsNewRelS := function(v)\n local tmp, i, j, cyc, cycr, v_cyc, r_cyc, r, r_cyc_inv;\n cyc := LongCycle(Length(v));\n for i in [0..Length(v)-1] do\n v_cyc := Permuted(v, cyc^i);\n if v_cyc[1] = v_cyc[Length(v)]^invs then return false; fi;\n for r in rels do\n cycr := LongCycle(Length(r));\n for j in [0..Length(r)-1] do\n r_cyc := Permuted(r, cycr^j){[1..Int(Length(r)/2)+1]};;\n r_cyc_inv := inverseS(Permuted(r, cycr^j)){[1..Int(Length(r)/2)+1]};;\n if PositionSublist(v_cyc, r_cyc) <> fail or PositionSublist(v_cyc, r_cyc_inv) <> fail then\n return false;\n fi;\n od;\n od;\n od;\n return true;\n end;\n#************************ FindGroupRelationsLocal itself ****************************************************\n\n rels := [];\n AssocWrels := [];\n inv := InversePerm(G);\n\n\n invslist := [];\n for i in [1..Length(subs)] do\n for j in [i..Length(subs)] do\n# Print(AssocW([Gi[2][i+1], Gi[2][j+1]])!.word, \"\\n\");\n if AG_IsOneList(Concatenation(subs[i], subs[j]), G) then\n invslist[i] := j; invslist[j] := i;\n if Length(AssocW([Gi[2][i+1], Gi[2][j+1]])!.word) > 0 then\n Add(rels, [i, j]);\n Add(AssocWrels, AssocW([Gi[2][i+1], Gi[2][j+1]]));\n Print( AssocW([Gi[2][i+1], Gi[2][j+1]])!.word, \"\\n\");\n fi;\n fi;\n od;\n od;\n\n invs := PermList(invslist);\n\n GrList := [1, Length(subs)+1];\n ElList := [];\n\n gr := 1; len := 1;\n\n for i in [1..Length(subs)] do\n Add(ElList, [i]);\n od;\n while GrList[len+1] > GrList[len] and len < max_len and Length(rels) < num_of_rels do\n for i in [GrList[len]..GrList[len+1]-1] do\n oldgr := Length(ElList);\n for j in [1..Length(subs)] do\n v := StructuralCopy(ElList[i]);\n if j <> v[Length(v)]^invs then\n Add(v, j);\n New := true;\n # k := 1;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n tmpv := StructuralCopy(v);\n Append(tmpv, inverseS(ElList[k]));\n if AG_IsOneWordSubs(tmpv, subs, G) then\n New := false;\n## show relations\n if IsNewRelS(tmpv) then\n# tmpv in the original generators\n tmpv_orig := [];\n for k in [1..Length(tmpv)] do\n tmpv_orig[k] := Gi[2][tmpv[k]+1];\n od;\n Add(rels, tmpv);\n if Length(AssocW(tmpv_orig)!.word) > 0 then\n Add(AssocWrels, AssocW(tmpv_orig));\n Print( AssocW(tmpv_orig)!.word, \"\\n\");\n fi;\n# Print(tmpv, \"\\n\");\n fi;\n fi;\n k := k+1;\n od;\n if New then Add(ElList, v); fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList)+1);\n # Print(\"ElList[\", len, \"] = \", ElList, \"\\n\");\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList) + 1, \" elements of length up to \", len + 1);\n len := len+1;\n od;\n return AssocWrels;\n end;\n\n#************************ FindGroupRelations itself ****************************************************\n\n gens := ShallowCopy(UnderlyingAutomFamily(G)!.automgens);\n\n Gi := StructuralCopy(AG_MinimizedAutomatonList(G));\n# Print(\"Gi = \", Gi, \"\\n\");\n H := Gi[1];\n\n track_s := Gi[2];\n track_l := Gi[3];\n rels0 := [];\n\n# for k in [1..Length(AutomatonList(G))] do\n# Print(\"Beam\\n\");\n# if track_l[k] = 1 then Add(rels0, AssocW([k]));\n# elif track_s[track_l[k]] <> k then Add(rels0, AssocW([k, track_s[track_l[k]]+Length(AutomatonList(G))]));\n# fi;\n# od;\n\n\n rels := FindGroupRelationsLocal(List([2..Length(H)], i -> [i]), AG_ChooseAutomatonList(G));\n Append(rels0, rels);\n# Print(rels0);\n return rels0;\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsAutomGroup, IsCyclotomic]\", true,\n [IsAutomatonGroup, IsCyclotomic],\nfunction(G, max_len)\n return FindGroupRelations(G, max_len, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsAutomGroup]\",\n [IsAutomatonGroup],\nfunction(G)\n return FindGroupRelations(G, infinity, infinity);\nend);\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection, IsCyclotomic, IsCyclotomic]\", true,\n [IsList and IsAutomCollection, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, max_len, num_of_rels)\n return FindGroupRelations(GroupWithGenerators(subs_words), max_len, infinity);\nend);\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection, IsCyclotomic]\", true,\n [IsList and IsAutomCollection, IsCyclotomic],\nfunction(subs_words, max_len)\n return FindGroupRelations(subs_words, max_len, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsList and IsAutomCollection]\",\n [IsList and IsAutomCollection],\nfunction(subs_words)\n return FindGroupRelations(subs_words, infinity, infinity);\nend);\n\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsGroup, IsCyclotomic, IsCyclotomic],\nfunction(G, max_len, num_of_rels)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, oldgr, New, k, rels, rel, F, relsF, ElListF, genf, f, fgens, all_relsF, rel1, new_rel, r, orig_fgens, \\\n IsNewRel, CyclicConjugates, ngens, FFhom_images, FFhom, FGhom_images, FGhom, ElList_inv, inv_gens, cur_rel;\n\n IsNewRel := function(rel)\n local rel1, r;\n rel1 := rel;\n repeat\n for r in all_relsF do\n if PositionWord(rel1, Subword(r,1,Int(Length(r)/2)+1), 1) <> fail then return false; fi;\n od;\n rel1 := rel1^Subword(rel1, 1, 1);\n until rel1 = rel;\n return true;\n end;\n\n\n CyclicConjugates := function(rel)\n local rel1, conjs;\n rel1 := rel; conjs := [];\n repeat\n rel1 := rel1^Subword(rel1, 1, 1);\n Add(conjs, rel1);\n until rel1 = rel;\n return conjs;\n end;\n\n\n\n orig_gens := ShallowCopy(GeneratorsOfGroup(G));\n ngens := Length(orig_gens);\n\n F := FreeGroup(ngens);\n orig_fgens := ShallowCopy(GeneratorsOfGroup(F));\n FFhom_images := ShallowCopy(GeneratorsOfGroup(F));\n FGhom_images := ShallowCopy(GeneratorsOfGroup(G));\n\n Append(orig_gens, List(orig_gens, x -> x^-1));\n Append(orig_fgens, List(orig_fgens, x -> x^-1));\n\n gens := [];\n fgens := [];\n rels := [];\n relsF := [];\n all_relsF := [];\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do\n if orig_gens[i] = orig_gens[j] then\n new_gen := false;\n if IsNewRel(orig_fgens[i]^-1*orig_fgens[j]) then\n if not IsIdenticalObj(orig_gens[i], orig_gens[j]) then\n Add(rels, orig_gens[i]^-1*orig_gens[j]);\n Print( orig_gens[i]^-1*orig_gens[j], \"\\n\");\n fi;\n Add(relsF, orig_fgens[i]^-1*orig_fgens[j]);\n Append(all_relsF, CyclicConjugates(orig_fgens[i]^-1*orig_fgens[j]));\n if i > ngens and j <= ngens then\n# hom_images[i-ngens] := orig_gens[j+ngens];\n# hom_images[j] := orig_gens[i];\n FFhom_images[i-ngens] := orig_fgens[j+ngens];\n FFhom_images[j] := orig_fgens[i];\n fi;\n fi;\n break;\n fi;\n od;\n if new_gen then\n Add(gens, orig_gens[i]);\n Add(fgens, orig_fgens[i]);\n if i <= ngens then\n FGhom_images[i] := orig_gens[i];\n fi;\n fi;\n else\n if not IsIdenticalObj(orig_gens[i], One(orig_gens[i])) then\n Add(rels, orig_gens[i]);\n Print( orig_gens[i], \"\\n\");\n fi;\n#\n# Add(relsF, orig_fgens[i]);\n fi;\n od;\n\n\n# inv_gens := [];\n# for i in [1..Length(gens)] do\n# for j in [1..i] do\n# if IsOne(gens[i]*gens[j]) then\n# inv_gens[i] := gens[j]; inv_gens[j] := gens[i];\n# fi;\n# od;\n# od;\n\n\n# Print(\"gens = \", gens, \"\\n\");\n# Print(\"inv_gens = \", inv_gens, \"\\n\");\n\n FFhom := GroupHomomorphismByImagesNC(F, F, GeneratorsOfGroup(F), FFhom_images);\n FGhom := GroupHomomorphismByImagesNC(F, G, GeneratorsOfGroup(F), FGhom_images);\n# Print(\"hom = \", hom, \"\\n\");\n\n ElList := [One(G)];\n# ElList_inv := [One(G)];\n ElListF := [One(F)];\n\n Append(ElList, ShallowCopy(gens));\n# Append(ElList_inv, ShallowCopy(inv_gens));\n Append(ElListF, ShallowCopy(fgens));\n\n GrList := [1, Length(gens)+1];\n\n len := 1;\n\n while GrList[len] <> GrList[len+1] and len < max_len and Length(rels) < num_of_rels do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for j in [1..Length(gens)] do\n f := ElListF[i]*fgens[j];\n if Length(f) > Length(ElListF[i]) then\n g := ElList[i]*gens[j];\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n if g = ElList[k] then\n New := false;\n fi;\n k := k+1;\n od;\n if New then\n Add(ElList, g);\n# Add(ElList_inv, inv_gens[j]*ElList_inv[i]);\n Add(ElListF, f);\n else\n new_rel := true;\n rel := CyclicallyReducedWord(Image(FFhom, f^-1)*ElListF[k-1]);\n if Length(rel) < Length(f)+Length(ElListF[k-1]) then new_rel := false; fi;\n\n\n if new_rel and IsNewRel(rel) and IsNewRel(Image(FFhom, rel^-1)) then\n# Add(rels, inv_gens[j]*ElList_inv[i]*ElList[k-1]);\n cur_rel := Image(FGhom, rel);\n Add(rels, cur_rel);\n Add(relsF, rel);\n Print( cur_rel, \"\\n\");\n Append(all_relsF, CyclicConjugates(rel));\n fi;\n\n fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n if GrList[len] = GrList[len+1] then\n SetSize(G, GrList[len]);\n fi;\n return rels;\nend);\n\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsGroup, IsCyclotomic]\", true,\n [IsGroup, IsCyclotomic],\nfunction(G, max_len)\n return FindGroupRelations(G, max_len, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsGroup]\",\n [IsGroup],\nfunction(G)\n return FindGroupRelations(G, infinity, infinity);\nend);\n\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList, IsCyclotomic, IsCyclotomic]\", true,\n [IsList, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, max_len, num_of_rels)\n return FindGroupRelations(GroupWithGenerators(subs_words), max_len, infinity);\nend);\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList, IsCyclotomic]\", true,\n [IsList, IsCyclotomic],\nfunction(subs_words, max_len)\n return FindGroupRelations(subs_words, max_len, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsList]\",\n [IsList],\nfunction(subs_words)\n return FindGroupRelations(subs_words, infinity, infinity);\nend);\n\n\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList, IsList, IsCyclotomic, IsCyclotomic]\", true,\n [IsList, IsList, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, names, max_len, num_of_rels)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, oldgr, New, k, rel, F, relsF, ElListF, genf, f, fgens, all_relsF, rel1, new_rel, r, orig_fgens, \\\n IsNewRel, CyclicConjugates, ngens, FFhom_images, FFhom;\n\n IsNewRel := function(rel)\n local rel1, r;\n rel1 := rel;\n repeat\n for r in all_relsF do\n if PositionWord(rel1, Subword(r,1,Int(Length(r)/2)+1), 1) <> fail then return false; fi;\n od;\n rel1 := rel1^Subword(rel1, 1, 1);\n until rel1 = rel;\n return true;\n end;\n\n\n CyclicConjugates := function(rel)\n local rel1, conjs;\n rel1 := rel; conjs := [];\n repeat\n rel1 := rel1^Subword(rel1, 1, 1);\n Add(conjs, rel1);\n until rel1 = rel;\n return conjs;\n end;\n\n\n\n if Length(subs_words) <> Length(names) then\n Error(\"The number of names must coincide with the number of generators\");\n fi;\n\n orig_gens := ShallowCopy(subs_words);\n\n F := FreeGroup(names);\n orig_fgens := ShallowCopy(GeneratorsOfGroup(F));\n ngens := Length(orig_gens);\n\n FFhom_images := ShallowCopy(GeneratorsOfGroup(F));\n\n\n Append(orig_gens, List(orig_gens, x -> x^-1));\n Append(orig_fgens, List(orig_fgens, x -> x^-1));\n\n gens := [];\n fgens := [];\n relsF := [];\n all_relsF := [];\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do\n if orig_gens[i] = orig_gens[j] then\n new_gen := false;\n if IsNewRel(orig_fgens[i]^-1*orig_fgens[j]) then\n Add(relsF, orig_fgens[i]^-1*orig_fgens[j]);\n Print(orig_fgens[i]^-1*orig_fgens[j], \"\\n\");\n\n Append(all_relsF, CyclicConjugates(orig_fgens[i]^-1*orig_fgens[j]));\n if i > ngens and j <= ngens then\n FFhom_images[i-ngens] := orig_fgens[j+ngens];\n FFhom_images[j] := orig_fgens[i];\n fi;\n fi;\n break;\n fi;\n od;\n if new_gen then\n Add(gens, orig_gens[i]);\n Add(fgens, orig_fgens[i]);\n fi;\n else\n Add(relsF, orig_fgens[i]);\n Print(orig_fgens[i], \"\\n\");\n fi;\n od;\n\n\n FFhom := GroupHomomorphismByImagesNC(F, F, GeneratorsOfGroup(F), FFhom_images);\n\n ElList := [One(subs_words[1])];\n ElListF := [One(F)];\n\n Append(ElList, ShallowCopy(gens));\n Append(ElListF, ShallowCopy(fgens));\n\n GrList := [1, Length(gens)+1];\n\n len := 1;\n\n while GrList[len] <> GrList[len+1] and len < max_len and Length(relsF) < num_of_rels do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for j in [1..Length(gens)] do\n f := ElListF[i]*fgens[j];\n if Length(f) > Length(ElListF[i]) then\n g := ElList[i]*gens[j];\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n if g = ElList[k] then\n New := false;\n fi;\n k := k+1;\n od;\n if New then\n Add(ElList, g);\n Add(ElListF, f);\n else\n new_rel := true;\n rel := CyclicallyReducedWord(Image(FFhom, f^-1)*ElListF[k-1]);\n if Length(rel) < Length(f)+Length(ElListF[k-1]) then new_rel := false; fi;\n\n\n if new_rel and IsNewRel(rel) and IsNewRel(Image(FFhom, rel^-1)) then\n Add(relsF, rel);\n Print( rel, \"\\n\");\n Append(all_relsF, CyclicConjugates(rel));\n fi;\n\n fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n return relsF;\nend);\n\n\n\nInstallMethod(FindGroupRelations, \"for [IsList, IsList, IsCyclotomic]\", true,\n [IsList, IsList, IsCyclotomic],\nfunction(subs_words, names, max_len)\n return FindGroupRelations(subs_words, names, max_len, infinity);\nend);\n\n\nInstallMethod(FindGroupRelations, \"for [IsList, IsList]\", true,\n [IsList, IsList],\nfunction(subs_words, names)\n return FindGroupRelations(subs_words, names, infinity, infinity);\nend);\n\n\n# InstallMethod(FindSemigroupRelations, \"for [IsAutomSemigroup, IsCyclotomic, IsCyclotomic]\", true,\n# [IsAutomSemigroup, IsCyclotomic, IsCyclotomic],\n# function(G, max_len, num_of_rels)\n# local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, oldgr, New, k, has_one, rels, rel;\n#\n# orig_gens := ShallowCopy(GeneratorsOfSemigroup(G));\n#\n# gens := [];\n# rels := [];\n# has_one := false;\n#\n# # select pairwise different generators\n# for i in [1..Length(orig_gens)] do\n# if not IsOne(orig_gens[i]) then\n# new_gen := true;\n# for j in [1..i-1] do\n# if orig_gens[i] = orig_gens[j] then\n# new_gen := false;\n# if not Word(orig_gens[i]) = Word(orig_gens[j]) then\n# Add(rels, [orig_gens[i], orig_gens[j]]);\n# fi;\n# break;\n# fi;\n# od;\n# if new_gen then Add(gens, orig_gens[i]); fi;\n# else\n# if not Word(orig_gens[i]) = Word(One(orig_gens[i])) then\n# Add(rels, [orig_gens[i], One(orig_gens[i])]);\n# fi;\n# has_one := true;\n# fi;\n# od;\n#\n# if has_one then\n# ElList := [One(G)];\n# GrList := [1];\n# else\n# ElList := [];\n# GrList := [0];\n# fi;\n#\n# Append(ElList, ShallowCopy(gens));\n# Add(GrList, Length(gens)+GrList[1]);\n# len := 1;\n#\n# while GrList[len] <> GrList[len+1] and len < max_len and Length(rels) < num_of_rels do\n# for i in [GrList[len]+1..GrList[len+1]] do\n# oldgr := Length(ElList);\n# for gen in gens do\n# g := ElList[i]*gen;\n# New := true;\n#\n# # Print(\"g = \", g, \"\\n\");\n# # Print(\"rels = \", rels, \"\\n\");\n#\n# # If g includes a longer part of some relation it can not represent\n# # neither a new element, nor be involved in a new relation\n#\n# for rel in rels do\n# if PositionWord(Word(g), Word(rel[1]), 1) <> fail then New := false; fi;\n# od;\n#\n# # Print(\"New el/rel:\", New, \"\\n\");\n# if New then\n#\n# k := 0;\n# while New and k < Length(ElList) do\n# k := k+1;\n# if g = ElList[k] then\n# New := false;\n# fi;\n# od;\n# # Print(\"New el:\", New, \"\\n\");\n# if New then\n# Add(ElList, g);\n# else\n# if not Word(g) = Word(ElList[k]) then\n# Add(rels, [g, ElList[k]]);\n# Print( g, \" = \", ElList[k], \"\\n\");\n# fi;\n# fi;\n# fi;\n# # Print(\"\\n\\n\\n\");\n# od;\n# od;\n# Add(GrList, Length(ElList));\n# Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n# len := len+1;\n# od;\n# if GrList[len] = GrList[len+1] then\n# SetSize(G, GrList[len]);\n# fi;\n# return rels;\n# end);\n#\n#\n#\n# InstallMethod(FindSemigroupRelations, \"for [IsAutomSemigroup, IsCyclotomic]\", true,\n# [IsAutomSemigroup, IsCyclotomic],\n# function(G, max_len)\n# return FindSemigroupRelations(G, max_len, infinity);\n# end);\n#\n#\n# InstallMethod(FindSemigroupRelations, \"for [IsAutomSemigroup]\",\n# [IsAutomSemigroup],\n# function(G)\n# return FindSemigroupRelations(G, infinity, infinity);\n# end);\n\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsSemigroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsSemigroup, IsCyclotomic, IsCyclotomic],\nfunction(G, max_len, num_of_rels)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, oldgr, New, k, has_one, rels, rel, F, relsF, ElListF, genf, f;\n\n orig_gens := ShallowCopy(GeneratorsOfSemigroup(G));\n\n gens := [];\n rels := [];\n relsF := [];\n has_one := false;\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do\n if orig_gens[i] = orig_gens[j] then\n new_gen := false;\n if not IsIdenticalObj(orig_gens[i], orig_gens[j]) then\n Add(rels, [orig_gens[i], orig_gens[j]]);\n fi;\n break;\n fi;\n od;\n if new_gen then Add(gens, orig_gens[i]); fi;\n else\n if not IsIdenticalObj(orig_gens[i], One(orig_gens[i])) then\n Add(rels, [orig_gens[i], One(orig_gens[i])]);\n fi;\n has_one := true;\n fi;\n od;\n\n F := FreeGroup(Length(gens));\n\n if has_one then\n ElList := [One(G)];\n ElListF := [One(F)];\n GrList := [1];\n else\n ElList := [];\n ElListF := [];\n GrList := [0];\n fi;\n\n Append(ElList, ShallowCopy(gens));\n Append(ElListF, GeneratorsOfGroup(F));\n Add(GrList, Length(gens)+GrList[1]);\n len := 1;\n\n while GrList[len] <> GrList[len+1] and len < max_len and Length(rels) < num_of_rels do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for j in [1..Length(gens)] do\n gen := gens[j];\n genf := GeneratorsOfGroup(F)[j];\n g := ElList[i]*gen;\n f := ElListF[i]*genf;\n New := true;\n\n# If g includes a longer part of some relation it can not represent\n# neither a new element, nor be involved in a new relation\n for rel in relsF do\n if PositionSublist(LetterRepAssocWord(f), LetterRepAssocWord(rel[1]) ) <> fail then New := false; fi;\n od;\n\n# Print(\"New = \", New, \"\\n\\n\");\n if New then\n\n k := 0;\n while New and k < Length(ElList) do\n k := k+1;\n if g = ElList[k] then\n New := false;\n fi;\n od;\n if New then\n Add(ElList, g);\n Add(ElListF, f);\n else\n Add(rels, [g, ElList[k]]);\n Add(relsF, [f, ElListF[k]]);\n # if Length(AssocW(v)) > 0 then\n Print(g, \" = \", ElList[k], \"\\n\");\n # fi;\n fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n if GrList[len] = GrList[len+1] then\n SetSize(G, GrList[len]);\n fi;\n return rels;\nend);\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsSemigroup, IsCyclotomic]\", true,\n [IsSemigroup, IsCyclotomic],\nfunction(G, max_len)\n return FindSemigroupRelations(G, max_len, infinity);\nend);\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsSemigroup]\",\n [IsSemigroup],\nfunction(G)\n return FindSemigroupRelations(G, infinity, infinity);\nend);\n\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList, IsCyclotomic, IsCyclotomic]\", true,\n [IsList, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, max_len, num_of_rels)\n return FindSemigroupRelations(SemigroupByGenerators(subs_words), max_len, num_of_rels);\nend);\n\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList, IsCyclotomic]\", true,\n [IsList, IsCyclotomic],\nfunction(subs_words, max_len)\n return FindSemigroupRelations(subs_words, max_len, infinity);\nend);\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList]\",\n [IsList],\nfunction(subs_words)\n return FindSemigroupRelations(subs_words, infinity, infinity);\nend);\n\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList, IsList, IsCyclotomic, IsCyclotomic]\", true,\n [IsList, IsList, IsCyclotomic, IsCyclotomic],\nfunction(subs_words, names, max_len, num_of_rels)\n local ElList, GrList, i, j, orig_gens, orig_fgens, gen, gens, fgens, new_gen, g, len, oldgr, New, k, has_one, rel, F, relsF, ElListF, genf, f;\n\n if Length(subs_words) <> Length(names) then\n Error(\"The number of names must coincide with the number of generators\");\n fi;\n F := FreeGroup(names);\n orig_fgens := GeneratorsOfGroup(F);\n\n\n orig_gens := ShallowCopy(subs_words);\n\n gens := [];\n fgens := [];\n relsF := [];\n has_one := false;\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do\n if orig_gens[i] = orig_gens[j] then\n new_gen := false;\n Add(relsF, [orig_fgens[i], orig_fgens[j]]);\n Print( orig_fgens[i], \" = \", orig_fgens[j], \"\\n\");\n break;\n fi;\n od;\n if new_gen then\n Add(gens, orig_gens[i]);\n Add(fgens, orig_fgens[i]);\n fi;\n else\n Add(relsF, [orig_fgens[i], One(orig_fgens[i])]);\n Print( orig_fgens[i], \" = \", One(F), \"\\n\");\n has_one := true;\n fi;\n od;\n\n\n if has_one then\n ElList := [One(gens[1])];\n ElListF := [One(F)];\n GrList := [1];\n else\n ElList := [];\n ElListF := [];\n GrList := [0];\n fi;\n\n Append(ElList, ShallowCopy(gens));\n Append(ElListF, fgens);\n Add(GrList, Length(gens)+GrList[1]);\n len := 1;\n\n while GrList[len] <> GrList[len+1] and len < max_len and Length(relsF) < num_of_rels do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for j in [1..Length(gens)] do\n gen := gens[j];\n genf := fgens[j];\n g := ElList[i]*gen;\n f := ElListF[i]*genf;\n New := true;\n\n# If g includes a longer part of some relation it can not represent\n# neither a new element, nor be involved in a new relation\n for rel in relsF do\n if PositionSublist(LetterRepAssocWord(f), LetterRepAssocWord(rel[1]) ) <> fail then New := false; fi;\n od;\n\n if New then\n k := 0;\n while New and k < Length(ElList) do\n k := k+1;\n if g = ElList[k] then\n New := false;\n fi;\n od;\n if New then\n Add(ElList, g);\n Add(ElListF, f);\n else\n Add(relsF, [f, ElListF[k]]);\n Print( f, \" = \", ElListF[k], \"\\n\");\n fi;\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n return relsF;\nend);\n\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList, IsList, IsCyclotomic]\", true,\n [IsList, IsList, IsCyclotomic],\nfunction(subs_words, names, max_len)\n return FindSemigroupRelations(subs_words, names, max_len, infinity);\nend);\n\n\nInstallMethod(FindSemigroupRelations, \"for [IsList, IsList]\", true,\n [IsList, IsList],\nfunction(subs_words, names)\n return FindSemigroupRelations(subs_words, names, infinity, infinity);\nend);\n\n\n\n\nInstallMethod(OrderUsingSections, \"for [IsAutom, IsCyclotomic]\", true,\n [IsAutom, IsCyclotomic],\nfunction(a, max_depth)\n local OrderUsingSections_LOCAL, cur_list, F, degs, vertex, AreConjugateUsingSmallRels, gens_ord2, CyclicallyReduce, res;\n\n CyclicallyReduce := function(w)\n local i, j, wtmp, reduced;\n\n for i in [1..Length(w)] do\n if -w[i] in gens_ord2 then w[i] := -w[i]; fi;\n od;\n\n repeat\n reduced := true;\n j := 1;\n while reduced and j < Length(w) do\n if w[j] = -w[j+1] or (w[j] = w[j+1] and w[j] in gens_ord2) then\n reduced := false;\n wtmp := ShallowCopy(w{[1..j-1]});\n Append(wtmp, w{[j+2..Length(w)]});\n w := wtmp;\n fi;\n j := j+1;\n od;\n until reduced;\n\n repeat\n if Length(w) < 2 then return w; fi;\n reduced := true;\n if w[1] = -w[Length(w)] or (w[1] = w[Length(w)] and w[1] in gens_ord2) then\n w := w{[2..Length(w)-1]};\n reduced := false;\n fi;\n until reduced;\n\n return w;\n end;\n\n AreConjugateUsingSmallRels := function(g, h)\n local i, g_list, h_list, long_cycle, l;\n g_list := CyclicallyReduce(LetterRepAssocWord(g));\n h_list := CyclicallyReduce(LetterRepAssocWord(h));\n if Length(g_list) <> Length(h_list) then return false; fi;\n l := [2..Length(g_list)];\n Add(l, 1);\n long_cycle := PermList(l);\n for i in [0..Length(g_list)-1] do\n if h_list = Permuted(g_list, long_cycle^i) then return true; fi;\n od;\n return false;\n end;\n\n OrderUsingSections_LOCAL := function(g)\n local i, el, orb, Orbs, res, st, reduced_word, loc_order;\n# Print(\"vertex=\",vertex,\"\\n\");\n# Print(\"g=\",g,\"\\n\");\n if IsOne(g) then return 1; fi;\n\n if IsActingOnBinaryTree(g) and\n not HasContainsSphericallyTransitiveElement(GroupOfAutomFamily(FamilyObj(g))) or\n (HasContainsSphericallyTransitiveElement(GroupOfAutomFamily(FamilyObj(g))) and\n ContainsSphericallyTransitiveElement(GroupOfAutomFamily(FamilyObj(g)))) then\n if IsSphericallyTransitive(g) then\n Info(InfoAutomGrp, 3, g!.word, \" acts transitively on levels and is obtained from (\", a!.word, \")^\", Product(degs{[1..Length(degs)]}), \"\\n by taking sections and cyclic reductions at vertex \", vertex);\n return infinity;\n fi;\n fi;\n for i in [1..Length(cur_list)] do\n el := cur_list[i];\n if (AreConjugateUsingSmallRels(g!.word, el!.word) or AreConjugateUsingSmallRels((g!.word)^(-1), el!.word)) then\n if Product(degs{[i..Length(degs)]}) > 1 then\n if i > 1 then Info(InfoAutomGrp, 3, el!.word, \" is obtained from (\", a!.word, \")^\", Product(degs{[1..i-1]}), \"\\n by taking sections and cyclic reductions at vertex \", vertex{[1..i-1]}); fi;\n Info(InfoAutomGrp, 3, g!.word, \" is obtained from (\", el!.word, \")^\", Product(degs{[i..Length(degs)]}), \"\\n by taking sections and cyclic reductions at vertex \", vertex{[i..Length(degs)]});\n SetIsFinite(GroupOfAutomFamily(FamilyObj(a)), false);\n return infinity;\n else\n# Info(InfoAutomGrp, 3, \"The group might not be contracting, \", g, \" has itself as a section.\");\n return 1;\n fi;\n fi;\n od;\n if Length(cur_list) >= max_depth then return fail; fi;\n Add(cur_list, g);\n Orbs := OrbitsPerms([g!.perm], [1..g!.deg]);\n loc_order := 1;\n\n for orb in Orbs do\n Add(degs, Length(orb));\n Add(vertex, orb[1]);\n# res := OrderUsingSections_LOCAL(Autom(CyclicallyReducedWord(Section(g^Length(orb), orb[1])!.word), FamilyObj(g)));\n# Print(g^Length(orb), \"\\n\");\n st := Section(g^Length(orb), orb[1]);\n reduced_word := AssocWordByLetterRep(FamilyObj(st!.word), CyclicallyReduce(LetterRepAssocWord(st!.word)));\n# Print(st!.word, \" at \", vertex, \"\\n\");\n res := OrderUsingSections_LOCAL(Autom(reduced_word, FamilyObj(g)));\n if res = infinity then return res;\n elif res=fail then\n loc_order:=fail;\n fi;\n if loc_order<>fail then\n loc_order := Lcm(loc_order, res*Length(orb));\n fi;\n Remove(degs);\n Remove(vertex);\n od;\n Remove(cur_list);\n return loc_order;\n end;\n\n F := FamilyObj(a)!.freegroup;\n gens_ord2 := GeneratorsOfOrderTwo(FamilyObj(a));\n cur_list := [];\n# degs traces at what positions we raise to what power\n degs := []; vertex := [];\n res := OrderUsingSections_LOCAL(a);\n if res = infinity then\n SetIsFinite(GroupOfAutomFamily(FamilyObj(a)), false);\n SetOrder(a, infinity);\n fi;\n return res;\nend);\n\n\n\nInstallMethod(OrderUsingSections, \"for [IsAutom]\", true,\n [IsAutom],\nfunction(a)\n return OrderUsingSections(a, infinity);\nend);\n\n\n\nInstallGlobalFunction(AG_SuspiciousForNoncontraction, function(arg)\n local AG_SuspiciousForNoncontraction_LOCAL, cur_list, F, vertex, print_info, a;\n\n AG_SuspiciousForNoncontraction_LOCAL := function(g)\n local i, res;\n if IsOne(g) or g!.perm <> () then return false; fi;\n\n if (g!.word in cur_list) or (g!.word^(-1) in cur_list) then\n if g = a or g = a^-1 then\n if print_info then\n Info(InfoAutomGrp, 3, a!.word, \" has \", g!.word, \" as a section at vertex \", vertex);\n else\n Info(InfoAutomGrp, 5, a!.word, \" has \", g!.word, \" as a section at vertex \", vertex);\n fi;\n return true;\n else return false; fi;\n fi;\n\n Add(cur_list, g!.word);\n\n for i in [1..FamilyObj(a)!.deg] do\n Add(vertex, i);\n res := AG_SuspiciousForNoncontraction_LOCAL(Section(g, i));\n if res then return true; fi;\n Unbind(vertex[Length(vertex)]);\n od;\n return false;\n end;\n\n a := arg[1];\n print_info := false;\n\n if Length(arg) > 1 then print_info := arg[2]; fi;\n if Length(arg) > 2 then Error(\"invalid arguments for IsNoncontracting\"); fi;\n\n F := FamilyObj(a)!.freegroup;\n cur_list := [];\n# degs traces at what positions we raise to what power\n vertex := [];\n return AG_SuspiciousForNoncontraction_LOCAL(a);\nend);\n\n\n\nInstallMethod(FindElement, \"for [IsAutomGroup, IsFunction, IsObject, IsCyclotomic]\", true,\n [IsAutomGroup, IsFunction, IsObject, IsCyclotomic],\nfunction(G, func, val, n)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, viewed, oldgr, New, k;\n\n if func(One(G)) = val then return One(G); fi;\n\n# produce a symmetric generating set\n orig_gens := ShallowCopy(GeneratorsOfGroup(G));\n Append(orig_gens, List(orig_gens, x -> x^-1));\n\n gens := [];\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do if orig_gens[i] = orig_gens[j] then new_gen := false; fi; od;\n if new_gen then Add(gens, orig_gens[i]); fi;\n fi;\n od;\n\n for g in gens do\n if func(g) = val then return g; fi;\n od;\n\n ElList := [One(G)]; Append(ElList, ShallowCopy(gens));\n GrList := [1, Length(gens)+1];\n len := 1;\n\n while len < n and GrList[len] <> GrList[len+1] do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for gen in gens do\n g := ElList[i]*gen;\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n if g = ElList[k] then New := false; fi;\n k := k+1;\n od;\n if New then\n if func(g) = val then return g; fi;\n Add(ElList, g);\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n if GrList[len] = GrList[len+1] then\n SetSize(G, GrList[len]);\n fi;\n return fail;\nend);\n\n\nInstallMethod(FindElements, \"for [IsAutomGroup, IsFunction, IsObject, IsCyclotomic]\", true,\n [IsGroup, IsFunction, IsObject, IsCyclotomic],\nfunction(G, func, val, n)\n local ElList, GrList, i, j, orig_gens, gen, gens, new_gen, g, len, viewed, oldgr, New, k, cur_els;\n\n# produce a symmetric generating set\n orig_gens := ShallowCopy(GeneratorsOfGroup(G));\n Append(orig_gens, List(orig_gens, x -> x^-1));\n\n gens := [];\n cur_els := [];\n\n# select pairwise different generators\n for i in [1..Length(orig_gens)] do\n if not IsOne(orig_gens[i]) then\n new_gen := true;\n for j in [1..i-1] do if orig_gens[i] = orig_gens[j] then new_gen := false; fi; od;\n if new_gen then Add(gens, orig_gens[i]); fi;\n fi;\n od;\n\n if func(One(G)) = val then Add(cur_els, One(G)); fi;\n for g in gens do\n if func(g) = val then Add(cur_els, g); fi;\n od;\n\n ElList := [One(G)]; Append(ElList, ShallowCopy(gens));\n GrList := [1, Length(gens)+1];\n len := 1;\n\n while len < n and GrList[len] <> GrList[len+1] do\n for i in [GrList[len]+1..GrList[len+1]] do\n oldgr := Length(ElList);\n for gen in gens do\n g := ElList[i]*gen;\n New := true;\n if len = 1 then k := 1; else k := GrList[len-1]; fi;\n while New and k <= oldgr do\n if g = ElList[k] then New := false; fi;\n k := k+1;\n od;\n if New then\n if func(g) = val then\n Add(cur_els, g);\n Info(InfoAutomGrp, 3, g);\n fi;\n Add(ElList, g);\n fi;\n od;\n od;\n Add(GrList, Length(ElList));\n Info(InfoAutomGrp, 3, \"There are \", Length(ElList), \" elements