{"text": "# An RZ_set is a subset of the circle R/Z that can be expressed as\n# a finite union of half-open intervals [u,v). Any such set can\n# be expressed uniquely as\n# [t[1],t[2]) u [t[3],t[4]) u ... u [t[2*n-1],t[2*n]) with\n# 0 <= t[0] < t[1] < ... < t[2*n] <= 1.\n\n`is_element/RZ_set` := proc(T)\n local n,i;\n \n if not type(T,list(realcons)) then return false; fi;\n n := nops(T)/2;\n if not(type(n,nonnegint)) then return false; fi;\n if n = 0 then return true; fi;\n if T[1] < 0 or T[2*n] > 1 then return false; fi;\n for i from 1 to 2*n-1 do\n if T[i+1] <= T[i] then return false; fi;\n od;\n return true;\nend:\n\n`is_equal/RZ_set` := proc(T,U)\n if nops(T) <> nops(U) then return false; fi;\n return evalb(simplify({0,op(T -~ U)}) = {0});\nend:\n\n`is_leq/RZ_set` := proc(T,U)\n evalb(`intersect/RZ_set`(T,`complement/RZ_set`(U)) = `empty/RZ_set`);\nend:\n\n`list_elements/RZ_set` := NULL:\n`count_elements/RZ_set` := NULL:\n\n`random_element/RZ_set` := proc()\n local n,S,T,i;\n \n n := rand(0..5)();\n S := {};\n while nops(S) < 2*n do\n S := {seq(rand(0..719)(),i=1..2*n)};\n od:\n T := sort([op(S)] /~ 720);\n T := `shift/RZ_set`(`random_element/RZ`())(T);\n return T;\nend:\n\n`length/RZ_set` := proc(T) local i; add((-1)^i * T[i],i=1..nops(T)); end:\n\n`bot/RZ_set` := []:\n`empty/RZ_set` := []:\n`top/RZ_set` := [0,1];\n`RZ/RZ_set` := [0,1];\n\n`complement/RZ_set` := proc(T)\n local n,U;\n n := nops(T)/2;\n if n = 0 then return [0,1]; fi;\n U := NULL;\n if T[1] > 0 then U := U,0,T[1]; fi;\n U := U,op(2..2*n-1,T);\n if T[2*n] < 1 then U := U,T[2*n],1; fi;\n U := [U];\n return U;\nend:\n\n`add_interval/RZ_set` := proc(T,u,v)\n local n,i,j,k,a,b;\n if nops(T) = 0 then return [u,v]; fi;\n n := nops(T)/2;\n i := 0;\n while i < n and T[2*i+2] < u do i := i+1; od;\n if i = n then return [op(T),u,v]; fi;\n j := i+1;\n while j <= n and T[2*j-1] <= v do j := j+1; od;\n a := min(u,T[2*i+1]);\n b := max(v,`if`(j = 1,0,T[2*j-2]));\n return [seq(T[k],k=1..2*i),a,b,seq(T[k],k=2*j-1..2*n)];\nend:\n\n`union/RZ_set` := proc()\n local U,T,n,i,j;\n if nargs = 0 then\n return `bot/RZ_set`;\n else\n U := args[1];\n for i from 2 to nargs do\n T := args[i];\n n := nops(T)/2;\n for j from 1 to n do\n U := `add_interval/RZ_set`(U,T[2*j-1],T[2*j]);\n od;\n od:\n return U;\n fi;\nend:\n\n`intersect/RZ_set` := proc()\n local T,U,V,n,m,i,j,a,b;\n if nargs = 0 then\n return `top/RZ_set`;\n elif nargs = 1 then\n return args[1];\n elif nargs > 2 then\n return `intersect/RZ_set`(args[1],`intersect/RZ_set`(args[2..-1]));\n else\n T := args[1];\n U := args[2];\n n := nops(T)/2;\n m := nops(U)/2;\n V := NULL;\n for i from 1 to n do\n for j from 1 to m do\n a := max(T[2*i-1],U[2*j-1]);\n b := min(T[2*i],U[2*j]);\n if a < b then\n V := V,[a,b];\n fi;\n od;\n od;\n V := sort([V],(x,y) -> (x[1] < y[1]));\n V := map(op,V);\n return V;\n fi;\nend:\n\n`symdiff/RZ_set` := proc(T,U)\n local A,B;\n \n A := `intersect/RZ_set`(T,`complement/RZ_set`(U));\n B := `intersect/RZ_set`(U,`complement/RZ_set`(T));\n return(`union/RZ_set`(A,B));\nend:\n\n`dist/RZ_set` := proc(T,U) `length/RZ_set`(`symdiff/RZ_set`(T,U)); end:\n\n`shift/RZ_set` := (t) -> proc(T)\n local U,n,i,j;\n if T = [] then return []; fi;\n \n U := T +~ t;\n U := U -~ floor(U[1]);\n n := nops(U)/2;\n if U[2*n] <= 1 then return U; fi;\n\n i := 0;\n while i < n and U[2*i+2] <= 1 do i := i+1; od;\n if U[2*i+1] < 1 then\n if U[2*n] - 1 = U[1] then\n return [0,seq(U[j]-1,j=2*i+2..2*n-1),seq(U[j],j=2..2*i+1),1];\n else\n return [0,seq(U[j]-1,j=2*i+2..2*n),seq(U[j],j=1..2*i+1),1];\n fi;\n else \n if U[2*n]-1 = U[1] then\n return [seq(U[j]-1,j=2*i+1..2*n-1),seq(U[j],j=2..2*i)];\n else\n return [seq(U[j]-1,j=2*i+1..2*n),seq(U[j],j=1..2*i)];\n fi;\n fi;\nend:\n\n`interval/RZ_set` := proc(a,b)\n local a0,b0;\n\n a0 := a - floor(a);\n b0 := b - floor(b);\n if a0 < b0 then\n return [a0,b0];\n elif a0 = b0 then\n return [];\n else \n return [0,b0,a0,1];\n fi;\nend:\n\n`unroll/RZ_set` := proc(T,k::posint := 2)\n local n,i,j,t;\n n := nops(T)/2;\n if n=0 then return []; fi;\n if k = 1 then return T; fi;\n\n if T[1] = 0 and T[2*n] = 1 then\n return [seq(T[i],i=1..2*n-1),\n seq(seq(T[i]+j,i=2..2*n-1),j=1..k-2),\n seq(T[i]+k-1,i=2..2*n)];\n else\n return [seq(seq(t+j,t in T),j=0..k-1)];\n fi;\nend:\n\n`starts/RZ_set` := proc(T)\n local n,i;\n n := nops(T)/2;\n\n if n = 0 then return {}; fi;\n\n if T[1] = 0 and T[2*n] = 1 then\n return {seq(T[2*i-1],i=2..n)};\n else\n return {seq(T[2*i-1],i=1..n)};\n fi;\nend:\n\n`boundary/RZ_set` := proc(T)\n local n,i;\n n := nops(T)/2;\n\n if n = 0 then return {}; fi;\n\n if T[1] = 0 and T[2*n] = 1 then\n return {seq(T[i],i=2..2*n-1)};\n else\n return {seq(T[i],i=1..2*n)};\n fi;\nend:\n\n`are_crossed/RZ_set` := proc(T,U)\n local A,B,n,i;\n if `intersect/RZ_set`(T,U) <> `empty/RZ_set` then\n return true;\n fi;\n\n if nops(T) = 0 or nops(U) = 0 then\n return false;\n fi;\n \n A := `shift/RZ_set`(-T[1])(T);\n B := `shift/RZ_set`(-T[1])(U);\n i := 1;\n n := nops(A)/2;\n while i < n and A[2*i+2] <= B[1] do \n i := i+1;\n od;\n if i = n then\n return false;\n else \n return evalb(B[nops(B)] > A[2*i+1]);\n fi;\nend:\n\n`centroid_C/RZ_set` := proc(T)\n local n,l,t,i;\n n := nops(T)/2;\n if n = 0 then error(\"T is empty\"); fi;\n l := `length/RZ_set`(T);\n evalf(add(int(exp(2*Pi*I*t),t=T[2*i-1]..T[2*i]),i=1..n)/l);\nend:\n\n`centroid_R2/RZ_set` := proc(T)\n local z;\n z := `centroid_C/RZ_set`(T);\n return([Re(z),Im(z)]);\nend:\n \n`flat_plot/RZ_set` := proc(T,y)\n local i;\n \n if T = [] then\n return NULL;\n else\n return \n display(seq(line([T[2*i-1],y],[T[2*i],y],args[3..-1]),i=1..nops(T)/2),\n scaling=constrained,axes=none);\n fi;\nend:\n\n`plot/RZ_set` := proc(T,r := 1,c := [0,0])\n local A,i,n,z,t;\n if nargs > 3 then \n A := args[4..-1];\n else\n A := NULL;\n fi;\n if T = [] then\n return NULL;\n else\n n := nops(T)/2;\n z := [seq(c +~ r *~ [cos(2*Pi*T[2*i-1]),sin(2*Pi*T[2*i-1])],i=1..n)];\n if T[1] = 0 and T[2*n] = 1 then\n z := [op(2..-1,z)];\n fi;\n return \n display(\n seq(plot([c[1]+r*cos(2*Pi*t),\n\t c[2]+r*sin(2*Pi*t),\n\t t = T[2*i-1]..T[2*i]],\n\t A),\n\ti=1..nops(T)/2),\n seq(line(0.95 *~ z[i],z[i],A),i=1..nops(z)),\n scaling=constrained,axes=none);\n fi;\nend:\n\n", "meta": {"hexsha": "ef260251c6518e01379f8e294b302250030ebb74", "size": 6066, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/RZ_set.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/RZ_set.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/RZ_set.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 20.7030716724, "max_line_length": 73, "alphanum_fraction": 0.5230794593, "num_tokens": 2571, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.782662489091802, "lm_q2_score": 0.7025300698514777, "lm_q1q2_score": 0.5498439331317951}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-7-input.txt\" ):\n\npos := parse~(StringTools:-Split(input,\",\")):\nanswer1 := min(seq(add(abs~(pos-~i)),i=min(pos)..max(pos)));\nanswer2 := min(seq( \n add(((pos[i]-j)^2+abs(pos[i]-j))/2, i=1..nops(pos)),\n j=min(pos)..max(pos)));\n", "meta": {"hexsha": "906d1d43b9a27b3e1b13429da37b79683a2b8d7f", "size": 279, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day7/AoC7-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day7/AoC7-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day7/AoC7-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.875, "max_line_length": 60, "alphanum_fraction": 0.5734767025, "num_tokens": 96, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8438950947024555, "lm_q2_score": 0.6513548511303338, "lm_q1q2_score": 0.5496751637795368}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* replace: \"mbrxc_x\\(\" -> \"xc_mgga_x_mbrxc_get_x(\" *)\n\n$include \"mgga_x_mbrxc_bg.mpl\"\n\ntask_alpha := (x, t) -> (t/K_FACTOR_C) * m_max(1 - x^2/(8*t), 1e-10):\n\nmggac_b1 := 3.712:\nmggac_b2 := 2.0:\nmggac_b4 := 0.1:\nmggac_b3 := 2.595 + 0.5197*mggac_b4 + 0.559*mggac_b2:\nmggac_b5 := -3*mggac_b3:\n\n(* new definition of Q. The rest of the functional remains the same *)\n(* We have Lambda = (32 Pi^2)^(2/3)/(6 Q) *)\nmbrxc_Q := (x, t) ->\n + (32*Pi)^(2/3)/6\n * (1 + mggac_b4*task_alpha(x, t) + mggac_b5*task_alpha(x, t)^2)\n / (mggac_b1 + mggac_b2*task_alpha(x, t) + mggac_b3*task_alpha(x, t)^2):", "meta": {"hexsha": "4d39f023caf621be4e1fe6bdacabfa6601b43987", "size": 860, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mggac.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mggac.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_mggac.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 31.8518518519, "max_line_length": 77, "alphanum_fraction": 0.6325581395, "num_tokens": 357, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8824278602705731, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.5492754557379045}} {"text": "read \"../ComputeIdentifiableFunctions.mpl\":\n\ncases := [\n [\n [PolynomialIdeal([a * x + b * y + c * y^2, d * y], variables={x, y}), PolynomialIdeal([a - a_aux, b - b_aux], variables={a_aux, b_aux})],\n PolynomialIdeal([x, y])\n ],\n [\n [PolynomialIdeal([a * x + b * z + c * y^2, d * y], variables={x, y, z}), PolynomialIdeal([a - a_aux, b - b_aux], variables={a_aux, b_aux})],\n PolynomialIdeal([a * x + b * z, y], variables={x, y, z})\n ],\n [\n [PolynomialIdeal([a - a_aux], variables={a_aux}), PolynomialIdeal([a - a_aux, b - b_aux], variables={a_aux, b_aux})],\n PolynomialIdeal([a - a_aux], variables={a_aux})\n ],\n [\n [PolynomialIdeal([-a - b + a_aux + b_aux, -a * a_aux + a * b + a_aux^2 - a_aux * b], variables={a_aux, b_aux}), PolynomialIdeal([-a + a_aux, -b + b_aux], variables={a_aux, b_aux})],\n PolynomialIdeal([-a - b + a_aux + b_aux, -a * a_aux + a * b + a_aux^2 - a_aux * b], variables={a_aux, b_aux})\n ],\n [\n [\n PolynomialIdeal([-a - b + a_aux + b_aux, -a * a_aux + a * b + a_aux^2 - a_aux * b], variables={a_aux, b_aux}), \n PolynomialIdeal([-a - b + a_aux + b_aux, -a * a_aux + a * b + a_aux^2 - a_aux * b, c - c_aux], variables={a_aux, b_aux, c_aux})\n ],\n PolynomialIdeal([-a - b + a_aux + b_aux, -a * a_aux + a * b + a_aux^2 - a_aux * b], variables={a_aux, b_aux})\n ]\n];\n\nnum_passed := 0:\nnum_failed := 0:\n\nfor case in cases do\n input := case[1]:\n correct := case[2]:\n if IdealsEq(FieldCoefficientRestriction(op(input)), correct) then\n printf(\"PASSED\\n\");\n num_passed := num_passed + 1:\n else\n printf(\"FAILED\\n\");\n num_failed := num_failed + 1:\n print(\"Expected: \", correct);\n print(\"Got: \", FieldCoefficientRestriction(op(input)));\n end if:\nend do:\n\nprintf(\"Passed: %a, failed %a \\n\", num_passed, num_failed);\n", "meta": {"hexsha": "4f5b6bce938c099f63a8b5ec6b2532dcbb0ed807", "size": 1905, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "tests/coeff_restriction.mpl", "max_stars_repo_name": "iliailmer/AllIdentifiableFunctions", "max_stars_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-03-19T18:42:30.000Z", "max_stars_repo_stars_event_max_datetime": "2021-03-19T18:42:30.000Z", "max_issues_repo_path": "tests/coeff_restriction.mpl", "max_issues_repo_name": "iliailmer/AllIdentifiableFunctions", "max_issues_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2021-03-20T15:22:40.000Z", "max_issues_repo_issues_event_max_datetime": "2021-03-21T01:07:04.000Z", "max_forks_repo_path": "tests/coeff_restriction.mpl", "max_forks_repo_name": "iliailmer/AllIdentifiableFunctions", "max_forks_repo_head_hexsha": "033d335b6a2e6d53d8d935c627f9724fd2a56ebd", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-03-04T20:30:13.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-04T20:30:13.000Z", "avg_line_length": 40.5319148936, "max_line_length": 189, "alphanum_fraction": 0.5538057743, "num_tokens": 601, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920020959544, "lm_q2_score": 0.6859494485880928, "lm_q1q2_score": 0.5492342373266159}} {"text": "######################################################################\n# Intervals in the set of positive integers\n\n`is_element/posint_intervals` := proc(J)\n global reason;\n\n if not(type(J,set(posint)) or type(J,list(posint))) then\n reason := [convert(procname,string),\"J is not a list or set of positive integers\",J];\n return false;\n fi;\n\n if nops(J) = 0 or nops(J) <> max(op(J)) - min(op(J)) + 1 then\n reason := [convert(procname,string),\"J is not an interval\",J];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/posint_intervals` := (J,K) -> evalb({op(J)} = {op(K)});\n\n`is_leq/posint_intervals` := (J,K) -> evalb({op(J)} minus {op(K)} = {});\n\n`random_element/posint_intervals` := proc()\n local a,b,i;\n a := rand(1..10)();\n b := rand(0..9)();\n [seq(i,i=a..a+b)];\nend:\n\n`list_elements/posint_intervals` := NULL;\n`count_elements/posint_intervals` := NULL;\n", "meta": {"hexsha": "1a38646820efe53bdbfc0dc7ab8d6c15f9f2cb04", "size": 863, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/posint_intervals.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/posint_intervals.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/posint_intervals.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 26.1515151515, "max_line_length": 87, "alphanum_fraction": 0.5874855156, "num_tokens": 247, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7745833841649233, "lm_q2_score": 0.7090191276365462, "lm_q1q2_score": 0.5491944353223777}} {"text": "# h := discrim(a1*x^4 + x^5 + a2*x^3 + a3*x^2 + a4*x + a5, x):\n\n# # (1)-(47) are from Wang Dongming - So1ving po1ynomia1 equations: Characteristic sets and triangu1ar systems\n# # \u517116\u4e2a\u4f8b\u5b50\n\nwangzero :=\n[\n [ #(2) wang_ex9\n [x^8 + 4*x^6*y^2 + 6*x^4*y^4 + 4*x^2*y^6 + y^8 - 2*x^6*y - 6*x^4*y^3 - 6*x^2*y^5 - 2*y^7 - 5*x^6 - 11*x^4*y^2 - 7*x^2*y^4 - y^6 + 10*x^4*y + 12*x^2*y^3 + 2*y^5 + 4*x^4 + 4*x^2*y^2 - 8*x^2*y,\n 8*x^7 + 24*x^5*y^2 + 24*x^3*y^4 + 8*x*y^6 - 12*x^5*y - 24*x^3*y^3 - 12*x*y^5 - 30*x^5 - 44*x^3*y^2 - 14*x*y^4 + 40*x^3*y + 24*x*y^3 + 16*x^3 + 8*x*y^2 - 16*x*y,\n 8*x^6*y + 24*x^4*y^3 + 24*x^2*y^5 + 8*y^7 - 2*x^6 - 18*x^4*y^2 - 30*x^2*y^4 - 14*y^6 - 22*x^4*y - 28*x^2*y^3 - 6*y^5 + 10*x^4 + 36*x^2*y^2 + 10*y^4 + 8*x^2*y - 8*x^2\n ],\n [x, y]\n ],\n [ #(7) wang_ex15\n [8*x^2-2*x*y-6*x*z+3*x+3*y^2-7*y*z+10*y+10*z^2-8*z-4,\n 10*x^2-2*x*y+6*x*z-6*x+9*y^2-y*z-4*y-2*z^2+5*z-9,\n 5*x^2+8*x*y+4*x*z+8*x+9*y^2-6*y*z+2*y-z^2-7*z+5\n ],\n [x, y, z]\n ],\n [\n #(8) wang_ex16\n [2 + 10*p^2 - 2*p*q - 2*q + c^2*(q - 1)^2 + 2*c*d*(1 - q)*(q - p) + 4*p*q*d*(d - c) + 4*d^2*(1 - 2*p) + 4*d^2*(p - q) + 4*d*c*(p - 1) + 4*p*q*(c + 1) - 8*p + d^2*(p - q)^2, \n d*(2*p + 1)*(q - p) + c*(p + 2)*(1 - q) - 6*p*d + 2*c*(-p*q + p + q - 1) + 6*p^2*d, \n -4*(p - 1)^2 + 2*p*(p - q) - 2*q + 2, \n 4 - 4*q^2 + 4*p + 3*c^2*(q - 1)^2 - 3*d^2*(p - q)^2 + 12*d^2*(p - 1)^2 + 4*p*(p - 2) + 12*d*c*(p + q + p*q - 1)\n ],\n [q, c, p, d]\n ],\n [\n #(10) wang_ex21\n [x + y + z + t + u,\n x*y + y*z + z*t + t*u + u*x,\n x*y*z + y*z*t + z*t*u + t*u*x + u*x*y,\n x*y*z*t + y*z*t*u + z*t*u*x + t*u*x*y + u*x*y*z,\n x*y*z*t*u + 1\n ],\n [x, y, z, t, u]\n ],\n [ #(13) wang_ex26\n [x^2 + y^2 + z^2,\n z*y*x,\n y^2*x^2 + z^2*x^2 + z^2*y^2,\n u^2 + 1/3*t^2,\n u^3 - t^2*u,\n 2*x^2*u - y^2*u - z^2*u + y^2*t - z^2*t, \n -y^2*x^2*u - z^2*x^2*u + 2*z^2*y^2*u - y^2*x^2*t + z^2*x^2*t,\n 2*x^2*u^2 - y^2*u^2 - z^2*u^2 - 2*y^2*t*u + 2*z^2*t*u - 2/3*x^2*t^2 + 1/3*y^2*t^2 + 1/3*z^2*t^2,\n - y^2*x^2*u^2 - z^2*x^2*u^2 + 2*z^2*y^2*u^2 + 2*y^2*x^2*t*u - 2*z^2*x^2*t*u + 1/3*y^2*x^2*t^2 + 1/3*z^2*x^2*t^2 - 2/3*z^2*y^2*t^2,\n - 3*y^2*x^4*t*u^2 + 3*z^2*x^4*t*u^2 + 3*y^4*x^2*t*u^2 - 3*z^4*x^2*t*u^2 - 3*z^2*y^4*t*u^2 + 3*z^4*y^2*t*u^2\n + 1/3*y^2*x^4*t^3 - 1/3*z^2*x^4*t^3 - 1/3*y^4*x^2*t^3 + 1/3*z^4*x^2*t^3 + 1/3*z^2*y^4*t^3 - 1/3*z^4*y^2*t^3\n ],\n [x, y, z, t, u]\n ],\n [ #(14) wang_ex27\n [y + u + v - 1,\n z + t + 2*u - 3,\n y + t + 2*v - 1,\n x - y - z - t - u - v,\n t*u*x^2 - 1569/31250*y*z^3,\n z*v - 587/15625*y*t\n ],\n [x, y, z, t, u, v]\n ],\n [\n #(15) wang_ex28\n [x^2 - x + 2*y^2 + 2*z^2 + 2*t^2, \n 2*x*y + 2*y*z + 2*z*t - y, \n 2*x*z + y^2 + 2*y*t - z, \n x + 2*y + 2*z + 2*t - 1\n ],\n [x, y, z, t]\n ],\n [ #(21) wang_ex34\n [B2*C2 + B3*C3 + B4*C4 + B5*C5 - 1/2,\n B2*C2^2 + B3*C3^2 + B4*C4^2 + B5*C5^2 - 1/3,\n B3*A32*C2 + B4*A42*C2 + B4*A43*C3 + B5*A52*C2 + B5*A53*C3 + B5*A54*C4 - 1/6,\n B2*C2^3 + B3*C3^3 + B4*C4^3 + B5*C5^3 - 1/4,\n B3*C3*A32*C2 + B4*C4*A42*C2 + B4*C4*A43*C3 + B5*C5*A52*C2 + B5*C5*A53*C3 + B5*C5*A54*C4 - 1/8,\n B3*A32*C2^2 + B4*A42*C2^2 + B4*A43*C3^2 + B5*A52*C2^2 + B5*A53*C3^2 + B5*A54*C4^2 - 1/12,\n B4*A43*A32*C2 + B5*A53*A32*C2 + B5*A54*A42*C2 + B5*A54*A43*C3-1/24,\n B2*C2^4 + B3*C3^4 + B4*C4^4 + B5*C5^4 - 1/5,\n B3*C3^2*A32*C2 + B4*C4^2*A42*C2 + B4*C4^2*A43*C3 + B5*C5^2*A52*C2 + B5*C5^2*A53*C3 + B5*C5^2*A54*C4 - 1/10,\n B3*C2^2*A32*C3 + B4*C2^2*A42*C4 + B4*C3^2*A43*C4 + B5*C2^2*A52*C2 + B5*C3^2*A53*C5 + B5*C4^2*A54*C5 - 1/15,\n B4*C4*A43*A32*C2 + B5*C5*A53*A32*C2 + B5*C5*A54*A42*C2\n + B5*C5*A54*A43*C3 - 1/30,\n B3*A32^2*C2^2 + B4*A42^2*C2^2 + 2*B4*A42*C2*A43*C3 + B4*A43^2*C3^2 + B5*A52^2*C2^2 + B5*A53^2*C3^2 + B5*A54^2*C4^2 + 2*B5*A52*C2*A53*C3 + 2*B5*A52*C2*A54*C4 + 2*B5*A53*C3*A54*C4 - 1/20,\n B3*A32*C2^3 + B4*A42*C2^3 + B4*A43*C3^3 + B5*A52*C2^3 + B5*A53*C3^3 + B5*A54*C4^3 - 1/20,\n B4*A43*C3*A32*C2 + B5*A53*C3*A32*C2 + B5*A54*C4*A42*C2 + B5*A54*C4*A43*C3- 1/40,\n B4*A43*A32*C2^2 + B5*A53*A32*C2^2 + B5*A54*A42*C2^2 + B5*A54*A43*C3^2- 1/60,\n B5*A54*A43*A32*C2-1/120\n ],\n [B2, B3, B4, B5, A32, A42, A43, A52, A53, A54, C4, C2, C3, C5]\n ],\n [ #(23) wang_ex36\n [U0^2 - U0 + 2*U1^2,\n U0 + 2*U1 - 1\n ],\n [U0, U1]\n ],\n [ #(24) wang_ex37\n [U0^2 - U0 + 2*U1^2 + 2*U2^2,\n 2*U0*U1 + 2*U1*U2 - U1,\n U0 + 2*U1 + 2*U2 - 1\n ],\n [U0, U1, U2]\n ],\n [ #(25) wang_ex38\n [U0^2 - U0 + 2*U1^2 + 2*U2^2 + 2*U3^2,\n 2*U0*U1 + 2*U1*U2 + 2*U2*U3 - U1,\n 2*U0*U2 + U1^2 + 2*U1*U3 - U2,\n U0 + 2*U1 + 2*U2 + 2*U3 - 1\n ],\n [U0, U1, U2, U3]\n ],\n [ #(26) wang_ex39\n [\n U0^2 - U0 + 2*U1^2 + 2*U2^2 + 2*U3^2 + 2*U4^2,\n 2*U0*U1 + 2*U1*U2 + 2*U2*U3 + 2*U3*U4 - U1,\n 2*U0*U2 + U1^2 + 2*U1*U3 + 2*U2*U4 - U2,\n 2*U0*U3 + 2*U1*U2 + 2*U1*U4 - U3,\n U0 + 2*U1 + 2*U2 + 2*U3 + 2*U4 - 1\n ],\n [U4, U3, U2, U1, U0]\n ],\n [ #(27) wang_ex40\n [U0^2 - U0 + 2*U1^2 + 2*U2^2 + 2*U3^2 + 2*U4^2 + 2*U5^2,\n 2*U0*U1 + 2*U1*U2 + 2*U2*U3 + 2*U3*U4 + 2*U4*U5 - U1,\n 2*U0*U2 + U1^2 + 2*U1*U3 + 2*U2*U4 + 2*U3*U5 - U2,\n 2*U0*U3 + 2*U1*U2 + 2*U1*U4 + 2*U2*U5 - U3,\n 2*U0*U4 + 2*U1*U3 + 2*U1*U5 + U2^2 - U4,\n U0 + 2*U1 + 2*U2 + 2*U3 + 2*U4 + 2*U5 - 1\n ],\n [U5, U4, U3, U2, U1, U0]\n ],\n [ #(28) wang_ex43\n [U4^4 - 20/7*A46^2,\n A46^2*U3^4 + 7/10*A46*U3^4 + 7/48*U3^4 - 50/27*A46^2 - 35/27*A46 - 49/216,\n A46^5*U4^3 + 7/5*A46^4*U4^3 + 609/1000*A46^3*U4^3 + 49/1250*A46^2*U4^3 - 27391/800000*A46*U4^3 - 1029/160000*U4^3 + 3/7*A46^5*U3*U4^2 + 3/5*A46^6*U3*U4^2 + 63/200*A46^3*U3*U4^2 + 147/2000*A46^2*U3*U4^2 + 4137/800000*A46*U3*U4^2 - 7/20*A46^4*U3^2*U4 - 77/125*A46^3*U3^2*U4 - 23863/60000*A46^2*U3^2*U4 - 1078/9375*A46*U3^2*U4 - 24353/1920000*U3^2*U4 - 3/20*A46^4*U3^3 - 21/100*A46^3*U3^3 - 91/800*A46^2*U3^3 - 5887/200000*A46*U3^3 - 343/128000*U3^3\n ],\n [U3, U4, A46]\n ],\n [ #(29) wang_ex45\n [45*P + 35*S - 165*B - 36,\n 35*P + 40*Z + 25*T - 27*S,\n 15*W + 25*P*S + 30*Z - 18*T - 165*B^2,\n -9*W + 15*P*T + 20*Z*S,\n W*P + 2*Z*T - 11*B^3,\n 99*W - 11*S*B + 3*B^2\n ],\n [W, P, Z, T, S, B]\n ],\n [ #(30) wang_ex46\n [45*P + 35*S - 165*B - 36,\n 35*P + 40*Z + 25*T - 27*S,\n 15*W + 25*P*S + 30*Z - 18*T - 165*B^2,\n -9*W + 15*P*T + 20*Z*S,\n W*P + 2*Z*T - 11*B^3,\n 99*W - 11*S*B + 3*B^2,\n B^2 + 33/50*B + 2673/10000\n ],\n [W, P, Z, T, S, B]\n ]\n]:", "meta": {"hexsha": "db410460e73b1ada4726d4f64572efbf7801e18c", "size": 7079, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Examples/wangzero.mpl", "max_stars_repo_name": "lihaokun/StrongSfTriDec", "max_stars_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2022-03-21T11:48:40.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-21T11:50:26.000Z", "max_issues_repo_path": "Examples/wangzero.mpl", "max_issues_repo_name": "lihaokun/StrongSfTriDec", "max_issues_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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": "Examples/wangzero.mpl", "max_forks_repo_name": "lihaokun/StrongSfTriDec", "max_forks_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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": 42.903030303, "max_line_length": 455, "alphanum_fraction": 0.3993501907, "num_tokens": 4133, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357563664174, "lm_q2_score": 0.6334102775181399, "lm_q1q2_score": 0.5491893590582028}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_x *)\n\nparams_a_kappa := 4.8827323:\nparams_a_mu := 0.3511128:\n$include \"gga_x_pbe.mpl\"\n\ndldf_a := [1, -0.1637571, -0.1880028, -0.4490609, -0.0082359]:\ncsi_HF := 1 - 0.6144129:\n\nf := (rs, x, t, u) ->\n + csi_HF*f_pbe(x)*mgga_series_w(dldf_a, 5, t):\n", "meta": {"hexsha": "eed801ae73a9cf32b9808f5be74d78d31f49ce56", "size": 508, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/hyb_mgga_x_dldf.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/hyb_mgga_x_dldf.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/hyb_mgga_x_dldf.