of length up to \", len+1);\n len := len+1;\n od;\n if GrList[len] = GrList[len+1] then\n SetSize(G, GrList[len]);\n fi;\n return cur_els;\nend);\n\n\nInstallMethod(FindElement, \"for [IsTreeHomomorphismSemigroup, IsFunction, IsObject, IsCyclotomic]\", true,\n [IsTreeHomomorphismSemigroup, IsFunction, IsObject, IsCyclotomic],\nfunction(G, func, val, max_len)\n local iter, g;\n iter := Iterator(G, max_len);\n while not IsDoneIterator(iter) do\n g := NextIterator(iter);\n if func(g) = val then return g; fi;\n od;\n return fail;\nend);\n\n\nInstallMethod(FindElements, \"for [IsTreeHomomorphismSemigroup, IsFunction, IsObject, IsCyclotomic]\", true,\n [IsTreeHomomorphismSemigroup, IsFunction, IsObject, IsCyclotomic],\nfunction(G, func, val, max_len)\n local iter, g, l;\n iter := Iterator(G, max_len);\n l := [];\n while not IsDoneIterator(iter) do\n g := NextIterator(iter);\n if func(g) = val then Add(l, g); fi;\n od;\n return l;\nend);\n\n\n\nInstallMethod(FindElementOfInfiniteOrder, \"for [IsTreeAutomorphismGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsTreeHomomorphismSemigroup, IsCyclotomic, IsCyclotomic],\nfunction(G, n, depth)\n local CheckOrder, res;\n\n if HasIsFinite(G) and IsFinite(G) then return fail; fi;\n\n CheckOrder := function(g) return OrderUsingSections(g, depth); end;\n res := FindElement(G, CheckOrder, infinity, n);\n if res <> fail then SetIsFinite(G, false); fi;\n return res;\nend);\n\n\nInstallMethod(FindElementsOfInfiniteOrder, \"for [IsAutomGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsAutomGroup, IsCyclotomic, IsCyclotomic],\nfunction(G, n, depth)\n local CheckOrder, res;\n if HasIsFinite(G) and IsFinite(G) then return []; fi;\n\n CheckOrder := function(g) return OrderUsingSections(g, depth); end;\n res := FindElements(G, CheckOrder, infinity, n);\n if res <> [] then SetIsFinite(G, false); fi;\n return res;\nend);\n\n\nInstallGlobalFunction(IsNoncontracting, function(arg)\n local IsNoncontrElement, res,\n G, n, depth;\n\n IsNoncontrElement := function(g)\n if AG_SuspiciousForNoncontraction(g) and OrderUsingSections( g, depth ) = infinity then\n if InfoLevel(InfoAutomGrp) > 2 then\n AG_SuspiciousForNoncontraction(g, true);\n fi;\n return true;\n fi;\n return false;\n end;\n\n G := arg[1];\n n := infinity;\n depth := 10;\n if Length(arg) > 1 then n := arg[2]; fi;\n if Length(arg) > 2 then depth := arg[3]; fi;\n if Length(arg) > 3 then Error(\"invalid arguments for IsNoncontracting\"); fi;\n\n if HasIsContracting(G) then return not IsContracting(G); fi;\n\n res := FindElement(G, IsNoncontrElement, true, n);\n if res <> fail then\n SetIsFinite(G, false);\n SetIsContracting(G, false);\n return true;\n fi;\n return fail;\nend);\n\n\n\nInstallMethod(IsGeneratedByAutomatonOfPolynomialGrowth, \"for [IsAutomatonGroup]\", true,\n [IsAutomatonGroup],\nfunction(G)\n local i, d, ver, nstates, cycles, cycle_of_vertex, IsNewCycle, known_vertices, aut_list, HasPolyGrowth, cycle_order, next_cycles, cur_cycles, cur_path, cycles_of_level, lev;\n\n IsNewCycle := function(C)\n local i, l, cur_cycle, long_cycle;\n l := [2..Length(C)];\n Add(l, 1);\n long_cycle := PermList(l);\n\n for cur_cycle in cycles do\n if Intersection(cur_cycle, C) <> [] then\n# if Length(C) <> Length(cur_cycle) then return fail; fi;\n# for i in [0..Length(C)-1] do\n# if cur_cycle = Permuted(C, long_cycle^i) then return false; fi;\n# od;\n Info(InfoAutomGrp, 5, \"cycle1 = \", cur_cycle, \"cycle2 = \", C);\n return fail;\n fi;\n od;\n return true;\n end;\n\n# Example:\n# cycles = [[1, 2, 4], [3, 5, 6], [7]]\n# cur_cycles = [1, 3] (the first and the third cycles)\n# cycle_order = [[2, 3], [3], []] (means 1 -> 2 -> 3, 1 -> 3)\n\n HasPolyGrowth := function(v)\n local i, v_next, is_new, C, ver;\n# Print(\"v = \", v, \"\\n\");\n Add(cur_path, v);\n for i in [1..d] do\n v_next := aut_list[v][i];\n if not (v_next in known_vertices or v_next = 2*nstates+1) then\n if v_next in cur_path then\n C := cur_path{[Position(cur_path, v_next)..Length(cur_path)]};\n is_new := IsNewCycle(C);\n if is_new = fail then\n return false;\n else\n Add(cycles, C);\n Add(cycle_order, []);\n for ver in C do\n# Print(\"next_cycles = \", next_cycles);\n UniteSet(cycle_order[Length(cycles)], next_cycles[ver]);\n cycle_of_vertex[ver] := Length(cycles);\n next_cycles[ver] := [Length(cycles)];\n od;\n fi;\n else\n if not HasPolyGrowth(v_next) then\n return false;\n fi;\n if cycle_of_vertex[v] = 0 then\n UniteSet(next_cycles[v], next_cycles[v_next]);\n elif cycle_of_vertex[v] <> cycle_of_vertex[v_next] then\n UniteSet(cycle_order[cycle_of_vertex[v]], next_cycles[v_next]);\n Info(InfoAutomGrp, 5, \"v = \", v, \"; v_next = \", v_next);\n Info(InfoAutomGrp, 5, \"cycle_order (local) = \", cycle_order);\n fi;\n fi;\n elif v_next in known_vertices then\n if cycle_of_vertex[v] = 0 then\n UniteSet(next_cycles[v], next_cycles[v_next]);\n elif cycle_of_vertex[v] = cycle_of_vertex[v_next] then\n return false;\n else\n UniteSet(cycle_order[cycle_of_vertex[v]], next_cycles[v_next]);\n fi;\n\n fi;\n od;\n Remove(cur_path);\n Add(known_vertices, v);\n return true;\n end;\n\n nstates := UnderlyingAutomFamily(G)!.numstates;\n aut_list := AutomatonList(G);\n d := UnderlyingAutomFamily(G)!.deg;\n cycles := [];\n cycle_of_vertex := List([1..nstates], x -> 0); #if vertex i is in cycle j, then cycle_of_vertex[i] = j\n next_cycles := List([1..nstates], x -> []); #if vertex i is not in a cycle, next_cycles[i] stores the list of cycles, that can be reached immediately (with no cycles in between) from this vertex\n known_vertices := [];\n cur_path := [];\n cycle_order := [];\n\n while Length(known_vertices) < nstates do\n ver := Difference([1..nstates], known_vertices)[1];\n if not HasPolyGrowth(ver) then\n SetIsGeneratedByBoundedAutomaton(G, false);\n return false;\n fi;\n od;\n\n# Now we find the longest chain in the poset of cycles\n cycles_of_level := [[]];\n for i in [1..Length(cycles)] do\n if cycle_order[i] = [] then Add(cycles_of_level[1], i); fi;\n od;\n\n lev := 1;\n\n while cycles_of_level[Length(cycles_of_level)] <> [] do\n Add(cycles_of_level, []);\n for i in [1..Length(cycles)] do\n if Intersection(cycles_of_level[lev], cycle_order[i]) <> [] then\n Add(cycles_of_level[lev+1], i);\n fi;\n od;\n lev := lev+1;\n od;\n\n if lev = 2 then\n SetIsGeneratedByBoundedAutomaton(G, true);\n SetIsAmenable(G, true);\n elif lev = 1 then\n SetIsGeneratedByBoundedAutomaton(G, true);\n SetIsFinite(G, true);\n else\n SetIsGeneratedByBoundedAutomaton(G, false);\n fi;\n SetPolynomialDegreeOfGrowthOfUnderlyingAutomaton(G, lev-2);\n Info(InfoAutomGrp, 5, \"Cycles = \", cycles);\n Info(InfoAutomGrp, 5, \"cycle_order = \", cycle_order);\n Info(InfoAutomGrp, 5, \"next_cycles = \", next_cycles);\n return true;\nend);\n\n\n\nInstallMethod(IsGeneratedByBoundedAutomaton, \"for [IsAutomatonGroup]\", true,\n [IsAutomatonGroup],\nfunction(G)\n local res;\n res := IsGeneratedByAutomatonOfPolynomialGrowth(G);\n return IsGeneratedByBoundedAutomaton(G);\nend);\n\n\n\n\nInstallMethod(PolynomialDegreeOfGrowthOfUnderlyingAutomaton, \"for [IsAutomatonGroup]\", true,\n [IsAutomatonGroup],\nfunction(G)\n local res;\n res := IsGeneratedByAutomatonOfPolynomialGrowth(G);\n if not res then\n Print(\"Error: the automaton generating has exponenetial growth\\n\");\n return fail;\n fi;\n return PolynomialDegreeOfGrowthOfUnderlyingAutomaton(G);\nend);\n\n\n\n\nInstallMethod(IsAmenable, \"for [IsAutomGroup]\", true,\n [IsAutomGroup],\nfunction(G)\n if HasIsFinite(G) and IsFinite(G) then return true; fi;\n if IsGeneratedByBoundedAutomaton(GroupOfAutomFamily(G)) then return true; fi;\n if IsAutomatonGroup(G) and IsAbelian(StabilizerOfLevel(G, 2)) then return true; fi;\n if IsAutomatonGroup(G) and IsOfSubexponentialGrowth(G)=true then return true; fi;\n TryNextMethod();\nend);\n\n\n\n\nInstallMethod(IsOfSubexponentialGrowth, \"for [IsAutomatonGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsAutomatonGroup, IsCyclotomic, IsCyclotomic],\nfunction(G, len, depth)\n local iter, res, g, cur_length;\n\n if (HasIsFinite(G) and IsFinite(G)) or IsAbelian(G) then return true; fi;\n iter := Iterator(G, len);\n\n cur_length := 1;\n res := false;\n\n while not IsDoneIterator(iter) do\n g := NextIterator(iter);\n\n if Length(Word(g)) > cur_length then\n if res then\n return true;\n SetIsAmenable(G, true);\n fi;\n res := true;\n cur_length := cur_length + 1;\n fi;\n\n if res and cur_length <= Sum( List(Sections(g, depth), x -> Length(Word(x))) ) then\n Info(InfoAutomGrp, 3, g, \" has sections \", Sections(g, depth));\n res := false;\n fi;\n\n od;\n\n if res then return true; fi;\n\n # if iterator has enumerated all (finitely many) elements of \n if HasIsFinite(G) and IsFinite(G) then return true; fi;\n if IsAbelian(StabilizerOfLevel(G, 2)) then return true; fi;\n return fail;\nend);\n\n\n\n\n\nInstallMethod(IsOfSubexponentialGrowth, \"for [IsSelfSimilarGroup, IsCyclotomic, IsCyclotomic]\", true,\n [IsSelfSimilarGroup, IsCyclotomic, IsCyclotomic],\nfunction(G, len, depth)\n local iter, res, g, cur_length, F;\n\n if (HasIsFinite(G) and IsFinite(G)) or IsAbelian(G) then return true; fi;\n F := UnderlyingFreeGroup(G);\n iter := Iterator(F);\n\n cur_length := 1;\n res := false;\n\n repeat\n g := NextIterator(iter);\n\n if Length(g) > cur_length then\n if res then\n return true;\n SetIsAmenable(G, true);\n fi;\n res := true;\n cur_length := cur_length + 1;\n fi;\n\n if res and cur_length <= Sum( List(Sections(SelfSim(g,One(G)), depth), x -> Length(Word(x))) ) then\n Info(InfoAutomGrp, 3, g, \" has sections \", Sections( SelfSim(g,One(G)), depth));\n res := false;\n fi;\n\n until Length(g)>len;\n\n # if iterator has enumerated all (finitely many) elements of \n if HasIsFinite(G) and IsFinite(G) then return true; fi;\n if IsAbelian(StabilizerOfLevel(G, 2)) then return true; fi;\n return fail;\nend);\n\n\n\n\nInstallMethod(IsOfSubexponentialGrowth, \"for [IsTreeAutomorphismGroup and IsSelfSimilar]\", true,\n [IsTreeAutomorphismGroup and IsSelfSimilar],\nfunction(G)\n return IsOfSubexponentialGrowth(G, 10, 6);\nend);\n\n\nInstallGlobalFunction(AG_GroupHomomorphismByImagesNC,\nfunction(G, H, gens_G, gens_H)\n\n local F, gens_in_freegrp, pi, pi_bar, hom_function, inv_hom_function;\n\n if Length(gens_G)<>Length(gens_H) then\n Error(\"Lengths of generating sets must coincide\");\n fi;\n\n F := FreeGroup(Length(gens_G));\n\n\n gens_in_freegrp := List(gens_G, Word);\n\n# pi\n# F ------> G ----> H\n# -------------->\n# pi_bar\n\n pi := GroupHomomorphismByImages(F, Group(gens_in_freegrp),\n GeneratorsOfGroup(F), gens_in_freegrp);\n\n pi_bar := GroupHomomorphismByImages(F, H,\n GeneratorsOfGroup(F), gens_H);\n\n hom_function := function(g)\n return Image(pi_bar, PreImagesRepresentative(pi, g!.word));\n end;\n\n if IsAutomGroup(G) then\n inv_hom_function := function(b)\n return Autom(Image(pi, PreImagesRepresentative(pi_bar, b)), UnderlyingAutomFamily(G));\n end;\n elif IsSelfSimGroup(G) then\n inv_hom_function := function(b)\n return SelfSim(Image(pi, PreImagesRepresentative(pi_bar, b)), UnderlyingSelfSimFamily(G));\n end;\n fi;\n\n return GroupHomomorphismByFunction(G, H, hom_function, inv_hom_function);\nend);\n\n\n#E\n", "meta": {"hexsha": "715755285fcbe40c3d17f04160215329a7cf02ed", "size": 99099, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/selfs.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/selfs.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/selfs.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.6330540306, "max_line_length": 218, "alphanum_fraction": 0.5779170325, "num_tokens": 30804, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6370307944803832, "lm_q2_score": 0.6513548782017745, "lm_q1q2_score": 0.4149331155495497}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# ==========================================================================\n# IDirSum(, , ) - Iterative direct sum.\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IDirSum, BaseIterative, rec(\n directOper := DirectSum,\n #-----------------------------------------------------------------------\n dims := self >> let(d:=self._children[1].dimensions,\n [d[1]* self.domain, d[2]*self.domain]),\n# dims := self >> _evInt(self.unroll().dims()),\n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n conjTranspose := self >> CopyFields(self, rec(\n _children := [self._children[1].conjTranspose()],\n dimensions := Reversed(self.dimensions))),\n #-----------------------------------------------------------------------\n inverse := self >> CopyFields(self, rec(\n _children := [self._children[1].inverse()],\n dimensions := Reversed(self.dimensions)))\n));\n\nDeclare(IColDirSum, IRowDirSum);\n\n# ==========================================================================\n# IRowDirSum(, , , ) - Iterative direct sum.\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IRowDirSum, BaseIterative, rec(\n directOper := RowDirectSum,\n transposeOper := self >> IColDirSum,\n abbrevs := [ (v, expr) -> [v, v.range, 0, expr] ],\n\n rChildren := self >> Concat([self.var, self.overlap, self._children], When(IsBound(self._setDims), [self._setDims],[])),\n rSetChild := rSetChildFields(\"var\", \"overlap\", \"_children\", \"_setDims\"),\n\n new := meth(self, var, domain, overlap, expr)\n local res;\n Constraint(IsSPL(expr));\n Constraint(not IsInt(domain) or domain > 0);\n var.isLoopIndex := true;\n res := SPL(WithBases(self, rec(_children := [expr], var := var, domain := domain, overlap := overlap)));\n res.dimensions := res.dims();\n return res;\n end,\n #-----------------------------------------------------------------------\n print := meth(self, indent, indentStep)\n Print(self.name, \"(\", self.var, \", \", self.domain, \", \", self.overlap, \",\");\n self._newline(indent + indentStep);\n SPLOps.Print(self._children[1], indent+indentStep, indentStep); #, \", \", self.nt_maps);\n self._newline(indent);\n Print(\")\");\n if IsBound(self._setDims) then\n Print(\".overrideDims(\", self._setDims, \")\");\n fi;\n end,\n #-----------------------------------------------------------------------\n _dims := self >> self.unroll().dims(),\n dims := self >> When(IsBound(self._setDims), self._setDims, let(d := Try(self._dims()), When(d[1], d[2], [errExp(), errExp()]))),\n #-----------------------------------------------------------------------\n unroll := self >> ApplyFunc(self.directOper, [self.overlap, self.unrolledChildren()]),\n #-----------------------------------------------------------------------\n transpose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).transpose()]),\n #-----------------------------------------------------------------------\n conjTranspose := self >> ApplyFunc(self.transposeOper(), [self.var, self.domain, self.overlap, self.child(1).conjTranspose()])\n));\n\n\n# ==========================================================================\n# IColDirSum(, , , ) - Iterative direct sum.\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IColDirSum, IRowDirSum, rec(\n directOper := ColDirectSum,\n transposeOper := self >> IRowDirSum\n));\n\n\n# ==========================================================================\n# IterCompose(, , ) - iterative compose\n# must be square\n# ==========================================================================\nClass(IterCompose, BaseIterative, rec(\n directOper := Compose,\n #-----------------------------------------------------------------------\n dims := self >> self._children[1].dimensions,\n #-----------------------------------------------------------------------\n unroll := self >> Compose(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n # NOTE: this is incorrect, one has to reverse the order\n transpose := self >> CopyFields(self, rec(\n _children := [self._children[1].transpose()],\n domain := self.domain,\n dimensions := self.dimensions))\n # NOTE: conjTranspose() is missing\n));\n\nDeclare(IterVStack);\n\n# ==========================================================================\n# IterHStack(, , )\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IterHStack, BaseIterative, rec(\n directOper := HStack,\n #-----------------------------------------------------------------------\n unroll := self >> HStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1],\n self.child(1).dimensions[2] * self.domain ],\n #-----------------------------------------------------------------------\n transpose := self >> IterVStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterVStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n# this is a HStack that is guaranteed not to perform any ops, and doesnt need ScatAcc in SumsGen\nClass(IterHStack1, IterHStack);\n# ==========================================================================\n# IterVStack(, , )\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IterVStack, BaseIterative, rec(\n directOper := VStack,\n #-----------------------------------------------------------------------\n unroll := self >> VStack(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [ self.child(1).dimensions[1] * self.domain,\n self.child(1).dimensions[2] ],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n\n#IterDirectSum := IDirSum;\n# ==========================================================================\n# IterDirectSum(, , )\n# Dimensions of are assumed to not depend on .\n# ==========================================================================\nClass(IterDirectSum, BaseIterative, rec(\n directOper := DirectSum, \n #-----------------------------------------------------------------------\n unroll := self >> DirectSum(self.unrolledChildren()),\n #-----------------------------------------------------------------------\n dims := self >> [self.child(1).dimensions[1] * self.domain, self.child(1).dimensions[2]*self.domain],\n #-----------------------------------------------------------------------\n transpose := self >> IterHStack(self.var, self.domain, self.child(1).transpose()),\n conjTranspose := self >> IterHStack(self.var, self.domain, self.child(1).conjTranspose())\n));\n", "meta": {"hexsha": "1603ccc9edf04657c1e08a4645385925d5a4bd46", "size": 8097, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/Iter.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/Iter.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/Iter.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 51.246835443, "max_line_length": 133, "alphanum_fraction": 0.4213906385, "num_tokens": 1527, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6297746213017459, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.4146546362958401}} {"text": "\n# Copyright 2018-2019, Carnegie Mellon University\n# See LICENSE for details\n\nClass(HCOLSumsGen, DefaultSumsGen, rec(\n OLCompose := (self, o, opts) >> Cond(o.isPermutation(), Prm(ApplyFunc(fCompose, List(Reversed(o.children()), c -> self(c, opts).func))),\n\t OLCompose(Map(o.children(), child -> self(child, opts)))),\n Reduction := (self, o, opts) >> o,\n Induction := (self, o, opts) >> o,\n ScalarProd := (self, o, opts) >> let(i := Ind(o.N), x := var.fresh_t(\"r\", TDouble), \n OLCompose(\n Reduction(o.N, (a,b)->add(a,b), V(0.0), False), \n PointWise(o.N, Lambda([x,i], mul(x,nth(o.scalars, i)))))),\n PointWise := (self, o, opts) >> o,\n\tCOND := (self, o, opts) >> let( #this is a recursive call.....must include check\n\t\ttest := o.cond,\n\t\tch := o.children(),\t\t\t\t\n\t\tCOND(self(test, opts), self(ch[1], opts), self(ch[2], opts))\n\t\t),\n IterVStack := (self, o, opts) >> let(\t\t\n \tch := o.children()[1],\n \tISumUnion(o.var, o.domain, \n\t OLCompose(\n\t ScatHUnion(Rows(o), Rows(ch), o.var*Rows(ch), 1), \n\t self(ch, opts)))), \n VStack := (self, o, opts) >> let(\n ch := o.children(),\n ApplyFunc(SUMUnion, List([1..Length(ch)], i->\n\t OLCompose(\n\t ScatHUnion(Rows(o), Rows(ch[i]), Sum(List(ch{[1..i-1]}, child->child.dims()[1])), 1),\n\t self(ch[i], opts)\n\t ) \n ))\n ),\n I := (self, o, opts) >> let (i := Ind(o.N()), \n ISumUnion(i, i.range, OLCompose(\n ScatHUnion(o.N(), 1, i, 1),\n GathH(o.N(), 1, i, o.N())\n\t))),\n IterDirectSum := (self, o, opts) >> let(\n ch := o.children(),\t\t\n\t ISumUnion(o.var, o.domain, #o.var.range, \n\t ApplyFunc(SUMUnion, List([1..Length(ch)], i->OLCompose(\n ScatHUnion(Rows(o), Rows(ch[i]), ch[1].dims()[1]*o.var, 1),\n self(ch[i], opts),\n GathH(Cols(o), Cols(ch[i]), ch[1].dims()[2]*o.var, 1)) )\n\t )\n\t )\n ),\n DirectSum := (self, o, opts) >> let(\n ch := o.children(),\n ApplyFunc(SUMUnion, List([1..Length(ch)], i->OLCompose(\n ScatHUnion(Rows(o), Rows(ch[i]), Sum(List(ch{[1..i-1]}, child->child.dims()[1])), 1),\n self(ch[i], opts),\n GathH(Cols(o), Cols(ch[i]), Sum(List(ch{[1..i-1]}, child->child.dims()[2])), 1))))),\n BinOp := (self, o, opts) >> When(o.N=1, o, let(i := Ind(o.N), \n ISumUnion(i, i.range, OLCompose(\n ScatHUnion(o.N, 1, i, 1),\n BinOp(1, o.op),\n GathH(2*o.N, 2, i, o.N)\n )))),\n Constant := (self, o, opts) >> o #Constant(o.value)\n));\n\n", "meta": {"hexsha": "472c75d7077a79539c55c75cbe1a6fc55bb893f1", "size": 2546, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "sumsgen.gi", "max_stars_repo_name": "spiral-software/spiral-package-hcol", "max_stars_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "sumsgen.gi", "max_issues_repo_name": "spiral-software/spiral-package-hcol", "max_issues_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "sumsgen.gi", "max_forks_repo_name": "spiral-software/spiral-package-hcol", "max_forks_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-11-26T05:21:02.000Z", "max_forks_repo_forks_event_max_datetime": "2019-11-26T05:21:02.000Z", "avg_line_length": 39.1692307692, "max_line_length": 140, "alphanum_fraction": 0.5090337785, "num_tokens": 846, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7122321842389469, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.41402276995444975}} {"text": "#\n# Read(\"~/Workspace/Chevalley.gap/init.gi\"); Read(Filename(test_dir,\"_allTests.gi\"));\n#\n\nLogTo(Filename(test_dir,\"_allTests.log\"));\n\n#\n# Polynomial stuff\n#\nPrint(\"[Polynomial stuff]\\n\");\nRead(Filename(test_dir,\"poly.test.init.gi\"));\nRead(Filename(test_dir,\"poly.test.gi\"));\n\n#\n# Root system\n#\nPrint(\"[Root system]\\n\");\nRead(Filename(test_dir,\"rsys.test.init.gi\"));\nRead(Filename(test_dir,\"rsys.test.gi\"));\n\n#\n# Parabolic system\n#\nPrint(\"[Parabolic system]\\n\");\nRead(Filename(test_dir,\"psys.test.init.gi\"));\nRead(Filename(test_dir,\"psys.test.gi\"));\n\n#\n# Chevalley group stuff\n#\nPrint(\"[Chevalley group stuff]\\n\");\nRead(Filename(home_dir,\"lib/chvadj.gd\"));\nRead(Filename(home_dir,\"lib/chvadj.gi\"));\nRead(Filename(test_dir,\"chvadj.test.gi\"));\n\n#\n# Nilpotent elements\n#\nPrint(\"[Nilpotent elements]\\n\");\nRead(Filename(home_dir,\"lib/nilchv.gd\"));\nRead(Filename(home_dir,\"lib/nilchv.gi\"));\nRead(Filename(test_dir,\"nilchv.test.gi\"));\n\n#\n# Algebraic unipotent Sylow stuff\n#\nPrint(\"[Algebraic unipotent Sylow stuff]\\n\");\nRead(Filename(home_dir,\"lib/algU.gd\"));\nRead(Filename(home_dir,\"lib/algU.gi\"));\nRead(Filename(test_dir,\"algU.test.gi\"));\n\n#\n# Unipotent elements\n#\nPrint(\"[Unipotent elements]\\n\");\nRead(Filename(home_dir,\"lib/unichv.gd\"));\nRead(Filename(home_dir,\"lib/witt.gd\"));\nRead(Filename(home_dir,\"lib/unialg.gd\"));\n#\nRead(Filename(home_dir,\"lib/unichv.gi\"));\nRead(Filename(test_dir,\"unichv.test.gi\"));\n\n#\n# Arithmetics modulo p\n#\nPrint(\"[Arithmetics modulo p]\\n\");\nRead(Filename(home_dir,\"lib/unimod.gd\"));\nRead(Filename(home_dir,\"lib/unimod.gi\"));\n#Read(Filename(test_dir,\"unimod.test.gi\"));\n\n#\n# Witt groups\n#\nPrint(\"[Witt groups]\\n\");\nRead(Filename(home_dir,\"lib/witt.gi\"));\nRead(Filename(test_dir,\"witt.test.gi\"));\n\n#\n# Unipotent elements over polynomials\n#\nPrint(\"[Unipotent elements over polynomials]\\n\");\nRead(Filename(home_dir,\"lib/unialg.gi\"));\nRead(Filename(test_dir,\"unialg.test.gi\"));", "meta": {"hexsha": "7f856f646feeeb01ee6056d99dfb4f40f23fdbe4", "size": 1898, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test/_allTests.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test/_allTests.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test/_allTests.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.8674698795, "max_line_length": 85, "alphanum_fraction": 0.7139093783, "num_tokens": 565, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6893056040203135, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4137131995058165}} {"text": "################################################################################\n##\n#W TY_data.gi GroupTheoretical Package\n##\n#W Paul Bruillard, Cesar Galindo, Siu-Hung Ng, Julia Plavnik, Eric Rowell, \n#W Zhenghan Wang\n##\n## Installation file for near_group_data functions of the GroupTheoretical Package\n##\n#Y Copyright (C) 2016, Battelle Memorial Institute\n##\n################################################################################\n\n\n################################################################################\n##\n#F near_group_data(,). . . . . . compute the data\n## . . . . . . . . . . . . . . . . . . . . . for a neargroup category k=0 is TY.\n##\nInstallGlobalFunction(near_group_data, function(G,k)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,g_idx,h_idx,g,h;\n\n if k < 0 or not(IsInt(k)) then\n Error(\"k must be a non-negative integer\\n\");\n fi;\n\n if k > 0 then\n\n Error(\"k > 0 is not currently supported. We need to unravel Siehler's paper 'Near-group categories\\n\");\n\n if Order(G) > k+1 then\n Error(\"near group categories only admit monoidal structure for |G| <= k+1\");\n fi;\n\n if Order(G) = k+1 and not(IsCyclic(G) and Size(Set(FactorsInt(Order(G)+1))) = 1) then\n Error(\"for |G| = k+1, the near group category only admits monoidal structure if G is the multiplicative group of a finite field.\");\n fi;\n\n if Order(G) = 1 and ( (k mod 4) = 2 or (k mod 4) = 3) then\n Error(\"For |G| = 1, the near group category does not admit monoidal structure if k = 2 or 3 mod 4.\");\n fi;\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := k;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,g*h)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2*Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n return [Simples, N, FPdim, FPdimC];\nend);\n\n################################################################################\n##\n#F TY_data(,,,,). . . . compute the data for TY(G,chi,tau,delta,Tsign)\n##\nInstallGlobalFunction(TY_data, function(G,chi,tau,delta,Tsign)\n local Simples,m,N,rank,x,FPdimC,FPdim,S,T,sigma1,sigma3_1,sigma3,sigma3_squared,sigma3_squared_trace,g_idx,h_idx,g,h;\n\n if not(IsInt(Tsign)) or Tsign^2 <> 1 then\n Error(\"Tsign must be +/-1\");\n fi;\n\n if Size(delta)<>Order(G)+1 or false in List(delta,x->(IsInt(x) and x^2=1)) then\n Error(\"delta must be a list of length |G|+1 and consist entirely of +/- 1\");\n fi;\n\n if (1/tau)^2 <> Order(G) then\n Error(\"tau must be a choice of squareroot of 1/|G|\");\n fi;\n\n Simples := ShallowCopy(AsSet(G));\n m:=\"m\";\n Add(Simples,m);\n rank:=Size(Simples);\n N:=List([1..rank],x->NullMat(rank,rank));\n # compute the fusion rules\n for g_idx in [1..rank] do\n g:=Simples[g_idx];\n for h_idx in [1..rank] do\n h:=Simples[h_idx];\n if g_idx = rank then\n if h_idx = rank then\n # m\\otimes m = Sum_{k\\in G}k+km\n N[g_idx][h_idx]:=List([1..rank],x->1);\n N[g_idx][h_idx][rank] := 0;\n else\n N[g_idx][h_idx][rank] := 1; # m\\otimes h = m\n fi;\n else\n if h_idx = rank then\n N[g_idx][h_idx][rank] := 1; # g\\otimes m = m\n else \n # g\\otimes h = gh\n N[g_idx][h_idx][Position(Simples,g*h)] := 1;\n fi;\n fi;\n od;\n od;\n\n FPdimC := 2*Order(G);\n FPdim := List([1..rank],x->1);\n FPdim[rank] := Sqrt(Order(G));\n\n if not(IsAbelian(G) and Exponent(G)=2) then\n # not braided. Return the fusion rules and simples (arxiv:math/0011037v1)\n Display(\"G is not an elementary abelian 2-group and so the associated category does not admit a braiding.\");\n return [Simples, N, FPdim, FPdimC];\n else\n # the category admits a braiding.\n # \n # need to compute the S-matrix and T-matrix\n #\n # First we compute T\n sigma1:=List([1..rank-1],x->delta[x]*Sqrt(chi[x][x]));\n sigma3_1:=delta[1]*Sqrt(tau*Sum(sigma1));\n T:=List([1..rank],x->0);\n for x in [1..rank-1] do\n T[x] := chi[x][x];\n od;\n T[rank]:=Tsign/sigma3_1;\n S:=NullMat(rank,rank);\n # sigma1 = sigma2 (Seihler section 2.3)\n # since delta[x] = pm1 we have sigma1[g]*sigma2[g] = chi[g][g]\n sigma3:=List([1..rank-1],x->sigma3_1*sigma1[x]*chi[x][x]);\n sigma3_squared:=List(sigma3,x->x^2);\n sigma3_squared_trace:=Sum(sigma3);\n for g in [1..rank-1] do\n for h in [1..rank-1] do\n # group elements are invertible\n #S[g][h] := chi[g][h]*chi[h][g]*FPdim[g]*FPdim[h];\n S[g][h] := chi[g][h]*chi[h][g];\n od;\n #S[g][m] := sigma1[g]*sigma2[g]*FPdim[g]*FPdim[rank];\n # group elements are invertible\n S[g][rank] := chi[g][g]*FPdim[rank];\n S[rank][g] := S[g][rank];\n od;\n S[rank][rank] := sigma3_squared_trace*FPdim[rank]*FPdim[rank];\n Display(\"VERIFY S and T\\n\");\n return [Simples,S,T,N,FPdim,FPdimC];\n fi;\nend);\n#E near_group_data.gi . . . . . . . . . . . . . . . . . . . . . . . . ends here\n", "meta": {"hexsha": "19e6999dc875f63c493675658423d5f92c2f7ca8", "size": 5573, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/near_group_data.gi", "max_stars_repo_name": "pnnl/GroupTheoretical", "max_stars_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "lib/near_group_data.gi", "max_issues_repo_name": "pnnl/GroupTheoretical", "max_issues_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-20T21:43:28.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-20T21:43:28.000Z", "max_forks_repo_path": "lib/near_group_data.gi", "max_forks_repo_name": "pnnl/GroupTheoretical", "max_forks_repo_head_hexsha": "d60aaec27d2ca98ec55b12b78213538a346eef27", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2017-12-07T13:46:25.000Z", "max_forks_repo_forks_event_max_datetime": "2020-12-12T22:39:35.000Z", "avg_line_length": 32.5906432749, "max_line_length": 138, "alphanum_fraction": 0.5420778755, "num_tokens": 1842, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7154240079185319, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4131540487156097}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(VIxL, VL, VPrm_x_I);\n\nRecursStep.isSymmetric := self >> self.child(1).isSymmetric();\nRTWrap.isSymmetric := self >> self.child(1).isSymmetric();\nRuleTreeClass.isSymmetric := self >> self.node.isSymmetric();\n\n# in-register permutations to change complex format\nClass(VIxL, BaseContainer, rec(\n new := (self, m, n, v) >> SPL(WithBases(self, rec(\n dimensions := [2*m*v, 2*m*v],\n m:=m,\n n:=n,\n v:=v\n ))),\n dims := self >> Replicate(2, 2*self.m*self.v),\n\n _children := [],\n rChildren := self >> [],\n from_rChildren := (self, rch) >> ObjId(self)(self.m, self.n, self.v),\n\n isPermutation := False,\n isReal := True,\n toAMat := self >> AMatSPL(Tensor(I(self.m), L(2*self.v, self.n))),\n sums := self >> self,\n print := (self,i,is) >> Print(self.name, \"(\", self.m, \", \", self.n, \", \", self.v, \")\"),\n\n implement := meth(self, isa)\n local t, hentry, sums;\n t := TL(2*self.v, self.n, 1, 1).withTags(isa.getTags());\n hentry := HashLookup(SIMD_ISA_DB.getHash(), t);\n if hentry=false then\n return Error(\"SIMD_ISA_DB lookup failed, tried \", t); \n\telse\n sums := Tensor(I(self.m), _SPLRuleTree(hentry[1].ruletree)).sums();\n sums := When(IsBound(sums.unroll), sums.unroll(), sums);\n return sums;\n\tfi;\n end,\n\n transpose := self >> VIxL(self.m, 2*self.v/self.n, self.v)\n));\n\n\n# in-register stride perm\nClass(VL, BaseContainer, rec(\n new := (self, mn, m) >> SPL(WithBases(self, rec(\n dimensions := [mn, mn],\n mn:=mn,\n m:=m\n ))),\n dims := self >> Replicate(2, self.mn),\n _children := [],\n\n rChildren := self >> [],\n from_rChildren := (self, rch) >> ObjId(self)(self.mn, self.m),\n\n isPermutation := False,\n isReal := True,\n toAMat := self >> AMatSPL(L(self.mn, self.m)),\n sums := self >> self,\n print := (self,i,is) >> Print(self.name, \"(\", self.mn, \", \", self.m, \")\"),\n implement := (self, isa) >> _SPLRuleTree(HashLookup(SIMD_ISA_DB.getHash(), TL(self.mn, self.m, 1, 1).withTags(isa.getTags()))[1].ruletree).sums(),\n transpose := self >> VL(self.mn, self.nm/self.m)\n));\n\n\n\n\n# Block diagonal permutation\n# NOTE: Franz pls make sure rChildren properly exposes all parameters\nClass(BlockVPerm, BaseContainer, rec(\n new := (self, n, vlen, spl, perm) >> SPL(WithBases(self, rec(\n _children := [spl],\n n := n,\n perm := perm,\n dimensions := n * spl.dimensions,\n vlen := vlen\n ))),\n\n from_rChildren := (self, rch) >> ObjId(self)(self.n, self.vlen, rch[1], self.perm),\n\n isPermutation := self >> self._children[1].isPermutation(),\n isReal := self >> self._children[1].isReal(),\n toAMat := self >> AMatSPL(Tensor(I(self.n), self._children[1])),\n\n print := (self,i,is) >> Print(self.name, \"(\", self.n, \", \", self._children[1].print(i+is, is), \")\"),\n sums := self >> self,\n dims := self>>self.dimensions,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n# code := (self, y, x) >> ApplyStrategy(\n# Tensor(I(self.n), self._children[1]).sums(),\n# VectorStrategySum, UntilDone).code(y, x);,\n transpose := self >> When(self.child(1).isSymmetric(), self, Error(\"transpose not supported\"))\n));\n\nClass(BlockVPerm2, BlockVPerm);\n\nDeclare(VPerm);\n\n# in-register permutations\nClass(VPerm, BaseContainer, rec(\n new := (self, spl, code, vlen, vcost) >> SPL(WithBases(self, rec(\n _children := [spl],\n dimensions := spl.dimensions,\n code:= code,\n vlen := vlen,\n _vcost := vcost\n ))),\n\n # NOTE: Franz pls make sure rChildren properly exposes all parameters\n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.code, self.vlen, self._vcost),\n\n isPermutation := False,\n isReal := True,\n toAMat := self >> AMatSPL(self._children[1]),\n\n printl := (self,i,is) >> Print(self.name, \"(\", self._children[1].print(i+is, is), \", \", self.code, \", \", self.vlen, \", \", self._vcost, \")\"),\n prints := (self,i,is) >> Print(self.name, \"(\", self._children[1].print(i+is, is), \")\"),\n\n sums := self >> self,\n vcost := self >> self._vcost,\n pshort := meth(self) self.print := self.prints; end,\n plong := meth(self) self.print := self.printl; end,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n transpose := self >> When(self.child(1).isSymmetric(), self, Error(\"transpose not supported\")),\n isSymmetric := self >> self.child(1).isSymmetric(),\n area := (self) >> self.dims()[1]\n));\n\nVPerm.pshort();\n\n# ==========================================================================\n# VPrm_x_I(, ) - permutation\n# ==========================================================================\nClass(VPrm_x_I, Prm, SumsBase, rec(\n #-----------------------------------------------------------------------\n abbrevs := [ (func, v) -> \n\tChecked(IsFunction(func) or IsFuncExp(func), IsInt(v), [func, v]) ],\n #-----------------------------------------------------------------------\n rChildren := self >> [self.func],\n rSetChild := rSetChildFields(\"func\"), \n from_rChildren := (self, rch) >> ObjId(self)(rch[1], self.v),\n #-----------------------------------------------------------------------\n area := self >> Rows(self) * self.v,\n #-----------------------------------------------------------------------\n new := (self, func, v) >> SPL(WithBases(self, rec(\n func := func, v := v))).setDims(), \n #-----------------------------------------------------------------------\n dims := self >> let(n := self.func.domain(), [n * self.v, n * self.v]),\n #-----------------------------------------------------------------------\n print := (self,i,is) >> Print(\n\tself.name, \"(\", self.func, \", \", self.v, \")\", self.printA()),\n #-----------------------------------------------------------------------\n toAMat := self >> let(f := self.func.lambda(),\n\tTensor(Perm(PermList(List(f.tolist(), EvalScalar) + 1),\n f.domain()), I(self.v)).toAMat()),\n #-----------------------------------------------------------------------\n sums := self >> self,\n needInterleavedLeft := False,\n needInterleavedRight := False,\n cannotChangeDataFormat := True,\n totallyCannotChangeDataFormat := True,\n transpose := self >> VPrm_x_I(self.func.transpose(), self.v)\n));\n", "meta": {"hexsha": "24d15a3b3e5a8e7b8d106331e25a96daf81ecd1e", "size": 6445, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/perm.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/perm.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/perm.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.4709302326, "max_line_length": 150, "alphanum_fraction": 0.5157486424, "num_tokens": 1734, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702642896702, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.41306924203674933}} {"text": "#############################################################################\n##\n#W mindeg.gi GAP 4 package SingerAlg Thomas Breuer\n##\n## This file contains the implementation for GAP functions related to\n## the numbers m(q,e).\n##\n\n\n#############################################################################\n##\n#M SingerAlgE( )\n#M SingerAlgE( [, ], )\n##\nInstallMethod( SingerAlgE,\n [ \"IsSingerAlgebra\" ],\n A -> CallFuncList( SingerAlgE, ParametersOfSingerAlgebra( A ) ) );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, z } -> (q^n-1) / z );\n\nInstallMethod( SingerAlgE,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, z } -> (q^OrderMod( q, z )-1) / z );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraGAP( )\n#M MinimalDegreeOfSingerAlgebraGAP( , )\n#M MinimalDegreeOfSingerAlgebraGAP( , , )\n##\n## If the \n## value of the Singer algebra A is known then use it.\n## If the cheap criteria suffice then take their result.\n## Otherwise call the hard method for q and e;\n## if the dimension of the algebra is small then use the algebra\n## also if just the parameters q and e are given.\n##\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoGAP\" ],\n A -> LoewyStructureInfoGAP( A ).m );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n return MinimalDegreeOfSingerAlgebraGAP( q, OrderModExt( q, e, n ), e );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> MinimalDegreeOfSingerAlgebraGAP( q, OrderMod( q, e ), e ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraGAP,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n function( q, n, e )\n local e_str, cache_e, m;\n\n q:= q mod e;\n e_str:= String( e ); # large integers cannot be record component names\n\n if not IsBound( MinimalDegreeOfSingerAlgebraCache.( e_str ) ) then\n cache_e:= rec();\n MinimalDegreeOfSingerAlgebraCache.( e_str ):= cache_e;\n else\n cache_e:= MinimalDegreeOfSingerAlgebraCache.( e_str );\n if IsBound( cache_e.( q ) ) then\n return cache_e.( q );\n fi;\n fi;\n\n m:= MinimalDegreeCheapGAP( q, n, e );\n if m = 0 then\n m:= MinimalDegreeHardGAP( q, n, e );\n fi;\n\n # Extend the cache.\n cache_e.( q ):= m;\n\n return m;\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeCheapGAP( , , )\n##\n## Return either 0 or the number m( q, e ),\n## which is the smallest number of powers of q\n## such that e divides the sum of these powers.\n##

\n## The return value 0 means that the cheap criteria from\n## the two papers and \n## do not suffice to determine m( q, e ).\n##

\n## We assume that\n## q is smaller than e,\n## the argument n is\n## OrderMod( q, e ).\n## The function does not use cached values of m( q, e )\n## or values known via the database of low dimensional Singer algebras.\n##\nInstallGlobalFunction( MinimalDegreeCheapGAP, function( q, n, e )\n local e1, e2, m;\n\n if e = 1 then\n return 1;\n fi;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n if q = 1 then\n # Example I.6.1.\n return e;\n elif IsEvenInt( n ) and PowerModInt( q, n/2, e ) = e-1 then\n # Decide the case m = 2, see Lemma I.6.3.\n return 2;\n elif n = 2 then\n # Prop. II.2.7.\n e1:= Gcd( e, q-1 );\n e2:= Gcd( e, q+1 );\n if e2 <= e1 or ( IsEvenInt( e ) and IsEvenInt( (q^2-1)/e ) ) then\n return e1;\n else\n return 2 * e1;\n fi;\n fi;\n\n # Deal with those cases where e is a prime power,\n # and where we know the value of m(q,e).\n if IsPrimePowerInt( e ) then\n # Let e = p^k for a prime p.\n if e mod 2 = 0 then\n # see Prop. II.2.9, note that here we have e > 4 and q mod e <> q-1.\n if q mod 4 = 1 then\n return Gcd( e, q-1 );\n else\n Assert( 1, ( q+1 ) mod e <> 0 );\n return 4;\n fi;\n else\n # see Prop. II.2.10, note that q \\equiv 1 \\pmod{p}\n # if and only if \\gcd( e, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m <> 1 then\n return m;\n elif n mod 3 = 0 then\n # Here we know that m(q,e) > 2 and thus p \\not= 3.\n # Hence \\gcd( e, q^{n/3}-1 ) = 1 holds,\n # because otherwise q^{n/3} would be a p-element in (Z/eZ)^*.\n # Thus Lemma I.6.4 yields m(q,e) \\leq 3.\n # (This is a generalization of Cor. II.2.11.)\n return 3;\n elif 2 * n = Phi( e ) then\n # Cor. II.2.14.\n return 3;\n elif e mod 11 = 0 then\n # Prop. II.2.16.\n return 5;\n fi;\n fi;\n fi;\n\n # Deal with those cases where e is twice an odd prime power,\n # and where we know the value of m(q,e).\n if IsEvenInt( e ) and IsPrimePowerInt( e/2 ) then\n # see Prop. II.2.17, note that the order of q mod e is a power of p\n # if and only if \\gcd( e/2, q-1 ) \\not= 1 holds.\n m:= Gcd( e, q-1 );\n if m > 2 then\n return m;\n fi;\n fi;\n\n # We give up.\n return 0;\n end );\n\n\n#############################################################################\n##\n#F VectorIterator( m, n, s )\n##\n## iterator for all vectors of length n\n## with entries in { 0, 1, 2, ... m }\n## and coefficient sum s, such that ...\n##\n## fill the first n positions in v with smallest partition of s into\n## numbers at most m\n## (we assume that s <= m*n)\n##\nBindGlobal( \"VectorIterator_ResetPrefix\", function( v, m, n, s )\n local rest, i, j;\n\n rest:= s;\n i:= 1;\n while m < rest do\n v[i]:= m;\n rest:= rest - m;\n i:= i + 1;\n od;\n v[i]:= rest;\n for j in [ i+1 .. n ] do\n v[j]:= 0;\n od;\n\n return v;\n end );\n\nBindGlobal( \"VectorIterator\", function( m, n, s )\n local next;\n\n if s > m*n then\n # The iterator is empty.\n next:= false;\n else\n # Initialize the coefficient vector.\n next:= VectorIterator_ResetPrefix( [], m, n, s );\n fi;\n\n return IteratorByFunctions( rec(\n NextIterator:= function( iter )\n local result, pos, succ;\n\n result:= iter!.next;\n # Find the first position with a nonzero value\n # such that the value on the right is smaller than m.\n pos:= First( [ 1 .. iter!.n - 1 ],\n i -> result[i] <> 0 and result[ i+1 ] < iter!.m );\n if pos = fail then\n succ:= false;\n else\n succ:= ShallowCopy( result );\n succ[ pos ]:= result[ pos ] - 1;\n succ[ pos + 1 ]:= result[ pos + 1 ] + 1;\n VectorIterator_ResetPrefix( succ, iter!.m, pos,\n Sum( succ{ [ 1 .. pos ] } ) );\n fi;\n iter!.next:= succ;\n return result;\n end,\n\n IsDoneIterator:= iter -> ( iter!.next = false ),\n\n ShallowCopy:= function( iter )\n end,\n\n m:= m,\n n:= n,\n s:= s,\n\n next:= next,\n ) );\n end );\n\n\n#############################################################################\n##\n#F MinimalDegreeHardGAP( , , )\n##\n## - assume that the cheap criteria do not yield the result\n## (e.g., m = 2 cannot occur here)\n## - assume q < e\n## - assume that n equals OrderMod( q, e )\n## - do not use the cache\n## - do not create the monomials by computing all q-adic expansions at once,\n## but create these coefficient vectors one by one, using an iterator\n## - for increasing values of m, run over those coefficient vectors\n## of length n and with entries in \\{ 0, 1, \\ldots, m \\}\n## such that the coefficient sum is s\n## and such that a largest entry is in the first position.\n##\nInstallGlobalFunction( MinimalDegreeHardGAP, function( q, n, e )\n local z, e1, m, powers, a, v;\n\n Assert( 2, PowerMod( q, n, e ) = 1 and OrderModExt( q, e, n ) = n );\n\n # If A[q,n,z] has small dimension and e is not very small\n # then enumerate its basis.\n # (For small e, we known that the m values are small,\n # so it is cheaper not to enumerate.)\n if e > 100 then\n z:= ( q^n - 1 ) / e;\n if z <= 10^5 then\n return LoewyStructureInfoGAP( q, n, z ).m;\n fi;\n fi;\n\n # m(q,e) is divisible by \\gcd( e, q-1 ), and m(q,e) \\geq 3.\n e1:= Gcd( e, q-1 );\n if e1 = 1 then\n m:= 3;\n elif e1 = 2 then\n m:= 4;\n else\n m:= e1;\n fi;\n\n powers:= List( [ 1 .. n-1 ], i -> PowerModInt( q, i, e ) );\n\n while true do\n for a in [ 1 .. m ] do\n for v in VectorIterator( a, n-1, m-a ) do\n if ( a + v * powers ) mod e = 0 then\n return m;\n fi;\n od;\n od;\n m:= m + e1;\n od;\n end );\n\n\n#############################################################################\n##\n#M MinimalDegreeOfSingerAlgebraJulia( )\n#M MinimalDegreeOfSingerAlgebraJulia( , )\n#M MinimalDegreeOfSingerAlgebraJulia( , , )\n##\n## Use the same criteria as for the &GAP; variant.\n## These methods are available only if &Julia; is available.\n##\nif IsPackageMarkedForLoading( \"JuliaInterface\", \"\" ) then\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra and HasLoewyStructureInfoJulia\" ],\n A -> JuliaToGAP( IsInt,\n Julia.Base.get( LoewyStructureInfoJulia( A ),\n JuliaSymbol( \"m\" ), 0 ) ));\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsSingerAlgebra\" ],\n function( A )\n local paras, q, n, e;\n\n # Note that we cannot assume that the parameter 'n' is equal to\n # the multiplicative order of 'q' modulo 'e'.\n paras:= ParametersOfSingerAlgebra( A );\n q:= paras[1];\n n:= paras[2];\n e:= SingerAlgE( A );\n\n # Supply 'A' as an argument in order to set the GAP attribute.\n return JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, OrderModExt( q, e, n ), e,\n A ) );\n end );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\" ],\n { q, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, GAPToJulia( e ) ) ) );\n\nInstallMethod( MinimalDegreeOfSingerAlgebraJulia,\n [ \"IsPosInt\", \"IsPosInt\", \"IsPosInt\" ],\n { q, n, e } -> JuliaToGAP( IsInt,\n Julia.SingerAlg.MinimalDegree( q, n, GAPToJulia( e ) ) ) );\n\nfi;\n\n\n#############################################################################\n##\n#E\n\n", "meta": {"hexsha": "c2162ad72bc30d4587b9d2cc1a5abfbb585ac241", "size": 11349, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/mindeg.gi", "max_stars_repo_name": "oscar-system/SingerAlg", "max_stars_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_stars_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-09-11T10:12:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T13:37:49.000Z", "max_issues_repo_path": "gap/mindeg.gi", "max_issues_repo_name": "oscar-system/SingerAlg", "max_issues_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_issues_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-05-04T21:41:17.000Z", "max_issues_repo_issues_event_max_datetime": "2021-05-04T21:41:17.000Z", "max_forks_repo_path": "gap/mindeg.gi", "max_forks_repo_name": "oscar-system/SingerAlg", "max_forks_repo_head_hexsha": "7d303756163638d97fa3bc93dd3546b400a4122f", "max_forks_repo_licenses": ["Naumen", "Condor-1.1", "MS-PL"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.264, "max_line_length": 78, "alphanum_fraction": 0.5167856199, "num_tokens": 3457, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.4120475972484857}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(TMDCT, TIMDCT);\n\n_DCT_CONST := 2.5;\n\n\nClass(TMDCT, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> MDCT(self.params[1]).dims(),\n isReal := True,\n terminate := self >> MDCT(self.params[1]).terminate(),\n transpose := self >> TIMDCT(self.params[1]),\n SmallRandom := () -> Random([2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32]),\n normalizedArithCost := (self) >> MDCT(self.params[1]).normalizedArithCost()\n));\n\nClass(TIMDCT, TaggedNonTerminal, rec(\n abbrevs := [ N -> Checked(IsInt(N), N >= 1, [N]) ] ,\n dims := self >> IMDCT(self.params[1]).dims(),\n isReal := True,\n terminate := self >> IMDCT(self.params[1]).terminate(),\n transpose := self >> TMDCT(self.params[1]),\n SmallRandom := () -> Random([2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32]),\n normalizedArithCost := (self) >> IMDCT(self.params[1]).normalizedArithCost()\n));\n\nNewRulesFor(TMDCT, rec(\n TMDCT_DCT4_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> let(tags := t.getTags(), n := t.params[1], [[\n TDCT4(n).withTags(tags),\n TTensorI(RowVec([1,1,1]), n, AVec, AVec).withTags(tags),\n TTensorI(ColVec([0,1]), n/2, AVec, AVec).withTags(tags),\n TCompose([TTensorI(RowVec(-1), n, AVec, AVec), TPrm(J(n)), TTensorI(RowVec(1), n, AVec, AVec)]).withTags(tags),\n TTensorI(ColVec([-1,0]), n/2, AVec, AVec).withTags(tags)\n ]]),\n apply := (self, t, C, Nonterms) >> C[1] * C[2] * DirectSum(C[3], C[4], C[5])\n )\n));\n\nNewRulesFor(TIMDCT, rec(\n TIMDCT_TMDCT_tSPL := rec(\n switch := false,\n applicable := (self, t) >> true,\n children := (self, t) >> [[ TMDCT(t.params[1]).withTags(t.getTags()) ]],\n apply := (self, t, C, Nonterms) >> C[1].transpose()\n )\n));\n", "meta": {"hexsha": "ec63ff7896e12cfae165cb6d7351f3b031172a25", "size": 2089, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/mdct.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/common/mdct.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/common/mdct.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 38.6851851852, "max_line_length": 147, "alphanum_fraction": 0.5193872666, "num_tokens": 666, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6688802735722128, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.41142013306853226}} {"text": "#\n# Read(\"~/Workspace/Chevalley.gap/init.gi\"); Read(Filename(home_dir,\"load.gi\")); Read(Filename(test_dir,\"unichv.test.gi\"));\n#\n# Read(\"~/Workspace/Chevalley.gap/init.gi\"); Read(Filename(test_dir,\"unichv.test.init.gi\")); Read(Filename(test_dir,\"unichv.test.gi\"));\n#\n# Read(Filename(test_dir,\"unichv.test.gi\"));\n#\n\nsys:=Unipotent(ChevalleyAdj(\"F\",4,GF(2)),[[1,1],[2,1]]);\nPrint(\"Created Unipotent \",sys,\"\\n\");\nPrint(\"\\t[\",IsUnipotent(sys)=true,\"] IsUnipotent(sys)=true\\n\");", "meta": {"hexsha": "01d63c091130bb8b6e1fbeb4723d2992c8f43b69", "size": 472, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test/unichv.test.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test/unichv.test.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test/unichv.test.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 42.9090909091, "max_line_length": 135, "alphanum_fraction": 0.6800847458, "num_tokens": 158, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7217432182679957, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.411287286570204}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n# DebugRewriting(true);\n# spiral.rewrite.RuleTrace := PrintLine;\n# spiral.rewrite.RuleStatus := Print;\n\n# s := SumsRuleTree(DFT(3), SpiralDefaults);\n# RecursiveFindBug(s, SpiralDefaults, (t,opts) -> t.free()=[]);\n# CompareCodeMat\n\n\n# If set to 1, the permutations will not use the patented\n# streaming permutation structures.\navoidPermPatent := 0; \n\n\nInitStreamHw := () -> CopyFields(\n StreamDefaults, \n\n # Other breakdown rules are set in StreamDefaults, in init.g\n rec( \n breakdownRules := rec(\n DFTDR := [DFTDR_tSPL_Pease ],\n DRDFT := [DRDFT_tSPL_Pease_Stream ],\n DFT := [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream, DFT_Stream1_Fold, DFT_tSPL_Bluestein_Stream_Rolled, DFT_tSPL_Mixed_Radix_It, DFT_PD], #, DFT_tSPL_StreamR2R4],\n MDDFT := [MDDFT_tSPL_HorReuse_Stream],\n TDiag := [TDiag_TC_Pease, TDiag_base, TDiag_tag_stream],\n WHT := [WHT_Base, WHT_tSPL_Pease, WHT_tSPL_STerm],\n TTensorI := [IxA_base, IxA_L_base, L_IxA_base, AxI_base, IxA_L_split, L_IxA_split, \n IxA_stream_base, TTensorI_Streamtag, TTensorI_Stream_Diag_Uneven, TTensorI_Stream_Perm_Uneven],\n TTensorInd := [TTensorInd_stream_base, TTensorInd_stream_prop],\n TCompose := [TCompose_tag],\n TICompose := [TICompose_tag],\n TDirectSum := [A_dirsum_B],\n TDR := [DR_StreamPerm],\n TRC := [TRC_stream],\n TCond := [TCond_tag],\n realDFTPerm := [realDFTPerm_Stream],\n TConjEven := [TConjEven_stream],\n TConjEvenStreamBB := [TConjEvenStreamBB_base],\n rDFTSkew := [rDFT_Skew_CT, rDFT_Skew_Base4, rDFT_Skew_Pease],\n PkRDFT1 := [PkRDFT1_rDFTSkew],\n InfoNt := [Info_Base],\n\n # Switch these lines to enable Jarvinen streaming perms\n TL := [L_base, L_StreamBase, L_StreamPerm],\n #TL := [L_base, L_Stream0, L_Stream1, L_Stream2],\n\n TPrm := [TPrm_stream, TPrm_flat],\n TPrmMulti := [TPrmMulti_stream],\n\n\t#Sort := [Sort_Stream],\n\tSort := [Sort_Stream, Sort_Stream_Iter, Sort_Stream4],\n\tSortVec := [Sort_Stream_Vec, Sort_Stream4_Vec],\n ),\n profile := spiral.profiler.default_profiles.fpga_splhdl\n));\n\nInitStreamHwRDFTtoDFT := function()\n local opts;\n\n opts := InitStreamHw();\n opts.breakdownRules.PkRDFT1 := [PkRDFT1_DFT];\n opts.breakdownRules.DFT := [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream_Trans, DFT_Stream1_Fold];\n return opts;\nend;\n\nInitStreamUnrollHw := () -> CopyFields(\n StreamDefaults, \n\n # Other breakdown rules are set in StreamDefaults, in init.g\n rec(\n breakdownRules := rec(\n DFTDR := [DFTDR_tSPL_Stream ],\n DRDFT := [DRDFT_tSPL_Stream ],\n DFT := [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream, DFT_tSPL_Fold_CT, DFT_tSPL_MultRadix_Stream, DFT_tSPL_Bluestein_Stream, DFT_tSPL_Mixed_Radix_Stream, DFT_tSPL_StreamFull, DFT_PD, DFT_Stream1_Fold], #, DFT_tSPL_StreamR2R4 ],\n MDDFT := [MDDFT_tSPL_Unroll_Stream],\n Sc_DCT2 := [Sc_DCT2_Stream], \n TDCT2 := [DCT2_Stream], \n TDiag := [TDiag_tag_stream, TDiag_TIFold_It, TDiag_base],\n WHT := [WHT_Base, WHT_tSPL_Pease, WHT_tSPL_STerm],\n TTensorI := [IxA_base, IxA_L_base, L_IxA_base, AxI_base, IxA_L_split, L_IxA_split, \n IxA_stream_base, TTensorI_Streamtag, TTensorI_Stream_Diag_Uneven, TTensorI_Stream_Perm_Uneven],\n TTensorInd := [TTensorInd_stream_base, TTensorInd_stream_prop],\n TCompose := [TCompose_tag],\n TICompose := [TICompose_tag],\n TDirectSum := [A_dirsum_B],\n TDR := [DR_StreamPerm],\n TRC := [TRC_stream],\n TCond := [TCond_tag],\n realDFTPerm := [realDFTPerm_Stream],\n TConjEven := [TConjEven_stream],\n TConjEvenStreamBB := [TConjEvenStreamBB_base],\n rDFTSkew := [rDFT_Skew_CT, rDFT_Skew_Base4, rDFT_Skew_Stream, rDFT_Skew_Stream_Mult_Radices],\n PkRDFT1 := [PkRDFT1_rDFTSkew],\n InfoNt := [Info_Base],\n\n # Switch these lines to enable Jarvinen streaming perms\n TL := [L_base, L_StreamBase, L_StreamPerm],\n# TL := [L_base, L_Stream0, L_Stream1, L_Stream2]\n# TPrm := [TPrm_stream_bit_perm, TPrm_stream_not_bit_perm],\n TPrm := [TPrm_stream, TPrm_flat],\n TPrmMulti := [TPrmMulti_stream],\n ),\n profile := spiral.profiler.default_profiles.fpga_splhdl\n));\n\n\nInitStreamUnrollHwRDFTtoDFT := function()\n local opts;\n\n opts := InitStreamUnrollHw();\n opts.breakdownRules.PkRDFT1 := [PkRDFT1_DFT];\n# opts.breakdownRules.DFT := [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream_Trans, DFT_Stream1_Fold, DFT_tSPL_Fold_CT];\n return opts;\nend;\n\n\n# a = 0 to make outer prod streaming, a=1 to make it HR\n# b = 0 to make inner prod streaming, b=1 to make it HR\nInitStreamMultiLevel := (a, b) -> CopyFields(\n StreamDefaults, \n\n # Other breakdown rules are set in StreamDefaults, in init.g\n rec(\n breakdownRules := rec(\n DFTDR := Cond(b=0, [DFTDR_tSPL_Stream], [DFTDR_tSPL_Pease]),\n DRDFT := Cond(b=0, [DRDFT_tSPL_Stream ], [DRDFT_tSPL_Pease_Stream]),\n DFT := Cond(a=0, \n [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream, DFT_tSPL_Fold_CT, DFT_tSPL_Bluestein_Stream], \n [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream, DFT_tSPL_Fold_CT, DFT_tSPL_Bluestein_Stream_Rolled]\n ),\n MDDFT := Cond(a=0, [MDDFT_tSPL_Unroll_Stream], [MDDFT_tSPL_HorReuse_Stream]),\n TDiag := [TDiag_tag_stream, TDiag_TIFold_It, TDiag_base, TDiag_TC_Pease],\n WHT := [WHT_Base, WHT_tSPL_Pease, WHT_tSPL_STerm],\n TTensorI := [IxA_base, IxA_L_base, L_IxA_base, AxI_base, IxA_L_split, L_IxA_split, \n IxA_stream_base, TTensorI_Streamtag],\n TCompose := [TCompose_tag],\n TICompose := [TICompose_tag],\n TDirectSum := [A_dirsum_B],\n TDR := [DR_StreamPerm],\n TRC := [TRC_stream],\n TCond := [TCond_tag],\n \n # Switch these lines to enable Jarvinen streaming perms\n TL := [L_base, L_StreamBase, L_StreamPerm],\n # TL := [L_base, L_Stream0, L_Stream1, L_Stream2]\n TPrm := [TPrm_stream, TPrm_flat],\n TPrmMulti := [TPrmMulti_stream],\n ),\n profile := spiral.profiler.default_profiles.fpga_splhdl\n));\n\n\nInitStreamAllHw := () -> CopyFields(\n StreamDefaults, \n\n # Other breakdown rules are set in StreamDefaults, in init.g\n rec(\n breakdownRules := rec(\n DFTDR := [DFTDR_tSPL_Stream, DFTDR_tSPL_Pease ],\n DRDFT := [DRDFT_tSPL_Stream ],\n DFT := [DFT_Base, DFT_HW_CT, DFT_tSPL_Stream, DFT_tSPL_Fold_CT] ,# DFT_tSPL_StreamR2R4],\n MDDFT := [MDDFT_tSPL_Unroll_Stream, MDDFT_tSPL_HorReuse_Stream],\n TDiag := [TDiag_tag_stream, TDiag_TIFold_It, TDiag_base, TDiag_TC_Pease],\n WHT := [WHT_Base, WHT_tSPL_Pease, WHT_tSPL_STerm],\n TTensorI := [IxA_base, IxA_L_base, L_IxA_base, AxI_base, IxA_L_split, L_IxA_split, \n IxA_stream_base, TTensorI_Streamtag],\n TCompose := [TCompose_tag],\n TICompose := [TICompose_tag],\n TDirectSum := [A_dirsum_B],\n TDR := [DR_StreamPerm],\n TRC := [TRC_stream],\n TCond := [TCond_tag],\n \n # Switch these lines to enable Jarvinen streaming perms\n TL := [L_base, L_StreamPerm]\n # TL := [L_base, L_Stream0, L_Stream1, L_Stream2]\n ),\n profile := spiral.profiler.default_profiles.fpga_splhdl\n));\n\n\n\nstreamRealDFT := function(trn, radix, opts, unroll)\n local rt, srt, srt2, srt3, srt4;\n\n rDFT_Skew_Pease.unroll_its := unroll;\n rDFT_Skew_Pease.radix := radix;\n rDFT_Skew_Stream.radix := radix;\n\n # set radix for complex DFT rules in case I am using half-size method\n DFT_tSPL_Stream.radix := radix;\n DFT_tSPL_Stream_Trans.radix := radix;\n DFTDR_tSPL_Pease.unroll_its := unroll;\n DRDFT_tSPL_Pease_Stream.unroll_its := unroll;\n\n rt := RandomRuleTree(trn, opts);\n srt := SumsRuleTreeStrategy(rt, SumStreamStrategy, opts);\n\n # I don't understand what's going on here.