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.4, "max_line_length": 68, "alphanum_fraction": 0.6633858268, "num_tokens": 200, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8558511469672595, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.5482889311530775}} {"text": "n_max := 6; # Number of generators to use in the dual Steenrod algebra\n\nbar := proc()\n local n,m,i,j,u,a,v,ac,av,x,y;\n n := nargs;\n for i from 1 to n do\n u := seq(args[j],j=1..i-1);\n a := args[i];\n v := seq(args[j],j=i+1..n);\n if type(a,`+`) then\n return map(t -> bar(u,t,v),a);\n elif type(a,integer) and modp(a,2) = 0 then\n return 0;\n elif type(a,`*`) then\n ac,av := selectremove(type,a,rational);\n ac := modp(ac,2);\n if ac <> 1 then\n return ac * bar(u,av,v);\n fi;\n elif type(a,specfunc(bar)) then\n return bar(u,op(a),v);\n fi;\n od;\n return 'procname'(args);\nend:\n\nsteenrod_length := proc(u::specfunc(nonnegint,Sq)) nops(u); end:\nsteenrod_deg := proc(u::specfunc(nonnegint,Sq)) `+`(op(u)); end:\nsteenrod_excess := proc(u::specfunc(nonnegint,Sq))\n add(op(i,u) - 2*op(i+1,u), i=1..nops(u)-1);\nend:\n\nis_admissible := proc(u::specfunc(nonnegint,Sq))\n local m,i;\n m := nops(u);\n for i from 1 to m-1 do\n if op(i,u) < 2*op(i+1,u) then return false; fi;\n od;\n return true;\nend:\n\nadmissible_basis := proc(n::nonnegint)\n option remember;\n local L,i,v;\n \n if n = 0 then return [Sq()]; fi;\n L := NULL;\n for i from 1 to n do\n for v in admissible_basis(n-i) do\n if i = n or i >= 2 * op(1,v) then\n L := L,Sq(i,op(v));\n fi;\n od;\n od;\n\n return [L];\nend:\n\nadmissible_lt := proc(u,v)\n local i;\n if steenrod_deg(u) < steenrod_deg(v) then return true; fi;\n if steenrod_deg(u) > steenrod_deg(v) then return false; fi;\n\n for i from 1 to min(nops(u),nops(v)) do\n if op(i,u) < op(i,v) then return true; fi;\n if op(i,u) > op(i,v) then return false; fi;\n od:\n\n if nops(u) > nops(v) then return true; fi;\n return false;\nend:\n\nmate := proc(u::specfunc(nonnegint,Sq))\n local m,i,t;\n \n if not(is_admissible(u)) then return FAIL; fi;\n\n m := nops(u);\n i := [op(u),0];\n return mul(a[t]^(i[t] - 2 * i[t+1]),t=1..m);\nend:\n\ncomate := proc(v)\n local r,alpha;\n r := n_max;\n while r > 0 and degree(v,a[r]) = 0 do r := r - 1; od;\n if r = 0 then return Sq(); fi;\n alpha := [seq(degree(v,a[t]),t=1..r)];\n return Sq(seq(add(2^(i-t)*alpha[i],i=t..r),t=1..r));\nend;\n\nadem_rhs := proc(k::nonnegint,j::nonnegint)\n modp(add(binomial(j-m-1,k-2*m) * Sq(j+k-m,m),m=0..floor(k/2)),2);\nend:\n\nadem_relation := (k,j) -> modp(Sq(k,j) + adem_rhs(k,j),2);\n\nadem_reduce0 := proc(u)\n local v,v0,v1,m,r,i;\n if type(u,list) or type (u,set) or type(u,specfunc(anything,bar)) then\n return(map(adem_reduce0,u));\n elif type (u,`+`) then\n return modp(expand(map(adem_reduce0,u)),2);\n elif type (u,`*`) then\n return modp(expand(map(adem_reduce0,u)),2);\n elif type(u,specfunc(nonnegint,Sq)) then\n v := remove(i -> i=0, [op(u)]);\n m := nops(v);\n if m < 2 then return Sq(op(v)); fi;\n i := 1;\n while i < m and v[i] >= 2 * v[i+1] do \n i := i + 1;\n od;\n if i = m then return Sq(op(v)); fi;\n r := adem_rhs(v[i],v[i+1]);\n if r = 0 then return 0; fi;\n if type(r,`+`) then r := [op(r)] else r := [r]; fi;\n v0 := op(1..i-1,v);\n v1 := op(i+2..-1,v);\n r := map(w -> Sq(v0,op(w),v1),r);\n return modp(`+`(op(r)),2);\n else\n return modp(u,2);\n fi;\nend:\n\nadem_reduce := proc(u)\n local v,w;\n v := u;\n w := adem_reduce0(u);\n while w <> v do \n v := w;\n w := adem_reduce0(v);\n od;\n return w;\nend:\n\nbullett_macdonald_series := (n,s,t) -> \n modp(expand(add(add(\n ((t^2+s*t)^i*s^(2*j) + (s^2+s*t)^i*t^(2*j)) * Sq(i,j),\n j=0..n-i),i=0..n)),2);\n\nbullett_macdonald_term := proc(i::nonnegint,j::nonnegint)\n local k0;\n k0 := modp(i,2);\n if modp(j,2) <> k0 then return 0; fi;\n return add(\n modp(binomial((j+k)/2,k),2) * Sq((j+k)/2,(i-k)/2),\n k=k0..min(i,j),2);\nend:\n\nbullett_macdonald_relation := proc(i::nonnegint,j::nonnegint)\n modp(bullett_macdonald_term(i,j) + bullett_macdonald_term(j,i),2);\nend:\n\nsinger_relation := proc(p::nonnegint,q::nonnegint)\n if p > 2*q then return 0; fi;\n\n return add(modp(binomial(p,i),2) * Sq(2*q-i+1,q-p+i+1),\n i = max(0,p-q-1)..p);\nend:\n\nsteenrod_mul := proc()\n local u,v;\n if nargs = 0 then \n return Sq();\n elif nargs = 1 then\n return modp(args[1],2);\n elif nargs > 2 then\n return steenrod_mul(steenrod_mul(args[1],args[2]),args[3..-1]);\n fi;\n\n u := modp(args[1],2);\n v := modp(args[2],2);\n if type(v,`+`) then\n return modp(expand(map(t -> steenrod_mul(u,t),v)),2);\n fi;\n if type(u,`+`) then\n return modp(expand(map(t -> steenrod_mul(t,v),u)),2);\n fi;\n\n if type(u,specfunc(nonnegint,Sq)) and type(v,specfunc(nonnegint,Sq)) then\n return Sq(op(u),op(v));\n else\n return u * v;\n fi;\nend:\n\nadem_mul := proc() adem_reduce(steenrod_mul(args)); end:\n\ntwo_power_Sq := proc(n::nonnegint)\n option remember;\n local m,p,s,t,rel;\n\n if n = 0 then return Sq(); fi;\n\n m := n;\n p := 1;\n while modp(m,2) = 0 do m := m/2; p := 2*p; od;\n if p = n then return Sq(n); fi;\n\n rel := bullett_macdonald_series(n,s,t);\n rel := coeff(coeff(rel,s,p),t,2*n-p) - Sq(n,0);\n\n return two_power_reduce(rel);\nend:\n\ntwo_power_reduce := proc(u)\n if type(u,list) or type(u,set) or type(u,specfunc(anything,bar)) then\n return map(two_power_reduce,u);\n elif type(u,`+`) or type(u,`*`) then\n return modp(expand(map(two_power_reduce,u)),2);\n elif type(u,specfunc(nonnegint,Sq)) then\n return steenrod_mul(op(map(two_power_Sq, [op(u)])));\n fi;\nend:\n\nmilnor_Q := proc(n::nonnegint)\n option remember;\n local u,v;\n\n if n = 0 then \n return Sq(1);\n else\n u := Sq(2^n);\n v := milnor_Q(n-1);\n return modp(adem_mul(u,v) + adem_mul(v,u),2);\n fi;\nend:\n\ncartan_psi := proc(u)\n local v,f,m,i,j,k;\n if type(u,list) or type(u,set) then \n return map(cartan_psi,u);\n elif type(u,`+`) or type(u,`*`) then\n return modp(expand(map(cartan_psi,u)),2);\n elif type(u,specfunc(nonnegint,Sq)) then\n v := [bar(Sq(),Sq())];\n f := (i,j) -> v -> bar(Sq(op(op(1,v)),i),Sq(op(op(2,v)),j));\n for k from 1 to nops(u) do\n m := op(k,u);\n v := [seq(seq(f(i,m-i)(x),x in v),i=0..m)];\n od:\n return `+`(op(v));\n else\n return u;\n fi;\nend:\n\na[0] := 1;\naL[0] := 1;\naR[0] := 1;\n\ndual_psi := (u) ->\n subs({seq(a[i] = add(aL[j] * aR[i-j]^(2^j),j=0..i),i=0..n_max)},u);\n\nsteenrod_pairing := proc(u,v)\n local m,c,i;\n\n if u = 0 or v = 0 then return 0; fi;\n\n if type(u,`+`) then \n return modp(expand(map(t -> steenrod_pairing(t,v),u)),2);\n fi;\n if type(v,`+`) then \n return modp(expand(map(t -> steenrod_pairing(u,t),v)),2);\n fi;\n\n if type(u,specfunc(nonnegint,Sq)) then\n m := nops(u);\n if m = 0 then\n c := v;\n for i from 1 to n_max do c := coeff(c,a[i],0); od;\n return modp(c,2);\n elif m = 1 then\n c := coeff(v,a[1],op(u));\n for i from 2 to n_max do c := coeff(c,a[i],0); od;\n return modp(c,2);\n else\n c := coeff(dual_psi(v),aR[1],op(1,u));\n for i from 2 to n_max do c := coeff(c,aR[i],0); od;\n c := eval(subs(aL = a,c));\n c := steenrod_pairing(Sq(op(2..-1,u)),c);\n return c;\n fi;\n else\n return FAIL;\n fi;\nend:\n\ndickson_fW := proc(n)\n local t;\n return unapply(add(W[n,i] * t^(2^i),i = 0..n-1) + t^(2^n),t);\nend:\n\ndickson_fx := proc(n)\n option remember;\n local t,g,h,i;\n \n if n = 0 then\n return unapply(t,t);\n else\n g := dickson_fx(n-1)(t);\n h := modp(expand(g * add(coeff(g,t,2^i) * (t^(2^i) + x[n-1]^(2^i)),i=0..n-1)),2);\n return unapply(h,t);\n fi;\nend:\n\ndickson_W_deg := (n,i) -> 2^n - 2^i;\n\ndickson_Wx := proc(n,k)\n option remember;\n return coeff(dickson_fx(n)(t),t,2^k);\nend:\n\nmui_Vx := (k) -> dickson_fx(k)(x[k]);\n\nmui_V_deg := (i) -> 2^i;\n\nmui_gV := (k) -> unapply(V[k] * t + t^2,t);\n\nmui_gx := (k) -> unapply(mui_Vx(k) * t + t^2,t);\n\ndickson_WV := proc(n,k)\n local L;\n if k > n then return 0; fi;\n \n L := combinat[choose]([seq(j,j=0..n-1)],n-k):\n return add(mul(V[i[t]]^(2^(t-i[t]+k-1)),t=1..n-k),i in L);\nend:\n\ndickson_WV_alt := proc(n,k)\n option remember;\n\n if k > n or k < 0 then return 0; fi;\n if k = n then return 1; fi;\n if k = 0 then return mul(V[i],i=0..n-1); fi;\n\n return modp(expand(V[n-1] * dickson_WV(n-1,k) + dickson_WV(n-1,k-1)^2),2); \nend:\n\nTSq_x := proc(n) local t; unapply(x[n] + t * x[n]^2, t); end;\n\nTSq_mui_V := proc(n)\n local t,u;\n u := t^(2^n) * V[n]^2 + add(t^(2^n - 2^i) * V[n] * dickson_WV(n,i),i=0..n);\n return unapply(u,t);\nend:\n\nTSq_dickson_W := proc(n,k)\n local t,u;\n u := subs(W[n,n] = 1,\n W[n,k]^2 * t^(2^n - 2^k) +\n add(add(W[n,i]*W[n,j]* t^(2^n+2^k-2^i-2^j),j=k+1..n),i=0..k));\n return unapply(u,t);\nend:\n\ndickson_w_deg := (n,k) -> 1 - 2^k;\n\ndickson_wW := proc(n::nonnegint,i::nonnegint)\n if i < n then\n return W[n,i]/W[n,0];\n elif i = n then\n return 1/W[n,0];\n else\n return 0;\n fi;\nend:\n\ndickson_Ww := proc(n,i)\n if i = 0 then\n return 1/w[n,n];\n elif i <= n then\n return w[n,i]/w[n,n];\n else\n return 0;\n fi;\nend:\n\ndickson_wx := (n,i) -> dickson_Wx(n,i)/dickson_Wx(n,0);\n\ndickson_wv := proc(n,k)\n local L;\n L := combinat[choose]([seq(j,j=0..n-1)],k):\n return add(mul(v[i[t]]^(-2^(k-t)),t=1..k),i in L);\nend:\n\ndickson_wv_alt := proc(n,k)\n option remember;\n local u;\n \n if k > n or k < 0 then return 0; fi;\n if k = 0 then return 1; fi;\n\n u := dickson_wv(n-1,k) + dickson_wv(n-1,k-1)^2/v[n-1];\n u := expand(modp(factor(u),2));\n return u;\nend:\n\ndickson_fw := (n) -> unapply(t + add(w[n,i] * t^(2^i),i=1..n),t);\n\nmui_v_deg := (i) -> 1;\n\nmui_vV := (i) -> V[i] / mul(V[j],j=0..i-1);\nmui_Vv := (i) -> mul(v[j] ^ (2^max(i-j-1,0)),j=0..i);\n\nmui_vx := (i) -> mui_Vx(i) / mul(mui_Vx(j),j=0..i-1);\n\nmui_gv := (i) -> unapply(t + t^2/v[i],t);\n\n######################################################################\n\ncheck_admissible := proc(m::nonnegint)\n local B,BB,n;\n\n B := admissible_basis(m);\n \n _ASSERT(\n `and`(op(map(is_admissible,B))),\n \"Admissible moomials are admissible\"\n );\n\n _ASSERT(\n B = sort(B,admissible_lt),\n \"Admissible monomials are sorted\"\n );\n\n _ASSERT(\n B = map(comate,map(mate,B)),\n \"comate o mate = 1\"\n );\n\n n := nops(B);\n _ASSERT(\n {1,op(map(u -> steenrod_pairing(u,mate(u)),B))} = {1},\n \" = 1\"\n );\n\n _ASSERT(\n {0,seq(seq(steenrod_pairing(B[j],mate(B[i])),j=i+1..n),i=1..n)} = {0},\n \" = 0 for A > B\"\n );\n\n BB := {seq(seq([u,v],v in B),u in B)};\n BB := select(uv -> steenrod_length(uv[1]) < steenrod_length(uv[2]),BB);\n BB := map(uv -> steenrod_pairing(uv[1],mate(uv[2])), BB);\n _ASSERT(\n BB = {0},\n \" = 0 for len(A) < len(B)\"\n );\n\nend:\n\ncheck_adem := proc(m::nonnegint)\n local err;\n \n err := \n {0, seq(seq(\n steenrod_pairing(adem_relation(i,m-i),mate(u)),\n i=0..m),u in admissible_basis(m))};\n\n _ASSERT(err = {0},\"Adem relations are compatible with pairing\");\nend:\n\ncheck_milnor_Q := proc(m)\n local i,Q;\n\n for i from 0 to m do Q[i] := milnor_Q(i); od;\n\n _ASSERT(\n {0,seq(adem_mul(Q[i],Q[i]),i=0..m)} = {0},\n \"Q_i^2 = 0\"\n );\n\n _ASSERT(\n {0,seq(seq(modp(adem_mul(Q[i],Q[j])+adem_mul(Q[j],Q[i]),2),j=i+1..m),i=0..m)} = {0},\n \"Q_i Q_j = Q_j Q_i\"\n );\n\n _ASSERT(\n {0,seq(modp(eval(adem_reduce(cartan_psi(Q[i]) + bar(Sq(),Q[i]) + bar(Q[i],Sq()))),2),i=0..m)} = {0}, \n \"Q_i is primitive\"\n );\nend:\n\ncheck_two_power := proc(m)\n local B,err;\n\n B := [seq(seq(seq(Sq(i,j,k),k=0..m),j=0..m),i=0..m)];\n\n err := {0,op(map(u -> adem_reduce(u + two_power_reduce(u)),B))};\n\n _ASSERT(err = {0},\"Two-power reduction is consistent\");\nend:\n\ncheck_bullett_macdonald := proc(m)\n local s,t;\n \n _ASSERT(\n adem_reduce(bullett_macdonald_series(m,s,t)) = 0,\n \"Bullett-Macdonald series\"\n );\n\n _ASSERT(\n {0,seq(seq(adem_reduce(bullett_macdonald_relation(i,j)),j=0..20),i=0..20)} = {0},\n \"Bullett-Macdonald relations\"\n );\n\n _ASSERT(\n {0,seq(seq(adem_reduce(singer_relation(p,q)),p=0..2*q),q=0..15)} = {0},\n \"Singer relations\"\n );\nend:\n\ncheck_dickson := proc(m::nonnegint)\n local t,err;\n \n _ASSERT(\n modp(expand(dickson_fx(m)(t) - add(dickson_Wx(m,i) * t^(2^i),i=0..m)),2) = 0,\n \"The Dickson polynomial is additive\"\n );\n\n _ASSERT(\n modp(expand(dickson_Wx(m,0) + mul(mui_Vx(i),i=0..m-1)),2) = 0,\n \"W_{m0} = prod_{i sort(expand(eval(subs(`bar/EA`=`d_bar/EA`,u))));\n\n`d_bar/EA` := proc()\n local n,i,q,a;\n a := args;\n n := nargs;\n if n = 0 then\n return FAIL;\n elif n = 1 then\n return 0;\n else \n return\n add((-1)^i*`bar/EA`(a[1..i-1],a[i]*a[i+1],a[i+2..n]),i=1..n-1) +\n (-1)^n*`bar/EA`(a[1..n-1]);\n fi;\nend:\n\n# The shuffle product in the bar complex is `mu/EA`\n\n`mu/EA` := proc()\n apply_linear_assoc(`mu0/EA`,`bar/EA`())(args);\nend:\n\n`mu0/EA` := proc(u,v)\n local n,m,uv,c,L,s,i;\n n := nops(u)-1;\n m := nops(v)-1;\n uv := [op(2..n+1,u),op(2..m+1,v)];\n c := op(1,u) * op(1,v);\n L := `list_elements/inverse_shuffles`(n,m);\n\n return add(`sgn/shuffles`(n,m)(s) *\n `bar/EA`(c,seq(uv[s[i]],i=1..n+m)),s in L):\nend:\n\n`mu_bar/EA` := proc()\n `mu/EA`(op(map(`bar/EA`,[args])));\nend:\n\n# We now give a chain homotopy of EA for the case where A is cyclic\n# of infinite order generated by a. This gives a retraction onto\n# a subcomplex concentrated in degrees 0 and 1.