\n # For some reason, this line messes everything up when I try the half-size complex\n # RDFT method, but I can't figure out what it is. \n#! srt2 := ApplyStrategy(srt, RuleRDFTStrategy, UntilDone, opts);\n \n # So, this is a temporary hack to make half-size compex gen. work\n srt2 := ApplyStrategy(srt, StreamStrategy, UntilDone, opts);\n\n\n srt3 := Process_fPrecompute(srt2, opts);\n srt4 := srt3.createCode();\n return srt4;\n \nend;\n \n\nstreamRDFTSkew := function(size, skew, radix, width, unroll)\n local k, m, logM, opts, t;\n\n k := radix/2;\n m := size/radix;\n logM := LogInt(m,k);\n\n if ((logM+1)/unroll = 1) then\n opts := InitStreamUnrollHw();\n else\n opts := InitStreamHw();\n fi;\n\n t := rDFTSkew(size,V(skew)).withTags([AStream(width)]);\n\n return streamRealDFT(t, radix, opts, unroll);\nend;\n\n\nstreamRDFTSkewUnroll := function(size, skew, radix, width)\n return streamRDFTSkew(size, skew, radix, width, LogInt((size/radix),(radix/2))+1);\nend;\n\n\nstreamRDFT := function(size, radix, width, unroll, method)\n # method = 1 for native RDFT algorithms, 2 for half-size complex RDFT\n\n local k, m, logM, opts, t;\n\n k := radix/2;\n m := size/radix;\n\n if (method = 1) then\n logM := LogInt(m,k);\n if ((logM+1)/unroll = 1) then\n opts := InitStreamUnrollHw();\n else\n opts := InitStreamHw();\n fi;\n fi;\n\n if (method = 2) then\n\n # Keep in mind that if you request an \"unrolling\" 1 basic block with an incompatible radix, it will\n # unroll here. E.g., (32,8,16,1,2)\n if (LogInt(size/2, radix) = unroll) then\n opts := InitStreamUnrollHwRDFTtoDFT();\n else\n opts := InitStreamHwRDFTtoDFT();\n fi;\n fi;\n \n\n t := PkRDFT1(size,1).withTags([AStream(width)]);\n\n return streamRealDFT(t, radix, opts, unroll);\nend;\n\n\nstreamRDFTPease := function(size, radix, width, unroll)\n return streamRealDFT(\n PkRDFT1(size,1).withTags([AStream(width)]),\n radix,\n InitStreamHw(), \n unroll);\nend;\n \nstreamRDFTUnroll := function(size, radix, width, method)\n return streamRDFT(size, radix, width, LogInt((size/radix),(radix/2))+1, method);\nend;\n\n\nstreamDFT := function(trn, radix, opts)\n local rt, srt, srt2, srt3, srt4, opts;\n \n# DFT_tSPL_Stream.minRadix := radix;\n# DFT_tSPL_Stream.maxRadix := radix;\n DFT_tSPL_Stream.radix := radix;\n\n \n rt := RandomRuleTree(trn, opts);\n srt := SumsRuleTreeStrategy(rt, SumStreamStrategy, opts);\n srt2 := ApplyStrategy(srt, StreamStrategy, UntilDone, opts);\n srt3 := Process_fPrecompute(srt2, opts);\n srt4 := srt3.createCode();\n \n return srt4; \nend;\n\n# Fully unrolled. \nstreamDFTNoFold := function(n,k)\n local t, r, s, s2, s3, s4, opts;\n \n opts := InitStreamHw();\n t := RC(DFT(n,k));\n r := RandomRuleTree(t, SpiralDefaults);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := Process_fPrecompute(s2, opts);\n s4 := s3.createCode();\n return s4;\nend;\n\n \nTestRandomPerm := function(size, width)\n local p, s;\n p := RandomPerm(size);\n s := StreamPerm([p], 1, width, 0);\n return MatSPL(p) - MatSPL(s.createCode());\nend;\n\nStreamRandomPerm := function(size, width)\n local s;\n s := StreamPerm([RandomPerm(size)], 1, width, 0);\n return s.createCode();\nend;\n\nStreamRandomPerms := function(size, width, number)\n local it, s, s2;\n it := Ind(number);\n s := StreamPerm(List([1..number], i->RandomPerm(size)), 1, width, it);\n s2 := ICompose(it, number, s);\n return s2.createCode();\nend;\n\n\nMyPermTest := function()\n local t0, t1, w, p, s, s2,h;\n p := RandomPerm(4096);\n Print(\"finished generating the random perm\\n\");\n\n # 0 = random\n# stream._whichMeth := 0;\n\n# for w in [2,4,8,16,32,64,128,256, 512] do\n \n# for h in [1,2] do\n# paradigms.stream._whichMeth := h;\n for w in [2,4,8,16,32,64] do\n t0 := TimeInSecs();\n s := StreamPerm(p, 1, w);\n s2 := s.createCode();\n t1 := TimeInSecs();\n Print(\"meth=\", stream._whichMeth, \", width=\", w, \", time=\", t1-t0, \"\\n\");\n od;\n# od;\nend;\n \nNewPermTest := function()\n local t0, t1, w,p,s,s2;\n \n p := RandomPerm(4096);\n\n t0 := TimeInSecs();\n s := StreamPerm(p, 1, 256);\n s2 := s.createCode();\n t1 := TimeInSecs();\n Print(\"time = \", t1-t0, \"\\n\");\nend;\n\nstreamGen := function(SPL, opts)\n local rt, srt, srt2, srt3, srt4;\n rt := RandomRuleTree(SPL, opts);\n srt := SumsRuleTreeStrategy(rt, SumStreamStrategy, opts);\n srt2 := ApplyStrategy(srt, StreamStrategy, UntilDone, opts);\n srt3 := Process_fPrecompute(srt2, opts);\n srt4 := srt3.createCode();\n \n return srt4; \nend;\n\n\nstreamDCTUnroll := function(size, width)\n return streamGen(TDCT2(size).withTags([AStream(width)]), InitStreamUnrollHw());\nend;\n\nstreamDFTUnroll := function(size, radix, width)\n return streamDFT(TRC(DFT(size, -1)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\nend;\n\n#streamIDFTUnroll := function(size, radix, width)\n# return streamDFT(TRC(DFT(size, 1)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\n#end;\n\nstreamDFTDRUnroll := function(size, radix, width)\n return streamDFT(TRC(DFTDR(size, 1, radix)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\nend;\n\nstreamDRDFTUnroll := function(size, radix, width)\n return streamDFT(TRC(DRDFT(size, 1, radix)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\nend;\n\nstreamIDFTUnroll := function(size, radix, width)\n if (width <= 2*size) then\n return streamDFT(TRC(DFT(size, -1)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\n else\n return streamDFT(TRC(TTensorI(DFT(size, -1), width/(2*size), APar, APar)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\n fi;\nend;\n\nstreamIDFTDRUnroll := function(size, radix, width)\n return streamDFT(TRC(DFTDR(size, -1, radix)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\nend;\n\nstreamDRIDFTUnroll := function(size, radix, width)\n return streamDFT(TRC(DRDFT(size, -1, radix)).withTags([AStream(width)]), radix, InitStreamUnrollHw());\nend;\n\n\nstreamDFTPease := function(size, radix, width, unroll)\n DFTDR_tSPL_Pease.unroll_its := unroll;\n return streamDFT(TRC(DFT(size, 1)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\nstreamDFTDRPease := function(size, radix, width)\n return streamDFT(TRC(DFTDR(size, 1, radix)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\nstreamDRDFTPease := function(size, radix, width)\n return streamDFT(TRC(DRDFT(size, 1, radix)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\nstreamIDFTPease := function(size, radix, width, unroll)\n DFTDR_tSPL_Pease.unroll_its := unroll;\n return streamDFT(TRC(DFT(size, -1)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\nstreamIDFTDRPease := function(size, radix, width)\n return streamDFT(TRC(DFTDR(size, -1, radix)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\nstreamDRIDFTPease := function(size, radix, width)\n return streamDFT(TRC(DRDFT(size, -1, radix)).withTags([AStream(width)]), radix, InitStreamHw());\nend;\n\n\n# countPerms := function(s)\n# local perms, l;\n# perms := Collect(s, BRAMPerm);\n# l := List([1..Length(perms)], i->perms[i].dimensions[1]);\n# Sort(l);\n# return Reversed(l);\n# end;\n\n\n\nHDLPrint := function(t, p, r, x)\n Print(\"points(\", p, \")\\n\");\n Print(\"threshold(\", t, \")\\n\");\n Print(\"radix(\", r, \")\\n\");\n Print(x);\nend;\n\nHDLPrint2 := function(w, w2, t, p, r, x)\n Print(\"points(\", p, \")\\n\");\n Print(\"threshold(\", t, \")\\n\");\n Print(\"radix(\", r, \")\\n\");\n Print(x);\nend;\n\nHDLPrint3 := HDLPrint;\n\n#! This is the code that changes how we deal with Complex mults.\n# RCDiag.code := meth(self, y, x)\n# local i, elt, re, im, rct;\n# i := Ind();\n# elt := self.element.lambda();\n# re := elt.at(2 * i);\n# im := elt.at(2*i+1);\n\n# rct := var(\"rct\");\n \n# return loop(i, Rows(self) / 2, \n# chain( \n# assign(nth(rct, (2*i)), mul(re, nth(x, (2*i)))),\n# assign(nth(rct, (2*i+1)), mul(im, nth(x, (2*i+1)))),\n# assign(nth(y, 2*i), nth(rct, 2*i) - nth(rct, 2*i+1)),\n# assign(nth(y, 2*i+1), mul((re + im), (nth(x, 2*i) + nth(x, 2*i+1))) - \n# nth(rct, 2*i) - nth(rct, 2*i+1))\n# )\n# );\n# end;\n\nCodeRCDiag42 := RCDiag.code;\nCodeRCDiag33 := meth(self, y, x)\n local i, elt, re, im, rct;\n i := Ind();\n elt := self.element.lambda();\n re := elt.at(2 * i);\n im := elt.at(2*i+1);\n rct := var(\"rct\");\n \n return loop(i, Rows(self) / 2, \n chain( \n assign(nth(rct, (2*i)), mul(re, nth(x, (2*i)))),\n assign(nth(rct, (2*i+1)), mul(im, nth(x, (2*i+1)))),\n assign(nth(y, 2*i), nth(rct, 2*i) - nth(rct, 2*i+1)),\n assign(nth(y, 2*i+1), mul((re + im), (nth(x, 2*i) + nth(x, 2*i+1))) - \n nth(rct, 2*i) - nth(rct, 2*i+1))\n )\n );\n end;\n\n# hack\nfCompose.dims := self >> [self.n, self.n];\nfCompose.sums := self >> self.child(1) * self.child(2);\n\n\n# n = size\n# r = radix\n# w = width\n# outer is the amount of times to unroll outer loop (1 or 2)\n# inner is the amount of times to unroll inner loop \nstream2DDFT := function(n, r, w, outer, inner)\n local srt, strat, strat2, opts;\n\n opts := InitStreamMultiLevel(Cond(outer=1, 1, 0), Cond(inner=LogInt(n, r), 0, 1));\n MDDFT_tSPL_Unroll_Stream.minRadix := r;\n MDDFT_tSPL_Unroll_Stream.maxRadix := r;\n MDDFT_tSPL_HorReuse_Stream.minRadix := r;\n MDDFT_tSPL_HorReuse_Stream.maxRadix := r;\n\n DFTDR_tSPL_Pease.unroll_its := inner;\n\n srt := SumsRuleTreeStrategy(\n RandomRuleTree(\n TRC(MDDFT([n,n])).withTags([AStream(w)]), \n opts), \n SumStreamStrategy, opts);\n\n strat := Process_fPrecompute(\n ApplyStrategy(srt, StreamStrategy, \n UntilDone, opts), \n opts);\n \n strat2 := strat.createCode();\n return strat2;\nend;\n\n\n# n = size\n# r = radix\n# w = width\n# outer is the amount of times to unroll outer loop (1 or 2)\n# inner is the amount of times to unroll inner loop \nstreamBluesteinDFT := function(n, r, w, outer, inner)\n local opts, t, r, s, s2, s3, s4, k;\n\n # Only works for non-two power n. \n k := 2^(Log2Int(2*n) + 1);\n\n opts := InitStreamMultiLevel(Cond(outer=1, 1, 0), Cond(inner=LogInt(k, r), 0, 1));\n DFT_tSPL_Stream.radix := r;\n\n DFTDR_tSPL_Pease.unroll_its := inner;\n DRDFT_tSPL_Pease_Stream.unroll_its := inner;\n\n t := TRC(DFT(n)).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := Process_fPrecompute(s2, opts);\n s4 := s3.createCode();\n\n return s4;\nend;\n\n\n_AbsFloatMat := function(v)\n local l, i, res, j;\n res := [];\n l := Length(v[1]);\n for i in [1..l] do\n res[i] := [];\n for j in [1..l] do\n res[i][j] := AbsFloat(v[i][j]);\n od;\n od;\n return res;\nend;\n\n_MaxAbsMat := function(m)\n local res, l, i, j;\n res := 0;\n l := Length(m[1]);\n for i in [1..l] do\n for j in [1..l] do\n if (res < AbsFloat(m[i][j])) then\n res := m[i][j];\n fi;\n od;\n od;\n return res;\nend;\n\n_MaxMat := function(m)\n local res, l, i, j;\n res := 0;\n l := Length(m[1]);\n for i in [1..l] do\n for j in [1..l] do\n if (res < m[i][j]) then\n res := m[i][j];\n fi;\n od;\n od;\n return res;\nend;\n\n_AvgMat := function(m)\n local res, l, i, j;\n res := 0;\n l := Length(m[1]);\n for i in [1..l] do\n for j in [1..l] do\n res := res + m[i][j];\n od;\n od;\n res := res / (l*l);\n return res;\nend;\n\n_MaxAbsVec := function(m)\n local res, l,i;\n res := 0;\n l := Length(m);\n for i in [1..l] do\n if (AbsFloat(m[i]) > res) then\n res := AbsFloat(m[i]);\n fi;\n od;\n return res;\nend;\n\n_setHDLDataType := function(t, w)\n spiral.profiler.default_profiles.fpga_splhdl.makeopts.DATATYPE := ConcatenationString(t, \" \", StringInt(w));\nend;\n\n_setHDLTwidWidth := function(w)\n spiral.profiler.default_profiles.fpga_splhdl.makeopts.TWIDTYPE := ConcatenationString(\"-fixtw\", \" \", StringInt(w));\nend;\n\n_setFixPointMode := function(w)\n spiral.paradigms.stream._setHDLDataType(\"fix\", w);\n spiral.profiler.default_profiles.fpga_splhdl.makeopts.TWIDTYPE := \"\";\nend;\n\n_setFloatMode := function()\n spiral.paradigms.stream._setHDLDataType(\"flt\", 1);\n spiral.profiler.default_profiles.fpga_splhdl.makeopts.TWIDTYPE := \"\";\nend;\n\n\n\n##\n## Note regarding E, omega:\n## omega(a,b) = E(a)^b = exp(2*pi*i*b/a)\n##\n## \n\n\nstreamTransDFT := (n,r,w) >> streamDFT(TRC(TCompose([TDR(n,r), DRDFT(n,-1,r)])).withTags([AStream(w)]), r, InitStreamHw());\n\nHDLCompile := function(t, name, dir)\n local opts;\n \n opts := InitStreamHw();\n\n opts.profile.outdir := ConcatenationString(\"/Users/pam/run/\", String(dir));\n opts.profile.makeopts.OUTNAME := ConcatenationString(String(name), \".v\");\n opts.profile.makeopts.GAP := ConcatenationString(String(name), \".spl\");\n opts.profile.makeopts.WRAP := \"-wrap -r -l\"; \n\n Print(name, \"\\n\");\n\n return CMeasure(t, opts);\n\nend;\n\nHDLCompileASIC := function(t, name, dir, freq)\n local opts;\n opts := InitStreamHw();\n\n opts.profile.outdir := ConcatenationString(\"/afs/scotch/usr/pam/run/\", String(dir));\n opts.profile.makeopts.OUTNAME := ConcatenationString(String(name), \".v\");\n opts.profile.makeopts.GAP := ConcatenationString(String(name), \".spl\");\n opts.profile.makeopts.WRAP := ConcatenationString(\"-r -l -bb -af \", String(freq)); \n\n Print(name, \"\\n\");\n\n return CMeasure(t, opts);\nend;\n\n\nHDLCompileFloat := function(t, name, dir)\n local opts;\n \n opts := InitStreamHw();\n\n opts.profile.outdir := ConcatenationString(\"/afs/scotch/usr/pam/run/\", String(dir));\n opts.profile.makeopts.OUTNAME := ConcatenationString(String(name), \".v\");\n opts.profile.makeopts.GAP := ConcatenationString(String(name), \".spl\");\n opts.profile.makeopts.DATATYPE := \"flt 1\";\n# opts.profile.makeopts.WRAP := \"-r -l -br 1152\"; \n opts.profile.makeopts.WRAP := \"-r -l -af 1000 -bb\"; \n\n Print(name, \"\\n\");\n\n return CMeasure(t, opts);\n\nend;\n\nHDLCompileDouble := function(t, name, dir)\n local opts;\n \n opts := InitStreamHw();\n\n opts.profile.outdir := ConcatenationString(\"/afs/scotch/usr/pam/run/\", String(dir));\n opts.profile.makeopts.OUTNAME := ConcatenationString(String(name), \".v\");\n opts.profile.makeopts.GAP := ConcatenationString(String(name), \".spl\");\n opts.profile.makeopts.DATATYPE := \"flt 2\";\n opts.profile.makeopts.WRAP := \"-r -l -br 1152\"; \n\n Print(name, \"\\n\");\n\n return CMeasure(t, opts);\n\nend;\n\nHDLCompileIntel := function(name, t, bw, freq)\n local opts, res;\n spiral.paradigms.stream._setHDLDataType(\"fix\", bw);\n\n opts := InitStreamHw();\n \n opts.profile.makeopts.OUTNAME := ConcatenationString(String(name), \".v\");\n opts.profile.makeopts.GAP := ConcatenationString(String(name), \".spl\");\n opts.profile.makeopts.WRAP := ConcatenationString(\"-lic -af \", String(freq), \" -s -r -v\");\n res := CMeasure(t, opts);\n\n return res;\nend;\n\n# For what we are doing now, we need to turn on scaling + license \n# also: get rid of wrapper\nrunIntel := function()\n local t;\n t := streamDFTNoFold(128,-1); # -1 for forward, 1 for inverse\n HDLCompileIntel(\"ifft-128-6.spl\", t, 6);\n HDLCompileIntel(\"ifft-128-8.spl\", t, 8);\n HDLCompileIntel(\"ifft-128-10.spl\", t, 10);\n HDLCompileIntel(\"ifft-128-12.spl\", t, 12);\n HDLCompileIntel(\"ifft-128-14.spl\", t, 14);\n HDLCompileIntel(\"ifft-128-16.spl\", t, 16);\nend;\n\n\ncheckRules := (rls, ob) >> Filtered(rls, i->i.applicable(ob));\n\n\npeaseSW := meth(n)\n local r, k, t, s, s2, s3, s4, opts;\n opts := InitStreamHw();\n k := Log2Int(n);\n t := RC(Compose(List([0..k-1], i->L(n,2) * Tensor(I(n/2), DFT(2)) * TDiag(fPrecompute(TC(n, 2, i, -1))))) * DR(n, 2));\n r := RandomRuleTree(t, spiral.SpiralDefaults);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := Process_fPrecompute(s2, opts);\n s4 := s3.createCode();\n return s4;\nend;\n\n# Generate fully unfolded Pease hardware\n# peaseSWR(n, r, inv, dir);\n# n: problem size\n# r: radix\n# inv: 0 for DFT, 1 for IDFT\n# dir: 0 for bit reversal on input side, 1 for bit reversal on output side\npeaseSWR := meth(n, r, inv, dir)\n local k, t, s, s2, s3, s4, invparam, opts, t;\n opts := InitStreamHw();\n k := LogInt(n,r);\n\n if (inv = 0) then\n invparam := -1;\n else\n invparam := 1;\n fi;\n\n if (dir = 0) then\n t := RC(Compose(List([0..k-1], i->L(n,r) * Tensor(I(n/r), DFT(r, invparam)) * TDiag(fPrecompute(TC(n, r, i, invparam))))) * DR(n, r));\n else\n t := RC(DR(n, r) * Compose(List([0..k-1], i->\n\t TDiag(fPrecompute(TC(n, r, k-1-i, invparam))) *\n\t\t Tensor(I(n/r), DFT(r, invparam)) * \n\t\t L(n,n/r) \n )));\n fi;\n\n r := RandomRuleTree(t, spiral.SpiralDefaults);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := Process_fPrecompute(s2, opts);\n s4 := s3.createCode();\n return s4;\nend;\n\nctSW := meth(n)\n local r, k, t, s, s2, s3, s4, opts;\n opts := InitStreamHw();\n k := Log2Int(n);\n t := RC(Compose(List([0..k-1], i-> Tensor(I(2^i), DFT(2), I(2^(k-i-1))) * Tensor(I(2^i), TDiag(fPrecompute(Tw1(2^(k-i), 2^(k-i-1), 1)))))) * DR(n, 2));\n r := RandomRuleTree(t, spiral.SpiralDefaults);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := Process_fPrecompute(s2, opts);\n s4 := s3.createCode();\n return s4;\nend;\n\n_splhdl_path := \"\";\n_synth_path := \"\";\n\n# HDLSynthesize(transform, platform, format, precision, frequency, filename)\n# platform: 0 for 65nm ASIC, 1 for FPGA\n# format: 0 for fixed point, 1 for floating point\n# precision: # bits precision, ignored for floating point\n# wrapper: 0 for normal mode, 1 to use a wrapper for synthesizing wide designs on FPGA\nHDLSynthesize := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n \n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := 1440;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n if (_synth_path = \"\") then\n\tError(\"Error: path to synthesis scripts not set: paradigms.stream._synth_path is not bound.\");\n fi;\n\n #cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -stb -o \", path, filename, \".v -r -l \");\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", frequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && \", _synth_path, \" \", filename, \".v \", StringDouble(\"%f\", frequency));\n fi;\n\n Exec(cmdString);\nend;\n\nHDLSynthesize_no_brams := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n \n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := 0;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n if (_synth_path = \"\") then\n\tError(\"Error: path to synthesis scripts not set: paradigms.stream._synth_path is not bound.\");\n fi;\n\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", frequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && \", _synth_path, \" \", filename, \".v \", StringDouble(\"%f\", frequency));\n fi;\n\n Exec(cmdString);\nend;\n\nHDLSynthesize_x5 := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n \n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := 1440;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n if (_synth_path = \"\") then\n\tError(\"Error: path to synthesis scripts not set: paradigms.stream._synth_path is not bound.\");\n fi;\n\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", frequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && \", _synth_path, \" \", filename, \".v \", StringDouble(\"%f\", frequency));\n fi;\n\n Exec(cmdString);\nend;\n\nHDLSynthesize_no_brams_x5 := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n \n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := 0;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n if (_synth_path = \"\") then\n\tError(\"Error: path to synthesis scripts not set: paradigms.stream._synth_path is not bound.\");\n fi;\n\n #cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -stb -o \", path, filename, \".v -r -l \");\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", frequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && \", _synth_path, \" \", filename, \".v \", StringDouble(\"%f\", frequency));\n fi;\n\n Exec(cmdString);\nend;\n\nHDLSynthesize_stb := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n \n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := 1440;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n if (_synth_path = \"\") then\n\tError(\"Error: path to synthesis scripts not set: paradigms.stream._synth_path is not bound.\");\n fi;\n\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -pp -stb -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", frequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && \", _synth_path, \" \", filename, \".v \", StringDouble(\"%f\", frequency));\n fi;\n\n Exec(cmdString);\nend;\n\n\n\n# HDLSynthesize2(transform, platform, format, precision, genfrequency, synthfrequency, filename)\n# platform: 0 for 65nm ASIC, 1 for FPGA\n# format: 0 for fixed point, 1 for floating point\n# precision: # bits precision, ignored for floating point\n# wrapper: 0 for normal mode, 1 to use a wrapper for synthesizing wide designs on FPGA\nHDLSynthesize2 := function(t, platform, format, precision, genfrequency, synthfrequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n\n path := \"/afs/scotch/usr/pam/res/\"; \n brams := 256;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n cmdString := ConcatenationString(\"/afs/scotch/usr/pam/splhdl/src/splhdl \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", genfrequency));\n else #FPGA\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\n # Ok, now file is generated. Time to synthesize.\n\n if (platform = 0) then\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/dc_scripts/run-synth.pl \", filename, \".v \", StringDouble(\"%f\", synthfrequency));\n else\n\tcmdString := ConcatenationString(\"cd \", path, \" && /afs/scotch/usr/pam/synth/synthfpga.pl \", filename, \".v \", StringDouble(\"%f\", synthfrequency));\n fi;\n\n Exec(cmdString);\nend;\n\n# HDLGen(transform, platform, format, precision, frequency, filename)\n# platform: 0 for 65nm ASIC, 1 for FPGA\n# format: 0 for fixed point, 1 for floating point, 2 for double\n# precision: # bits precision, ignored for floating point\n# wrapper: 0 for normal mode, 1 to use a wrapper for synthesizing wide designs on FPGA\nHDLGen := function(t, platform, format, precision, frequency, wrapper, filename)\n local opts, cmdString, path, brams, wrapString;\n\n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n MakeDir(path);\n brams := -1;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -r -l \");\n\n if (wrapper = 1) then\n\twrapString := \" -wrap\";\n else\n\twrapString := \"\";\n fi;\n\n # ASIC\n if (platform = 0) then\n\tcmdString := ConcatenationString(cmdString, \"-bb -af \", StringDouble(\"%f\", frequency));\n elif (brams = -1) then\n\tcmdString := ConcatenationString(cmdString, \" \", wrapString);\n else\n\tcmdString := ConcatenationString(cmdString, \"-br \", StringInt(brams), \" \", wrapString);\n fi;\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n elif (format = 1) then\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 2 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\treturn path;\nend;\n\nsortVecAlg1 := function(size, w)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.SortVec := [Sort_Stream_Vec];\n\n t := SortVec(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortVecAlg5 := function(size, w, d)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.SortVec := [Sort_Stream4_Vec];\n Sort_Stream4_Vec.depth := d;\n\n t := SortVec(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg1 := function(size, w)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream];\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg6 := function(size, w)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream6];\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg2 := function(size, w, d)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream_Iter];\n Sort_Stream_Iter.depth_params := d;\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg5 := function(size, w, d)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream5];\n Sort_Stream5.depth_params := d;\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg3 := function(size, w, d_out, d_in)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream3];\n Sort_Stream3.depth_out := d_out;\n Sort_Stream3.depth_in := d_in;\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortAlg4 := function(size, w, d)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Sort_Stream4];\n Sort_Stream4.depth := d;\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\nsortLinear := function(size,w)\n local opts, t, r, s, s2, s3;\n opts := InitStreamHw();\n opts.breakdownRules.Sort := [Linear_Sort];\n\n t := Sort(size).withTags([AStream(w)]);\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := ApplyStrategy(s, StreamStrategy, UntilDone, opts);\n s3 := s2.createCode();\n return s3;\nend;\n\n\n\nrunThisOFDMTx := function(size, radix, w, bits, freqs)\n local t, i, name;\n\n t := streamIDFTUnroll(size, radix, 2*w);\n for i in [1..Length(bits)] do\n name := ConcatenationString(\"ifft\", String(size), \"w\", String(w), \"b\", String(bits[i]), \"f\", String(freqs[i]));\n HDLGen(t, 0, 0, bits[i], freqs[i], 0, name);\n od;\nend;\n\nrunThisOFDMRx := function(size, radix, w, bits, freqs)\n local t, i, name;\n\n t := streamDFTUnroll(size, radix, 2*w);\n for i in [1..Length(bits)] do\n name := ConcatenationString(\"fft\", String(size), \"w\", String(w), \"b\", String(bits[i]), \"f\", String(freqs[i]));\n HDLGen(t, 0, 0, bits[i], freqs[i], 0, name);\n od;\nend;\n \nrunJobsOFDMTx := function()\n runThisOFDMTx(128, 16, 128,[12, 12, 14, 14, 14, 14, 15], [250, 167.2, 125, 100, 83.6, 71.1, 62.5]);\n runThisOFDMTx(128, 16, 64, [12, 12, 14, 14, 14, 14, 15], [500, 334.4, 250, 200, 167.2, 142.2, 125]);\n runThisOFDMTx(128, 16, 32, [12, 12, 14, 14, 14, 14, 15], [1000, 668.8, 500, 400, 334.4, 284.4, 250]);\n runThisOFDMTx(128, 16, 16, [12, 14, 14, 14, 14, 15], [1337.5, 1000, 800, 668.8, 568.8, 500]);\n runThisOFDMTx(128, 8, 8, [14, 14, 15], [1337.5, 1137.5, 1000]);\nend;\n\nrunJobsOFDMRx := function()\n runThisOFDMRx(128, 16, 128, [14, 14, 15, 15, 16, 16, 16], [250, 167.2, 125, 100, 83.6, 71.1, 62.5]);\n runThisOFDMRx(128, 16, 64, [14, 14, 15, 15, 16, 16, 16], [500, 334.4, 250, 200, 167.2, 142.2, 125]);\n runThisOFDMRx(128, 16, 32, [14, 14, 15, 15, 16, 16, 16], [1000, 668.8, 500, 400, 334.4, 284.4, 250]);\n runThisOFDMRx(128, 16, 16, [14, 15, 15, 16, 16, 16], [1337.5, 1000, 800, 668.8, 568.8, 500]);\n runThisOFDMRx(128, 8, 8, [16, 16, 16], [1337.5, 1137.5, 1000]);\nend;\n\n# I needed to increase the pipelining of mults for the fast cores.\nreRunOFDMTx := function()\n runThisOFDMTx(128, 16, 32, [12], [1000]);\n runThisOFDMTx(128, 16, 16, [12], [1337.5]);\n runThisOFDMTx(128, 16, 16, [14], [1000]);\n runThisOFDMTx(128, 8, 8, [14], [1337.5]);\n runThisOFDMTx(128, 8, 8, [14], [1137.5]);\n runThisOFDMTx(128, 8, 8, [15], [1000]);\nend;\n\nfourStepTest := (n, u) >> let(\n t0 := Tensor(L(n^2/u, n), I(u)),\n t1 := Tensor(I(n/u), L(n*u, n) * Tensor(I(u), DFT(n)) * (Tensor(L(n,u), I(u)))),\n t2 := Tensor(Tensor(I(n/u), L(n, n/u)), I(u)),\n t3 := Tensor(L(n*n/u, n), I(u)),\n p := Tensor(L(n*n/u, n), I(u)) * Tensor(I(n*n/(u*u)), L(u*u,u)) * Tensor(I(n/u), L(n, n/u), I(u)) * Tensor(L(n*n/u, n), I(u)),\n t4 := TransposedSPL(p) * Diag(Tw1(n*n,n,1)) * p,\n t5 := Tensor(I(n/u), L(n*u, n) * Tensor(I(u), DFT(n)) * L(n*u,u)),\n t6 := Tensor(L(n*n/u, n/u), I(u)),\n t0*t1*t2*t3*t4*t5*t6\n);\n\nfourStepTest2 := (n, u) >> let(\n t0 := Tensor(L(n^3/u, n), I(u)),\n t1 := Tensor(I(n*n/u), L(n*u, n) * Tensor(I(u), DFT(n)) * (Tensor(L(n,u), I(u)))),\n t2 := Tensor(Tensor(I(n*n/u), L(n, n/u)), I(u)),\n t3 := Tensor(L(n*n*n/u, n), I(u)),\n p2 := Tensor(L(n*n*n/u, n), I(u)) * Tensor(I(n*n*n/(u*u)), L(u*u,u)) * Tensor(I(n*n/u), L(n, n/u), I(u)) * Tensor(L(n*n*n/u, n), I(u)),\n t4 := TransposedSPL(p2) * Diag(Tw1(n*n*n,n*n,1)) * p2,\n t5 := Tensor(I(n*n/u), L(n*u, n) * Tensor(I(u), DFT(n)) * L(n*u,u)),\n t6 := Tensor(L(n*n*n/u, n*n/u), I(u)),\n t7 := Tensor(L(n*n,n), I(n)),\n t8 := Tensor(L(n*n*n/u, n), I(u)),\n p := Tensor(L(n*n, n), I(n)) * Tensor(L(n*n*n/u, n), I(u)),\n t9 := TransposedSPL(p) * Tensor(Diag(Tw1(n*n,n,1)), I(n)) * p,\n t10 := Tensor(I(n*n/u), L(n*u, n) * Tensor(I(u), DFT(n)) * L(n*u,u)),\n t11 := Tensor(L(n*n*n/u, n*n/u), I(u)),\n t0 * t1 * t2 * t3 * t4 * t5 * t6 * t7 * t8 * t9 * t10 * t11\n);\n\nrunRachid2 := function(size, radix, w, bits)\n local t, i, name;\n\n t := streamDFTUnroll(size, radix, 2*w);\n for i in [1..Length(bits)] do\n name := ConcatenationString(\"fft\", String(size), \"-w\", String(w), \"-b\", String(bits[i]));\n HDLGen(t, 1, 0, bits[i], 0, 0, name);\n od;\nend;\n\nrunRachid3 := function(size, radix, w, bits)\n local t, i, name;\n\n t := streamIDFTUnroll(size, radix, 2*w);\n for i in [1..Length(bits)] do\n name := ConcatenationString(\"ifft\", String(size), \"-w\", String(w), \"-b\", String(bits[i]));\n HDLGen(t, 1, 0, bits[i], 0, 0, name);\n od;\nend;\n\nrunOFDMExp := function()\nHDLGen(streamDFTUnroll(64, 64, 128), 0, 0, 14, 250, 0, \"fft64w64b14f250\");\nHDLGen(streamDFTUnroll(64, 64, 128), 0, 0, 14, 500, 0, \"fft64w64b14f500\");\nHDLGen(streamDFTUnroll(64, 32, 64), 0, 0, 14, 1000, 0, \"fft64w32b14f1000\");\nHDLGen(streamDFTUnroll(128, 128, 256), 0, 0, 14, 250, 0, \"fft128w128b14f250\");\nHDLGen(streamDFTUnroll(128, 64, 128), 0, 0, 14, 500, 0, \"fft128w64b14f500\");\nHDLGen(streamDFTUnroll(128, 32, 64), 0, 0, 14, 1000, 0, \"fft128w32b14f1000\");\nHDLGen(streamDFTUnroll(256, 128, 256), 0, 0, 14, 250, 0, \"fft256w128b14f250\");\nHDLGen(streamDFTUnroll(256, 64, 128), 0, 0, 14, 500, 0, \"fft256w64b14f500\");\nHDLGen(streamDFTUnroll(256, 32, 64), 0, 0, 14, 1000, 0, \"fft256w32b14f1000\");\nHDLGen(streamDFTUnroll(512, 128, 256), 0, 0, 14, 250, 0, \"fft512w128b14f250\");\nHDLGen(streamDFTUnroll(512, 64, 128), 0, 0, 14, 500, 0, \"fft512w64b14f500\");\nHDLGen(streamDFTUnroll(512, 32, 64), 0, 0, 14, 1000, 0, \"fft512w32b14f1000\");\nHDLGen(streamDFTUnroll(1024, 128, 256), 0, 0, 14, 250, 0, \"fft1024w128b14f250\");\nHDLGen(streamDFTUnroll(1024, 64, 128), 0, 0, 14, 500, 0, \"fft1024w64b14f500\");\nHDLGen(streamDFTUnroll(1024, 32, 64), 0, 0, 14, 1000, 0, \"fft1024w32b14f1000\");\nHDLGen(streamDFTUnroll(2048, 128, 256), 0, 0, 14, 250, 0, \"fft2048w128b14f250\");\nHDLGen(streamDFTUnroll(2048, 64, 128), 0, 0, 14, 500, 0, \"fft2048w64b14f500\");\nHDLGen(streamDFTUnroll(2048, 32, 64), 0, 0, 14, 1000, 0, \"fft2048w32b14f1000\");\nend;\n\n#runForRachid := function()\n\n#end;\n\nrunRachid := function()\n runRachid2(256, 16, 128, [8, 10, 12]);\n runRachid2(512, 16, 128, [8, 10, 12]);\n runRachid3(256, 16, 128, [12, 13, 14, 15, 16, 17, 18]);\n runRachid3(512, 16, 128, [12, 13, 14, 15, 16, 17, 18]);\nend;\n\nrunRachidECOC2012 := function()\n runRachid3(32, 32, 32, [10, 11, 12]);\n runRachid3(32, 32, 128, [10, 11, 12]);\n runRachid3(64, 32, 64, [10, 11, 12]);\n runRachid3(64, 32, 128, [10, 11, 12]);\nend;\n\n# genBRAMPermMem(perm, w, format, bits, name)\n# Will generate Verilog for a Permutation Memory, performing permutation perm\n# with streaming width w. The file will reside in /tmp/spiral/[PID] where [PID]\n# is Spiral's process ID.\n#\n# format: 0 for fixed point, 1 for single precision floating point, 2 for double\n# bits: number of bits of precision, ignored for floating point\n#\n# Note that if you want the permutation to take complex data, you will need to wrap\n# perm in TRC( ), and that your streaming width is given in *real* words.\n#\n# So, to generate L(32,2) on complex data with streaming width 2 complex (= 4 real),\n# 16 bit fixed point data, storing in file.v:\n# genBRAMPermMem(TRC(TPrm(TL(32,2,1,1))), 4, 0, 16, \"file\");\n\ngenBRAMPermMem := function(perm, w, format, bits, name)\n local opts,path;\n opts := InitStreamUnrollHw();\n\n # Rather than having separate functions in Spiral for streaming perms and streaming perm memories,\n # just adapt the BRAMPerm to generate a memory by making this change.\n BRAMPerm.print := (self, i, is) >> Print(self.name, \"Mem(\", BitMatrixToInts(self._children[1]), \", \", BitMatrixToInts(self._children[2]), \", \", self.streamSize, \")\");\n\n \n path := HDLGen(streamGen(perm.withTags([AStream(w)]), opts), 1, format, bits, 0, 0, name);\n\n\n\n # Put BRAMPerm.print back to normal.\n BRAMPerm.print := (self,i,is) >> Print(self.name, \"(\", BitMatrixToInts(self._children[1]), \", \", BitMatrixToInts(self._children[2]), \", \", self.streamSize, \")\");\n\treturn path;\nend;\n\nrunBerkin := function()\n local opts;\n opts := InitStreamUnrollHw();\n BRAMPerm.print := (self,i,is) >> Print(self.name, \"Mem(\", BitMatrixToInts(self._children[1]), \", \", BitMatrixToInts(self._children[2]), \", \", self.streamSize, \")\");\n\n HDLGen(streamGen(TRC(TPrm(TL(512, 32, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L512_32-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(1024, 64, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L1024_64-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(2048, 128, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L2048_128-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(4096, 256, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L4096_256-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(8192, 512, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L8192_512-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(16384, 1024, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L16384_1024-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(32768, 2048, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L32768_2048-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(65536, 4096, 1, 1))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L65536_4096-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(32, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L32_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(64, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L64_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(128, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L128_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(256, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L256_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(512, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L512_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(1024, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L1024_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(2048, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L2048_16_t16-dbl-w2\");\n HDLGen(streamGen(TRC(TPrm(TL(4096, 16, 1, 16))).withTags([AStream(4)]), opts), 1, 2, 0, 0, 0, \"L4096_16_t16-dbl-w2\");\n\n# NB: TL is much better in the TPrm than Tensor(T .. .because TL has a fast function to turn it to a bit matrix, while\n# Tensor has to do it by brute force.\n\n BRAMPerm.print := (self,i,is) >> Print(self.name, \"(\", BitMatrixToInts(self._children[1]), \", \", BitMatrixToInts(self._children[2]), \", \", self.streamSize, \")\");\n HDLGen(streamDFTUnroll(32,2,4), 1, 2, 0, 0, 0, \"dft32-dbl-w2\");\n HDLGen(streamDFTUnroll(64,2,4), 1, 2, 0, 0, 0, \"dft64-dbl-w2\");\n HDLGen(streamDFTUnroll(128,2,4), 1, 2, 0, 0, 0, \"dft128-dbl-w2\");\n HDLGen(streamDFTUnroll(256,2,4), 1, 2, 0, 0, 0, \"dft256-dbl-w2\");\n HDLGen(streamDFTUnroll(512,2,4), 1, 2, 0, 0, 0, \"dft512-dbl-w2\");\n HDLGen(streamDFTUnroll(1024,2,4), 1, 2, 0, 0, 0, \"dft1024-dbl-w2\");\n HDLGen(streamDFTUnroll(2048,2,4), 1, 2, 0, 0, 0, \"dft2048-dbl-w2\");\n HDLGen(streamDFTUnroll(4096,2,4), 1, 2, 0, 0, 0, \"dft4096-dbl-w2\");\nend;\n\n# HDLSimPerm(transform, format, precision, filename)\n# format: 0 for fixed point, 1 for floating point, 2 for double\n# precision: # bits precision, ignored for floating point\nHDLSimPerm := function(t, format, precision, filename)\n local opts, cmdString, path, brams, wrapString;\n\n path := Concat(\"/tmp/spiral/\", String(GetPid()), \"/\");\n Exec(\"rm -f \"::path::\"log\");\n MakeDir(path);\n brams := -1;\n\n opts := InitStreamHw();\n PrintTo(ConcatenationString(path, filename, \".spl\"), HDLPrint(1024, t.dims(), -1, t));\n\n if (_splhdl_path = \"\") then\n\tError(\"Error: path to SPLHDL compiler not set: paradigms.stream._splhdl_path is not bound.\");\n fi;\n\n cmdString := ConcatenationString(_splhdl_path, \" \", path, filename, \".spl -o \", path, filename, \".v -ptb\");\n\n if (format = 0) then\n\tcmdString := ConcatenationString(cmdString, \" -fix \", StringInt(precision));\n elif (format = 1) then\n\tcmdString := ConcatenationString(cmdString, \" -flt 1 \");\n else\n\tcmdString := ConcatenationString(cmdString, \" -flt 2 \");\n fi;\n\n Print(cmdString, \"\\n\");\n Exec(cmdString);\n\n cmdString := \"cd \"::path::\" && iverilog \"::filename::\".v && vvp a.out > out\";\n Exec(cmdString);\n\n return ReadVal(path::\"/log\");\n\nend;\n\n\n# Generate a random full-rank bit matrix. I.e., a bit matrix that\n# represents a permutation.\nRandomBitMatrix := function(size)\n local res, i, j, trow, rank;\n rank := 0;\n \n while (rank < size) do\n res := [];\n for i in [1..size] do\n trow := [];\n for j in [1..size] do\n Append(trow, [Random(GF(2))]);\n od;\n Append(res, [trow]);\n od;\n rank := Rank(res);\n od;\n\n return res;\nend;\n \nRandomBitPerm := function(size, width)\n # the L is a hack, but should't matter because toAMat in StreamPermBit does not use LinearBits.child(2).\n return StreamPerm([LinearBits(RandomBitMatrix(size), L(4,2))], 1, width, 0);\nend;\n\nsimRandomPerm := function(n, w)\n local p, t, c, res;\n p := RandomBitPerm(Log2Int(n), w);\n c := p.createCode(); \n res := 1;\n\n res := HDLSimPerm(c, 0, 16, \"test\");\n \n if (res <> 0) then\n PrintBitMatrix(p.child(1)[1].child(1));\n fi;\n\n return res; \nend;\n\ntestPerms := function(n, w)\n local res, count, it;\n count := 100;\n res := 0;\n for it in [1..count] do\n Print(it);\n res := simRandomPerm(n, w);\n if (res <> 0) then\n\t Error();\n fi;\n od;\nend;\n\nsimPerm := function(t)\n local res, r, s, opts, s2;\n opts := InitStreamUnrollHw();\n r := RandomRuleTree(t, opts);\n s := SumsRuleTreeStrategy(r, SumStreamStrategy, opts);\n s2 := s.createCode();\n\n res := 1;\n res := HDLSimPerm(s2, 0, 16, \"test\");\n \n Print(\"Errors: \"::String(res) :: \"\\n\");\n\n if (res <> 0) then\n Print(t);\n fi;\n\n return res; \nend;\n\nrandomStridePerm := function(maxN, maxW)\n local n, ln, w, lw, ls, s;\n ln := Random([2..Log2Int(maxN)]);\n n := 2^ln;\n ls := Random([1..ln-1]);\n s := 2^ls;\n lw := Random([1..Min2(Log2Int(maxW), ln-1)]);\n w := 2^lw;\n \n Print(\" L(\"::String(n)::\", \"::String(s)::\"), w=\"::String(w)::\" \");\n return TPrm(TL(n, s)).withTags([AStream(w)]);\n\nend;\n\nrandomVPerm := function(maxN, maxW)\n local n, ln, w, lw;\n ln := Random([2..Log2Int(maxN)]);\n n := 2^ln;\n lw := Random([1..Min2(Log2Int(maxW), ln-1)]);\n w := 2^lw;\n \n Print(\" V(\"::String(n)::\"), w=\"::String(w)::\" \");\n return TPrm(SortIJPerm(n)).withTags([AStream(w)]);\n\nend;\n\ntestStridePerms := function(maxN, maxW)\n local res, count, it;\n count := 100;\n res := 0;\n for it in [1..count] do\n Print(it);\n res := simPerm(randomStridePerm(maxN, maxW));\n if (res <> 0) then\n\t Error();\n fi;\n od;\nend;\n\ntestVPerms := function(maxN, maxW)\n local res, count, it;\n count := 100;\n res := 0;\n for it in [1..count] do\n Print(it);\n res := simPerm(randomVPerm(maxN, maxW));\n if (res <> 0) then\n\t Error();\n fi;\n od;\nend;\n\n#runPermTests := function()\n# testPerms(16,2);\n# testPerms(16,4);\n# testPerms(16,8);\n# testPerms(32,2);\n# testPerms(32,4);\n# testPerms(32,8);\n# testPerms(32,16);\n#testPerms(256,2);\n#testPerms(256,4);\n#testPerms(256,8);\n#testPerms(256,16);\n#testPerms(256,32);\n#testPerms(256,64);\n#testPerms(256,128);\n#end;\n\n#testStridePerms(256,64)\n#testVPerm\n\n\n\n# To compile normal C code:\n# opts := SpiralDefaults;\n# t := WHT(8);\n# r := RandomRuleTree(t, opts);\n# c := CodeRuleTree(r, opts);\n# _StandardMeasure(c, opts);\n# code ends up in /tmp/spiral/PID\n", "meta": {"hexsha": "1f1f4dfe05b11ad3d6f56e0e09af3cf6382ceba2", "size": 57834, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/stream/hacks.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/stream/hacks.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/stream/hacks.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.314516129, "max_line_length": 234, "alphanum_fraction": 0.6186499291, "num_tokens": 19607, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6584175139669997, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.40983812539548636}} {"text": "#\n# walrus: Computational Methods for Finitely Generated Monoids and Groups\n#\n\nInstallGlobalFunction(NewPregroupWord,\nfunction(pg, word)\n local maxk, rel;\n maxk := MaxPowerK(word);\n return Objectify(IsPregroupRelatorType,\n rec( pregroup := pg\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1]) ) );\nend);\n\nInstallGlobalFunction(NewPregroupRelator,\nfunction(pres, word, id)\n local maxk, rel;\n maxk := MaxPowerK(word);\n rel := Objectify(IsPregroupRelatorType,\n rec( pres := pres\n , base := maxk[1]\n , exponent := maxk[2]\n , baselen := Length(maxk[1])\n , __ID := id)\n );\n return rel;\nend);\n\nInstallMethod(Base, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.base);\n\nInstallMethod(Exponent, \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep ],\n r -> r!.exponent);\n\nInstallMethod(Inverse, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\n r -> Objectify(IsPregroupRelatorType,\n rec( pres := r!.pres\n , base := List(Reversed(r!.base), PregroupInverse)\n , exponent := r!.exponent\n , baselen := r!.baselen\n , __ID := -r!.__ID)\n ));\nInstallMethod(PregroupPresentationOf,\n \"for pregroup relators\",\n [IsPregroupRelator],\n r -> r!.pres);\n\nInstallMethod(Locations, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n return List([1..r!.baselen], i -> NewLocation(r, i));\nend);\n\nInstallMethod(\\[\\], \"for a pregroup relator\",\n [IsPregroupRelator and IsPregroupRelatorRep, IsInt],\nfunction(r, p)\n local i, l;\n i := RemInt(p - 1, r!.baselen);\n if i < 0 then\n i := i + r!.baselen;\n fi;\n return r!.base[i + 1];\nend);\n\nInstallMethod(Length, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n return r!.baselen * r!.exponent;\nend);\n\n# we could possibly store this on creation\n# But this is run at most once anyway\nInstallMethod(Places, \"for a pregroup relator\",\n [ IsPregroupRelator and IsPregroupRelatorRep ],\nfunction(r)\n local P, res;\n\n res := [];\n\n for P in Places(PregroupPresentationOf(r)) do\n if Relator(P) = r then\n Add(res, P);\n fi;\n od;\n return res;\nend);\n\nInstallMethod(ViewString, \"for a pregroup relator\",\n [IsPregroupRelator],\nfunction(r)\n if Exponent(r) > 1 then\n return STRINGIFY(\"\");\n else\n return STRINGIFY(\"\");\n fi;\nend);\n\nInstallMethod(IsBound\\[\\], \"for a pregroup relator, and an position\",\n [IsPregroupRelator, IsInt], ReturnTrue );\n\n\nInstallMethod(\\=, \"for a pregroup relator, and a pregroup relator\",\n [IsPregroupRelator, IsPregroupRelator],\nfunction(l,r)\n # id is uniqe wrt pregroup presentation. We should probably\n # make a family of relators for each presentation etc\n return l!.__ID = r!.__ID;\n return (l!.exponent = r!.exponent)\n and (l!.base = r!.base);\nend);\n\nInstallMethod(\\in, \"for a generator and a pregroup relator\",\n [ IsElementOfPregroup, IsPregroupRelator and IsPregroupRelatorRep],\nfunction(e,r)\n return e in r!.base;\nend);\n\n#T redo and move to pregroup files\nInstallGlobalFunction(ReduceUPregroupWord,\nfunction(word)\n local rw, rw2, i, j, one;\n\n if Length(word) = 0 then\n return [];\n fi;\n\n one := PregroupOf(word[1])[1];\n rw := ShallowCopy(word);\n\n for i in [2..Length(rw)] do\n if rw[i-1] * rw[i] <> fail then\n rw[i] := rw[i-1] * rw[i];\n rw[i-1] := one;\n fi;\n od;\n\n i := 1; j := 1;\n rw2 := [];\n while i <= Length(rw) do\n if rw[i] <> one then\n rw2[j] := rw[i];\n j := j + 1;\n fi;\n i := i + 1;\n od;\n\n return rw2;\nend);\n\n\n", "meta": {"hexsha": "6c6c84d3a5ffc56e47950eb2fe19144738114982", "size": 4467, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/relator.gi", "max_stars_repo_name": "RussWoodroofe/walrus", "max_stars_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T14:55:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T14:55:52.000Z", "max_issues_repo_path": "gap/relator.gi", "max_issues_repo_name": "RussWoodroofe/walrus", "max_issues_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 26, "max_issues_repo_issues_event_min_datetime": "2018-11-22T11:15:07.000Z", "max_issues_repo_issues_event_max_datetime": "2022-02-21T13:31:01.000Z", "max_forks_repo_path": "gap/relator.gi", "max_forks_repo_name": "RussWoodroofe/walrus", "max_forks_repo_head_hexsha": "f7a4e3597f288c6d9518aaa39091826dadc864b8", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-02-11T14:47:47.000Z", "max_forks_repo_forks_event_max_datetime": "2021-05-20T10:22:09.000Z", "avg_line_length": 28.0943396226, "max_line_length": 82, "alphanum_fraction": 0.5374972017, "num_tokens": 1195, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6825737214979746, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.40967280198000144}} {"text": "MEMO_Base64Digits :=\n \"0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz-_\";\n\nInstallGlobalFunction(MEMO_Digits,\nfunction(n, base, args...)\n local minlen, len, digits, str;\n # Adapted from the DigitsNumber function in GAPDoc-1.6.1\n if Length(args) = 0 then\n minlen := 0;\n elif Length(args) = 1 then\n minlen := args[1];\n else\n return fail;\n fi;\n digits := MEMO_Base64Digits;\n str := \"\";\n while n <> 0 do\n Add(str, digits[(n mod base) + 1]);\n n := QuoInt(n, base);\n od;\n if Length(str) < minlen then\n # Pad with zeroes\n Append(str, ListWithIdenticalEntries(minlen - Length(str), digits[1]));\n fi;\n return Reversed(str);\nend);\n\nInstallGlobalFunction(MEMO_Hash,\nfunction(key)\n local str, ints, sum, i;\n IO_ClearPickleCache(); # In case IO_Pickle was recently interrupted\n str := IO_Pickle(key); # Pickle the key to a string\n ints := SHA256String(str); # Get the SHA-256 checksum in 32-bit chunks\n sum := 0; # Bring all 256 bits together into a single integer\n for i in [1..Length(ints)] do\n sum := sum + ints[i] * 2 ^ (32 * (i-1));\n od;\n str := MEMO_Digits(sum, 64, 43); # Make into a padded base-64 string\n return str;\nend);\n", "meta": {"hexsha": "6486b6644034bb56e30018e056958a561f2bc4f8", "size": 1187, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/hashing.gi", "max_stars_repo_name": "gap-packages/Memoisation", "max_stars_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2019-08-20T21:02:33.000Z", "max_stars_repo_stars_event_max_datetime": "2019-12-19T09:25:15.000Z", "max_issues_repo_path": "gap/hashing.gi", "max_issues_repo_name": "gap-packages/Memoisation", "max_issues_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2018-08-06T11:56:51.000Z", "max_issues_repo_issues_event_max_datetime": "2020-02-04T15:04:36.000Z", "max_forks_repo_path": "gap/hashing.gi", "max_forks_repo_name": "gap-packages/Memoisation", "max_forks_repo_head_hexsha": "0b1c1c172d52d57376876fd345aaa7db81792df1", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.9512195122, "max_line_length": 75, "alphanum_fraction": 0.6663858467, "num_tokens": 369, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.4083828936343597}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(VContainer);\n\n###############################################################################\n#F VContainer(, )\n#F\n#F self.child(1) -- spl\n#F self.isa -- isa\n#F\nClass(VContainer, VRC, rec(\n #-----------------------------------------------------------------------\n new := (self, spl, isa) >> SPL(WithBases(self, rec(\n _children := [spl], isa := isa))).setDims(), \n #-----------------------------------------------------------------------\n dims := self >> self.child(1).dims(),\n #-----------------------------------------------------------------------\n toAMat := (self) >> AMatMat(MatSPL(self.child(1))),\n #-----------------------------------------------------------------------\n isReal := self >> self.child(1).isReal(),\n #-----------------------------------------------------------------------\n conjTranspose := self >> ObjId(self)(self.child(1).conjTranspose(), self.isa),\n #-----------------------------------------------------------------------\n # NOTE: make sure rChildren properly exposes all parameters\n from_rChildren := (self, rch) >> VContainer(rch[1], self.isa),\n #-----------------------------------------------------------------------\n print := (self, i, is) >> Print(self.name, \"(\\n\", Blanks(i+is), \n\tself.child(1).print(i+is,is), \",\\n\", Blanks(i+is), self.isa, \")\", \n\tself.printA()),\n #-----------------------------------------------------------------------\n unroll := self >> self,\n #-----------------------------------------------------------------------\n transpose := self >> VContainer(self.child(1).transpose(), self.isa),\n #-----------------------------------------------------------------------\n vcost := self >> self.child(1).vcost()\n));\n\nClass(VirtualPad, BaseContainer, SumsBase, rec(\n #-----------------------------------------------------------------------\n new := (self, rows, cols, ch) >> SPL(WithBases(self, rec(\n dimensions := [rows, cols], _children := [ch]))).setDims(),\n #-----------------------------------------------------------------------\n dims := self >> self.dimensions,\n #-----------------------------------------------------------------------\n toAMat := self >> let(m := MatSPL(self.child(1)), ch := self.child(1),\n\tAMatMat(\n\t List(m, x -> x :: Replicate(Cols(self)-Cols(ch), 0)) ::\n\t Replicate(Rows(self)-Rows(ch), Replicate(Cols(self), 0)))),\n #-----------------------------------------------------------------------\n rChildren := self >> [self.dimensions[1], self.dimensions[2], self._children[1]],\n #-----------------------------------------------------------------------\n rSetChild := meth(self, n, what)\n if n=1 then self.dimensions[1] := Checked(IsIntSym(what), what);\n elif n=2 then self.dimensions[2] := Checked(IsIntSym(what), what);\n\telif n=3 then self._children[1] := Checked(IsSPL(what), what);\n\telse Error(\" must be in [1..3]\");\n\tfi;\n end,\n));\n", "meta": {"hexsha": "c41acda4cb691c50d7dd3c6dbe0c355f9cdf69a2", "size": 3047, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vcontainer.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vcontainer.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/sigmaspl/vcontainer.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 48.3650793651, "max_line_length": 85, "alphanum_fraction": 0.3590416803, "num_tokens": 624, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952052, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.4083828936343596}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F DiagFunc - base class for diagonal generating functions\n#F Required fields in subclasses:\n#F .abbrevs = [ (p1) -> [parlist1],\n#F (p1,...) -> [parlist2] ]\n#F Mapping from various lengths of parameter lists to a\n#F fixed signature .def\n#F\n#F .lambda(self) - must return Lambda() object representing the actual\n#F function. One should use .params field here\n#F\n#F .domain(self) -- must return the domain of the function (integer or type)\n#F .range(self) -- must return the range of the function (integer or type)\n#F\n#F Optional:\n#F .def(self, p1, ...) - this method is called from the constructor \n#F before the instance object is created. \n#F = class in this case\n#F .def() must return a record, all fields of the record\n#F will be copied to the resulting instance object,\n#F which will also have the field .params := [p1, ...].\n#F additional error checking can be performed in .def\n#F NB: parameter lists are normalized here, using .abbrevs\nClass(DiagFunc, Function, Sym, rec(\n isSPL := false,\n\n range := self >> Error(ObjId(self), \" does not implement .range()\"), \n domain := self >> Error(ObjId(self), \" does not implement .domain()\"), \n\n tensor_op := (v,rows,cols,fl,gl) ->\n Lambda(v, fl.at(idiv(v, cols)) * gl.at(imod(v, cols))),\n\n sums := self >> self,\n rSetChild := meth(self, n, newChild)\n self.params[n] := newChild;\n end,\n\n print := meth(self, i, is)\n local params;\n params := let(p:=self.params, When(IsList(p), p, [p]));\n Print(self.name, \"(\",\n DoForAllButLast(params, x -> Print(x, \", \")),\n Last(params), \")\");\n end,\n\n def := arg -> rec(),\n\n fromDef := meth(arg)\n local result, self, params, h, lkup;\n self := arg[1];\n params := arg{[2..Length(arg)]};\n params := self.canonizeParams(params);\n self.checkParams(params);\n params := When(IsList(params), params, [params]);\n\n h := self.hash;\n if h<>false then\n lkup := h.objLookup(self, params);\n if lkup[1] <> false then return lkup[1]; fi;\n fi;\n\n result := SPL(WithBases(self, CopyFields(\n rec(params := params),\n ApplyFunc(self.def,params))));\n\n if h<>false then return h.objAdd(result, lkup[2]);\n else return result;\n fi;\n end,\n\n free := self >> Union(List(self.params, FreeVars)),\n __call__ := ~.fromDef,\n\n isReal := self >> not IsComplexT(self.range())\n));\n\n#F II - interval diagonal function\n#F\n#F II() - diagonal of N 1's\n#F II(, ) - diagonal with 1's from 0.., and 0's after\n#F II(, , ) - diagonal with 1's in .., 0's elsewhere\n#F\nClass(II, DiagFunc, rec(\n abbrevs := [ (N) -> [N,0,N],\n (N,to) -> [N,0,to],\n (N,from,to) -> [N,from,to] ],\n\n def := (N, from, to) -> Checked(\n\tIsPosInt0Sym(N), IsPosInt0Sym(from), IsPosInt0Sym(to), rec()),\n\n lambda := self >> let(\n i := Ind(self.params[1]), from := self.params[2], to := self.params[3],\n Lambda(i, cond(leq(from, i, to-1), 1, 0))),\n\n domain := self >> self.params[1],\n range := self >> TInt, \n));\n\n#F fConst(, , ) - constant diagonal function, values of of type \n#F\nClass(fConst, DiagFunc, rec(\n abbrevs := [ (N,c) -> Checked( IsPosInt0Sym(N), [TReal, N,c]),\n (t,N,c) -> Checked(IsType(t), IsPosInt0Sym(N), [t, N, c]) ],\n range := self >> self.params[1],\n domain := self >> self.params[2], \n lambda := self >> let(i := Ind(self.params[2]), Lambda(i, self.params[3]))\n));\n\n#F fUnk(, ) - dummy diagonal that denotes an \"unknown\" function, values of type \n#F To be used for .hashAs methods of transforms\n#F\nClass(fUnk, DiagFunc, rec(\n abbrevs := [ N -> Checked(IsIntSym(N), [TReal, N]), \n\t (t, N) -> Checked(IsType(t), IsIntSym(N), [t, N]) ],\n range := self >> self.params[1],\n domain := self >> self.params[2],\n lambda := self >> let(N:=self.params[2], i:=Ind(N), \n\tCond(IsIntT(self.params[1]), Lambda(i, i+1), \n\t Lambda(i, self.params[1].one()/N*(i+1))))\n));\n\n# FUnk is for backwards compatibility, use fUnk\nFUnk := n -> fUnk(TReal, n);\n\nDeclare(LD);\n\n# UD(, ) - upper diagonal\n#\nClass(UD, Sym, rec(\n def := (n,k) -> Checked(k < n, Z(n,k) * Diag(II(n, k, n))),\n transpose := self >> ApplyFunc(LD, self.params)\n));\n\n# LD(, ) - lower diagonal\n#\nClass(LD, Sym, rec(\n def := (n,k) -> Checked(k < n, Z(n,n-k) * Diag(II(n, 0, n-k))),\n transpose := self >> ApplyFunc(UD, self.params)\n));\n\n# [ 1 1\n# 1 1\n# ... ]\nClass(S, Sym, rec(\n def := n -> SUM(I(n), UD(n,1))));\n\n\n# Class(fComputeOnline, PlaceholderExp);\nClass(fComputeOnline, FuncClassOper, rec(\n range := self >> self._children[1].range(),\n domain := self >> self._children[1].domain(),\n lambda := self >> self._children[1].lambda(),\n tolist := self >> self._children[1].tolist(),\n free := self >> self._children[1].free(),\n ev := self >> self._children[1].ev(),\n eval := self >> self._children[1].eval(),\n));\n\nDeclare(fPrecompute);\n\n# fPrecompute()\n#\n# Marks functions that should be precomputed by either generating a\n# table (opts.generateInitCode := true) or runtime initialization code\n# (opts.generateInitCode := true).\n#\n# Actual precomputation is done by Process_fPrecompute. Which uses\n# options record 'opts' to determine the precomputation strategy.\n#\nClass(fPrecompute, FuncClassOper, rec(\n def := func -> rec(t := TPtr(func.range())),\n range := self >> self._children[1].range(),\n domain := self >> self._children[1].domain(),\n lambda := self >> self._children[1].lambda(),\n tolist := self >> self._children[1].tolist(),\n free := self >> self._children[1].free(),\n isReal := self >> self._children[1].isReal()\n));\n\n\n# diagAdd(, ,...) : i -> f1(i) + f2(i) + ...\n# Pointwise addition of several diagonal functions\nClass(diagAdd, FuncClassOper, rec(\n domain := self >> self.child(1).domain(),\n range := self >> UnifyTypes(List(self.children(), x->x.range())),\n lambda := self >> let(v := Ind(self.domain()), \n\tLambda(v, ApplyFunc(add, List(self.children(), i->i.at(v))))),\n));\n\n# diagMul(, ,...) : i -> f1(i) * f2(i) * ...\n# Pointwise multiplication of several diagonal functions\nClass(diagMul, FuncClassOper, rec(\n domain := self >> self.child(1).domain(),\n range := self >> UnifyTypes(List(self.children(), (x) -> x.range())),\n lambda := self >> let(v := Ind(self.domain()), \n\tLambda(v, ApplyFunc(mul, List(self.children(), i->i.at(v))))),\n));\n\nClass(diagCond, FuncClassOper, rec(\n domain := self >> self.child(2).domain(),\n range := self >> UnifyTypes(List(Drop(self.children(), 1), x->x.range())),\n lambda := self >> let(v := Ind(self.domain()), \n\tLambda(v, cond(self.child(1), self.child(2).at(v), self.child(3).at(v))))\n));\n\n#F fCast(, ) -- symbolic type cast function \n#F\n#F Example: fCast(TReal, TInt)\n#F\nClass(fCast, DiagFunc, rec(\n abbrevs := [ (toT, fromT) -> Checked(IsType(toT), IsType(fromT), [toT, fromT]) ], \n range := self >> self.params[1],\n domain := self >> self.params[2],\n lambda := self >> let(i:=TempVar(self.domain()), Lambda(i, tcast(self.range(), i))), \n));\n", "meta": {"hexsha": "3f3cf76483958fd5e6e44262a8faa2ed723af2de", "size": 7664, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/spl/diags.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/spl/diags.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/spl/diags.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 34.8363636364, "max_line_length": 93, "alphanum_fraction": 0.5658924843, "num_tokens": 2219, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.658417500561683, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.4074158665820999}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F ResolveMemos()\n#F This function removes all precomputed variables (with Data(v, expr, ...))\n#F by inserting the corresponding expressions\n#F\nResolveMemos := o ->\n SubstTopDown(o, @(1,var,e->IsBound(e.mapping)), e->e.mapping);\n\n_GenerateData := function(map, free, lambda)\n local newlambda, v, val, d, free1;\n if free = [] then\n\tnewlambda := Copy(lambda);\n\t# NOTE: hardcoded [var, param] is ugly\n\tnewlambda.expr := SubstParamsCustom(newlambda.expr, map, [var, param]);\n\treturn newlambda.tolist();\n else\n\tv := free[1];\n\td := [];\n\tfree1 := Drop(free, 1);\n\tfor val in [0..v.range-1] do\n\t map.(v.id) := V(val);\n\t Append(d, _GenerateData(map, free1, lambda));\n\tod;\n\treturn d;\n fi;\nend;\n\n#Declare(fComputeOnline);\n\n# PrecalculatedData - accumulating precalculated data variables so\n# same constant data table (variable) could be reused in different places in code.\n# Beware: search for table by key is inefficient here.\n\nClass(PrecalculatedData, rec(\n\n # _tables is a list of rec(key, data, opts) items.\n _tables := [],\n\n __call__ := (self) >> self._tables,\n\n # keyForFunc - returns search key for function 'func' that has 'var' variables.\n # The key is just the same function with unnamed variables.\n\n keyForFunc := meth( self, func, vars)\n local i, j, map;\n map := rec();\n i := 1; j := Length(vars);\n while j>0 do\n map.(vars[i].id) := ind(vars[i].range, j);\n i := i+1; j := j-1;\n od;\n\t# NOTE: hardcoded [var, param] is ugly\n return SubstParamsCustom( Copy(func), map, [var, param]);\n end,\n\n # find(key, opts) - searching if data table already exists.\n find := meth( self, key, opts)\n local item;\n for item in self._tables do \n #NOTE: opts.dataType - just to distinguish single precision from double \n if item.key=key and item.opts.dataType=opts.dataType then\n return item.data;\n fi;\n od;\n return false;\n end,\n\n # add - remember data table assosiated with key, data is FData object.\n add := meth( self, key, data, opts)\n Add(self._tables, rec( key := key, data := data, opts := opts));\n end,\n\n clear := meth(self) \n self._tables := []; \n end,\n\n));\n\nGenerateData := function ( func, opts )\n local f, n, free, lambda, data, t, olvars, key, map, i;\n\n if ObjId(func)=FDataOfs then return func; fi;\n\n olvars := [];\n map := rec();\n\n func := SubstTopDown(Copy(func), fComputeOnline, \n function(s)\n local v;\n v := var.fresh_t(\"o\", s._children[1].t);\n v.range := s._children[1].range();\n Add(olvars, v);\n map.(v.id) := s._children[1];\n return v;\n end\n );\n\n lambda := func.lambda();\n # NOTE: Collect is a hack\n # NOTE: hardcoded 'param' is ugly\n free := Difference(lambda.expr.free() :: Collect(lambda.expr, param), lambda.vars);\n free := Filtered(free, IsLoopIndex);\n\n for i in free do map.(i.id) := fBase(i); od;\n\n Append(free, olvars);\n\n Constraint(ForAll(free, v->IsBound(v.range)));\n Sort(free, (x,y) -> DoubleString(Drop(x.id,1)) <= DoubleString(Drop(y.id,1)));\n\n if IsBound(opts.dataSharing) and opts.dataSharing.enabled then\n key := PrecalculatedData.keyForFunc(func, free);\n data := PrecalculatedData.find(key, opts);\n if ObjId(data)=false then \n data := FData(_GenerateData(tab(), free, lambda));\n PrecalculatedData.add(key, data, opts);\n fi;\n else data := FData(_GenerateData(tab(), free, lambda));\n fi;\n\n n := lambda.domain();\n\n if (free=[] and olvars=[]) then return data.part(n,0);\n else return data.part(n, n * fTensor(List(free, i->map.