\n\n`s0/EA` := (a) -> proc(u)\n local n,k,s,i;\n if type(u,specfunc(anything,`bar/EA`)) then\n n := nops(u);\n if n <= 1 then return 0; fi;\n k := degree(op(n,u),a);\n if op(n,u) <> a^k then\n return FAIL;\n fi;\n if k >= 0 then \n return add((-1)^n*`bar/EA`(op(1..n-1,u),a^i,a),i=0..k-1);\n else\n return add((-1)^(n+1)*`bar/EA`(op(1..n-1,u),a^(-i),a),i=1..abs(k));\n fi:\n else\n return FAIL;\n fi;\nend:\n\n`s/EA` := (a) -> apply_linear(`s0/EA`(a));\n\n`p0/EA` := (a) -> proc(u)\n local n,i,k;\n if type(u,specfunc(anything,`bar/EA`)) then\n n := nops(u);\n if n <= 1 then\n return u;\n elif n = 2 then\n k := degree(op(2,u),a);\n if op(n,u) <> a^k then\n return FAIL;\n fi;\n if k >= 0 then\n return add(`bar/EA`(a^i*op(1,u),a),i=0..k-1);\n else\n return add(-`bar/EA`(a^(-i)*op(1,u),a),i=1..abs(k));\n fi;\n else\n return 0;\n fi;\n else\n return FAIL;\n fi;\n\nend:\n\n`p/EA` := (a) -> apply_linear(`p0/EA`(a));\n\n\n######################################################################\n\n# Given elements a[i] in A we have elements 1 - a[i] in the group ring.\n# The tensor product of these is represented by `bar/BA`(a[1],...,a[n])\n\n`bar/BA` := proc ()\n local i;\n for i to nargs do\n if args[i] = 1 then return 0 fi;\n od;\n return '`bar/BA`'(args);\nend:\n\n# The standard differential in the bar complex is `d/BA`\n\n`d/BA` := (u) -> sort(expand(eval(subs(`bar/BA`=`d_bar/BA`,u))));\n\n`d_bar/BA` := proc()\n local n,i,q;\n n := nargs;\n if n = 0 then\n return 0;\n else \n return -`bar/BA`(args[2..n]) + \n (-1)^(n+1)*`bar/BA`(args[1..n-1]) +\n add((-1)^(i+1)*`bar/BA`(args[1..i-1],args[i]*args[i+1],args[i+2..n]),\n i=1..n-1);\n fi;\nend:\n\n# The shuffle product in the bar complex is `mu/BA`\n\n`mu/BA` := proc()\n apply_linear_assoc(`mu0/BA`,`bar/BA`())(args);\nend:\n\n`mu0/BA` := proc(u,v)\n local n,m,uv,L,s,i;\n n := nops(u);\n m := nops(v);\n uv := [op(u),op(v)];\n L := `list_elements/inverse_shuffles`(n,m);\n\n return add(`sgn/shuffles`(n,m)(s) * `bar/BA`(seq(uv[s[i]],i=1..n+m)),s in L):\nend:\n\n`mu_bar/BA` := proc()\n `mu/BA`(op(map(`bar/BA`,[args])));\nend:\n\n`proj_bar/EA` := proc() `bar/BA`(args[2..-1]); end:\n`lift_bar/BA` := proc() `bar/EA`(1,args); end: \n`proj/EA/BA` := (u) -> eval(subs(`bar/EA` = `proj_bar/EA`,u));\n`lift/BA/EA` := (u) -> eval(subs(`bar/BA` = `lift_bar/BA`,u));\n\n######################################################################\n# The element u = `tau/BA`(n,a) has du = n[a] - [a^n].\n# Thus, if a^n = 1 then u is a 2-cycle modulo n.\n\n`tau/BA` := proc(n,a)\n local k;\n add(-`bar/BA`(a^k,a),k=0..n-1);\nend:\n\n`zeta/BA` := proc(n,m,a)\n local i,j;\n - add(add(`bar/BA`(a^(m*i),a^j,a),j=0..m-1),i=0..n-1);\nend:\n\n# The element `sigma/BA`(n,a,b) is a chain of dimension 3.\n# It is symmetric in a and b, and is a cycle if a^n = b^n = 1.\n\n`sigma/BA` := proc(n,a,b)\n `mu/BA`(`tau/BA`(n, a), `bar/BA`(b)) +\n `mu/BA`(`tau/BA`(n, b), `bar/BA`(a))\nend:\n\n# The element u = `gamma/BA`(n,a) is a chain of dimension 2n+1.\n# It is a cycle if a^n = 1.\n\n`gamma/BA` := proc(n,k,a)\n local u,v,i;\n u := `bar/BA`(a);\n v := `tau/BA`(n,a);\n for i from 1 to k do\n u := `mu/BA`(u,v);\n od;\n u := expand(u/k!);\n return u;\nend:\n\n`xi/BA` := proc(n,m,a)\n local i,j;\n \n add(add(-`bar/BA`(a^i,a,a^j,a),i=1..m-1),j=1..n*m-1) +\n add(add(-`bar/BA`(a^m,a^(i*m),a^j,a),j=1..m-1),i=1..n-1);\nend:\n\n`rho/BA` := proc(n,a,b)\n `tau/BA`(n,a) +\n `tau/BA`(n,b) -\n `tau/BA`(n,a*b) +\n n*`bar/BA`(a, b);\nend:\n\n`omega/BA` := proc (n,a,b)\n local i,j;\n \n -add(add(`bar/BA`(a^i*b^j,b,a), j = i .. n-1), i = 0 .. n-1) +\n add(add(`bar/BA`(a^i*b^j,a,b), j = i+1 .. n-1), i = 0 .. n-2);\nend:\n\n######################################################################\n# We now introduce the standard DGA for H_*(BZ/n).\n\n# The k'th chain group is freely generated over Z[Z/n] by\n# `e/EC`(n)(k,0). The orbit of this consists of elements `e/EC`(n)(k,i).\n\n`de/EC` := (n::posint) -> proc(k::nonnegint,i::nonnegint)\n local j;\n \n if k = 0 then\n return 0;\n elif modp(k,2) = 0 then\n return(add(`e/EC`(n)(k-1,j),j=0..n-1));\n else\n return `e/EC`(n)(k-1,modp(i+1,n)) - `e/EC`(n)(k-1,i);\n fi;\nend:\n\n`d/EC` := (n) -> (u) -> eval(subs(`e/EC` = `de/EC`,u));\n\n`mu/EC` := (n) -> proc()\n apply_linear_assoc(`mu0/EC`(n),`e/EC`(n)(0,0))(args);\nend:\n\n`mu0/EC` := (n) -> proc(a,b)\n local ka,kb,ia,ib,la,lb;\n if type(a,specfunc(anything,`e/EC`(n))) and\n type(b,specfunc(anything,`e/EC`(n))) then\n ka,ia := op(a);\n kb,ib := op(b);\n if modp(ka,2) = 1 and modp(kb,2) = 1 then\n return 0;\n fi;\n la := floor(ka/2);\n lb := floor(kb/2);\n return binomial(la+lb,la) * `e/EC`(n)(ka+kb,modp(ia+ib,n));\n else\n return('`mu/EC`'(n)(args))\n fi;\nend:\n\n\n##################################################\n\n`de/BC` := (n::posint) -> proc(k::nonnegint)\n if k = 0 or modp(k,2) = 1 then\n return 0;\n else\n return n * `e/BC`(n)(k-1);\n fi;\nend:\n\n`d/BC` := (n) -> (u) -> eval(subs(`e/BC` = `de/BC`,u));\n\n`mu/BC` := (n) -> proc()\n apply_linear_assoc(`mu0/BC`(n),`e/BC`(n)(0))(args);\nend:\n\n`mu0/BC` := (n) -> proc(a,b)\n local ka,kb,la,lb;\n if type(a,specfunc(anything,`e/BC`(n))) and\n type(b,specfunc(anything,`e/BC`(n))) then\n ka := op(a);\n kb := op(b);\n if modp(ka,2) = 1 and modp(kb,2) = 1 then\n return 0;\n fi;\n la := floor(ka/2);\n lb := floor(kb/2);\n return binomial(la+lb,la) * `e/BC`(n)(ka+kb);\n else\n return('`mu/BC`'(n)(args))\n fi;\nend:\n\n`e/BC/BA` := (n::posint) -> proc(k::nonnegint)\n option remember;\n\n if k = 0 then\n return `bar/BA`();\n elif k = 1 then\n return `bar/BA`(a);\n else\n return expand(`mu/BA`(`tau/BA`(n,a),`e/BC/BA`(n)(k-2))/floor(k/2));\n fi;\nend:\n\n`phi/BC/BA` := proc(u)\n eval(subs(`e/BC` = `e/BC/BA`,u));\nend:\n\n######################################################################\n\ncheck_homology_BA := proc()\n local i,j,k,n,m,a,b,c,t,u,v,w,T,ok,err,exp_rel,diff_rel;\n\n ok := true;\n for i from 0 to 4 do\n for j from 0 to 4 do \n u := `bar/EA`(seq(a[m],m=1..i+1)); \n v := `bar/EA`(seq(a[m],m=i+2..i+j+2));\n err := `mu/EA`(u,v) - (-1)^(i*j) * `mu/EA`(v,u);\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`mu/EA` is graded-commutative\");\n\n ok := true;\n for i from 0 to 4 do\n for j from 0 to 4 do \n for k from 0 to 4 do \n u := `bar/EA`(seq(a[m],m=1..i+1)); \n v := `bar/EA`(seq(a[m],m=i+2..i+j+2));\n w := `bar/EA`(seq(a[m],m=i+j+3..i+j+k+3));\n err := `mu/EA`(`mu/EA`(u,v),w) - `mu/EA`(u,`mu/EA`(v,w));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`mu/EA` is associative\");\n\n ok := true;\n for i from 0 to 3 do\n for j from 0 to 3 do \n u := `bar/EA`(seq(a[m],m=1..i+1)); \n v := `bar/EA`(seq(a[m],m=i+2..i+j+2));\n err := `d/EA`(`mu/EA`(u,v)) - `mu/EA`(`d/EA`(u),v) - (-1)^i*`mu/EA`(u,`d/EA`(v));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`d/EA` and `mu/EA` satisfy the Leibniz rule\");\n\n ok := true;\n for i from 0 to 4 do\n for j from 0 to 4 do \n u := `bar/BA`(seq(a[m],m=1..i)); \n v := `bar/BA`(seq(a[m],m=i+1..i+j));\n err := `mu/BA`(u,v) - (-1)^(i*j) * `mu/BA`(v,u);\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`mu/BA` is graded-commutative\");\n\n ok := true;\n for i from 0 to 4 do\n for j from 0 to 4 do \n for k from 0 to 4 do \n u := `bar/BA`(seq(a[m],m=1..i)); \n v := `bar/BA`(seq(a[m],m=i+1..i+j));\n w := `bar/BA`(seq(a[m],m=i+j+1..i+j+k));\n err := `mu/BA`(`mu/BA`(u,v),w) - `mu/BA`(u,`mu/BA`(v,w));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`mu/BA` is associative\");\n\n ok := true;\n for i from 0 to 4 do\n for j from 0 to 4 do \n u := `bar/BA`(seq(a[m],m=1..i)); \n v := `bar/BA`(seq(a[m],m=i+1..i+j));\n err := `d/BA`(`mu/BA`(u,v)) - `mu/BA`(`d/BA`(u),v) - (-1)^i*`mu/BA`(u,`d/BA`(v));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`d/BA` and `mu/BA` satisfy the Leibniz rule\");\n\n n := 5;\n err := `d/BA`(`tau/BA`(n,a)) - n * `bar/BA`(a);\n exp_rel := `bar/BA`(a^n);\n err := err + exp_rel;\n \n _ASSERT(err = 0,\"d(tau_n(a))\");\n\n err := \n `d/BA`(`mu/BA`(`tau/BA`(n,a),`bar/BA`(b))) - n * `mu_bar/BA`(a,b);\n exp_rel := `mu_bar/BA`(a^n,b); \n err := err + exp_rel;\n\n _ASSERT(err = 0,\"d(tau_n(a) b)\");\n\n _ASSERT(\n {seq(seq(\n `tau/BA`(i*j,a) - `tau/BA`(i,a^j) - i * `tau/BA`(j,a) - `d/BA`(`zeta/BA`(i,j,a)),\n j=1..4),i=1..4)} = {0},\n \"tau_{ij}(a)\"\n );\n\n err := `d/BA`(`sigma/BA`(n,a,b));\n exp_rel := `mu_bar/BA`(a^n,b) - `mu_bar/BA`(a,b^n);\n err := err + exp_rel;\n\n _ASSERT(err = 0,\"d(sigma_n(a,b))\");\n\n _ASSERT(`sigma/BA`(n,a,b) = `sigma/BA`(n,b,a),\"sigma_n is symmetric\");\n \n err :=\n `sigma/BA`(n,a,b*c) - `sigma/BA`(n,a,b) - `sigma/BA`(n,a,c) +\n `mu/BA`(`bar/BA`(a),`rho/BA`(n,b,c));\n diff_rel := - `mu/BA`(`tau/BA`(n,a),`bar/BA`(b,c));\n exp_rel := - `mu/BA`(`bar/BA`(a^n),`bar/BA`(b,c));\n err := err + `d/BA`(diff_rel) + exp_rel;\n\n _ASSERT(err = 0,\"First formula for sigma_n(a,bc)\");\n\n err := \n `sigma/BA`(n,a,b*c)-`sigma/BA`(n,a,b)-`sigma/BA`(n,a,c)+\n binomial(n+1,2)*`mu_bar/BA`(a,b,c);\n \n diff_rel := -(`mu/BA`(`bar/BA`(a),`omega/BA`(n,b,c))+\n \t `mu/BA`(`tau/BA`(n,a),`bar/BA`(b,c)));\n exp_rel := \n - `mu/BA`(`bar/BA`(a^n),`bar/BA`(b,c)) - \n add(`bar/BA`(a,b^i,b)-`bar/BA`(a,b^i*c^n,b),i=0..n-1)- \n add(`bar/BA`(b^i,b,a)-`bar/BA`(b^i*c^n,b,a),i=0..n-1)+\n add(`bar/BA`(b^i,a,b)-`bar/BA`(b^i*c^n,a,b),i=0..n-1);\n\n err := err + `d/BA`(diff_rel) + exp_rel;\n\n _ASSERT(err = 0,\"Second formula for sigma_n(a,bc)\");\n\n for k from 1 to 5 do\n err := `d/BA`(`gamma/BA`(n,k,a));\n T := [[]]:\n for i from 1 to k-1 do\n T := [seq(seq([op(t),a,a^j],j=1..n-1),t in T)]:\n od:\n exp_rel := (-1)^k*add(`mu/BA`(`bar/BA`(op(t),a),`bar/BA`(a^n)),t in T);\n err := err + exp_rel;\n _ASSERT(err = 0,sprintf(\"d(gamma_{n,%d}(u))\",k));\n od:\n\n _ASSERT(simplify(`sigma/BA`(n,a,a) - 2 * `gamma/BA`(n,1,a)) = 0,\n \"sigma_n(a,a) = 2 gamma_{n,1}(a)\");\n\t \n err := \n `gamma/BA`(n,1,a*b) - `gamma/BA`(n,1,a) - `gamma/BA`(n,1,b) -\n `sigma/BA`(n,a,b);\n\n diff_rel :=\n n*`bar/BA`(a,b,a,b) -\n `mu/BA`(`bar/BA`(a,b),`tau/BA`(n,a*b)) +\n `mu/BA`(`omega/BA`(n,a,b),`bar/BA`(a)+`bar/BA`(b));\n \n exp_rel := \n add(`bar/BA`(a^i,b,a) - `bar/BA`(a^i*b^n,b,a),i=0..n-1) -\n add(`bar/BA`(a^i,a,b) - `bar/BA`(a^i*b^n,a,b),i=0..n-1) -\n add(`bar/BA`(b,a^i,a) - `bar/BA`(b,a^i*b^n,a),i=0..n-1) -\n add(`bar/BA`(a,a^i,a) - `bar/BA`(a,a^i*b^n,a),i=0..n-1) -\n `mu/BA`(`bar/BA`(a^n*b^n),`bar/BA`(a,b));\n\n err := err + `d/BA`(diff_rel) + exp_rel;\n\n _ASSERT(err = 0,\"gamma_{n,1}(ab)\");\n\n _ASSERT(\n {seq(seq(\n `gamma/BA`(i,1,a^j) - j * `gamma/BA`(i*j,1,a) +\n `mu/BA`(`bar/BA`(a^(i*j)),`tau/BA`(j,a)) -\n `d/BA`(`xi/BA`(i,j,a)),\n j=1..4),i=1..4)} = {0},\n \"gamma_{ij,1}(a)\"\n );\nend:\n\n######################################################################\n\ncheck_homology_BZ := proc()\n local U,i,j,u,du,sdu,su,dsu,pu,ok,err;\n \n U := [seq(`bar/EA`(a^j),j=-2..2)]:\n for i from 1 to 4 do\n U := [op(U),\n\tseq(seq(`bar/EA`(op(u),a^j),j=1..2),u in U),\n\tseq(seq(`bar/EA`(op(u),a^(-j)),j=1..2),u in U)]:\n od:\n\n ok := true;\n \n for u in U do\n du := `d/EA`(u);\n sdu := `s/EA`(a)(du);\n su := `s/EA`(a)(u); \n dsu := `d/EA`(su);\n pu := `p/EA`(a)(u);\n err := sdu + dsu - u + pu;\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n\n _ASSERT(ok,\"ds + ds = 1 - p\",[u,du,sdu,su,dsu,pu]);\nend:\n\n######################################################################\n\ncheck_homology_BC := proc()\n local n,ok,u,v,w,ku,kv,kw,err;\n \n n := 5;\n\n ok := true;\n for ku from 0 to 4 do\n for kv from 0 to 4 do\n u := `e/BC`(n)(ku);\n v := `e/BC`(n)(kv);\n err := `mu/BC`(n)(u,v) - (-1)^(ku*kv) * `mu/BC`(n)(v,u);\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"`mu_BC` is graded-commutative\");\n\n ok := true;\n for ku from 0 to 4 do\n for kv from 0 to 4 do\n for kw from 0 to 4 do\n u := `e/BC`(n)(ku);\n v := `e/BC`(n)(kv);\n w := `e/BC`(n)(kw);\n err := `mu/BC`(n)(`mu/BC`(n)(u,v),w) - `mu/BC`(n)(u,`mu/BC`(n)(v,w));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n od:\n \n _ASSERT(ok,\"`mu_BC` is associative\",[u,v,w,err]);\n\n ok := true;\n for ku from 0 to 4 do\n for kv from 0 to 4 do\n u := `e/BC`(n)(ku);\n v := `e/BC`(n)(kv);\n err := `d/BC`(n)(`mu/BC`(n)(u,v)) - `mu/BC`(n)(`d/BC`(n)(u),v) - (-1)^ku * `mu/BC`(n)(u,`d/BC`(n)(v));\n if err <> 0 then\n ok := false;\n break;\n fi;\n od:\n if not(ok) then break; fi;\n od:\n\n _ASSERT(ok,\"Leibniz rule for BC\");\nend:\n", "meta": {"hexsha": "7728fd182d176c01e266be04fe98047827166823", "size": 13820, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/abelian_group_homology.