(i.id))).at(0));\n fi;\nend;\n\n_GenerateInitCode := function(data, N, idx, free, lambda)\n local i, v, res;\n if free = [] then\n\ti := lambda.vars[1];\n\tres := loop(i, lambda.domain(), \n\t\tassign(nth(data, idx+i), \n\t\t When(data.t.t = lambda.expr.t, \n\t\t\t lambda.expr,\n\t\t\t # else\n\t\t\t\ttcast(data.t.t, lambda.expr))));\n\n # ObjId<>loop, when i.range was 1, loop just returned its body\n\tif i.range <= 16 and ObjId(res)=loop then return SReduceSimple(res.unroll()); \n\telse return SReduceSimple(res);\n\tfi;\n else\n\tv := free[1];\n # careful here, since N and v.range can be symbols we have to use div ,\n # since N/v.range will become an fdiv (floating point division) in the code,\n # div = integer division with divisible arguments (allows normal simplification as in fdiv)\n\tN := div(N, v.range); \n\treturn loop(v, v.range,\n\t _GenerateInitCode(data, N, idx+v*N, Drop(free,1), lambda));\n fi;\nend;\n\nGenerateInitCode := function ( func, data_container, opts )\n local f, N, n, free, lambda, data, map, initcode, res, range, key;\n if ObjId(func)=FDataOfs then return func; fi;\n lambda := func.lambda();\n\n # NOTE: Collect is a hack\n # NOTE: hardcoded 'param' is ugly\n free := Difference(lambda.expr.free() :: Collect(lambda.expr, param), lambda.vars);\n free := Filtered(free, IsLoopIndex);\n\n Constraint(ForAll(free, v->IsBound(v.range)));\n Sort(free, (x,y) -> DoubleString(Drop(x.id,1)) <= DoubleString(Drop(y.id,1)));\n\n n := func.domain();\n N := n * Product(free, x->x.range);\n\n range := func.range();\n\n if IsBound(opts.dataSharing) and opts.dataSharing.enabled then\n key := PrecalculatedData.keyForFunc(func, free);\n data := PrecalculatedData.find(key, opts);\n else\n data := false;\n fi;\n\n if data=false then \n if IsInt(range) or IsSymbolic(range) then \n data := data_container(TInt, N); # index mapping function, not diag\n else \n\t if opts.unifyStoredDataType = \"input\" then\n\t\trange := UnifyTypes([range, opts.XType.t]);\n\t elif opts.unifyStoredDataType = \"output\" then\n\t\trange := UnifyTypes([range, opts.YType.t]);\n\t elif IsType(opts.unifyStoredDataType) then \n\t\trange := UnifyTypes([range, opts.unifyStoredDataType]);\n\t fi;\n data := data_container(range, N);\n fi;\n data.init := _GenerateInitCode(data, N, 0, free, lambda);\n\n if IsBound(opts.dataSharing) and opts.dataSharing.enabled then \n PrecalculatedData.add(key, data, opts);\n fi;\n fi;\n\n if free=[] then\n res := FData(data).part(n,0);\n else\n res := FData(data).part(n, n * fTensor(List(free, fBase)).at(0));\n fi;\n res := res.setRange(range);\n res.init := res.var.init;\n \n return res;\nend;\n\n_Process_fPrecompute := (o, precompute_func, precond) -> SubstBottomUpRules(o, [\n [ [fPrecompute, @(1)],\n (e,cx) -> When(precond(e,cx) and e.rank()=0, precompute_func(ResolveMemos(e)), e),\n \"ContextDependentLocalize_fPrecompute\"],\n]);\n\n# Process_fPrecompute(, )\n#\nProcess_fPrecompute := function(sums, opts)\n local bb, b, has_free_vars, precompute_func;\n\n # Autolib needs ability to disable fPrecompute when it uses strategies from LocalConfig.bench\n if IsBound(opts.disablePrecompute) and opts.disablePrecompute then\n return sums;\n fi;\n\n if IsBound(opts.dataSharing) and opts.dataSharing.enabled then\n \tsums := ApplyStrategy(sums, opts.dataSharing.precomputeStrategy, UntilDone, opts);\n fi;\n\n bb := Collect(sums, @(1, [BB, RecursStep]));\n for b in bb do\n b.precomputed_free := b.free();\n od;\n\n has_free_vars := (e, cxentry) -> \n (CollectNR(e, param) <> []) or\n (Intersection(e.free(), cxentry[1].precomputed_free)<>[]);\n\n precompute_func := When(opts.generateInitFunc, \n e -> GenerateInitCode(e, Dat1d, opts), \n e -> GenerateData(e, opts));\n\n sums := _Process_fPrecompute(sums, precompute_func,\n (e, cx) -> (\n ((not IsBound(cx.BB) or cx.BB=[]) and \n (not IsBound(cx.RecursStep) or cx.RecursStep=[]) and\n (not IsBound(cx.RS) or cx.RS=[]) and \n (not IsBound(cx.RSBase) or cx.RSBase=[])) or \n (IsBound(cx.BB) and cx.BB<>[] and has_free_vars(e, cx.BB)) or \n\t (IsBound(cx.RecursStep) and cx.RecursStep<>[] and has_free_vars(e, cx.RecursStep)) \n )\n );\n return sums;\nend;\n", "meta": {"hexsha": "413b59832df18d7983ee63548ac084e6d7068020", "size": 8386, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/sigma/precompute.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/sigma/precompute.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/sigma/precompute.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 32.3783783784, "max_line_length": 104, "alphanum_fraction": 0.6013594085, "num_tokens": 2270, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7122321842389469, "lm_q2_score": 0.5698526514141571, "lm_q1q2_score": 0.4058673986110603}} {"text": "#\n#\n#\n\nRead(\"~/Workspace/Chevalley.gap/init.gi\");\n\nRead(Filename(home_dir,\"lib/poly.gd\"));\nRead(Filename(home_dir,\"lib/poly.gi\"));\n", "meta": {"hexsha": "80305bee2fd89fab7da1fb71d8003ab65ace6eda", "size": 131, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "test/poly.test.init.gi", "max_stars_repo_name": "iuliansimion/Chevalley.gap", "max_stars_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "test/poly.test.init.gi", "max_issues_repo_name": "iuliansimion/Chevalley.gap", "max_issues_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "test/poly.test.init.gi", "max_forks_repo_name": "iuliansimion/Chevalley.gap", "max_forks_repo_head_hexsha": "dd237f36d69a42bcd6cb6a24c5e4bf7dfb3da186", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 14.5555555556, "max_line_length": 42, "alphanum_fraction": 0.679389313, "num_tokens": 40, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6297746074044134, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.40571661351751986}} {"text": "\n# Copyright 2018-2019, Carnegie Mellon University\n# See LICENSE for details\n\nDeclare(OLCompose);\n\nClass(OLCompose, Compose, rec(\n printSeparationChar := \" o \",\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], OLCompose(DropLast(self._children, 1)).toOperator()(Last(self._children).toOperator()(vec))))\n));\n\nClass(LinearSystem, BaseMat, rec(\n abbrevs := [ (A, b) -> [A, b] ],\n new := (self, A, b) >> SPL(WithBases(self, rec(\n mat := A, rhs := b, dimensions := [Rows(A), Cols(A)]))),\n print := (self, i, is) >> Print(\"LinearSystem(\", self.mat, \", \", self.rhs, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.mat, self.rhs],\n rSetChild := rSetChildFields(\"mat\", \"rhs\"),\n isReal := True\n));\n\nClass(Reduction, BaseMat, rec(\n abbrevs := [ (N, op, idval, isSaturated) -> [N, op, idval, isSaturated] ],\n new := (self, N, op, idval, isSaturated) >> SPL(WithBases(self, rec(\n N := N, op := op, idval := idval, isSaturated := isSaturated, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"Reduction(\", self.N, \", \", self.op, \", \", self.idval, \", \", self.isSaturated, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.idval, self.isSaturated],\n rSetChild := rSetChildFields(\"N\", \"op\", \"idval\", \"isSaturated\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], [RulesStrengthReduce(FoldL(vec, self.op, self.idval)).v]))\n));\n\nClass(Induction, BaseMat, rec(\n abbrevs := [ (N, op, initval) -> [N, op, initval] ],\n new := (self, N, op, initval) >> SPL(WithBases(self, rec(\n N := N, op := op, initval := initval, dimensions := [N, 1]))),\n print := (self, i, is) >> Print(\"Induction(\", self.N, \", \", self.op, \", \", self.initval, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op, self.initval],\n rSetChild := rSetChildFields(\"N\", \"op\", \"initval\"),\n isReal := True,\n recurrence := self >> ((j,v)->When(j=0, self.initval, self.op.at(self.recurrence()(j-1,v),v))),\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..self.N-1], i->_unwrap(RulesStrengthReduce(self.recurrence()(i,vec[1]))))))\n));\n\nClass(PointWise, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, N]))),\n print := (self, i, is) >> Print(\"PointWise(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n transpose := self >> self,\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([0..Length(vec)-1], j->RulesStrengthReduce(self.op.at(vec[j+1], j)).v)))\n));\n\nClass(BinOp, BaseMat, rec(\n abbrevs := [ (N, op) -> [N, op] ],\n new := (self, N, op) >> SPL(WithBases(self, rec(\n N := N, op := op, dimensions := [N, 2*N]))),\n print := (self, i, is) >> Print(\"BinOp(\", self.N, \", \", self.op, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.op],\n rSetChild := rSetChildFields(\"N\", \"op\"),\n isReal := True,\n toOperator := self >> (vec -> Checked(Length(vec)=self.dims()[2], List([1..Length(vec)/2], j->RulesStrengthReduce(self.op.at(vec[j], vec[j+self.N])).v)))\n));\n\nClass(ScalarProd, BaseMat, rec(\n abbrevs := [ (N, scalars) -> [N, scalars] ],\n new := (self, N, scalars) >> SPL(WithBases(self, rec(\n N := N, scalars := scalars, dimensions := [1, N]))),\n print := (self, i, is) >> Print(\"ScalarProd(\", self.N, \", \", self.scalars, \")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.N, self.scalars],\n rSetChild := rSetChildFields(\"N\", \"scalars\"),\n isReal := True,\n toOperator := self >>(vec -> Checked(Length(vec)=self.dims()[2], [_unwrapVec(self.scalars) * vec]))\n));\n\nClass(Constant, BaseMat, rec(\n abbrevs := [ x -> [x]],\n new := (self, x) >> SPL(WithBases(self, rec(\n value := x, dimensions := [1,0]))),\n print := (self, i ,is) >> Print(\"Constant(\",self.value,\")\"),\n dims := self >> self.dimensions,\n rChildren := self >> [self.value],\n rSetChild := rSetChildFields(\"value\"),\n isReal := True\n));\t\t\n\nspiral.spl.IterVStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[2], \n Flat(List([0..self.var.range-1], \n j->RulesStrengthReduce(\n SubstVars(Copy(self._children[1]), \n rec((self.var.id):=V(j))\n )\n ).toOperator()(vec) )\n )\n )\n );\n\nspiral.spl.HStack.toOperator := \n self >> (vec -> Checked(Length(vec)=self.dims()[1]*Length(self.children()), \n \t \t Sum(List([1..Length(self.children())], \n\t i->self.children()[i].toOperator()(vec{[(i-1)*self.dims()[1] + 1..i*self.dims()[1]]})\n\t\t ))\n\t \t )\n );\n\nspiral.spl.DirectSum.toOperator := self >> (vec -> Checked(Length(vec)=Sum(List(self.children(), i->i.dims()[2])), \n ApplyFunc(Concat, List([1..Length(self.children())], \n i->self.children()[i].toOperator()(vec{\n [Sum(List(self.children(){[1..i-1]}, j->j.dims()[2]))+1..Sum(List(self.children(){[1..i]}, j->j.dims()[2]))]\n })))));\n\n\n\nspiral.spl.I.N := self >> self.params[1];\n", "meta": {"hexsha": "415716060653413e3b29aa137cee928de1a506cc", "size": 5515, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "spl.gi", "max_stars_repo_name": "spiral-software/spiral-package-hcol", "max_stars_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "spl.gi", "max_issues_repo_name": "spiral-software/spiral-package-hcol", "max_issues_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "spl.gi", "max_forks_repo_name": "spiral-software/spiral-package-hcol", "max_forks_repo_head_hexsha": "b4a0118382e3bba91ecd82a6c667f2cdb6389ceb", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2019-11-26T05:21:02.000Z", "max_forks_repo_forks_event_max_datetime": "2019-11-26T05:21:02.000Z", "avg_line_length": 43.7698412698, "max_line_length": 163, "alphanum_fraction": 0.5410698096, "num_tokens": 1673, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952054, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.4057078520494534}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nImportAll(paradigms.smp); # for AParSMP\nImportAll(paradigms.vector); # for VRCLR\nImport(approx); # for CeilingRat.\n\n_swrap := (nt) -> let(t:=nt.firstTag(), ScratchWrap(t.size,t.nsgmts,t.linesize));\n\n_nodeFitsTensorDoesnt := (nt) -> let (\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2],\n n := nt.params[2],\n\n 2*m <= k and m*n >= k\n);\n\n_isALStoreTag := (nt) -> nt.isTag(1,ALStore) or nt.isTag(1,ALStoreCx);\n\nNewRulesFor(TTensorI, rec(\n# (In x Am)_{LS(<=k)} -> In x (Am)_{LS(<=k)} for m > k\n IxA_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n and IsParPar(nt.params) \n and nt.params[1].dims()[2] > nt.getTag(1).size,\n\n children := nt -> [[ nt.params[1].withTags(nt.getTags()) ]],\n apply := (nt, c, cnt) -> Tensor(I(nt.params[2]), c[1])\n ),\n \n AxI_scratch_push := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsVecVec(nt.params)\n and nt.params[1].dims()[2] > nt.getTag(1).size,\n children := nt -> [[nt.params[1].withTags(nt.getTags())]],\n apply := (nt, c, cnt) -> Tensor(c[1], I(nt.params[2]))\n ),\n\n# ==========================================================\n# synchronous rules\n\n# (In x Am)_{LS(<=k)} -> Imn/k x (Ik/m x Am) for m|k and k|mn\n IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / nt.params[1].dims()[2], \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(m*n/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/m)\n )))\n ),\n\n# (Am x In)_{LS(<=k)} -> (L^m^2n/k_m x Ik/m) (Imn/k x (Am x Ik/m)) (L^m^2n/k_mn/k x Ik/m) for m|k and k|mn\n AxI_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]*nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / nt.params[1].dims()[2], \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(m^2*n/k, m), fId(k/m))) *\n Tensor(\n I(m*n/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/m)\n ) *\n Prm(fTensor(L(m^2*n/k, m*n/k), fId(k/m))))\n )\n ),\n\n IxAL_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ nt.params[1].dims()[2])\n and IsPosInt(nt.params[1].dims()[2]*nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/m, \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(m*n/k),\n LSKernel(c[1],nt.normalizedArithCost() * k/m)\n ) *\n Prm(fTensor(L(m^2*n/k,m*n/k),fId(k/m)))\n )\n ),\n ),\n\n L_IxA_scratch := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / nt.params[1].dims()[2], \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(m^2*n/k, m*n/k), fId(k/m))\n ) * Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/m\n ), I(m*n/k))\n )\n )\n ),\n#====================================================================\n# SWP Rules - double buffering is applied\n IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsParPar(nt.params)\n and IsPosInt(nt.getTag(1).size / (2 * nt.params[1].dims()[2]))\n and IsPosInt(2 * nt.params[1].dims()[2] * nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1],\n nt.getTag(1).size / (2 * nt.params[1].dims()[2]), \n APar, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n apply := (nt, c, cnt) -> let(k := nt.getTag(1).size, m := nt.params[1].dims()[2], n:= nt.params[2],\n DMAFence(Tensor(\n I(2*m*n/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2*m))\n )))\n ),\n\n AxI_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt)\n\t and IsVecVec(nt.params) \n and IsPosInt(nt.getTag(1).size / (2*nt.params[1].dims()[2]))\n and IsPosInt(2*nt.params[1].dims()[2]*nt.params[2] / nt.getTag(1).size),\n\n children := nt -> [[ let(t := nt.firstTag(),\n TTensorI(\n nt.params[1], \n t.size / (2*nt.params[1].dims()[2]), \n AVec, AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt))\n ) ]],\n\n apply := (nt, c, cnt) -> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence(Prm(fTensor(L(2*m^2*n/k, 2*m), fId(k/(2*m)))) *\n Tensor(\n I(2*m*n/k),\n LSKernel(c[1], nt.params[1].normalizedArithCost() * k/(2*m))\n ) *\n Prm(fTensor(L(2*m^2*n/k, 2*m*n/k), fId(k/(2*m)))))\n )\n ),\n\n IxAL_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags()\n and _isALStoreTag(nt)\n and IsParVec(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2*nt.params[1].dims()[2]))\n and IsPosInt(2*nt.params[1].dims()[2]*nt.params[2]/nt.getTag(1).size),\n children := nt -> let(\n k := nt.firstTag().size,\n m := nt.params[1].dims()[2],\n\n [[ TTensorI(\n nt.params[1], \n k/(2*m), \n APar,AVec\n ).withTags(Drop(nt.getTags(),1)).setWrap(_swrap(nt)) \n ]]),\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size, \n m := nt.params[1].dims()[2], \n n := nt.params[2],\n\n DMAFence(\n Tensor(\n I(2*m*n/k),\n LSKernel(c[1],nt.normalizedArithCost() * k/(2*m))\n ) *\n Prm(fTensor(L(2*m^2*n/k,2*m*n/k),fId(k/(2*m))))\n )\n ),\n ),\n\n L_IxA_scratch_swp := rec(\n forTransposition := false,\n applicable := nt -> nt.hasTags() \n and _isALStoreTag(nt) \n\t and IsVecPar(nt.params)\n and IsPosInt(nt.getTag(1).size/ (2*nt.params[1].dims()[2]))\n and IsPosInt(2*nt.params[1].dims()[2]*nt.params[2]/nt.getTag(1).size),\n\n children := nt -> [[ \n TTensorI(\n nt.params[1], \n nt.getTag(1).size / (2*nt.params[1].dims()[2]), \n AVec, APar\n ).withTags(Drop(nt.getTags(),1)).setWrap(\n _swrap(nt)\n )\n ]],\n\n apply := (self, nt, c, cnt) >> let(\n k := nt.getTag(1).size,\n m := nt.params[1].dims()[2], \n n:= nt.params[2],\n\n DMAFence( \n Prm(fTensor(L(2*m^2*n/k, 2*m*n/k), fId(k/(2*m)))\n ) * Tensor(LSKernel(\n c[1], nt.normalizedArithCost() * k/(2*m)\n ), I(2*m*n/k))\n )\n )\n )\n));\n", "meta": {"hexsha": "30680d70d4a8a18801d2f33da0edacb57129f681", "size": 9722, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/scratchpad/breakdown.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/scratchpad/breakdown.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/scratchpad/breakdown.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 33.8745644599, "max_line_length": 108, "alphanum_fraction": 0.4279983542, "num_tokens": 2720, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.752012562644147, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.4053221530115411}} {"text": "#############################################################################\n##\n#W selfsim.gi automgrp package Yevgen Muntyan\n#W Dmytro Savchuk\n##\n#Y Copyright (C) 2003 - 2018 Yevgen Muntyan, Dmytro Savchuk\n##\n\n\n###############################################################################\n##\n#R IsSelfSimRep\n##\n## This is how IsSelfSim object is stored in GAP:\n## IsSelfSim object is a thing of kind \"w = (w_1, w_2, ..., w_d)\\pi\", where\n## deg = d - arity of tree;\n## perm = \\pi - permutation on first level;\n## w, w_1, ..., w_d - elements of free group representing elements of\n## automata group;\n## word = w;\n## states = [w_1, ..., w_d].\n##\nDeclareRepresentation(\"IsSelfSimRep\",\n IsComponentObjectRep and IsAttributeStoringRep,\n [\"word\", \"states\", \"perm\", \"deg\"]);\n\n\nInstallGlobalFunction(__AG_CreateSelfSim,\nfunction(family, word, states, perm, invertible)\n local a, cat;\n\n if invertible then\n cat := IsInvertibleSelfSim and IsSelfSimRep;\n\n if perm^-1=fail then\n Error(perm, \" is not invertible\");\n else\n perm := AG_PermFromTransformation(perm);\n fi;\n else\n cat := IsSelfSim and IsSelfSimRep;\n fi;\n\n a := Objectify(NewType(family, cat),\n rec(word := word,\n states := states,\n perm := perm,\n deg := family!.deg));\n\n SetIsActingOnBinaryTree(a, a!.deg = 2);\n\n return a;\nend);\n\n###############################################################################\n##\n#M SelfSim( , )\n##\nInstallMethod(SelfSim, \"for [IsAssocWord, IsSelfSimFamily]\",\n [IsAssocWord, IsSelfSimFamily],\nfunction(w, fam)\n local exp, wstates, curstate, newstate, curletter, newletter,\n nperm, i, j, perm, a, wtmp, reduced, invertible;\n\n if fam!.use_rws then\n w := AG_ReducedForm(fam!.rws, w);\n fi;\n\n if Length(w) = 0 then\n return One(fam);\n elif Length(w) = 1 then\n if ExponentSyllable(w, 1) = 1 then\n return fam!.recurgens[GeneratorSyllable(w, 1)];\n else\n if IsBound(fam!.recurgens[GeneratorSyllable(w, 1) + fam!.numstates]) then\n return fam!.recurgens[GeneratorSyllable(w, 1) + fam!.numstates];\n else\n Error(fam!.recurgens[GeneratorSyllable(w, 1)], \" is not invertible\");\n fi;\n fi;\n fi;\n\n exp := LetterRepAssocWord(w);\n for i in [1..Length(exp)] do\n if exp[i] < 0 then\n if IsBound(fam!.recurlist[-exp[i] + fam!.numstates]) then\n exp[i] := -exp[i] + fam!.numstates;\n else\n Error(fam!.recurgens[-exp[i]], \" is not invertible\");\n fi;\n fi;\n od;\n wstates := [];\n nperm := ();\n for i in [1..Length(exp)] do\n nperm := nperm * fam!.recurlist[exp[i]][fam!.deg+1];\n od;\n\n for i in [1..fam!.deg] do\n wstates[i] := One(fam!.freegroup);\n perm := ();\n\n for j in [1..Length(exp)] do\n wstates[i] := wstates[i]*fam!.recurgens[exp[j]]!.states[i^perm];\n perm := perm * fam!.recurlist[exp[j]][fam!.deg+1];\n od;\n\n# if fam!.use_rws and Length(wstates[i]) > 0 then\n# wstates[i] := AG_ReducedForm(fam!.rws, wstates[i]);\n# fi;\n od;\n\n invertible := true;\n if not fam!.isgroup then\n for i in exp do\n if i <= fam!.numstates and not IsInvertibleSelfSim(fam!.recurgens[i]) then\n invertible := false;\n break;\n fi;\n od;\n fi;\n\n return __AG_CreateSelfSim(fam, w, wstates, nperm, invertible);\nend);\n\n\n###############################################################################\n##\n#M SelfSim( , )\n##\nInstallMethod(SelfSim, \"for [IsAssocWord, IsSelfSim]\", [IsAssocWord, IsSelfSim],\nfunction(w, a)\n return SelfSim(w, FamilyObj(a));\nend);\n\n\nInstallMethod(MappedWord, [IsAssocWord,\n IsList and IsAssocWordCollection,\n IsList and IsSelfSimCollection],\nfunction(w, fgens, agens)\n local img;\n img := MappedWord(w, fgens, List(agens, a -> a!.word));\n return SelfSim(img, FamilyObj(agens[1]));\nend);\n\n\n###############################################################################\n##\n#M SelfSim( , )\n##\nInstallMethod(SelfSim, \"for [IsAssocWord, IsList]\",\n [IsAssocWord, IsList],\nfunction(w, list)\n local fam;\n fam := SelfSimFamily(list);\n if fam = fail then\n return fail;\n fi;\n return SelfSim(w, fam);\nend);\n\n\n###############################################################################\n##\n#M PrintObj( )\n##\nInstallMethod(PrintObj, \"for [IsSelfSim]\",\n [IsSelfSim],\nfunction (a)\n local deg, printword, i;\n\n printword := function(w)\n if IsOne(w) then Print(AG_Globals.identity_symbol);\n else Print(w); fi;\n end;\n\n if true then\n View(a);\n return;\n fi;\n\n deg := a!.deg;\n printword(a!.word);\n Print(\" = (\");\n for i in [1..deg] do\n printword(a!.states[i]);\n if i <> deg then Print(\", \"); fi;\n od;\n Print(\")\");\n if not IsOne(a!.perm) then AG_PrintTransformation(a!.perm); fi;\nend);\n\n\n###############################################################################\n##\n#M ViewObj( )\n##\nInstallMethod(ViewObj, \"for [IsSelfSim]\",\n [IsSelfSim],\nfunction (a)\n if IsOne(a!.word) then Print(AG_Globals.identity_symbol);\n else Print(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M String( )\n##\nInstallMethod(String, \"for [IsSelfSim]\",\n [IsSelfSim],\nfunction (a)\n if IsOne(a!.word) then return AG_Globals.identity_symbol;\n else return String(a!.word); fi;\nend);\n\n\n###############################################################################\n##\n#M Perm( )\n##\nInstallMethod(Perm, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return a!.perm;\nend);\n\n\n###############################################################################\n##\n#M Word()\n##\nInstallMethod(Word, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return a!.word;\nend);\n\n\n###############################################################################\n##\n#M * \n##\nInstallMethod(\\*, \"for [IsSelfSim, IsSelfSim]\", [IsSelfSim, IsSelfSim],\nfunction(a1, a2)\n local a, i, fam, word, states;\n\n fam := FamilyObj(a1);\n word := a1!.word * a2!.word;\n\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n fi;\n\n if IsOne(word) then\n return One(a1);\n fi;\n\n states := List([1..a1!.deg], i -> a1!.states[i] * a2!.states[i^(a1!.perm)]);\n\n if fam!.use_rws then\n for i in [1..a1!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateSelfSim(FamilyObj(a1), word, states, a1!.perm * a2!.perm,\n IsInvertibleSelfSim(a1) and IsInvertibleSelfSim(a2));\nend);\n\n\n\n\n\n###############################################################################\n##\n#M a1 < a2\n##\nInstallMethod(\\<, \"for [IsSelfSim, IsSelfSim]\", IsIdenticalObj, [IsSelfSim, IsSelfSim],\nfunction(a1, a2)\n local d, checked, checked_words, p, pos, np, np_words, i, perm1, perm2, cmp, G1, G2;\n\n G1 := GroupOfSelfSimFamily(FamilyObj(a1));\n G2 := GroupOfSelfSimFamily(FamilyObj(a2));\n\n # if a1 or a2 are elements of semigroup, which is not a group, then G1 or G2 is `fail'\n\n if IsIdenticalObj(G1, G2) and HasIsFinite(G1) and IsFinite(G1) and a1 = a2 then\n return false;\n fi;\n\n d := a1!.deg;\n\n checked := [[a1, a2]];\n checked_words := [[a1!.word, a2!.word]];\n pos := 0;\n\n while Length(checked) <> pos do\n pos := pos + 1;\n p := checked[pos];\n perm1 := p[1]!.perm;\n perm2 := p[2]!.perm;\n cmp := AG_TrCmp(perm1, perm2, d);\n if cmp < 0 then\n return true;\n elif cmp > 0 then\n return false;\n fi;\n for i in [1..d] do\n np := [Section(p[1], i), Section(p[2], i)];\n np_words := List(np, x -> x!.word);\n if not np_words in checked_words then\n Add(checked, np);\n Add(checked_words, np_words);\n fi;\n od;\n od;\n\n return false;\nend);\n\n\n###############################################################################\n##\n#M InverseOp( )\n##\nInstallMethod(InverseOp, \"for [IsInvertibleSelfSim]\", [IsInvertibleSelfSim],\nfunction(a)\n local i, inv, fam, word, states;\n\n fam := FamilyObj(a);\n word := a!.word ^ -1;\n if fam!.use_rws then\n word := AG_ReducedForm(fam!.rws, word);\n if IsOne(word) then\n return One(a);\n fi;\n fi;\n\n states := List([1..a!.deg], i -> a!.states[i^(a!.perm^-1)]^-1);\n\n if fam!.use_rws then\n for i in [1..a!.deg] do\n states[i] := AG_ReducedForm(fam!.rws, states[i]);\n od;\n fi;\n\n return __AG_CreateSelfSim(FamilyObj(a), word, states, a!.perm^-1, true);\nend);\n\n\n###############################################################################\n##\n#M OneOp( )\n##\nInstallMethod(OneOp, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return One(FamilyObj(a));\nend);\n\n\n###############################################################################\n##\n#M StatesWords( )\n##\nInstallMethod(StatesWords, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return a!.states;\nend);\n\n\n###############################################################################\n##\n#M Sections( )\n##\nInstallMethod(Sections, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return List(a!.states, s -> SelfSim(s, a));\nend);\n\n\n###############################################################################\n##\n#M Section( , )\n##\nInstallMethod(Section, \"for [IsSelfSim, IsPosInt]\", [IsSelfSim, IsPosInt],\nfunction(a, k)\n if k > a!.deg then\n Error(\"in Section(IsSelfSim, IsPosInt): invalid vertex \", k);\n fi;\n return SelfSim(a!.states[k], a);\nend);\n\n\n###############################################################################\n##\n#M Section(a, seq)\n##\n## TODO\nInstallMethod(Section, \"for [IsSelfSim, IsList]\", [IsSelfSim, IsList],\nfunction(a, v)\n if Length(v) = 0 then\n return a;\n fi;\n\n if Length(v) = 1 then\n return Section(a, v[1]);\n fi;\n\n return Section(Section(a, v[1]), v{[2..Length(v)]});\nend);\n\n\n###############################################################################\n##\n#M k ^ a\n##\nInstallMethod(\\^, \"for [IsPosInt, IsSelfSim]\", [IsPosInt, IsSelfSim],\nfunction(k, a)\n return k ^ Perm(a);\nend);\n\n\n###############################################################################\n##\n#M seq ^ a\n##\nInstallMethod(\\^, \"for [IsList, IsSelfSim]\", [IsList, IsSelfSim],\nfunction(seq, a)\n local i, deg, img, cur;\n\n deg := DegreeOfTree(a);\n for i in seq do\n if not IsInt(i) or i < 1 or i > deg then\n Print(\"\\^(IsList, IsFGSelfSim): \",\n i, \"is out of range 1..\", deg, \"\\n\");\n return seq;\n fi;\n od;\n\n if Length(seq) = 0 then return []; fi;\n if Length(seq) = 1 then return [seq[1]^Perm(a)]; fi;\n\n return Concatenation([seq[1]^Perm(a)], seq{[2..Length(seq)]}^Section(a, seq[1]));\nend);\n\n\n###############################################################################\n##\n#M PermOnLevelOp( , )\n##\n## TODO\nInstallMethod(PermOnLevelOp, \"for [IsInvertibleSelfSim, IsPosInt]\",\n [IsInvertibleSelfSim, IsPosInt],\nfunction(a, k)\n local dom, perm;\n\n if k = 1 then\n return a!.perm;\n fi;\n\n dom := AsList(Tuples([1..a!.deg], k));\n perm := List(dom, s -> s^a);\n perm := PermListList(dom, perm);\n\n return perm;\nend);\n\nInstallMethod(TransformationOnFirstLevel, [IsSelfSim],\nfunction(a)\n return AsTransformation(a!.perm);\nend);\n\n\n###############################################################################\n##\n#M IsActingOnBinaryTree( )\n##\nInstallMethod(IsActingOnBinaryTree, \"for [IsSelfSim]\",\n [IsSelfSim],\nfunction(a)\n return a!.deg = 2;\nend);\n\n\n###############################################################################\n##\n#M IsOne( )\n##\nInstallMethod(IsOne, \"for [IsSelfSim]\",\n [IsSelfSim],\nfunction(a)\n local st, state_words, IsOneLocal, G;\n\n G := GroupOfSelfSimFamily(FamilyObj(a));\n\n if HasIsFinite(G) and IsFinite(G) then\n return IsOne(Image(IsomorphismPermGroup(G), a));\n fi;\n\n\n if HasIsContracting(G) and IsContracting(G) then\n return IsOne(Image(MonomorphismToAutomatonGroup(G), a));\n fi;\n\n IsOneLocal := function(s)\n local i, triv;\n if not IsOne(Perm(s)) then return false; fi;\n if s!.word in state_words then return true; fi;\n\n Add(state_words, s!.word);\n triv := true;\n i := 1;\n while triv and i<=s!.deg do\n triv := IsOneLocal(Section(s, i));\n i := i+1;\n od;\n return triv;\n end;\n\n state_words := [];\n\n return IsOneLocal(a);\nend);\n\n\n\n###############################################################################\n##\n#M a1 = a2\n##\n##\nInstallMethod(\\=, \"for [IsSelfSim, IsSelfSim]\", IsIdenticalObj, [IsSelfSim, IsSelfSim],\nfunction(a1, a2)\n local areequalstates, d, checked_pairs, G1, G2;\n\n G1 := GroupOfSelfSimFamily(FamilyObj(a1));\n G2 := GroupOfSelfSimFamily(FamilyObj(a2));\n\n # if a1 or a2 are elements of semigroup, which is not a group, then G1 or G2 is `fail'\n\n if IsIdenticalObj(G1, G2) and HasIsFinite(G1) and IsFinite(G1) then\n return IsOne(Image(IsomorphismPermGroup(G1), a1*a2^-1));\n fi;\n\n d := a1!.deg;\n\n areequalstates := function(a, b)\n local j;\n\n if a!.word = b!.word then\n return true;\n fi;\n\n if [a!.word, b!.word] in checked_pairs then\n return true;\n else\n if a!.perm <> b!.perm then\n return false;\n fi;\n AddSet(checked_pairs, [a!.word, b!.word]);\n for j in [1..d] do\n if not areequalstates(Section(a, j), Section(b, j)) then\n return false;\n fi;\n od;\n return true;\n fi;\n end;\n\n checked_pairs := [];\n return areequalstates(a1, a2);\nend);\n\n\n\nInstallMethod(OrderUsingSections, \"[IsSelfSim, IsCyclotomic]\", true,\n [IsSelfSim, IsCyclotomic],\nfunction(a, max_depth)\n local OrderUsingSections_LOCAL, cur_list, F, degs, vertex, AreConjugateUsingSmallRels, gens_ord2, CyclicallyReduce, res;\n\n CyclicallyReduce := function(w)\n local i, j, wtmp, reduced;\n\n for i in [1..Length(w)] do\n if -w[i] in gens_ord2 then w[i] := -w[i]; fi;\n od;\n\n repeat\n reduced := true;\n j := 1;\n while reduced and jLength(h_list) then return false; fi;\n l := [2..Length(g_list)];\n Add(l, 1);\n long_cycle := PermList(l);\n for i in [0..Length(g_list)-1] do\n if h_list=Permuted(g_list, long_cycle^i) then return true; fi;\n od;\n return false;\n end;\n\n OrderUsingSections_LOCAL := function(g)\n local i, el, orb, Orbs, res, st, reduced_word, loc_order;\n if IsOne(g) then return 1; fi;\n\n if IsActingOnBinaryTree(g) and IsSphericallyTransitive(g) then\n Info(InfoAutomGrp, 3, g!.word, \" acts transitively on levels and is obtained from (\", a!.word, \")^\", Product(degs{[1..Length(degs)]}), \"\\n by taking sections and cyclic reductions at vertex \", vertex);\n return infinity;\n fi;\n\n for i in [1..Length(cur_list)] do\n el := cur_list[i];\n if (AreConjugateUsingSmallRels(g!.word, el!.word) or AreConjugateUsingSmallRels((g!.word)^(-1), el!.word)) then\n if Product(degs{[i..Length(degs)]})>1 then\n if i>1 then Info(InfoAutomGrp, 3, \"(\", a!.word, \")^\", Product(degs{[1..i-1]}), \" has \", el!.word, \" as a section at vertex \", vertex{[1..i-1]}); fi;\n Info(InfoAutomGrp, 3, \"(\", el!.word, \")^\", Product(degs{[i..Length(degs)]}), \" has conjugate of \", g!.word, \" as a section at vertex \", vertex{[i..Length(degs)]});\n SetIsFinite(GroupOfSelfSimFamily(FamilyObj(a)), false);\n return infinity;\n else\n# Info(InfoAutomGrp, 3, \"The group might not be contracting, \", g, \" has itself as a section.