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/abelian_group_homology.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/abelian_group_homology.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 22.9950083195, "max_line_length": 105, "alphanum_fraction": 0.4908104197, "num_tokens": 5925, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8152324893520001, "lm_q2_score": 0.672331699179286, "lm_q1q2_score": 0.5481066447921894}} {"text": "make_octahedron_complex := proc()\n global octahedron_complex,cube_complex;\n local OC,CC,vO,vC,vOi,vCi,i,j,k,dp,CF,f,G,G0,G1,r,g,h,eqs,sol,sc,OS,s,t;\n\n CC := table():\n OC := table():\n \n CC[\"vertices\"] := [seq(i,i=1..8)];\n OC[\"vertices\"] := [seq(i,i=1..6)];\n\n vO := table([\n 1 = [1,0,0], 2 = [0,1,0], 3 = [0,0,1], 4 = [0,0,-1], 5 = [0,-1,0], 6 = [-1,0,0]\n ]);\n\n vC := table([\n 1 = [ 1, 1, 1], 2 = [ 1, 1,-1], 3 = [ 1,-1, 1], 4 = [ 1,-1,-1],\n 5 = [-1, 1, 1], 6 = [-1, 1,-1], 7 = [-1,-1, 1], 8 = [-1,-1,-1]\n ]);\n\n vOi := table():\n vCi := table():\n\n for i from 1 to 6 do vOi[vO[i]] := i; od;\n for i from 1 to 8 do vCi[vC[i]] := i; od;\n\n OC[\"embedding_dim\"] := 3;\n CC[\"embedding_dim\"] := 3;\n\n OC[\"embedding\"] := eval(vO);\n OC[\"normalised_embedding\"] := copy(vO);\n OC[\"dual_embedding\"] := copy(vO);\n\n CC[\"embedding\"] := eval(vC);\n CC[\"normalised_embedding\"] := table([seq(i = vC[i] *~ (sqrt(3)/3), i = 1 .. 8)]);\n CC[\"dual_embedding\"] := table([seq(i = vC[i] /~ 3, i = 1 .. 8)]);\n\n dp := (u,v) -> add(u[i] * v[i],i=1..3);\n \n OC[\"faces\"] := [seq(select(i -> dp(vO[i],vC[j]) = 1,OC[\"vertices\"]),j = 1..8)];\n CC[\"squares\"] := [seq(select(j -> dp(vO[i],vC[j]) = 1,CC[\"vertices\"]),i = 1..6)];\n\n OC[\"edges\"] := {op(map(op,map(f -> [[f[1],f[2]],[f[1],f[3]],[f[2],f[3]]],OC[\"faces\"])))};\n OC[\"edges\"] := sort([op(OC[\"edges\"])]);\n\n CC[\"short_edges\"] := [[1,2],[1,3],[1,5],[1,6],\n [2,4],[2,6],[3,4],[3,7],[5,6],[5,7],\n\t\t [4,8],[5,8],[6,8],[7,8]];\n \n CC[\"long_edges\"] := [[1,4],[1,6],[1,7],[2,8],[3,8],[5,8]];\n\n CC[\"edges\"] := sort([op(CC[\"short_edges\"]),op(CC[\"long_edges\"])]);\n sc := [1,6,4,2,7,5,3,8];\n CC[\"six_cycle\"] := sc;\n\n CF := NULL;\n OS := NULL;\n for s in CC[\"squares\"] do\n i := op({op(s)} minus {seq(sc[j],j in s)});\n if member(1,s) then\n CF := CF,[1,s[2],s[4]],[1,s[3],s[4]];\n OS := OS,[1,i,sc[i],sc[sc[i]]];\n else\n CF := CF,[s[1],s[2],8],[s[1],s[3],8];\n OS := OS,[sc[sc[i]],sc[i],i,8];\n fi;\n od:\n OS := [OS];\n \n CC[\"faces\"] := sort([CF]);\n CC[\"oriented_squares\"] := OS;\n CC[\"square_plot\"] :=\n display(\n seq(polygon(map(j -> vC[j],OS[i]),colour=standard_colour(i)),i=1..6),\n scaling=constrained,axes=none);\n\n OC[\"max_simplices\"] := OC[\"faces\"];\n CC[\"max_simplices\"] := CC[\"faces\"];\n\n OC[\"edge_index\"] := make_index(OC[\"edges\"]):\n OC[\"face_index\"] := make_index(OC[\"faces\"]):\n\n CC[\"edge_index\"] := make_index(CC[\"edges\"]):\n CC[\"face_index\"] := make_index(CC[\"faces\"]):\n\n `plot/simplicial_complex`(OC);\n `plot/simplicial_complex`(CC);\n\n OC[\"edge_centres\"] :=\n map(e -> (vO[e[1]] +~ vO[e[2]]) /~ 2,OC[\"edges\"]);\n\n OC[\"face_centres\"] :=\n map(f -> (vO[f[1]] +~ vO[f[2]] +~ vO[f[3]]) /~ 3, OC[\"faces\"]);\n\n CC[\"short_edge_centres\"] :=\n map(e -> (vC[e[1]] +~ vC[e[2]]) /~ 2,CC[\"short_edges\"]);\n\n CC[\"square_centres\"] :=\n map(f -> (vC[f[1]] +~ vC[f[2]] +~ vC[f[3]] +~ vC[f[4]]) /~ 4, CC[\"squares\"]);\n\n f := (u) -> simplify(rationalize(u /~ sqrt(add(u[i]^2,i=1..3))));\n\n OC[\"poles\"] := table([\n 2 = map(f,OC[\"edge_centres\"]),\n 3 = map(f,OC[\"face_centres\"]),\n 4 = map(i -> f(vO[i]),OC[\"vertices\"])\n ]);\n\n CC[\"poles\"] := copy(OC[\"poles\"]);\n \n OC[\"pole_plots\"] := table([\n 2 = map(u -> line(1.1 *~ u, -1.1 *~ u,color=green,thickness=4),CC[\"poles\"][2]),\n 3 = map(u -> line(1.1 *~ u, -1.1 *~ u,color=red ,thickness=4),CC[\"poles\"][3]),\n 4 = map(u -> line(1.2 *~ u, -1.2 *~ u,color=blue ,thickness=4),CC[\"poles\"][4])\n ]);\n\n OC[\"all_poles_plot\"] := display(\n op(OC[\"pole_plots\"][2]),op(OC[\"pole_plots\"][3]),op(OC[\"pole_plots\"][4]),\n scaling=constrained,axes=none\n );\n\n CC[\"pole_plots\"] := table([\n 2 = map(u -> line(1.6 *~ u, -1.6 *~ u,color=green,thickness=4),CC[\"poles\"][2]),\n 3 = map(u -> line(1.9 *~ u, -1.9 *~ u,color=red ,thickness=4),CC[\"poles\"][3]),\n 4 = map(u -> line(1.2 *~ u, -1.2 *~ u,color=blue ,thickness=4),CC[\"poles\"][4])\n ]);\n\n CC[\"all_poles_plot\"] := display(\n op(CC[\"pole_plots\"][2]),op(CC[\"pole_plots\"][3]),op(CC[\"pole_plots\"][4]),\n scaling=constrained,axes=none\n );\n\n G0 := [];\n G1 := [[2,4,1,3,6,8,5,7],[1,3,5,7,2,4,6,8]];\n G := [[1,2,3,4,5,6,7,8]];\n\n while G <> G0 do\n G0 := G;\n G := sort([op({seq(seq(`o/permutations`(8)(g,h),g in G1),h in G)})]);\n od:\n\n r := table([1 = 1, 2 = 2, 3 = 3, 4 = 4, 5 = 4, 6 = 3, 7 = 2, 8 = 1]):\n\n CC[\"vertex_action\"] := table():\n CC[\"short_edge_action\"] := table():\n CC[\"square_action\"] := table():\n CC[\"rotation_matrix\"] := table():\n \n OC[\"vertex_action\"] := table():\n OC[\"edge_action\"] := table():\n OC[\"face_action\"] := table():\n OC[\"rotation_matrix\"] := table():\n \n for s in G do\n t := [r[s[1]],r[s[2]],r[s[3]],r[s[4]]];\n CC[\"vertex_action\"][t] := s;\n OC[\"face_action\"][t] := s;\n\n CC[\"short_edge_action\"][t] :=\n map(e -> CC[\"short_edge_index\"][sort([s[e[1]],s[e[2]]])],CC[\"short_edges\"]);\n\n CC[\"square_action\"][t] :=\n map(e -> CC[\"square_index\"][sort([s[e[1]],s[e[2]],s[e[3]],s[e[4]]])],CC[\"squares\"]);\n\n OC[\"vertex_action\"][t] := CC[\"square_action\"][t];\n\n OC[\"edge_action\"][t] :=\n map(e -> OC[\"edge_index\"][sort([s[e[1]],s[e[2]]])],OC[\"edges\"]);\n\n g := Matrix(3,3,[seq(x[i],i=1..9)]);\n eqs := map(op,[seq(convert(g . Vector(vC[i]) - Vector(vC[s[i]]),list),i = 1..8)]);\n sol := solve(eqs);\n CC[\"rotation_matrix\"][t] := subs(sol,convert( g,listlist));\n OC[\"rotation_matrix\"][t] := CC[\"rotation_matrix\"][s];\n od:\n \n octahedron_complex := eval(OC);\n cube_complex := eval(CC);\n return eval(OC);\nend:\n\nmake_octahedron_complex():\n\noctosphere_complex := proc(n::nonnegint)\n local T,T0,E,v,x,i,j;\n \n T := eval(octahedron_complex);\n\n for i from 1 to n do\n T0 := eval(T);\n T := eval(`triangular_subdivision/simplicial_complex`(T0));\n T0 := eval(T);\n T := eval(`condense/simplicial_complex`(T0));\n E := T[\"embedding\"];\n for v in T[\"vertices\"] do\n x := E[v];\n x := evalf(x /~ sqrt(add(x[j]^2,j=1..3)));\n E[v] := x;\n od:\n od:\n\n return eval(T):\nend:", "meta": {"hexsha": "dd2d2b698eeb35f43e8ac3f58d74ce6e20713717", "size": 5844, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/octahedron_complex.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/octahedron_complex.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/octahedron_complex.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 28.9306930693, "max_line_length": 90, "alphanum_fraction": 0.5114647502, "num_tokens": 2341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7981867873410141, "lm_q2_score": 0.6859494614282923, "lm_q1q2_score": 0.5475157968957475}} {"text": "single_case_Partition := module()\n uses Domain, Domain_Type;\n\n export SimplName := \"Single case partition\";\n export SimplOrder := 11;\n\n export ModuleApply := proc(vs :: DomBound, sh :: DomShape, $)\n subsindets(sh, DomSplit, x->do_simp(op(x)));\n end proc;\n\n local do_simp := proc(p:: Partition,$)::DomShape;\n local r := Partition:-Simpl:-single_nonzero_piece_cps(\n proc(c,v) if v::DomConstrain then DConstrain(conv_bool(c),op(v)) else p end if\n end proc,p,_testzero=(x->x=DSum()));\n if r :: Partition then DSplit(r) else r end if;\n end proc;\n\n local conv_bool := proc(r, $)\n if r :: {specfunc(`And`), `and`} then\n op(map(conv_bool,r))\n else\n r\n end if;\n end proc;\nend module;\n\nPartition_simpl := module()\n uses Domain, Domain_Type;\n\n export SimplName := \"Partition simpl\";\n export SimplOrder := (10+1/2);\n\n local TRY := proc(bnds, kb, kb_rn, as, pr)\n local r, ns;\n r := subs(kb_rn, op(1,pr));\n\n ns := op(1,bnds);\n ns := select(b->op(3,b) in {`Int`,`Ints`}, ns);\n ns := map(curry(op,1), ns);\n\n r := Partition:-Simpl(r, kb, _name_cands=ns, _testequal=`=`) assuming op(as);\n if not r :: Partition then r else DSplit(r) end if;\n end proc;\n\n export ModuleApply := proc(vs :: DomBound, sh :: DomShape, $)\n local as := Domain:-Bound:-toConstraints(vs, 'bound_types');\n subsindets(sh, DomSplit, curry(TRY,vs, op(Domain:-Bound:-toKB(vs)),as));\n end proc;\nend module;\n", "meta": {"hexsha": "09b9fc131edceb8e2d000ee5c58143c708370a53", "size": 1500, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 30.0, "max_line_length": 90, "alphanum_fraction": 0.5973333333, "num_tokens": 447, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7981867777396212, "lm_q2_score": 0.6859494614282923, "lm_q1q2_score": 0.5475157903096772}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_x_m05_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_m05_params * )(p->params);\n*)\n\n$define gga_x_pbe_params\n$include \"gga_x_pbe.mpl\"\n\nm05_f := (x, u, t) ->\n + params_a_csi_HF*pbe_f(x)*mgga_series_w(params_a_a, 12, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(m05_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "ed4f9f1020d924d822cfa111e4debfabef1ccd7f", "size": 620, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_m05.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_m05.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_m05.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 24.8, "max_line_length": 68, "alphanum_fraction": 0.6580645161, "num_tokens": 230, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8947894717137996, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5470581528992138}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\n(* This is the definition in the paper *)\nth_f0 := (x, u, t) -> -27*Pi/(10*t) * (1 + 7*x^2/(108*t)):\n\n(* Since we write this as an enhancement functional, we need to divide\n out the LDA prefactor. The paper also defines tau without one half *)\nth_f := (x, u, t) -> -th_f0(x,u,2*t) / X_FACTOR_C:\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(th_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "b9070f5e15cecf76a4066a2f2b15f9f0c871e9eb", "size": 659, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_th.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_th.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_th.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 32.95, "max_line_length": 72, "alphanum_fraction": 0.6418816388, "num_tokens": 233, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9230391685381605, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.5470544856419431}} {"text": "make_platonic := proc()\n global platonic_complexes,tetrahedron_complex,cube_complex,\n octahedron_complex,dodecahedron_complex,icosahedron_complex;\n local AC,TC,CC,OC,DC,IC,t0,t1,t2,s0,s1,AV,p,q,u,v,ui,s,t,n,m,d,M,A5,dp,nm,dd,r,k,i,E,g,\n E0,E1,E2,F1,F2,F3,C0,P0,PP0,PM,pole_colours,c;\n\n AC := [seq(table(),i=1..5)];\n IC := eval(AC[1]); OC := eval(AC[2]); TC := eval(AC[3]); CC := eval(AC[4]); DC := eval(AC[5]);\n\n t0 := (sqrt(5) + 1)/2;\n t1 := (sqrt(5) - 1)/2;\n t2 := expand(t1^2);\n s0 := sqrt(2/(5 + sqrt(5)));\n s1 := sqrt(2/(5 - sqrt(5)));\n \n dp := (u,v) -> simplify(expand(add(u[i] * v[i],i=1..3)));\n nm := (u) -> simplify(sqrt(dp(u,u)));\n dd := (u,v) -> nm(u -~ v);\n \n AV := [\n [\n [ 0, t2, t1],[ 0, t2,-t1],[ 0,-t2, t1],[ 0,-t2,-t1],\n [ t1, 0, t2],[-t1, 0, t2],[ t1, 0,-t2],[-t1, 0,-t2],\n [ t2, t1, 0],[ t2,-t1, 0],[-t2, t1, 0],[-t2,-t1, 0]\n ],\n [\n [ 1, 0, 0],[ 0, 1, 0],[ 0, 0, 1],\n [ 0, 0,-1],[ 0,-1, 0],[-1, 0, 0]\n ],\n [\n [ 1, 1, 1],[ 1,-1,-1],[-1, 1,-1],[-1,-1, 1]\n ],\n [\n [ 1, 1, 1],[ 1,-1,-1],[-1, 1,-1],[-1,-1, 1],\n [-1, 1, 1],[ 1,-1, 1],[ 1, 1,-1],[-1,-1,-1]\n ],\n [\n [ 1, 1, 1],[ 1, -1, -1],[ -1, 1, -1],[ -1, -1, 1],\n [ 0, t0, t1],[ 0, t0,-t1],[ 0,-t0, t1],[ 0,-t0,-t1],\n [ t1, 0, t0],[-t1, 0, t0],[ t1, 0,-t0],[-t1, 0,-t0],\n [ t0, t1, 0],[ t0,-t1, 0],[-t0, t1, 0],[-t0,-t1, 0],\n [ -1, 1, 1],[ 1, -1, 1],[ 1, 1, -1],[ -1, -1, -1]\n ]];\n\n for p from 1 to 5 do\n n := nops(AV[p]);\n AC[p][\"num_vertices\"] := n;\n AC[p][\"vertices\"] := [seq(i,i=1..AC[p][\"num_vertices\"])];\n r := simplify(sqrt(dp(AV[p][1],AV[p][1])));\n AC[p][\"vertex_radius\"] := r;\n AC[p][\"embedding\"] := table([seq(i = AV[p][i],i=1..n)]);\n AC[p][\"normalised_embedding\"] := table([seq(i = evalf(AV[p][i] /~ r),i=1..n)]);\n AC[p][\"embedding_index\"] := table():\n for i from 1 to n do\n AC[p][\"embedding_index\"][AV[p][i]] := i;\n od:\n od:\n \n for p from 1 to 5 do\n q := 6 - p;\n u := AV[p]; v := AV[q]; n := nops(u); m := nops(v);\n k := `if`(p = 5,\"pentagons\",`if`(p = 4,\"squares\",\"faces\"));\n AC[p][k] := [seq(select(i -> dp(u[i],v[j]) = -1,[seq(i,i=1..n)]),j = 1..m)];\n AC[p][cat(\"oriented_\",k)] :=\n [seq(orient_face(f,AC[p][\"embedding\"]),f in AC[p][k])];\n AC[p][\"facets\"] := AC[p][k];\n AC[p][\"oriented_facets\"] := AC[p][cat(\"oriented_\",k)];\n AC[p][cat(\"num_\",k)] := m;\n AC[p][\"num_facets\"] := m;\n AC[p][\"plot\"] := display(\n seq(polygon(map(j -> u[j],AC[p][\"oriented_facets\"][i]),colour=standard_colour(i)),i=1..m),\n scaling=constrained,axes=none);\n AC[p][\"grey_plot\"] := display(\n seq(polygon(map(j -> u[j],AC[p][\"oriented_facets\"][i]),colour=grey),i=1..m),\n scaling=constrained,axes=none);\n AC[p][\"wireframe_plot\"] := display(\n seq(polygon(map(j -> u[j],AC[p][\"oriented_facets\"][i]),colour=grey,style=wireframe),i=1..m),\n scaling=constrained,axes=none);\n od;\n\n for p from 1 to 3 do\n u := AV[p];\n E := {op(map(op,map(f -> [[f[1],f[2]],[f[1],f[3]],[f[2],f[3]]],AC[p][\"faces\"])))};\n AC[p][\"edges\"] := sort([op(E)]);\n AC[p][\"short_edges\"] := AC[p][\"edges\"];\n AC[p][\"long_edges\"] := [];\n r := dd(u[E[1][1]],u[E[1][2]]);\n AC[p][\"short_edge_length\"] := r;\n od:\n\n u := AV[4];\n r := 2;\n CC[\"short_edge_length\"] := r;\n CC[\"short_edges\"] :=\n select(e -> dd(u[e[1]],u[e[2]]) = r,[seq(seq([i,j],j=i+1..8),i=1..8)]);\n CC[\"long_edges\"] := [[1,2],[1,3],[1,4],[5,8],[6,8],[7,8]];\n CC[\"edges\"] := sort([op(CC[\"short_edges\"]),op(CC[\"long_edges\"])]);\n CC[\"faces\"] := [];\n \n u := AV[5];\n r := sqrt(5) - 1;\n DC[\"short_edge_length\"] := r;\n DC[\"short_edges\"] :=\n select(e -> dd(u[e[1]],u[e[2]]) = 2,[seq(seq([i,j],j=i+1..20),i=1..20)]);\n\n A5 := eval(alternating_five);\n\n for p from 1 to 5 do\n u := AV[p];\n ui := AC[p][\"embedding_index\"];\n AC[p][\"rotation_group\"] := NULL;\n AC[p][\"vertex_permutation\"] := table();\n for g in A5[\"elements\"] do\n M := Matrix(A5[\"matrix\"][g]);\n s := [seq(ui[expand(convert(M . Vector(u[i]),list))],i=1..nops(u))];\n if type(s,list(posint)) then\n AC[p][\"rotation_group\"] := AC[p][\"rotation_group\"],g;\n AC[p][\"vertex_permutation\"][g] := s;\n fi;\n od:\n AC[p][\"rotation_group\"] := [AC[p][\"rotation_group\"]];\n od:\n\n for p from 2 to 4 do\n AC[p][\"poles\"] := table([2 = {}, 3 = {}, 5 = {}]);\n\n for g in AC[p][\"rotation_group\"] do\n if g = [1,2,3,4,5] then continue; fi;\n d := A5[\"element_order\"][g];\n AC[p][\"poles\"][d] := {op(AC[p][\"poles\"][d]),A5[\"axis\"][g],-~ A5[\"axis\"][g]};\n od;\n\n for d in [2,3,5] do\n AC[p][\"poles\"][d] := [op(AC[p][\"poles\"][d])];\n od:\n od:\n\n PM := [1,-1];\n IC[\"poles\"] := table():\n IC[\"poles\"][2] := [\n [1,0,0],[0,1,0],[0,0,1],[-1,0,0],[0,-1,0],[0,0,-1],\n seq(seq(seq([i,j * t1,k * t0]/~2,k in PM),j in PM),i in PM),\n seq(seq(seq([k * t0,i,j * t1]/~2,k in PM),j in PM),i in PM),\n seq(seq(seq([j * t1,k * t0,i]/~2,k in PM),j in PM),i in PM)\n ];\n\n IC[\"poles\"][3] := expand([seq(DC[\"embedding\"][i] *~ sqrt(3)/3,i=1..20)]);\n\n IC[\"poles\"][5] := [\n [ 0, s0, s1],[ 0, s0,-s1],[ 0,-s0, s1],[ 0,-s0,-s1],\n [ s1, 0, s0],[-s1, 0, s0],[ s1, 0,-s0],[-s1, 0,-s0],\n [ s0, s1, 0],[ s0,-s1, 0],[-s0, s1, 0],[-s0,-s1, 0]\n ];\n\n DC[\"poles\"] := copy(IC[\"poles\"]);\n \n E0 := NULL:\n E1 := NULL:\n E2 := NULL:\n F1 := NULL:\n F2 := NULL:\n F3 := NULL:\n for s in DC[\"rotation_group\"] do \n t := DC[\"vertex_permutation\"][s];\n E0 := E0,sort([t[1],t[ 5]]);\n od:\n for s in CC[\"rotation_group\"] do \n t := DC[\"vertex_permutation\"][s];\n E1 := E1,sort([t[1],t[10]]);\n E2 := E2,sort([t[1],t[17]]);\n F1 := F1,sort([t[1],t[ 9],t[10]]);\n F2 := F2,sort([t[1],t[ 5],t[17]]);\n F3 := F3,sort([t[1],t[10],t[17]]);\n od:\n E0 := sort([op({E0})]);\n E1 := sort([op({E1})]);\n E2 := sort([op({E2})]);\n F1 := sort([op({F1})]);\n F2 := sort([op({F2})]);\n F3 := sort([op({F3})]);\n\n DC[\"short_edges\"] := E0;\n DC[\"long_edges_a\"] := E1;\n DC[\"long_edges_b\"] := E2;\n DC[\"edges\"] := sort([op(E0),op(E1),op(E2)]);\n\n DC[\"faces_a\"] := F1;\n DC[\"faces_b\"] := F2;\n DC[\"faces_c\"] := F3;\n DC[\"faces\"] := sort([op(F1),op(F2),op(F3)]);\n\n DC[\"inscribed_cubes\"] := [\n [3, 5, 8, 10, 11, 13, 16, 18], \n [4, 5, 8, 9, 12, 14, 15, 19],\n [2, 6, 7, 9, 12, 13, 16, 17], \n [1, 6, 7, 10, 11, 14, 15, 20], \n [1, 2, 3, 4, 17, 18, 19, 20] \n ];\n\n v := DC[\"embedding\"];\n \n DC[\"all_edges_plot\"] := \n display(\n seq(line(v[e[1]],v[e[2]],colour=blue) ,e in DC[\"short_edges\"]),\n seq(line(v[e[1]],v[e[2]],colour=red) ,e in DC[\"long_edges_a\"]),\n seq(line(v[e[1]],v[e[2]],colour=green),e in DC[\"long_edges_b\"]),\n scaling=constrained,axes=none\n );\n\n DC[\"triangle_plot\"] := \n display(\n seq(polygon([v[e[1]],v[e[2]],v[e[3]]],colour=blue ),e in DC[\"faces_a\"]),\n seq(polygon([v[e[1]],v[e[2]],v[e[3]]],colour=red ),e in DC[\"faces_b\"]),\n seq(polygon([v[e[1]],v[e[2]],v[e[3]]],colour=green),e in DC[\"faces_c\"]),\n scaling=constrained,axes=none\n );\n\n PP0 := NULL:\n for k from 1 to 5 do \n C0 := DC[\"inscribed_cubes\"][k];\n E0 := [seq(seq([C0[i],C0[j]],j=i+1..8),i=1..7)]:\n E0 := select(e -> simplify(expand(dd(v[e[1]],v[e[2]]))) = 2,E0);\n P0 := display(seq(line(v[e[1]],v[e[2]],colour=standard_colour(k)),e in E0),\n scaling=constrained,axes=none);\n PP0 := PP0,P0;\n od:\n DC[\"cubes_plot\"] := display(DC[\"grey_plot\"],PP0);\n\n pole_colours := table([2 = green, 3 = red, 5 = blue]):\n \n IC[\"pole_length\"] := table([2 = 0.8, 3 = 0.8, 5 = 0.9]):\n OC[\"pole_length\"] := table([2 = 1.2, 3 = 0.8, 5 = 0.9]):\n TC[\"pole_length\"] := table([2 = 1.3, 3 = 1.2, 5 = 0.9]):\n CC[\"pole_length\"] := table([2 = 1.3, 3 = 2.0, 5 = 0.9]):\n DC[\"pole_length\"] := table([2 = 2.0, 3 = 2.0, 5 = 1.7]):\n\n for p from 1 to 5 do \n AC[p][\"unit_pole_plot\"] := table():\n AC[p][\"pole_plot\"] := table():\n for d in [2,3,5] do \n r := AC[p][\"pole_length\"][d];\n c := pole_colours[d];\n AC[p][\"pole_plot\"][d] := \n map(u -> line(-r *~ u,r *~u,colour = c,thickness=4),AC[p][\"poles\"][d]);\n AC[p][\"unit_pole_plot\"][d] := \n map(u -> line(-1.1 *~ u,1.1 *~u,colour = c,thickness=4),AC[p][\"poles\"][d]);\n od:\n AC[p][\"all_poles_plot\"] := \n display(seq(op(AC[p][\"pole_plot\"][d]),d in [2,3,5]),\n\t scaling=constrained,axes=none);\n AC[p][\"all_unit_poles_plot\"] := \n display(seq(op(AC[p][\"unit_pole_plot\"][d]),d in [2,3,5]),\n\t scaling=constrained,axes=none);\n if p >= 2 and p <= 4 then \n AC[p][\"sample_poles_plot\"] := \n display(AC[p][\"pole_plot\"][2][1],\n\t AC[p][\"pole_plot\"][3][1],\n\t scaling=constrained,axes=none);\n else\n AC[p][\"sample_poles_plot\"] := \n display(AC[p][\"pole_plot\"][2][1],\n\t AC[p][\"pole_plot\"][3][1],\n\t AC[p][\"pole_plot\"][5][1],\n\t scaling=constrained,axes=none);\n fi:\n od:\n\n IC[\"dual_factor\"] := 3;\n OC[\"dual_factor\"] := 3;\n TC[\"dual_factor\"] := 3;\n CC[\"dual_factor\"] := 1;\n DC[\"dual_factor\"] := 5 - 2 * sqrt(5);\n\n for p from 1 to 5 do \n q := 6 - p;\n v := AC[q][\"embedding\"];\n m := nops(AC[q][\"oriented_facets\"]);\n r := AC[p][\"dual_factor\"];\n\n AC[p][\"dual_plot\"] := display(\n AC[p][\"wireframe_plot\"],\n seq(polygon(map(j -> evalf(v[j] /~ (-r)),AC[q][\"oriented_facets\"][i]),colour=standard_colour(i)),i=1..m),\n scaling=constrained,axes=none\n );\n od:\n\n platonic_complexes := eval(AC);\n icosahedron_complex := eval(IC);\n octahedron_complex := eval(OC);\n tetrahedron_complex := eval(TC);\n cube_complex := eval(CC);\n dodecahedron_complex := eval(DC);\n NULL;\nend:\n", "meta": {"hexsha": "fe39add646cf5e8aa7b6936c57bba1583057ba2b", "size": 9177, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/platonic.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/platonic.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/platonic.