\");\n return 1;\n fi;\n fi;\n od;\n if Length(cur_list)>=max_depth then return fail; fi;\n Add(cur_list, g);\n Orbs := OrbitsPerms([g!.perm], [1..g!.deg]);\n loc_order := 1;\n\n for orb in Orbs do\n Add(degs, Length(orb));\n Add(vertex, orb[1]);\n st := Section(g^Length(orb), orb[1]);\n reduced_word := AssocWordByLetterRep(FamilyObj(st!.word), CyclicallyReduce(LetterRepAssocWord(st!.word)));\n# Print(st!.word, \" at \", vertex, \"\\n\");\n res := OrderUsingSections_LOCAL(SelfSim(reduced_word, FamilyObj(g)));\n if res = infinity then return res;\n elif res=fail then\n loc_order:=fail;\n fi;\n if loc_order<>fail then\n loc_order := Lcm(loc_order, res*Length(orb));\n fi;\n Remove(degs);\n Remove(vertex);\n od;\n Remove(cur_list);\n return loc_order;\n end;\n\n F := FamilyObj(a)!.freegroup;\n if IsObviouslyFiniteState(FamilyObj(a)) then\n gens_ord2 := GeneratorsOfOrderTwo(FamilyObj(a));\n else\n gens_ord2 := [];\n fi;\n cur_list := [];\n# degs traces at what positions we raise to what power\n degs := []; vertex := [];\n res := OrderUsingSections_LOCAL(a);\n if res=infinity then\n SetIsFinite(GroupOfSelfSimFamily(FamilyObj(a)), false);\n SetOrder(a, infinity);\n fi;\n return res;\nend);\n\n\n\nInstallMethod(OrderUsingSections, \"for [IsSelfSim]\", true,\n [IsSelfSim],\nfunction(a)\n return OrderUsingSections(a, infinity);\nend);\n\n\n\nInstallMethod(SphericalIndex, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n # XXX check uses of SphericalIndex everywhere\n return rec(start := [], period := [a!.deg]);\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(DegreeOfTree, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return a!.deg;\nend);\n\n# XXX check uses of this everywhere\nInstallMethod(TopDegreeOfTree, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n return a!.deg;\nend);\n\n\n###############################################################################\n##\n#M CanEasilyTestSphericalTransitivity( )\n##\nInstallTrueMethod(CanEasilyTestSphericalTransitivity,\n IsActingOnBinaryTree and IsSelfSim and IsFiniteState);\n\n\n###############################################################################\n##\n#M IsSphericallyTransitive( )\n##\nInstallMethod(IsSphericallyTransitive, \"for [IsInvertibleSelfSim]\",\n [IsInvertibleSelfSim],\nfunction(a)\n local w, i, ab, abs;\n\n if IsOne(Word(a)) then\n Info(InfoAutomGrp, 3, \"IsSphericallyTransitive(a): false\");\n Info(InfoAutomGrp, 3, \" IsOne(Word(a)): a = \", a);\n return false;\n fi;\n\n TryNextMethod();\nend);\n\n\n#########################################################################\n##\n#M Order( )\n##\nInstallMethod(Order, \"for [IsInvertibleSelfSim]\", true,\n [IsInvertibleSelfSim],\nfunction(a)\n local ord_loc;\n if HasIsFiniteState(GroupOfSelfSimFamily(FamilyObj(a))) and IsFiniteState(GroupOfSelfSimFamily(FamilyObj(a))) then\n if IsGeneratedByBoundedAutomaton(UnderlyingAutomatonGroup(GroupOfSelfSimFamily(FamilyObj(a)))) then\n return OrderUsingSections(a, infinity);\n fi;\n fi;\n if IsActingOnBinaryTree(a) and IsSphericallyTransitive(a) then\n return infinity;\n fi;\n ord_loc := OrderUsingSections(a, 10);\n if ord_loc <> fail then\n return ord_loc;\n fi;\n return OrderUsingSections(a, infinity);\nend);\n\n\n#########################################################################\n##\n#M IsTransitiveOnLevel( , )\n##\nInstallMethod(IsTransitiveOnLevel, \"for [IsInvertibleSelfSim, IsPosInt]\",\n [IsInvertibleSelfSim, IsPosInt],\nfunction(a, lev)\n return Length(OrbitPerms([PermOnLevel(a, lev)], 1)) = a!.deg^lev;\nend);\n\n\n#########################################################################\n##\n#M IsFiniteState( )\n##\nInstallMethod(IsFiniteState, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n local st, state_words, find_all_sections;\n\n find_all_sections := function(s)\n local i;\n if not s!.word in state_words then\n Add(state_words, s!.word);\n for i in [1..s!.deg] do find_all_sections(Section(s, i)); od;\n fi;\n end;\n\n state_words := [];\n find_all_sections(a);\n SetAllSections(a, List(state_words, x -> SelfSim(x, FamilyObj(a))));\n return true;\nend);\n\n\n#########################################################################\n##\n#M AllSections( )\n##\nInstallMethod(AllSections, \"for [IsSelfSim]\", [IsSelfSim],\nfunction(a)\n if IsFiniteState(a) then return AllSections(a); fi;\nend);\n\n\n\n#E\n", "meta": {"hexsha": "1e4bb8d082e134804a4aa5f63bb12226f920b4cd", "size": 20909, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "gap/selfsim.gi", "max_stars_repo_name": "gap-packages/automgrp", "max_stars_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-10-02T15:00:11.000Z", "max_stars_repo_stars_event_max_datetime": "2021-10-02T15:00:11.000Z", "max_issues_repo_path": "gap/selfsim.gi", "max_issues_repo_name": "gap-packages/automgrp", "max_issues_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2019-09-21T22:10:40.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-26T23:51:41.000Z", "max_forks_repo_path": "gap/selfsim.gi", "max_forks_repo_name": "gap-packages/automgrp", "max_forks_repo_head_hexsha": "1beb0cbc96c9748cf912433c27c661e1f87ef5dc", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.5299145299, "max_line_length": 210, "alphanum_fraction": 0.5381414702, "num_tokens": 5864, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.66192288918838, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.40468772216055754}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\n#F _IPCodeSums(, )\n#F\n#F Generates unoptimize inplace loop code for \n#F if we know how (i.e. 'ipcode' methods exist for )\n#F\n_IPCodeSums := function(sums, x)\n local code;\n code := sums.ipcode(x);\n code.dimensions := sums.dimensions;\n code.root := sums;\n return code;\nend;\n\nInplace.ipcode := (self, x) >> _IPCodeSums(self.child(1), x);\n\nInplace.code := (self, y, x) >> self.child(1).code(y,x);\n#let(i := Ind(),\n# chain(self.child(1).ipcode(x),\n#\t loop(i, Rows(self), assign(nth(y,i), nth(x,i)))));\n#\nLStep.ipcode := (self, x) >> _CodeSumsAcc(self.child(1), x, x);\n\nCompose.ipcode := (self, x) >> chain(\n List(Reversed(self.children()), c->_IPCodeSums(c, x)));\n\nSUM.ipcode := (self, x) >> chain(\n List(self.children(), c->_IPCodeSums(c, x)));\n\n\n#2x2 inplace blockmat (one entry must be 0)\n#A B \n#0 C\n#Inplace(A%G0 + S0''*B*G1 + C%G1);\nBB.ipcode := (self, x) >> MarkForUnrolling(_CodeSums(self.child(1), x, x));\nBlk.ipcode := (self, x) >> MarkForUnrolling(_CodeSums(self, x, x));\nISum.ipcode := (self, x) >> _CodeSums(self,x,x);\n\n", "meta": {"hexsha": "32e1946b9f3e69fdb3eeee95ddc7f8ddd53a822b", "size": 1185, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/compiler/sums2ipcode.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/compiler/sums2ipcode.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/compiler/sums2ipcode.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 27.5581395349, "max_line_length": 75, "alphanum_fraction": 0.6303797468, "num_tokens": 408, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943925708561, "lm_q2_score": 0.5621765008857982, "lm_q1q2_score": 0.4039768811716395}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nNewRulesFor(TRaderMid, rec(\n Pad_vec := rec(\n applicable := (self, t) >> t.isTag(1, AVecReg) or t.isTag(1, AVecRegCx),\n forTransposition := false,\n apply := (t, C, Nonterms) -> let(\n v := t.firstTag().v,\n ds := Rows(t)-1,\n When(IsInt(ds/v),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), I(ds))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), I(ds)),\n DelayedDirectSum(VScat_sv(fId(1), v , 1), VScat_sv(fId(ds), v, 1))\n * VecRaderMid(t.params[1], t.params[2], t.params[3], v)\n * DelayedDirectSum(VGath_sv(fId(1), v , 1), VGath_sv(fId(ds), v, 1))\n )\n )\n )\n));\n", "meta": {"hexsha": "fc452e6cddff6bf6917c5eb061d675215195ec82", "size": 860, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tradermid.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tradermid.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/vector/breakdown/tradermid.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.8333333333, "max_line_length": 84, "alphanum_fraction": 0.511627907, "num_tokens": 276, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7490872131147275, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.4037454387005374}} {"text": "# Code must be in 0 .. 255.\nCharInt(65);\n# 'A'\nIntChar('Z');\n# 90\n", "meta": {"hexsha": "a1b966c4cc8528614622f3c6eca5fb247d58f09f", "size": 66, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Character-codes/GAP/character-codes.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Character-codes/GAP/character-codes.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Character-codes/GAP/character-codes.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 11.0, "max_line_length": 27, "alphanum_fraction": 0.5454545455, "num_tokens": 29, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.672331699179286, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.4035256594090414}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(UTwid, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(N*da*db)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), omega(da*db,k), omega(N*da*db, k*(i*da+na)*(j*db+nb)))))\n));\nClass(UTwid1, DiagFunc, rec(\n def := (N, n, k, a, b, i) -> rec(size:=n),\n lambda := self >> let(N:=self.params[1], n:=self.size, k:=self.params[3],\n\ta := self.params[4], b := self.params[5], i := self.params[6],\n\tna := Numerator(a), nb := Numerator(b),\n\tda := Denominator(a), db := Denominator(b),\n\tw := E(N*da*db)^k, j := Ind(n),\n\tLambda(j, cond(eq(j,n/2), 1, omega(N*da*db, k*(i*da+na)*(j*db+nb)))))\n));\n\nClass(UDFT_NonTerm, DFT_NonTerm, rec(\n isReal := False,\n));\n\nClass(UDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4*r*c,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) *\n\tDFT(n,k).terminate()),\n\n conjTranspose := self >> ObjId(self)(self.params[1], -self.params[2]).transpose()\n));\nUDFT1 := UDFT;\n\nClass(UDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 2=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2*n))]) ],\n omega4pow := (r,c)->2*r*(2*c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I(n-2))^L(n,n/2) *\n\tDFT2(n,k).terminate()),\n));\n\nClass(UUDFT, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod n)]) ],\n omega4pow := (r,c)->4*r*c,\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT(2))^-1,\n\tDirectSum(Mat(m), I((n-4)/2), Mat(m), I((n-4)/2))^L(n,n/2) *\n\tDFT(n,k).terminate()),\n));\nUUDFT1 := UUDFT;\n\nClass(UUDFT2, UDFT_NonTerm, rec(\n abbrevs := [ \n (n) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), [n, 1]),\n (n,k) -> Checked(IsPosIntSym(n), AnySyms(n) or (n mod 4=0), \n\t IsIntSym(k), AnySyms(n,k) or Gcd(n,k)=1, \n\t\t [n, When(AnySyms(n,k), k, k mod (2*n))]) ],\n omega4pow := (r,c)->2*r*(2*c+1),\n terminate := self >> let(\n\tn:=self.params[1], k:=self.params[2], m:=MatSPL(DFT2(2,k))^-1,\n\tDirectSum(Mat(m), I((n-2)/2), Mat(m), I((n-2)/2))^L(n,n/2) *\n\tDFT2(n,k).terminate()),\n));\n", "meta": {"hexsha": "0f61c691bb7e9a2e56a15a697cbd3f0d38d9256b", "size": 3168, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/transforms/dft/udft.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/transforms/dft/udft.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/transforms/dft/udft.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 37.7142857143, "max_line_length": 84, "alphanum_fraction": 0.5299873737, "num_tokens": 1233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.757794360334681, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.4025474672995523}} {"text": "for i in [1 .. 5] do\n for j in [1 .. i] do\n Print(\"*\");\n od;\n Print(\"\\n\");\nod;\n\n# *\n# **\n# ***\n# ****\n# *****\n", "meta": {"hexsha": "95f3b7fd2725fa0eccc1f344c80e2aa4525ea920", "size": 126, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "Task/Loops-For/GAP/loops-for.gap", "max_stars_repo_name": "LaudateCorpus1/RosettaCodeData", "max_stars_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_stars_repo_licenses": ["Info-ZIP"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2018-11-09T22:08:38.000Z", "max_stars_repo_stars_event_max_datetime": "2018-11-09T22:08:38.000Z", "max_issues_repo_path": "Task/Loops-For/GAP/loops-for.gap", "max_issues_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_issues_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_issues_repo_licenses": ["Info-ZIP"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Task/Loops-For/GAP/loops-for.gap", "max_forks_repo_name": "seanwallawalla-forks/RosettaCodeData", "max_forks_repo_head_hexsha": "9ad63ea473a958506c041077f1d810c0c7c8c18d", "max_forks_repo_licenses": ["Info-ZIP"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-11-09T22:08:40.000Z", "max_forks_repo_forks_event_max_datetime": "2018-11-09T22:08:40.000Z", "avg_line_length": 9.6923076923, "max_line_length": 24, "alphanum_fraction": 0.2777777778, "num_tokens": 48, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.5926666143433998, "lm_q2_score": 0.6791787121629465, "lm_q1q2_score": 0.4025265478717239}} {"text": "############################################################################\n##\n## recognizeprim.gi IRREDSOL Burkhard H\u00f6fling\n##\n## Copyright \u00a9 2003\u20132016 Burkhard H\u00f6fling\n##\n\n\n###########################################################################\n##\n#F IdPrimitiveSolubleGroup()\n##\n## see IRREDSOL documentation\n## \nInstallMethod(IdPrimitiveSolubleGroup, \"for soluble group\",\n true, [IsSolvableGroup and IsFinite], 0,\n G -> IdIrreducibleSolubleMatrixGroup(IrreducibleMatrixGroupPrimitiveSolubleGroup(G)));\n\n\nRedispatchOnCondition(IdPrimitiveSolubleGroup, true, [IsGroup],\n [IsFinite and IsSolvableGroup], 0);\n\n\n###########################################################################\n##\n#F IdPrimitiveSolubleGroupNC()\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(IdPrimitiveSolubleGroupNC,\n function(G)\n local id;\n id := IdIrreducibleSolubleMatrixGroup(IrreducibleMatrixGroupPrimitiveSolubleGroupNC(G));\n SetIdPrimitiveSolubleGroup(G, id);\n return id;\n end);\n \n\n############################################################################\n##\n#F RecognitionPrimitiveSolubleGroup()\n##\n## see IRREDSOL documentation\n## \nInstallGlobalFunction(RecognitionPrimitiveSolubleGroup,\n function(G, wantiso)\n \n local N, F, p, pcgsN, C, pcgsC, one, i, mat, mats, CC, H, hom, infomat, info, rep, ext, imgs, g, r;\n \n N := FittingSubgroup(G);\n \n pcgsN := Pcgs(N);\n p := Set(RelativeOrders(pcgsN));\n if Length(p) <> 1 then\n Error(\"G must be primitive\");\n fi;\n \n p := p[1];\n \n if not IsAbelian(N) or ForAny(pcgsN, g -> g^p <> One(G)) then\n Error(\"G must be primitive\");\n fi;\n \n # now we know that N is elementary abelian of exponent p\n \n F := GF(p); \n one := One(F);\n \n mats := [];\n \n C := ComplementClassesRepresentatives(G, N);\n if Length(C) <> 1 then\n Error(\"G must be primitive\");\n fi;\n \n C := C[1];\n \n # N is complemented\n \n pcgsC := Pcgs(C);\n for g in pcgsC do\n mat := [];\n for i in [1..Length(pcgsN)] do\n mat[i] := ExponentsOfPcElement(pcgsN, pcgsN[i]^g)*one;\n od;\n Add(mats, ImmutableMatrix(F, mat));\n od;\n \n if not MTX.IsIrreducible(GModuleByMats(mats, F)) then\n Error(\"G must be primitive\");\n fi;\n \n H := Group(mats);\n \n # the recognition part works best if the source of the representation isomorphism is a pc group\n \n if IsPcGroup(C) then\n CC := C;\n else\n CC := PcGroupWithPcgs(Pcgs(C));\n fi;\n \n SetSize(H, Size(C));\n hom := GroupGeneralMappingByImagesNC(CC, H, Pcgs(CC), mats);\n SetIsGroupHomomorphism(hom, true);\n SetIsBijective(hom, true);\n SetRepresentationIsomorphism(H, hom);\n\n infomat := RecognitionIrreducibleSolubleMatrixGroup(H, wantiso, wantiso, wantiso);\n\n info := rec(id := infomat.id);\n if not wantiso then\n return info;\n fi;\n\n rep := RepresentationIsomorphism(infomat.group);\n \n ext := PcGroupExtensionByMatrixAction(Pcgs(Source(rep)), rep);\n \n imgs := [];\n for g in Pcgs(CC) do\n Add(imgs, ImageElm(ext.embed, ImageElm(infomat.iso, g)));\n od;\n for r in infomat.mat do\n g := PcElementByExponents(ext.pcgsV, List(r, IntFFE));\n Add(imgs, g);\n od;\n \n info.group := ext.E;\n info.iso := GroupHomomorphismByImages(G, ext.E,\n Concatenation(pcgsC, pcgsN), imgs);\n if info.iso = fail or not IsBijective(info.iso) then\n Error(\"wrong group homomorphism\");\n fi;\n return info;\n end);\n \n\n############################################################################\n##\n#E\n##\n\n ", "meta": {"hexsha": "167d02f2742c7185075551315af080672498b8ae", "size": 4102, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "lib/recognizeprim.gi", "max_stars_repo_name": "fingolfin/irredsol", "max_stars_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_stars_repo_licenses": ["BSD-2-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2017-09-01T16:53:11.000Z", "max_stars_repo_stars_event_max_datetime": "2017-09-01T16:53:11.000Z", "max_issues_repo_path": "lib/recognizeprim.gi", "max_issues_repo_name": "fingolfin/irredsol", "max_issues_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_issues_repo_licenses": ["BSD-2-Clause"], "max_issues_count": 7, "max_issues_repo_issues_event_min_datetime": "2017-08-02T16:19:58.000Z", "max_issues_repo_issues_event_max_datetime": "2021-07-01T08:57:23.000Z", "max_forks_repo_path": "lib/recognizeprim.gi", "max_forks_repo_name": "fingolfin/irredsol", "max_forks_repo_head_hexsha": "c7ab06f5123650049142a5ae3a1c1e05a38d2151", "max_forks_repo_licenses": ["BSD-2-Clause"], "max_forks_count": 2, "max_forks_repo_forks_event_min_datetime": "2016-02-17T18:26:09.000Z", "max_forks_repo_forks_event_max_datetime": "2019-10-02T10:40:35.000Z", "avg_line_length": 28.4861111111, "max_line_length": 107, "alphanum_fraction": 0.4953681131, "num_tokens": 980, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7154239957834733, "lm_q2_score": 0.5621765008857982, "lm_q1q2_score": 0.40219455859928904}} {"text": "#!/usr/bin/gap\n\n# time gap -o 8g clifford.gap\n\n# Build clifford groups, up to 3 qubits, and\n# search for T operators defined by field extensions......\n\n\nPrint(\"running clifford.gap\\n\");;\n\n# See:\n# https://www.mathstat.dal.ca/~selinger/papers/clifford.pdf\n\nr2 := Sqrt(2);;\nir2 := 1/r2;;\n\ni := [[1, 0], [0, 1]];;\nw := [[E(4), 0], [0, E(4)]];;\nx := [[0, 1], [1, 0]];;\nz := [[1, 0], [0, -1]];;\ns := [[1, 0], [0, E(4)]];;\nh := [[ir2, ir2], [ir2, -ir2]];;\n\nCliff1 := Group(w, s, h);; # Order 192\nPauli1 := Group(w, x, z);; # Order 32\n\nfor U in Cliff1 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli1 do\n if (U*g*Inverse(U)*Inverse(g) in Pauli1) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\nxi := KroneckerProduct(x, i);;\nix := KroneckerProduct(i, x);;\nzi := KroneckerProduct(z, i);;\niz := KroneckerProduct(i, z);;\nsi := KroneckerProduct(s, i);;\nis := KroneckerProduct(i, s);;\nhi := KroneckerProduct(h, i);;\nih := KroneckerProduct(i, h);;\nwi := KroneckerProduct(w, i);;\n\n\ncz := [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, -1]];;\n\nCliff2 := Group(si, is, hi, ih, wi, cz);; # Order 92160\n#for g in Cliff2 do Print(g, \"\\n\"); od;\nPauli2 := Group(wi, xi, ix, zi, iz);;\n\n# Works:\nfor U in Cliff2 do\n found := false;;\n #Udag := Inverse(U);\n #Print(\"found? \");\n for g in Pauli2 do\n if (U*g*Inverse(U)*Inverse(g) in Pauli2) then found:=true; break; fi;\n od;\n if not found then Print(\"Not found\\n\"); fi;\nod;\n\na := [\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n [-1, 0, 0, 0]];; # a in G2 = true\n\n#Print(a*a, \"\\n\");\n#Print(a*a*a, \"\\n\");\n#Print(a*a*a*a, \"\\n\");\n\n# Print(Order(G2));\n\n\nxii := KroneckerProduct(xi, i);;\nixi := KroneckerProduct(i, xi);;\niix := KroneckerProduct(i, ix);;\n\nzii := KroneckerProduct(zi, i);;\nizi := KroneckerProduct(i, zi);;\niiz := KroneckerProduct(i, iz);;\n\nsii := KroneckerProduct(si, i);;\nisi := KroneckerProduct(i, si);;\niis := KroneckerProduct(i, is);;\n\nhii := KroneckerProduct(hi, i);;\nihi := KroneckerProduct(i, hi);;\niih := KroneckerProduct(i, ih);;\n\nwii := KroneckerProduct(wi, i);;\n\nicz := KroneckerProduct(i, cz);;\nczi := KroneckerProduct(cz, i);;\n\nca := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0]];;\n\ncb := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0]];;\n\ncc := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, -1, 0, 0, 0],\n [0, 0, 0, 0, 0, -1, 0, 0],\n [0, 0, 0, 0, 0, 0, -1, 0]];;\n\n\nTofolli := [\n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 1],\n [0, 0, 0, 0, 0, 0, 1, 0]];;\n\n\nCliff3 := Group(sii, isi, iis, hii, ihi, iih, wii, icz, czi);; # Order 743178240\nPauli3 := Group(wii, xii, ixi, iix, zii, izi, iiz);; # Order 256\n\n# Print(Order(Pauli3), \"\\n\");;\n\n# ca in Cliff3 = false\n# ca in third level of clifford hierarchy = true\n\n\nCliff3_12 := Group(sii, isi, hii, ihi, wii, czi);;\nCliff3_13 := Group(sii, iis, hii, iih, wii);; # cz on 1&3 ??\nCliff3_23 := Group(isi, iis, ihi, iih, wii, icz);;\n\n#SmCliff3 := Group(sii, isi, iis, hii, ihi, iih, icz, czi);; # Order 743178240\n\nPrint(\"warming up...\\n\");\nOrder(Cliff3);; # need this line otherwise membership test eats all memory...!\nPrint(\"Ok\\n\");\n\nin_third_level := function(U)\n # Is U in the third level of the clifford hierarchy ?\n local A;\n for g in Pauli3 do\n A := U*g*Inverse(U)*Inverse(g);\n if A in Cliff3_12 then continue; fi;\n if A in Cliff3_13 then continue; fi;\n if A in Cliff3_23 then continue; fi;\n if A in Cliff3 then continue; fi;\n return false; # no\n od;\n return true; # yes\nend;;\n\n\nPrint(\"in_third_level(ca):\", in_third_level(ca), \"\\n\"); # true\nPrint(\"in_third_level(cb):\", in_third_level(cb), \"\\n\"); # true\nPrint(\"in_third_level(cc):\", in_third_level(cc), \"\\n\"); # true\nPrint(\"in_third_level(Tofolli):\", in_third_level(Tofolli), \"\\n\"); # true\nPrint(\"in_third_level(Tofolli*ca):\", in_third_level(Tofolli*ca), \"\\n\"); # false\n\nU3 := [ \n [1, 0, 0, 0, 0, 0, 0, 0],\n [0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 0, 0]];\n\nPrint(\"# Where do control control 1-qubit Pauli gates live ?\\n\");\nfor g in Pauli1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control control 1-qubit clifford gates live ?\\n\");\nfor g in Cliff1 do \n #Print(g, \"\\n\");\n U3{[7,8]}{[7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit Pauli gates live ?\\n\");\nfor g in Pauli2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\nPrint(\"\\n\");\n\nPrint(\"# Where do control 2-qubit clifford gates live ?\\n\");\nfor g in Cliff2 do \n #Print(g, \"\\n\");\n U3{[5,6,7,8]}{[5,6,7,8]} := g;\n if U3 in Pauli3 then Print(\"1\\c\"); continue; fi;\n if U3 in Cliff3 then Print(\"2\\c\"); continue; fi;\n if in_third_level(U3) then Print(\"3\\c\"); else Print(\".\\c\"); fi;\nod;\n\nPrint(\"\\n\");\n\nPrint(\"Done.\\n\");\n\n\n", "meta": {"hexsha": "99b868878e0cf5e0ad4958cda6de0234c36a9d5d", "size": 6194, "ext": "gap", "lang": "GAP", "max_stars_repo_path": "bruhat/dev/clifford.gap", "max_stars_repo_name": "punkdit/bruhat", "max_stars_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 3, "max_stars_repo_stars_event_min_datetime": "2020-04-07T13:21:30.000Z", "max_stars_repo_stars_event_max_datetime": "2020-07-15T02:07:20.000Z", "max_issues_repo_path": "bruhat/dev/clifford.gap", "max_issues_repo_name": "punkdit/bruhat", "max_issues_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "bruhat/dev/clifford.gap", "max_forks_repo_name": "punkdit/bruhat", "max_forks_repo_head_hexsha": "3231eacc49fd3464542f7eb72684751371d9876c", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 25.9163179916, "max_line_length": 80, "alphanum_fraction": 0.5182434614, "num_tokens": 2859, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.8221891392358015, "lm_q2_score": 0.48828339529583464, "lm_q1q2_score": 0.40146130448141687}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nDeclare(GT);\nDeclare(ListProduct);\n\nListProduct := function(l)\n local prod, i;\n if Length(l) <=0 then return 0; fi;\n prod := 1;\n for i in l do\n prod := prod * i;\n od;\n return(prod);\nend;\n\nGTVec := XChain([0,1]);\nGTPar := XChain([1,0]);\n\nTTensorI_GT := function(gt)\n local spl, g, s, v, tags;\n [spl,g,s,v] := gt.params;\n tags := gt.getTags();\n Constraint(IsList(v) and Length(v)=1 and IsPosInt(v[1]));\n g := When(g=XChain([0,1]), AVec, APar);\n s := When(s=XChain([0,1]), AVec, APar);\n return TTensorI(spl, v[1], s, g).withTags(tags);\nend;\n\nGT_TTensorI := function(tt)\n local spl, g, s, v, tags;\n [spl,v,s,g] := tt.params;\n tags := tt.getTags();\n g := When(g=AVec, GTVec, GTPar);\n s := When(s=AVec, GTVec, GTPar);\n return GT(spl, g, s, [v]).withTags(tags);\nend;\n\nIsGT := x -> IsRec(x) and IsBound(x.isGT) and x.isGT;\n\nClass(GTBase, rec(\n isGT := true,\n\n freeTags := self >> Filtered(self.tags, x -> not x.isSticky),\n stickyTags := self >> Filtered(self.tags, x -> x.isSticky),\n\n stickyRank := self >> Length(self.stickyTags()),\n freeRank := self >> self.rank() - self.stickyRank(),\n freeLoops := self >> [self.stickyRank()+1 .. self.rank()],\n\n transposedTags := self >> List(self.tags, x->x.transpose()),\n\n getSpl := self >> self.params[1],\n setSpl := (self, spl) >> ApplyFunc(ObjId(self), Concatenation([spl], Drop(self.params, 1)))\n .withTags(self.tags),\n\n # need setIts(its) and getIts()\n _fmanip := meth(self, func_manip, gt_manip, newits) \n local cpy, z;\n\t cpy := Copy(self);\n \t z := SubstTopDownNR_named(cpy, @.cond(x -> (not Same(x, cpy) and IsGT(x)) or IsFunction(x) or IsFuncExp(x) or ObjId(x)=ind), \n\t e -> When(IsGT(e), gt_manip(e), func_manip(e)), \"__GT._fmanip\");\n return z.setIts(newits);\n end,\n\n bodyRank := self >> Maximum( [0] ::\n\tList(Collect(self.getSpl(), @.cond(e->IsFunction(e) or IsFuncExp(e))), _rank)),\n\n downRankFull := (self, inds) >> let(thisrank := self.rank(), \n\tself._fmanip(f -> f.downRankFull(inds), \n\t e -> Cond(e.bodyRank()=0, e, Error(\".downRankFull does not work with nested GTs\")),\n\t\t [])),\n\n\n downRank := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid, ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t ListWithout(self.getIts(), loopid)),\n # downRankOuter: notification that downRank performed on some outer GT, \n # so that this GT can update its functions and notify children.\n downRankOuter := (self, loopid, ind) >>\n self._fmanip(f -> f.downRank(loopid + self.rank(), ind), \n\t e -> e.downRankOuter(loopid + e.rank(), ind), \n\t self.getIts()),\n\n rotate := (self, n) >> When(n=1, self, let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n), \n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res,\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [stags[n]] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n \t Error(\"Can't make non-sticky rank an inner loop, because sticky tags exist\")\n # it could look like this instead: res.setTags( [ANoTag] :: tags )\n\t))),\n\n rotateIntoSticky := (self, n, newtag) >> let(\n\tits := self.getIts(), \n\ttags := self.getTags(),\tstags := self.stickyTags(), ftags := self.freeTags(),\n res := self._fmanip(\n\t f -> f.rotate(n),\n\t e -> Cond(e.bodyRank() <= e.rank(), e, \n\t\t Error(\".rotate() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\t [its[n]] :: its{[1..n-1]} :: its{[n+1..Length(its)]}),\n\tCond(self.stickyRank() = 0, \n\t res.setTags(tags :: [newtag]),\n\t n <= self.stickyRank(),\n\t res.setTags( ftags :: [newtag] :: stags{[1..n-1]} :: stags{[n+1..Length(stags)]}),\n\t # else, n > self.stickyRank(),\n res.setTags( ftags :: [newtag] :: stags )\n\t)),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRank := self >> self._fmanip(\n\tf -> f.upRank(), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRank() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation([0], self.getIts())),\n\n # NOTE: upRank() leaves GT in inconsistent state, because sticky tags still need to be shifted\n upRankBy := (self, n) >> self._fmanip(\n\tf -> f.upRankBy(n), \n\te -> Cond(e.bodyRank() <= e.rank(), e, \n\t Error(\".upRankBy() doesn't support nested GTs where inner GTs depend on outer indices\")),\n\tConcatenation(Replicate(n, 0), self.getIts())),\n\n split := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid, inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n Concatenation(its{[1..loopid-1]}, [inner_its, outer_its], its{[loopid+1..Length(its)]}))),\n # splitOuter: notification that some outer GT is splitting loop, \n # so that this GT can update its functions and notify children.