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 31.1084745763, "max_line_length": 108, "alphanum_fraction": 0.5050670154, "num_tokens": 3945, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339516289534, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.5469647944187678}} {"text": "input := ImportMatrix(\"AoC-2021-1-input.txt\" ):\n\nscan := (v,d)->ifelse(d[2]<0,[v,0],\n [v, ifelse(v<=d[1], d[2], d[2]+1)]);\n \nrtable_scanblock(input, [], noindex, scan, [-1,-1] )[2]; # part 1 answer\n\nwindows := Array([seq(input[i]+input[i+1]+input[i+2],\n i=1..numelems(input)-2)]);\n \nrtable_scanblock(windows, [], noindex, scan, [-1,-1])[2]; # part 2 answer\n", "meta": {"hexsha": "96aab19d142e16d2c1ebb4160c84655a5dcd89a3", "size": 408, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day1/AoC1-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day1/AoC1-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day1/AoC1-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 34.0, "max_line_length": 73, "alphanum_fraction": 0.5147058824, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7606506635289835, "lm_q2_score": 0.7185943805178139, "lm_q1q2_score": 0.546599292349074}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_x_rlda_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_rlda_params * )(p->params);\n*)\n\n(* the extra factor of 1/2 comes from the spin sum rule *)\nrlda_a1 := (5/4) * 3*Pi * params_a_prefactor/X_FACTOR_C:\n\n(* the functional is inherently unstable but that's how it is *)\nrlda_f := (x, u, t) -> rlda_a1/(2*t - u/4):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(rlda_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "a4cc27db3e8a0ec4ef46fac1d17c569ac5d8e928", "size": 713, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_rlda.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_rlda.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_rlda.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.52, "max_line_length": 68, "alphanum_fraction": 0.6507713885, "num_tokens": 249, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.916109606718245, "lm_q2_score": 0.5964331462646254, "lm_q1q2_score": 0.5463981350582114}} {"text": "# https://www.reddit.com/r/adventofcode/comments/ra88up/2021_day_6_part_4_day_googolplex/\n# Calculate the population at the googolplex generation mod nextprime(10^8)\ninput := \"4,1,7,7,4,7,6,2,5,4,3,1,4,7,2,4,5,2,2,1,3,7,4,5,1,3,3,5,5,7,6,3,3,3,7,7,5,4,6,3,1,7,6,1,3,5,1,2,6,6,5,5,4,3,2,6,5,3,7,5,4,2,1,3,6,2,7,2,2,6,5,6,7,6,3,3,1,1,1,3,7,3,3,5,4,7,2,1,4,4,1,2,5,5,4,3,4,4,7,4,2,1,2,2,4\":\ntally := table(sparse=0,Statistics:-Tally(StringTools:-Split(input,\",\"))):\nlanternfish := Vector([seq(tally[cat(\"\",i)],i=0..8)]):\n\nU := Matrix([\n [0, 1, 0, 0, 0, 0, 0, 0, 0],\n [0, 0, 1, 0, 0, 0, 0, 0, 0],\n [0, 0, 0, 1, 0, 0, 0, 0, 0],\n [0, 0, 0, 0, 1, 0, 0, 0, 0],\n [0, 0, 0, 0, 0, 1, 0, 0, 0],\n [0, 0, 0, 0, 0, 0, 1, 0, 0],\n [1, 0, 0, 0, 0, 0, 0, 1, 0],\n [0, 0, 0, 0, 0, 0, 0, 0, 1],\n [1, 0, 0, 0, 0, 0, 0, 0, 0]]):\n\nminpoly := LinearAlgebra:-MinimalPolynomial(U,x);\n# x^9 - x^2 - 1\n\nq := 100000007:\n\n# look for a power of x that is 1 modulo the minpoly in F_q[x]\nfor i from 1 to 100 do\n qq := q^i-1;\n # x^qq ( mod minpoly ) in F_q[x]\n if Powmod(x, qq, minpoly, x) mod q = 1 then\n break;\n end if;\nend do:\ni, qq;\n# i=8, qq=10000005600001372000192080016807000941192032941720658834405764800\n\n# qq is the period of powers of U mod q\n\n# calculate googolplex mod qq\nn := Power(10, 10^100) mod qq;\n# 7308711993169798294967234678458568672383628022002873653735230400\n# so U^googolplex = U^n mod q\n\n# I like computing powers of U using the minpoly\ng := Powmod(x, n, minpoly, x) mod q;\n# 46714893*x^8+75968618*x^7+86556894*x^6+35145482*x^5+7013179*x^4\n# +30172454*x^3+81311138*x^2+30235098*x+46689635\n\n# g(U) = U^googolplex mod q\n\nadd(eval(g, x=U) . lanternfish) mod q;\n# 52292574\n\n", "meta": {"hexsha": "56f3401780fb21ee73bd9a6492758b398ec5ebca", "size": 1676, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day6/Part4-reddit.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day6/Part4-reddit.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day6/Part4-reddit.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 32.862745098, "max_line_length": 221, "alphanum_fraction": 0.6103818616, "num_tokens": 899, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213772699436, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5463629461763692}} {"text": "make_fgl_Lazard := proc(d)\n global a,m,ma,am;\n local T,u,x,y,q,i,k,Fm,sol;\n\n T := table();\n T[\"degree\"] := d;\n Order := d+2;\n\n T[\"log_m\"] := unapply(x + add(m[i]*x^(i+1),i=1..d-1),x);\n T[\"exp_m\"] := \n unapply(\n convert(\n solve(x = series(T[\"log_m\"](y) + sin(y)^(d+1),y=0,d+1),y),\n polynom,x\n ),\n x\n );\n\n T[\"sum_m\"] :=\n unapply(\n subs(u=1,expand(convert(series(T[\"exp_m\"](T[\"log_m\"](u*x)+T[\"log_m\"](u*y)),u=0,d+1),polynom,u))),\n x,y\n ):\n\n Fm := T[\"sum_m\"](x,y);\n am[1] := m[1];\n for k from 2 to d-1 do\n q := igcd_alt([seq(binomial(k+1,i),i=1..k)])[2];\n am[k] := -add(q[i]*coeff(coeff(Fm,x,i),y,k+1-i),i=1..k);\n od:\n sol := solve({seq(a[i]=am[i],i=1..d-1)},{seq(m[i],i=1..d-1)}):\n for i from 1 to d-1 do ma[i] := subs(sol,m[i]); od:\n\n T[\"log_a\"] := unapply(collect(expand(eval(subs(m = ma,T[\"log_m\"](x)))),x),x);\n T[\"exp_a\"] := unapply(collect(expand(eval(subs(m = ma,T[\"exp_m\"](x)))),x),x);\n T[\"sum_a\"] := unapply(collect(expand(eval(subs(m = ma,T[\"sum_m\"](x,y)))),{x,y}),x,y);\n\n return eval(T);\nend:\n\n", "meta": {"hexsha": "2136ae7a582ce6c6414fbf9d92d3c5b657258181", "size": 1024, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/scratch/MU.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/scratch/MU.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/scratch/MU.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 24.9756097561, "max_line_length": 100, "alphanum_fraction": 0.5185546875, "num_tokens": 427, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8824278602705731, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.5460290941258827}} {"text": "\n# Acceleration Calculation for the Robot based on MDH frames\n# Introduction\n# Berechnung der Beschleunigung von Koordinatensystemen und Schwerpunkten\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# tree -> Berechnung f\u00fcr eine beliebige Baumstruktur (ohne Schleifen)\n# acceleration_mdh_angles -> Berechnung der Beschleunigung der MDH-Koordinaten (Drehung und Verschiebung in z-Richtung. Diese k\u00f6nnen zeitabh\u00e4ngig sein.)\n# Sources\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I (WS 2014/15)\n# Initialization\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"Generiere Beschleunigung f\u00fcr %s\\n\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Absch\u00e4tzen der Komplexit\u00e4t\n;\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(5)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardm\u00e4\u00dfig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # standardm\u00e4\u00dfig simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(5): # f\u00fcnfter Eintrag ist f\u00fcr Beschleunigung\nend if:\n\n# Ergebnisse der Geschwindigkeit laden\nread sprintf(\"../codeexport/%s/tmp/velocity_mdh_angles_maple.m\", robot_name):\nthetaD:= thetaD:\ndD:=dD:\n# Lade Marker f\u00fcr Existenz kinematischer Zwangsbedingungen (Verkn\u00fcpfung von MDH-Gelenkwinkeln durch verallgemeinerte Koordinaten)\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nkin_constraints_exist := kin_constraints_exist:\n\n\n# Zeitableitung der Drehwinkelgeschwindigkeit berechnen\n# Im Falle kinematischer Zwangsbedingungen wurden diese schon im Arbeitsblatt f\u00fcr die Geschwindigkeit eingesetzt\n# und m\u00fcssen hier nicht mehr betrachtet werden.\n# Zeitableitung der Geschwindigkeit in Abh\u00e4ngigkeit der verallgemeinerten Koordinaten \nthetaD_qt := thetaD:\ndD_qt := dD:\nthetaDD := Matrix(NJ, 1):\ndDD:= Matrix(NJ, 1):\n\nfor i from 1 to NJ do:\n thetaDD(i,1):= diff(thetaD_qt(i,1),t):\n dDD(i,1) := diff(dD_qt(i,1),t):\nend do:\nif kin_constraints_exist then # ist nur rechenaufw\u00e4ndig, wenn ZB vorliegen\n printf(\"%s. Zweite Zeitableitung der MDH-Winkel gebildet.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n# Terme vereinfachen\n\nif use_simplify>=1 and kin_constraints_exist then # ist nur sinnvoll, wenn ZB vorliegen\n tmp_t0 := time():\n tmp_l0 := length(thetaDD)+length(dDD):\n printf(\"%s: Vereinfache MDH-Beschleunigungen. L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l0):\n for i from 1 to NJ do\n tmp_t1 := time():\n tmp_l1 := length(thetaDD(i,1)) + length(dDD(i,1)): # es kann sowieso nur einer der beiden Informationen enthalten\n printf(\"%s: Vereinfache MDH-Beschl. %d. L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1):\n thetaDD(i,1) := simplify2(thetaDD(i,1)):\n dDD(i,1) := simplify2(dDD(i,1)):\n tmp_t2 := time():\n tmp_l2 := length(thetaDD(i,1)) + length(dDD(i,1)):\n printf(\"%s: MDH-Beschl. %d vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end do:\n tmp_l3 := length(thetaDD)+length(dDD):\n printf(\"%s: MDH-Beschleunigungen vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l0, tmp_l3, tmp_t2-tmp_t0):\nend if:\n# Ausdruck f\u00fcr Zeitableitungen der Beschleunigungen exportieren\nif codegen_act then\n MatlabExport(convert_t_s(thetaDD), sprintf(\"../codeexport/%s/tmp/acceleration_mdh_angles_matlab.m\", robot_name), codegen_opt):\n MatlabExport(convert_t_s(dDD), sprintf(\"../codeexport/%s/tmp/acceleration_mdh_deltaz_matlab.m\", robot_name), codegen_opt):\nend if:\n# Ausdruck f\u00fcr Maple speichern\nsave thetaDD, dDD, sprintf(\"../codeexport/%s/tmp/acceleration_mdh_angles_maple.m\", robot_name):\nsave thetaDD, dDD, sprintf(\"../codeexport/%s/tmp/acceleration_mdh_angles_maple\", robot_name):\n\n", "meta": {"hexsha": "c4c22ce6a7daad48c7263f1617306c9ca70af1ab", "size": 4616, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_kinematics/robot_tree_acceleration_mdh_angles.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_kinematics/robot_tree_acceleration_mdh_angles.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_kinematics/robot_tree_acceleration_mdh_angles.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 45.2549019608, "max_line_length": 153, "alphanum_fraction": 0.7461005199, "num_tokens": 1432, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8289388167733099, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.5457878294145353}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_b94_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_b94_params * ) (p->params);\n*)\n\n(* replace: \"br89_x\\(\" -> \"xc_mgga_x_br89_get_x(\" *)\n\n$define mgga_x_br89_params\n$include \"mgga_x_br89.mpl\"\n\n(* This is a fake parameter in libxc *)\nparams_a_at := 0:\n\n(* Equation 9, same-spin correlation *)\nb94_css := (rs, z, xs, us, ts) ->\n - 0.01 * (1 + z)^(8/3) * 2^(-8/3) * n_total(rs)^(5/3) * (2*ts - xs^2/4)\n * b94_zss(params_a_css, br89_f, rs, z, xs, us, ts)^4 * (\n 1 - 2*log(1 + b94_zss(params_a_css, br89_f, rs, z, xs, us, ts)/2)\n / b94_zss(params_a_css, br89_f, rs, z, xs, us, ts)\n ):\n\n(* Same-spin correlation overall *)\nb94_par := (rs, z, xs0, xs1, us0, us1, ts0, ts1) ->\n + my_piecewise3(screen_dens(rs, z), 0, b94_css(rs, z_thr( z), xs0, us0, ts0))\n + my_piecewise3(screen_dens(rs, -z), 0, b94_css(rs, z_thr(-z), xs1, us1, ts1)):\n\n(* Equation 8, opposite-spin correlation *)\nb94_cab := (rs, z, xs0, xs1, us0, us1, ts0, ts1) ->\n - 0.8 * (1 - z^2)/4 * n_total(rs)\n * b94_zab(params_a_cab, br89_f, rs, z, xs0, xs1, us0, us1, ts0, ts1) * (\n b94_zab(params_a_cab, br89_f, rs, z, xs0, xs1, us0, us1, ts0, ts1)\n - log(1 + b94_zab(params_a_cab, br89_f, rs, z, xs0, xs1, us0, us1, ts0, ts1))\n ):\n\n(* Whole functional *)\nb94_c_f := (rs, z, xs0, xs1, us0, us1, ts0, ts1) ->\n + b94_cab(rs, z, xs0, xs1, us0, us1, ts0, ts1)\n + b94_par(rs, z, xs0, xs1, us0, us1, ts0, ts1):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n b94_c_f(rs, z, xs0, xs1, us0, us1, ts0, ts1):\n", "meta": {"hexsha": "e824c39119756984f5b599bcf44ef6cda883bdf9", "size": 1782, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b94.