\n splitOuter := (self, loopid, inner_its, outer_its) >> let(its := self.getIts(),\n self._fmanip(\n\t f -> f.split(loopid + self.rank(), inner_its, outer_its),\n\t e -> e.splitOuter(loopid + e.rank(), inner_its, outer_its), \n its)),\n\n getGath := self >> Error(\"Must be implemented in a subclass\"),\n\n getScat := self >> Error(\"Must be implemented in a subclass\"),\n\n isReal := self >> self.params[1].isReal(),\n toAMat := self >> self.toSpl().toAMat(),\n # when self.getIts() returns empty list it actually means single iteration,\n # that's why [1] appended to the list\n normalizedArithCost := self >> self.getSpl().normalizedArithCost() * ListProduct(self.getIts() :: [1]),\n\n children := self >> [self.params[1]],\n child := (self, n) >> Checked( n = 1, self.params[1] ),\n\n # overrideing withTags() to make sure non-sticky/sticky tags order is preserved\n # returns a copy of the object with 'tags' added on to any existing tags.\n withTags := (self, tags) >> self.setTags(Flat(TransposedMat(\n List([self.tags, tags], t -> SplitBy(t, e -> not e.isSticky))))),\n));\n\n# GT(, , , ) - generalized problem spec\n#\n# NOTE: assumes tightly packed data, i.e. Dims(GT(spl)) = Dims(spl) * Product(v)\n# (if gath/scat functions have domain&range == 0)\nClass(GT, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, gath, scat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, gath, scat, v]\n ) ],\n\n dims := self >> let(p := self.params, r := range(p[3]), c := range(p[2]), d := p[1].dims(),\n When(r<>0 and c<>0,\n [r, c],\n let(prod := Product(p[4]), [d[1]*prod, d[2]*prod]))), # NOTE: assumes XChain.\n\n advdims := self >> let(p := self.params, [p[3].advrange(), p[2].advrange()]),\n\n getIts := self >> self.params[4],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], its).withTags(self.tags),\n getGath := self >> self.params[2],\n getScat := self >> self.params[3],\n\n rank := self >> Length(self.params[4]),\n\n _scat := Scat,\n _gath := Gath,\n\n # NOTE: toSpl doesn't work with nested GTs. It should use downRank method for function manipulations\n toSpl := self >> self.toSplCx([]),\n toSplCx := (self, outer_inds) >> let(\n p := self.params, spl := Copy(p[1]), g := Copy(p[2]), s := Copy(p[3]), dims := p[4],\n inds := List(dims, Ind), allinds := Concatenation(inds, outer_inds),\n kernel := self._scat(s.toSpl(allinds, Rows(spl))) * spl * self._gath(g.toSpl(allinds, Cols(spl))),\n kerneld := Cond(inds=[], kernel, # downRank only if not rank-0\n SubstTopDownNR(kernel, @.cond(e->IsFunction(e) or IsFuncExp(e)), e->e.downRankFull(allinds))),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kerneld)\n ),\n\n toISums := self >> let(\n inds := List(self.getIts(), Ind),\n kernel := self._scat(self.getScat()) * self.params[1] * self._gath(self.getGath()),\n FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel)\n ),\n\n transpose := self >> let(p:=self.params,\n GT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n conjTranspose := self >> let(p:=self.params,\n GT(p[1].conjTranspose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4]).withTags(self.tags)),\n));\n\nDeclare(GTAccT, GTAcc0T);\n\n# GTAcc(, , , ) - generalized problem spec with accumulation on output side\n#\nClass(GTAcc, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAccT(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc\n));\n\nClass(GTAcc0, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0T(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n _scat := ScatAcc,\n\n toSplCx := (self, outer_inds) >> Checked(self.rank()=1, let( # NOTE: works only for rank-1\n dims := self.getIts(),\n inds0 := Concatenation(List(DropLast(dims,1), Ind), [0]),\n inds := Concatenation(List(DropLast(dims,1), Ind), [Ind(Last(dims)-1)]),\n inds_shft := Concatenation(DropLast(inds,1), [Last(inds)+1]),\n\n dr0 := self.downRankFull(Concatenation(inds0, outer_inds)),\n dr := self.downRankFull(Concatenation(inds_shft, outer_inds)),\n kernel0 := Scat(dr0.getScat()) * dr0.params[1] * self._gath(dr0.getGath()),\n kernel := ScatAcc(dr.getScat()) * dr .params[1] * self._gath(dr .getGath()),\n When(Last(dims)=1,\n kernel0,\n SUM(kernel0, FoldL(inds, (ker, idx) -> ISum(idx.setAttr(\"GT\"), ker), kernel))))\n ),\n));\n\n# GTAccT == GTAcc.transpose(), even though semantically GTAccT == GT, we need a separate object, so that\n# GTAccT.transpose() is back to GTAcc itself.\nClass(GTAccT, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nClass(GTAcc0T, GT, rec(\n transpose := self >> let(p:=self.params,\n GTAcc0(p[1].transpose(), p[3], p[2], p[4]).withTags(self.transposedTags())),\n));\n\nDeclare(GTInplace);\n\nClass(GTInplace, GTBase, Tagged_tSPL, rec(\n abbrevs := [ (spl, gathscat, v) -> Checked(\n IsSPL(spl), IsIndexMapping(gathscat), IsList(v), ForAll(v, IsPosInt0Sym),\n [spl, gathscat, v]) ],\n\n dims := self >> let(p := self.params, rc := range(p[2]), d := p[1].dims(),\n When(rc<>0,\n [rc, rc],\n let(prod:=Product(p[3]), [d[1]*prod, d[2]*prod]))), # NOTE: assumes XChain.\n\n getIts := self >> self.params[3],\n setIts := (self,its) >> GTInplace(self.params[1], self.params[2], its).withTags(self.tags),\n\n getGath := self >> self.params[2],\n getScat := self >> self.params[2],\n\n rank := self >> Length(self.params[3]),\n toGT := self >> let(p:=self.params, GT(p[1], p[2], p[2], p[3]).withTags(self.tags)),\n toNonInplace := self >> self.toGT(),\n toSpl := self >> Inplace(self.toGT().toSpl()),\n isInplace := self >> true,\n\n conjTranspose := self >> let(p:=self.params,\n GTInplace(p[1].conjTranspose(), p[2], p[3]).withTags(self.transposedTags())),\n\n transpose := self >> let(p:=self.params,\n GTInplace(p[1].transpose(), p[2], p[3]).withTags(self.transposedTags())),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3]).withTags(self.tags))\n));\n\n\n#\n# NOTE: what if there is no SUM scatters or gathers\n#\n\nClass(GTPS, GTBase, Tagged_tSPL, rec(\n abbrevs := [\n (spl, fb_cnt, gath, scat, v) -> Checked(\n IsSPL(spl), IsPosInt(fb_cnt), IsIndexMapping(gath), IsIndexMapping(scat), IsList(v),\n ForAll(v, IsPosInt0Sym),\n [spl, fb_cnt, gath, scat, v]\n ) ],\n\n dims := self >> let( p := self.params, r := range(p[4]), c := range(p[3]), \n d := p[1].dims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n advdims := self >> let(p := self.params, r := p[4].advrange(), c := p[3].advrange(), \n d := p[1].advdims(), \n [ StripList(Flat([d[1]]){[1..p[2]]} :: Flat([r])), \n StripList(Flat([d[2]]){[1..p[2]]} :: Flat([c])) ]),\n\n getIts := self >> self.params[5],\n setIts := (self,its) >> ObjId(self)(self.params[1], self.params[2], self.params[3], self.params[4], its).withTags(self.tags),\n getGath := self >> fCross(List(Flat([self.params[1].advdims()[1]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[3]]),\n getScat := self >> fCross(List(Flat([self.params[1].advdims()[2]]){[1..self.params[2]]}, e -> fId(e)) :: [self.params[4]]),\n\n rank := self >> Length(self.params[5]),\n\n toSpl := self >> let(\n inds := List(self.params[5], Ind),\n kernel := FoldR([1..self.rank()], (ker, i) -> ker.downRank(i, inds[i]), Copy(self)),\n spl := Scat(kernel.getScat()) * kernel.child(1) * Gath(kernel.getGath()),\n FoldL(inds, (ker, idx) -> IParSeq(idx.setAttr(\"GT\"), kernel.params[2], ker), spl)),\n\n hashAs := self >> let(p:=self.params,\n ObjId(self)(HashAsSPL(p[1]), p[2], p[3], p[4], p[5]).withTags(self.tags)),\n \n));\n\n# Useful identities:\n#\n# Tr(m,n) = GT(I(m), XChain([0,1]), XChain([1,0]), [n]) =\n# GT(I(n), XChain([1,0]), XChain([0,1]), [m]) = L(m*n, n)\nGT_Tr1 := (m,n) -> GT(I(m), XChain([0,1]), XChain([1,0]), [n]);\nGT_Tr2 := (m,n) -> GT(I(n), XChain([1,0]), XChain([0,1]), [m]);\n\nGT_Tr1u := (m,n,u) -> let(uu:=When(m mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([1,0,2]), XChain([2,1,0]), [m/uu, n]));\n\nGT_Tr2u := (m,n,u) -> let(uu:=When(n mod u = 0, u, 1),\n GT(BB(I(uu)), XChain([2,1,0]), XChain([1,0,2]), [n/uu, m]));\n\n\nNewRulesFor(GT, rec(\n GT_Base := rec(\n\tswitch := false,\n\ta := rec(maxSize := false),\n # requiredFirstTag := ANoTag,\n\tapplicable := (self, t) >> let(rank := Length(t.params[4]), spl := t.params[1],\n rank = 0 and (self.a.maxSize=false\n\t\tor Rows(spl) <= self.a.maxSize or Cols(spl) <= self.a.maxSize)),\n freedoms := (self, t) >> [],\n\tchild := (t, fr) -> [ t.params[1].withTags(t.getTags()) ],\n\tapply := (t, C, Nonterms) -> let(\n g := t.params[2], s := t.params[3],\n Scat(s.toSpl([], Rows(C[1]))) * C[1] * Gath(g.toSpl([], Cols(C[1])))\n )\n ),\n\n GT_NthLoop := rec(\n\t requiredFirstTag := [ANoTag, ALimitNthLoop],\n\t applicable := t -> let(rank := Length(t.params[4]), rank > 0), \n\n # restrict to innermost first (i.e. loop interchange)\n\t # to search over loop orders use [1..nloops]\n\n # Limit tag reduces the number of loop interchanges.\n # it is useful when you don't want the number of potential\n # ruletrees to explode, and you are not overtly concerned\n # with having access to all the potential ones.\n freedoms := t -> let(\n fr := [1..Length(t.params[4])], \n When(t.hasTag(ALimitNthLoop),\n [[1]],\n [fr]\n )\n ),\n\n\t child := (t, fr) -> let(\n\t spl := t.params[1], \n g := t.params[2], \n s := t.params[3], \n loopid := fr[1],\n\t [ \n GT(spl, g.without(loopid), \n s.without(loopid), ListWithout(t.params[4], loopid)), \n InfoNt(loopid) \n ]\n ),\n\n\t apply := (t, C, Nonterms) -> let(\n\t loopid := Nonterms[2].params[1], \n dft := Nonterms[1].params[1], \n\t g := t.params[2], \n s := t.params[3],\n\t loop_dims := t.params[4],\n\t i := Ind(loop_dims[loopid]),\n\n\t ISum(i, Scat(s.part(loopid, i, Rows(dft), loop_dims)) \n * C[1] \n * Gath(g.part(loopid, i, Cols(dft), loop_dims)))\n )\n ),\n\n GT_BufReshape := rec(\n bufIters := [2, 4, 8, 16, 32],\n requiredFirstTag := ANoTag,\n\n applicable := (self, t) >> Length(t.params[4])=1 and let(\n N := Minimum(t.params[1].dimensions), its := t.params[4][1],\n PatternMatch(t, [GT, @, @(2,XChain), @(3,XChain), ...], empty_cx()) and\n (@(2).val.params[1] = [0,1] or @(3).val.params[1] = [0,1]) and\n ForAny(self.bufIters, bi -> bi < its and IsInt(its/bi))),\n\n u := [2,4,8,16],\n\n children := (self, t) >> let(\n spl := t.params[1], its := t.params[4][1],\n bufiters := Filtered(self.bufIters, bi -> (bi < its) and IsInt(its/bi)),\n Map2(Cartesian(bufiters, self.u), (bi, u) ->\n [ GT(spl, XChain([1,0]), XChain([1,0]), [bi]),\n InfoNt(u) ])),\n\n apply := (self, t, C, Nonterms) >> let(\n g := t.params[2].params[1], s := t.params[3].params[1],\n gg := When(g=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n ss := When(s=[0,1], XChain([0,1,2]), XChain([1,2,0])),\n spl := t.params[1], its := t.params[4][1], inner := Nonterms[1].params[4][1],\n i := Ind(its / inner),\n u := When(IsBound(Nonterms[2]), Nonterms[2].params[1], 4),\n\n ISum(i, Scat(ss.part(1, i, Rows(spl), [i.range, inner])) *\n When(s=[0,1], GT_Tr2u(inner, Rows(spl), u).toSpl(), I(Rows(spl)*inner)) *\n C[1] *\n When(g=[0,1], GT_Tr1u(Cols(spl), inner, u).toSpl(), I(Cols(spl)*inner)) *\n Gath(gg.part(1, i, Cols(spl), [i.range, inner]))\n )\n )\n )\n));\n", "meta": {"hexsha": "96647f9fa2ada3b111abfb5b8f18a7e91e0d4333", "size": 17897, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/gt.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/common/gt.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/common/gt.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 39.5951327434, "max_line_length": 129, "alphanum_fraction": 0.5567413533, "num_tokens": 5721, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6688802603710086, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.40145414601361434}} {"text": "IsSymInf := x -> IsSymbolic(x) and IsBound(x.isSymInf) and x.isSymInf;\n\nClass(SymInf, Symbolic, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := rec(Print := x-> When(IsBound(x.print), x.print(), Print(x.__name__)))\n )),\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n isSymInf := true,\n isValue := true,\n ev := self >> self,\n computeType := self >> self.t\n));\n\n# ==========================================================================\n# Semiring\n# ==========================================================================\n\nIsSemiring := x -> IsType(x) and IsBound(x.isSemiring) and x.isSemiring;\n\nIsSemiring_Arithmetic := x -> IsSemiring(x) and IsBound(x.isSemiring_Arithmetic) and x.isSemiring_Arithmetic;\n\nIsSemiring_MinPlus := x -> IsSemiring(x) and IsBound(x.isSemiring_MinPlus) and x.isSemiring_MinPlus;\n\nIsSemiring_MinTimes := x -> IsSemiring(x) and IsBound(x.IsSemiring_MinTimes) and x.isSemiring_MinTimes;\n\nisSemiring_Boolean := x -> IsSemiring(x) and IsBound(x.isSemiring_Boolean) and x.isSemiring_Boolean;\n\nClass(TSemiring, CompositeTyp, rec(\n __call__ := (self, t) >> WithBases(self, rec(\n t := Checked(IsType(t), t),\n operations := TypOps\n )),\n base_t := self >> self.t,\n isSemiring := true,\n\n print := self >> Print(self.__name__, \"(\", self.t, \")\"),\n\n check := (self, v) >> Cond(\n UnifyTypes([self.t, InferType(v)]) = self.t,\n v,\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n rChildren := self >> [self.t],\n rSetChild := rSetChildFields(\"t\"),\n from_rChildren := (self, rch) >> self,\n\n zero := self >> Error(\"method on undefined semiring\"),\n one := self >> Error(\"method on undefined semiring\"),\n\n sum := self >> Error(\"method on undefined semiring\"),\n product := self >> Error(\"method on undefined semiring\")\n));\n\nClass(TSemiring_Arithmetic, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"+\",\n OpenMP_product := \"*\",\n\n isSemiring_Arithmetic := true\n));\n\nClass(TSemiring_MinPlus, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n IsSymInf(v1) or IsSymInf(v2),\n SymInf(self.t),\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.sum(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"+\",\n\n isSemiring_MinPlus := true\n));\n\n\nClass(TSemiring_MinTimes, TSemiring, rec(\n zero := self >> SymInf(self.t),\n one := self >> self.t.zero(),\n\n sum := (self, v1, v2) >> Cond(\n IsSymInf(v1) and IsSymInf(v2),\n SymInf(self.t),\n IsSymInf(v1) and UnifyTypes([self.t, v2.t]) = self.t,\n v2,\n IsSymInf(v2) and UnifyTypes([self.t, v1.t]) = self.t,\n v1,\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n min(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(\n UnifyTypes([self.t, InferType(v1), InferType(v2)]) = self.t,\n self.t.product(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"min\",\n OpenMP_product := \"*\",\n\n isSemiring_MinTimes := true\n));\n\n\nClass(TSemiring_Boolean, TSemiring, rec(\n zero := self >> self.t.zero(),\n one := self >> self.t.one(),\n\n sum := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_or(v1, v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n product := (self, v1, v2) >> Cond(let(\n l := UnifyTypes([self.t, InferType(v1), InferType(v2)]), Cond(IsArrayT(l), l.t = self.t, l = self.t)),\n logic_and(v1,v2),\n Error(\"type mismatch: semiring is type \", self.t)\n ),\n\n OpenMP_sum := \"||\",\n OpenMP_product := \"&&\",\n\n isSemiring_Boolean := true\n));", "meta": {"hexsha": "3c71b4c37e44edc5087c34108be0e49e1848c05e", "size": 4619, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/packages/graph/semiring.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": 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"max_line_length": 109, "alphanum_fraction": 0.5916865122, "num_tokens": 1437, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7341195269001831, "lm_q2_score": 0.5467381519846138, "lm_q1q2_score": 0.4013711534732251}} {"text": "\n#\n# Read(\"~/Workspace/groupsSB/epi/B2/handle.gi\");\n#\n\ntype:=\"B\";\nrank:=2;\nnr_pos_roots:=4;\n\nRead(\"~/Workspace/groupsSB/epi/group.gi\");\n\n\n#sList(rels,r->Value(r,[vars[22]],[vars[2]+vars[12]]);\n\n#\n# c_1, c_2 not 0 => c_3=c_1/2\n#\n# a test that the coeffs are right\n#a:=root_group(1,xvars[1]);\n#b:=root_group(2,xvars[2]);\n#c:=root_group(3,xvars[3]);\n#d:=root_group(4,xvars[4]);\n#test1:=evaluate_U(a*b*c*d,[[[xvars[1]],[One(APR)]],[[xvars[2]],[One(APR)]],[[xvars[3]],[-One(APR)/2]],[[xvars[4]],[-2*One(APR)/3]]]);\n#test2:=evaluate_U(a*b*c*d,[[[xvars[1]],[One(APR)*2]],[[xvars[2]],[One(APR)*2]],[[xvars[3]],[-One(APR)*2]],[[xvars[4]],[-16*One(APR)/3]]]);\n#Set(Concatenation(test2-test1^2));\nhandleReg:=function()\n\tlocal ua,ub,uab,uabb,u,e,nn,vals,rels,i,v;\n\tua:=root_group(1,1);\n\tub:=root_group(2,1);\n\tuab:=root_group(3,-1/2);\n\tuabb:=root_group(4,-2/3);\n\tu:=ua*ub*uab*uabb;\n\te:=u-id_mat;\n\n\tnn:=List([1..2*nr_pos_roots+rank],i->xvars[i]);\n\n\tvals:=[];\n \tAppend(vals,[[[xvars[6]],[Zero(APR)]]]);\n# \tAppend(vals,[[[xvars[4]],[Zero(APR)]]]);\n \tAppend(vals,[[[xvars[5]],[Zero(APR)]]]);\n \tAppend(vals,[[[xvars[7]],[Zero(APR)]]]);\n \tAppend(vals,[[[xvars[8]],[Zero(APR)]]]);\n \tAppend(vals,[[[xvars[9]],[2*xvars[10]]]]);\n \tAppend(vals,[[[xvars[10]],[Zero(APR)]]]);\n \tAppend(vals,[[[xvars[2]],[xvars[1]]]]);\n \tAppend(vals,[[[xvars[3]],[Zero(APR)]]]);\n# \tAppend(vals,[[[xvars[3]],[-2*xvars[1]/3]]]);\n# \t##\n\t#Append(vals,[[[xvars[1]],[Zero(APR)]]]);\n\t#Append(vals,[[[xvars[3]],[Zero(APR)]]]);\n\t#Append(vals,[[[xvars[7]],[Zero(APR)]]]);\n\n\t#\n\t# atentie la ordinea transpunerilor\n\t#\n\trels:=nn*TransposedMat(u)-nn;\n\trels:=evaluate_rels(rels,vals);\n\tnn:=evaluate_rels(nn,vals);\n\t\n\treturn [u,nn,rels,vals];\nend;\n\n#\n# Done\n#\nhandleRegModule:=function()\n\tlocal ua,ub,uab,uabb,u,e,nn,vals,rels,i,v;\n\tua:=root_group(1,1);\n\tub:=root_group(2,1);\n\tuab:=root_group(3,-1/2);\n\tuabb:=root_group(4,-2/3);\n\tu:=ua*ub*uab*uabb;\n\t\n\tnn:=One(APR)*[0,0,0,0,xvars[1],xvars[2],xvars[3],0,0,0];\n\t#\n\t# atentie la ordinea transpunerilor\n\t#\n\tnn:=nn*TransposedMat(u);\n\t\n\trels:=[];\n\tAppend(rels,[nn[1]-nn[2]]);\n\t# Append(rels,[nn[3]-2*nn[1]/3]);\n\t\n\tvals:=[];\n\tAppend(vals,[[[xvars[3]],[-6*xvars[1]/5+8*xvars[2]/5]]]); # because I want the projection on U3 to be trivial\n\tAppend(vals,[[[xvars[2]],[3*xvars[1]/4]]]); # because I want the projections on U1 and U2 to be equal\n#\tAppend(vals,[[[xvars[3]],[13*xvars[1]/2-2*xvars[2]]]]);\n#\tAppend(vals,[[[xvars[2]],[203*3*xvars[1]/(4*85)]]]);\n\n\trels:=evaluate_rels(rels,vals);\n\tnn:=evaluate_rels(nn,vals);\n\t\n\treturn [u,nn,rels,vals];\nend;\n\n#\n# c_2=0 c_3=0\n#\n#\n#\nhandle23:=function()\n\tlocal ua,ub,uab,uabb,u,e,nn,vals,rels,i,v;\n\tua:=root_group(1,1);\n\tuabb:=root_group(4,1);\n\tu:=ua*uabb;\n\tid_mat:=u^0;\n\te:=u-id_mat;\n\n\tnn:=List([1..2*nr_pos_roots+rank],i->xvars[i]);\n\n\tvals:=[];\n\tAppend(vals,[[[xvars[7]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[8]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[5]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[10]],[Zero(APR)]]]); # for p>2\n\tAppend(vals,[[[xvars[9]],[Zero(APR)]]]); # for p>2\n\tAppend(vals,[[[xvars[2]],[-xvars[6]]]]);\n\t# ###\n\t# Append(vals,[[[xvars[1]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[3]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[4]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[8]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[9]],[Zero(APR)]]]);\n\n\n\t#\n\t# atentie la ordinea transpunerilor\n\t#\n\trels:=nn*TransposedMat(u)-nn;\n\trels:=evaluate_rels(rels,vals);\n\tnn:=evaluate_rels(nn,vals);\n\n\treturn [u,nn,rels,vals];\nend;\n\n#\n# c_2=0 c_4=0\n#\nhandle24:=function()\n\tlocal ua,ub,uab,uabb,u,e,nn,vals,rels,i,v;\n\tua:=root_group(1,1);\n\tuab:=root_group(3,1);\n\tu:=ua*uab;\n\tid_mat:=u^0;\n\te:=u-id_mat;\n\n\tnn:=List([1..2*nr_pos_roots+rank],i->xvars[i]);\n\n\tvals:=[];\n\tAppend(vals,[[[xvars[7]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[8]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[5]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[2]],[Zero(APR)]]]); # for p>2\n\tAppend(vals,[[[xvars[9]],[Zero(APR)]]]);\n\tAppend(vals,[[[xvars[10]],[-xvars[6]]]]); # for p>2\n\t# # ###\n\t# Append(vals,[[[xvars[1]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[3]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[4]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[8]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[9]],[Zero(APR)]]]);\n\n\n\t#\n\t# atentie la ordinea transpunerilor\n\t#\n\trels:=nn*TransposedMat(u)-nn;\n\trels:=evaluate_rels(rels,vals);\n\tnn:=evaluate_rels(nn,vals);\n\n\treturn [u,nn,rels,vals];\nend;\n\n\n#\n# c_2=0\n#\nhandle2:=function()\n\tlocal ua,ub,uab,uabb,u,e,nn,vals,rels,i,v;\n\tua:=root_group(1,1);\n\tuab:=root_group(3,1);\n\tuabb:=root_group(4,1);\n\tu:=ua*uab*uabb;\n\tid_mat:=u^0;\n\te:=u-id_mat;\n\n\tnn:=List([1..2*nr_pos_roots+rank],i->xvars[i]);\n\n\tvals:=[];\n\tAppend(vals,[[[xvars[5]],[xvars[8]]]]);\n\tAppend(vals,[[[xvars[7]],[-xvars[8]]]]);\n\tAppend(vals,[[[xvars[2]],[-xvars[6]+xvars[9]]]]);\n\tAppend(vals,[[[xvars[6]],[xvars[9]-xvars[10]]]]); # only in char 2\n\t###\n\t# Append(vals,[[[xvars[1]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[3]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[4]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[8]],[Zero(APR)]]]);\n\t# Append(vals,[[[xvars[9]],[Zero(APR)]]]);\n\n\n\t#\n\t# atentie la ordinea transpunerilor\n\t#\n\trels:=nn*TransposedMat(u)-nn;\n\tfor i in [1..Length(rels)] do\n\t\tfor v in vals do\n\t\t\tPrint(rels[i],\"\\n\");\n\t\t\trels[i]:=One(APR)*Value(rels[i],v[1],v[2]);\n\t\t\tnn[i]:=One(APR)*Value(nn[i],v[1],v[2]);\n\t\tod;\n\tod;\n\n\treturn [u,nn,rels,vals];\nend;\n\n\n#\n# regular\n# c_1, c_2 not, c_3 not 0\n#\nhandle1:=function()\n\nend;\n\n", "meta": {"hexsha": "08c47e72c6a56f02d1b437d38063eb35d0bb1487", "size": 5382, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "epi/B2/handle.gi", "max_stars_repo_name": "iuliansimion/groupsSB", "max_stars_repo_head_hexsha": "db7494e81bb03f76c20fa181e358ba1cc2d28975", "max_stars_repo_licenses": ["MIT"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "epi/B2/handle.gi", "max_issues_repo_name": "iuliansimion/groupsSB", "max_issues_repo_head_hexsha": "db7494e81bb03f76c20fa181e358ba1cc2d28975", "max_issues_repo_licenses": ["MIT"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "epi/B2/handle.gi", "max_forks_repo_name": "iuliansimion/groupsSB", "max_forks_repo_head_hexsha": "db7494e81bb03f76c20fa181e358ba1cc2d28975", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 23.814159292, "max_line_length": 139, "alphanum_fraction": 0.5832404311, "num_tokens": 2304, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943805178139, "lm_q2_score": 0.5583269943353745, "lm_q1q2_score": 0.4012106406208014}} {"text": "Declare(CUFFTCall);\n\nClass(CUFFTCall, BaseMat, SumsBase, rec(\n dims := self >> self.L.dims(),\n isReal := self >> self.L.isReal(),\n #-----------------------------------------------------------------------\n rChildren := self >> [self.L, self.codegen],\n rSetChild := rSetChildFields(\"L\", \"codegen\"),\n #-----------------------------------------------------------------------\n new := (self, L, codegen) >> SPL(WithBases(self,\n rec(L := L,\n codegen := CopyFields(codegen, rec(\n plan_var := var.fresh_t(\"plan\", TSym(\"cufftHandle\")),\n size_var := var.fresh_t(\"size\", TInt),\n data := (self, c) >> data(self.size_var, V(self.N), c),\n init := self >> call(rec(id:=\"cufftPlanMany\"), addrof(self.plan_var), V(1), addrof(self.size_var), addrof(self.size_var), V(1), V(self.M),\n \t addrof(self.size_var), V((self.N * self.K) / (self.p1 * self.p2)), V(1), \"CUFFT_Z2Z\", V((self.N * self.K) / (self.p1 * self.p2))),\n )),\n dimensions := L.dims())\n )),\n\n #-----------------------------------------------------------------------\n transpose := self >> CUFFTCall(self.L.transpose(), self.codegen),\n #-----------------------------------------------------------------------\n\n print := (self,i,is) >> Print(self.name, \"(\",\n self.L.print(i+is,is), \", )\"),\n #-----------------------------------------------------------------------\n toAMat := self >> self.L.toAMat(),\n #-----------------------------------------------------------------------\n isPermutation := False\n));\n\nRewriteRules(RulesRC, rec(\n RC_CUFFTCall := Rule([RC, @(1, CUFFTCall)], e -> CUFFTCall(RC(@(1).val.L), @(1).val.codegen)),\n));\n\n\nCudaCodegen.CUFFTCall := (self, o, y, x, opts) >> simt_block(\n call(rec(id := \"cufftExecZ2Z\", codegen := o.codegen), o.codegen.plan_var,\n tcast(TPtr(TSym(\"cufftDoubleComplex\")), x), tcast(TPtr(TSym(\"cufftDoubleComplex\")), y), When(o.codegen.k = 1, \"CUFFT_INVERSE\", \"CUFFT_FORWARD\")));\n\n", "meta": {"hexsha": "85fc367d8e405f4b23aa3582d07ee4918a6f3c66", "size": 2055, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "library/cufft/spl.gi", "max_stars_repo_name": "franzfranchetti/spiral-package-fftx", "max_stars_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "library/cufft/spl.gi", "max_issues_repo_name": "franzfranchetti/spiral-package-fftx", "max_issues_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "library/cufft/spl.gi", "max_forks_repo_name": "franzfranchetti/spiral-package-fftx", "max_forks_repo_head_hexsha": "3149606d3d60a9b50c225ec1e8450628d543698b", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 47.7906976744, "max_line_length": 154, "alphanum_fraction": 0.4364963504, "num_tokens": 526, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718434978390747, "lm_q2_score": 0.519521321952093, "lm_q1q2_score": 0.4009891543374835}} {"text": "\n# Copyright (c) 2018-2021, Carnegie Mellon University\n# See LICENSE for details\n\n\nClass(RulesId, RuleSet);\n\nRewriteRules(RulesId, rec(\n\n IdISumRight := ARule( Compose,\n [ @(1, Id), @(2, ISum, canReorder) ],\n e -> [ ISum(@2.val.var, @2.val.domain, @1.val * @2.val.child(1)).attrs(@(2).val) ]),\n\n IdISumLeft := ARule( Compose,\n [ @(1, ISum, canReorder), @(2, Id) ],\n e -> [ ISum(@1.val.var, @1.val.domain, @1.val.child(1) * @2.val).attrs(@(1).val) ]),\n\n IdIComposeRight := ARule( Compose,\n [ @(1, Id), @(2, ICompose, canReorder) ],\n e -> [ ICompose(@2.val.var, @2.val.domain, @1.val * @2.val.child(1)).attrs(@(2).val) ]),\n\n IdIComposeLeft := ARule( Compose,\n [ @(1, ICompose, canReorder), @(2, Id) ],\n e -> [ ICompose(@1.val.var, @1.val.domain, @1.val.child(1) * @2.val).attrs(@(1).val) ]),\n\n # Gath * Id\n CommuteGathId := ARule( Compose,\n [ @(1, Gath), @(2, Id) ], # o 1-> 2->\n e -> [ Id(fCompose(@2.val.element, @1.val.func)).attrs(@(2).val), @1.val ]),\n\n # Prm * Id\n CommutePrmId := ARule( Compose,\n [ @(1, Prm), @(2, Id) ], # o 1-> 2->\n e -> [ Id(fCompose(@2.val.element, @1.val.func)).attrs(@(2).val), @1.val ]),\n\n # Id * Scat\n CommuteIdScat := ARule( Compose,\n [ @(1, Id), @(2, Scat) ], # <-1 <-2 o\n e -> [ @2.val, Id(fCompose(@1.val.element, @2.val.func)).attrs(@(1).val) ]),\n\n #(A X B) o (C X D) -> (A o C) X (B o D)\n CommuteIdTensorfTensor := Rule([fCompose, [idTensor, @(1), @(2)],\n [@(5, fTensor).cond(e->Length(e.children()) = 2), @(3).cond(e->e.range() = @1.val.domain()), @(4).cond(e->e.range() = @2.val.domain())]],\n e -> idTensor(fCompose(@(1).val, @(3).val), fCompose(@(2).val, @(4).val))\n ),\n\n IdNoDiagPullinRight := ARule( Compose,\n [ @(1, Id), @(2, NoDiagPullinRight) ],\n e -> [ NoDiagPullinRight(@(1).val * @2.val.child(1)) ]),\n\n IdNoDiagPullinLeft := ARule( Compose,\n [ @(1, NoDiagPullinLeft), @(2, Id) ],\n e -> [ NoDiagPullinLeft(@1.val.child(1) * @(2).val) ]),\n\n\n#(A X B) o ((C X D) X E) -> (A o (C X D)) X (B o E)\n CommuteIdTensorfTensor2 := Rule([fCompose, [idTensor, @(1), @(2)],\n [@(3, fTensor).cond(e->\n Length(e.children()) = 3 and\n fTensor(e.child(1), e.child(2)).range() = @1.val.domain() and\n e.child(3).range() = @2.val.domain()\n ),\n @(4), @(5), @(6)\n ]], e->\n\n idTensor(fCompose(@(1).val, fTensor(@(3).val.child(1), @(3).val.child(2))),\n fCompose(@(2).val, @(3).val.child(3)))\n ),\n\n\n # i o (j)n = (j)1->N, where i is an idId\n IdComposeConst := Rule([fCompose, @(1, idId), @(2, fBase)],\n e -> idConst(1, @2.val.params[2])\n ),\n \n idTensorId1 := ARule(idTensor, [@(1), [@(2,[idId]), 1]], e -> [@(1).val]),\n idTensorId2 := ARule(idTensor, [[@(2,[idId,J]), 1], @(1)], e -> [@(1).val]),\n\n # This is a special-puprose modification of the IdComposeConst rule, above.\n # It's possible that this is not the best way to do this. I'd be willing\n # to change it later (Peter).\n # i o ((j)n X (k)m ) = (j)1->N X (k)1->N\n# IdComposeTensConst := Rule([fCompose,\n# @(1, idId),\n# @(2, fTensor).cond(e->\n# Length(e.children()) = 2 and\n# ObjId(e.child(1)) = fBase and\n# ObjId(e.child(2)) = fBase)],\n# e -> @(2).val\n# ),\n\n\n # id(a x b) = id(c) where c is derived from merging a and b and\n # computing corresponding domains and ranges.\n FoldConstants := ARule(idTensor, [@(1, idConst), @(2, idConst)],\n e -> [idConst(@1.val.domain()*@2.val.domain(), @1.val.params[2]*@2.val.params[2])]\n )\n\n));\n", "meta": {"hexsha": "1982ca24de8d3921126eb995f23e2cf61c8ad2d8", "size": 3530, "ext": "gi", "lang": "GAP", "max_stars_repo_path": "namespaces/spiral/paradigms/common/id/rewrite.gi", "max_stars_repo_name": "sr7cb/spiral-software", "max_stars_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_stars_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2019-09-01T19:29:39.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-17T12:26:12.000Z", "max_issues_repo_path": "namespaces/spiral/paradigms/common/id/rewrite.gi", "max_issues_repo_name": "sr7cb/spiral-software", "max_issues_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_issues_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_issues_count": 12, "max_issues_repo_issues_event_min_datetime": "2020-11-20T16:15:52.000Z", "max_issues_repo_issues_event_max_datetime": "2022-01-07T21:17:28.000Z", "max_forks_repo_path": "namespaces/spiral/paradigms/common/id/rewrite.gi", "max_forks_repo_name": "sr7cb/spiral-software", "max_forks_repo_head_hexsha": "349d9e0abe75bf4b9a4690f2dbee631700f8361a", "max_forks_repo_licenses": ["BSD-2-Clause-FreeBSD"], "max_forks_count": 21, "max_forks_repo_forks_event_min_datetime": "2019-08-20T19:27:52.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-01T22:11:18.000Z", "avg_line_length": 35.3, "max_line_length": 143, "alphanum_fraction": 0.5288951841, "num_tokens": 1296, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6757645879592642, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.40050310071518}}