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b94.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b94.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 33.6226415094, "max_line_length": 82, "alphanum_fraction": 0.6077441077, "num_tokens": 761, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8918110511888303, "lm_q2_score": 0.611381973294151, "lm_q1q2_score": 0.5452372002813581}} {"text": "######################################################################\n\n`is_element/cubes` := (k::posint) -> (A::set) -> proc(f)\n local n,i,j;\n global reason;\n\n if not type(f,table) then\n reason := [convert(procname,string),\"f is not a table\",f];\n return false;\n fi;\n\n if map(op,{indices(f)}) <> A then\n reason := [convert(procname,string),\"f is not indexed by A\",f,A];\n return false;\n fi;\n \n n := nops(A);\n for i from 1 to n do\n if not `is_element/single_cubes`(k)(f[A[i]]) then\n reason := [convert(procname,string),\"f(a) is not a single cube\",A[i],f(A[i]),reason];\n return false;\n fi;\n\n for j from 1 to i-1 do\n if `overlap/single_cubes`(k)(f[A[j]],f[A[i]]) then\n reason := [convert(procname,string),\"subcubes f(a) and f(b) overlap\",A[i],A[j],f(A[i]),f(A[j])];\n return false;\n fi;\n od;\n od;\n\n return true;\nend;\n\n`is_equal/cubes` := (k::posint) -> (A::set) -> proc(f,g)\n local a;\n global reason;\n\n for a in A do \n if not `is_equal/single_cubes`(k)(f[a],g[a]) then\n reason := [convert(procname,string),\"f[a] <> g[a]\",a,f[a],g[a]];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n`is_leq/cubes` := NULL;\n\n`random_element/cubes` := (N::posint) -> (A::set) -> proc()\n local d,f,a;\n\n d := 5;\n\n while true do\n d := d+1;\n f := table();\n for a in A do \n f[a] := `random_element/single_cubes`(N)(d);\n od;\n\n if `is_element/cubes`(N)(A)(f) then\n return(eval(f));\n fi;\n\n if d > 1000 then return FAIL; fi;\n od;\nend;\n\n`list_elements/cubes` := NULL;\n`count_elements/cubes` := NULL;\n\n`draw/cubes` := (A::set) -> proc(f)\n local P,a;\n\n P := rectangle([0,0],[1,1],colour=blue,style=line);\n for a in A do\n P := P,rectangle(f[a][1],f[a][2],colour=red);\n od;\n display(P,scaling=constrained,axes=none);\nend;\n\n`centres/cubes` := (k::posint) -> (A::set) -> proc(f)\n local g,a;\n\n g := table();\n for a in A do \n g[a] := `centre/single_cubes`(k)(f[a]);\n od;\n\n return eval(g);\nend;\n\n", "meta": {"hexsha": "c7ae78d04c863864541a46c916c528b727291e54", "size": 1893, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/cubes.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/cubes.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/cubes.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 19.9263157895, "max_line_length": 100, "alphanum_fraction": 0.5636555732, "num_tokens": 632, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7981867777396212, "lm_q2_score": 0.6825737279551494, "lm_q1q2_score": 0.5448213244862414}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_x_scan_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_scan_params * )(p->params);\n*)\n\nscan_p := x -> X2S^2*x^2:\nscan_alpha := (x, t) -> (t - x^2/8)/K_FACTOR_C:\n\n(* The interpolating functions are nasty for a -> 1, so we need to\n truncate them. The natural choice is to cut off the functions to\n zero when the exponential term reaches machine epsilon.\n\n The left cutoff is |log epsilon|/(|log epsilon| + c1) < 1\n and the right one is (|log epsilon| + c2)/|log epsilon| > 1,\n so we don't even really need the step function.\n*)\nscan_f_alpha_left0 := a -> exp(-params_a_c1*a/(1 - a)):\nscan_f_alpha_left_cutoff := -log(DBL_EPSILON)/(-log(DBL_EPSILON) + params_a_c1):\nscan_f_alpha_left := a -> my_piecewise3(a > scan_f_alpha_left_cutoff, 0, scan_f_alpha_left0(m_min(scan_f_alpha_left_cutoff, a))):\n\nscan_f_alpha_right0 := a -> -params_a_d*exp(params_a_c2/(1 - a)):\nscan_f_alpha_right_cutoff := (-log(DBL_EPSILON/abs(params_a_d)) + params_a_c2)/(-log(DBL_EPSILON/abs(params_a_d))):\nscan_f_alpha_right := a -> my_piecewise3(a < scan_f_alpha_right_cutoff, 0, scan_f_alpha_right0(m_max(scan_f_alpha_right_cutoff, a))):\nscan_f_alpha := a -> my_piecewise3(\n a <= 1, scan_f_alpha_left(a), scan_f_alpha_right(a)\n ):\n\nscan_h1x := x -> 1 + params_a_k1*(1 - params_a_k1/(params_a_k1 + x)):\n\nscan_b2 := sqrt(5913/405000):\nscan_b1 := (511/13500)/(2*scan_b2):\nscan_b3 := 1/2:\nscan_b4 := MU_GE^2/params_a_k1 - 1606/18225 - scan_b1^2:\nscan_y := (x, a) -> MU_GE*scan_p(x) + scan_b4*scan_p(x)^2*exp(-scan_b4*scan_p(x)/MU_GE)\n + (scan_b1*scan_p(x) + scan_b2*(1 - a)*exp(-scan_b3*(1 - a)^2))^2:\n\nscan_a1 := 4.9479:\nscan_gx := x -> 1 - exp(-scan_a1/sqrt(X2S*x)):\n\nscan_h0x := 1.174:\nscan_f := (x, u, t) -> (scan_h1x(scan_y(x, scan_alpha(x, t)))*(1 - scan_f_alpha(scan_alpha(x, t)))\n + scan_h0x*scan_f_alpha(scan_alpha(x, t)))*scan_gx(x):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) -> mgga_exchange(scan_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "4ef7dbcb1b40bca12780047923571698dc3347f2", "size": 2231, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_scan.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_scan.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_scan.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 39.8392857143, "max_line_length": 133, "alphanum_fraction": 0.6786194532, "num_tokens": 789, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9005297914570319, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.5438586082795002}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_tpss_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_tpss_params * )(p->params);\n*)\n\n(* beta is taken from the params *)\nparams_a_gamma := (1 - log(2))/Pi^2:\nparams_a_BB := 1:\n$include \"gga_c_pbe.mpl\"\n\n$include \"tpss_c.mpl\"\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n + tpss_f(f_pbe, rs, z, xt, xs0, xs1, ts0, ts1):\n\n\n\n\n", "meta": {"hexsha": "1d4d29b1fc4481bd4d5b5da4f485f2c2933e8435", "size": 629, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_tpss.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_tpss.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_tpss.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 20.9666666667, "max_line_length": 68, "alphanum_fraction": 0.6422893482, "num_tokens": 221, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357529306639, "lm_q2_score": 0.6261241772283034, "lm_q1q2_score": 0.5428720474312345}} {"text": "\n\nwith(Groebner):\nwith(PolynomialIdeals):\n\nJ := PolynomialIdeal({x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 + x10, x1*x2 + x1*x3 + x1*x4 + x1*x5 + x1*x6 + x1*x7 + x1*x8 + x1*x9 + x1*x10 + x2*x3 + x2*x4 + x2*x5 + x2*x6 + x2*x7 + x2*x8 + x2*x9 + x2*x10 + x3*x4 + x3*x5 + x3*x6 + x3*x7 + x3*x8 + x3*x9 + x3*x10 + x4*x5 + x4*x6 + x4*x7 + x4*x8 + x4*x9 + x4*x10 + x5*x6 + x5*x7 + x5*x8 + x5*x9 + x5*x10 + x6*x7 + x6*x8 + x6*x9 + x6*x10 + x7*x8 + x7*x9 + x7*x10 + x8*x9 + x8*x10 + x9*x10, x1*x2*x3 + x1*x2*x4 + x1*x2*x5 + x1*x2*x6 + x1*x2*x7 + x1*x2*x8 + x1*x2*x9 + x1*x2*x10 + x1*x3*x4 + x1*x3*x5 + x1*x3*x6 + x1*x3*x7 + x1*x3*x8 + x1*x3*x9 + x1*x3*x10 + x1*x4*x5 + x1*x4*x6 + x1*x4*x7 +\nx1*x4*x8 + x1*x4*x9 + x1*x4*x10 + x1*x5*x6 + x1*x5*x7 + x1*x5*x8 + x1*x5*x9 + x1*x5*x10 + x1*x6*x7 + x1*x6*x8 + x1*x6*x9 + x1*x6*x10 + x1*x7*x8 + x1*x7*x9 + x1*x7*x10 + x1*x8*x9 + x1*x8*x10 + x1*x9*x10 + x2*x3*x4 + x2*x3*x5 + x2*x3*x6 + x2*x3*x7 + x2*x3*x8 + x2*x3*x9 + x2*x3*x10 + x2*x4*x5 + x2*x4*x6 + x2*x4*x7 + x2*x4*x8 + x2*x4*x9 + x2*x4*x10 + x2*x5*x6 + x2*x5*x7 + x2*x5*x8 + x2*x5*x9 + x2*x5*x10 + x2*x6*x7 + x2*x6*x8 + x2*x6*x9 + x2*x6*x10 + x2*x7*x8 + x2*x7*x9 + x2*x7*x10 + x2*x8*x9 + x2*x8*x10 + x2*x9*x10 + x3*x4*x5 + x3*x4*x6 + x3*x4*x7 + x3*x4*x8 + x3*x4*x9 + x3*x4*x10 + x3*x5*x6 + x3*x5*x7 + x3*x5*x8 + x3*x5*x9 + x3*x5*x10 + x3*x6*x7 + x3*x6*x8 + x3*x6*x9 + x3*x6*x10 + x3*x7*x8 + x3*x7*x9 + x3*x7*x10 + x3*x8*x9 + x3*x8*x10 + x3*x9*x10 + x4*x5*x6 + x4*x5*x7 + x4*x5*x8 + x4*x5*x9 + x4*x5*x10 + x4*x6*x7 + x4*x6*x8 + x4*x6*x9 + x4*x6*x10 + x4*x7*x8 + x4*x7*x9 + x4*x7*x10 + x4*x8*x9 + x4*x8*x10 + x4*x9*x10 + x5*x6*x7 + x5*x6*x8 + x5*x6*x9 + x5*x6*x10 + x5*x7*x8 + x5*x7*x9 + x5*x7*x10 + x5*x8*x9 + x5*x8*x10 + x5*x9*x10 + x6*x7*x8 + x6*x7*x9 + x6*x7*x10 + x6*x8*x9 + x6*x8*x10 + x6*x9*x10 + x7*x8*x9 + x7*x8*x10 + x7*x9*x10 + x8*x9*x10, x1*x2*x3*x4 + x1*x2*x3*x5 + x1*x2*x3*x6 + x1*x2*x3*x7 + x1*x2*x3*x8 + x1*x2*x3*x9 + x1*x2*x3*x10 + x1*x2*x4*x5 + x1*x2*x4*x6 + x1*x2*x4*x7 + x1*x2*x4*x8 + x1*x2*x4*x9 + x1*x2*x4*x10 + x1*x2*x5*x6 + x1*x2*x5*x7 + x1*x2*x5*x8 + x1*x2*x5*x9 + x1*x2*x5*x10 + x1*x2*x6*x7 + x1*x2*x6*x8 + x1*x2*x6*x9 + x1*x2*x6*x10 + x1*x2*x7*x8 + x1*x2*x7*x9 + x1*x2*x7*x10 + x1*x2*x8*x9 + x1*x2*x8*x10 + x1*x2*x9*x10 +\nx1*x3*x4*x5 + x1*x3*x4*x6 + x1*x3*x4*x7 + x1*x3*x4*x8 + x1*x3*x4*x9 + x1*x3*x4*x10 + x1*x3*x5*x6 + x1*x3*x5*x7 + x1*x3*x5*x8 + x1*x3*x5*x9 + x1*x3*x5*x10 + x1*x3*x6*x7 + x1*x3*x6*x8 + x1*x3*x6*x9 + x1*x3*x6*x10 + x1*x3*x7*x8 + x1*x3*x7*x9 + x1*x3*x7*x10 + x1*x3*x8*x9 + x1*x3*x8*x10 + x1*x3*x9*x10 + x1*x4*x5*x6 + x1*x4*x5*x7 + x1*x4*x5*x8 + x1*x4*x5*x9 + x1*x4*x5*x10 + x1*x4*x6*x7 + x1*x4*x6*x8 + x1*x4*x6*x9 + x1*x4*x6*x10 + x1*x4*x7*x8 + x1*x4*x7*x9 + x1*x4*x7*x10 + x1*x4*x8*x9 + x1*x4*x8*x10 + x1*x4*x9*x10 + x1*x5*x6*x7 + x1*x5*x6*x8 + x1*x5*x6*x9 + x1*x5*x6*x10 + x1*x5*x7*x8 + x1*x5*x7*x9 + x1*x5*x7*x10 + x1*x5*x8*x9 + x1*x5*x8*x10 + x1*x5*x9*x10 + x1*x6*x7*x8 + x1*x6*x7*x9 + x1*x6*x7*x10 + x1*x6*x8*x9 + x1*x6*x8*x10 + x1*x6*x9*x10 + x1*x7*x8*x9 + x1*x7*x8*x10 + x1*x7*x9*x10 + x1*x8*x9*x10 + x2*x3*x4*x5 + x2*x3*x4*x6 + x2*x3*x4*x7 + x2*x3*x4*x8 + x2*x3*x4*x9 + x2*x3*x4*x10\n+ x2*x3*x5*x6 + x2*x3*x5*x7 + x2*x3*x5*x8 + x2*x3*x5*x9 + x2*x3*x5*x10 + x2*x3*x6*x7 + x2*x3*x6*x8 + x2*x3*x6*x9 + x2*x3*x6*x10 + x2*x3*x7*x8 + x2*x3*x7*x9 + x2*x3*x7*x10 + x2*x3*x8*x9 + x2*x3*x8*x10 + x2*x3*x9*x10 + x2*x4*x5*x6 + x2*x4*x5*x7 + x2*x4*x5*x8 + x2*x4*x5*x9 + x2*x4*x5*x10 + x2*x4*x6*x7 + x2*x4*x6*x8 + x2*x4*x6*x9 + x2*x4*x6*x10 + x2*x4*x7*x8 + x2*x4*x7*x9 + x2*x4*x7*x10 + x2*x4*x8*x9 + x2*x4*x8*x10 + x2*x4*x9*x10 + x2*x5*x6*x7\n+ x2*x5*x6*x8 + x2*x5*x6*x9 + x2*x5*x6*x10 + x2*x5*x7*x8 + x2*x5*x7*x9 + x2*x5*x7*x10 + x2*x5*x8*x9 + x2*x5*x8*x10 + x2*x5*x9*x10 + x2*x6*x7*x8 + x2*x6*x7*x9 + x2*x6*x7*x10 + x2*x6*x8*x9 + x2*x6*x8*x10 + x2*x6*x9*x10 + x2*x7*x8*x9 + x2*x7*x8*x10 + x2*x7*x9*x10 + x2*x8*x9*x10 + x3*x4*x5*x6 + x3*x4*x5*x7 + x3*x4*x5*x8 + x3*x4*x5*x9 + x3*x4*x5*x10 + x3*x4*x6*x7 + x3*x4*x6*x8 + x3*x4*x6*x9 + x3*x4*x6*x10 + x3*x4*x7*x8 + x3*x4*x7*x9 + x3*x4*x7*x10 + x3*x4*x8*x9 + x3*x4*x8*x10 + x3*x4*x9*x10 + x3*x5*x6*x7 + x3*x5*x6*x8 + x3*x5*x6*x9 + x3*x5*x6*x10 + x3*x5*x7*x8 + x3*x5*x7*x9 + x3*x5*x7*x10 + x3*x5*x8*x9 + x3*x5*x8*x10 + x3*x5*x9*x10 + x3*x6*x7*x8 + x3*x6*x7*x9 + x3*x6*x7*x10 + x3*x6*x8*x9 + x3*x6*x8*x10 + x3*x6*x9*x10 + x3*x7*x8*x9 + x3*x7*x8*x10 + x3*x7*x9*x10 + x3*x8*x9*x10 + x4*x5*x6*x7 + x4*x5*x6*x8 + x4*x5*x6*x9 + x4*x5*x6*x10 + x4*x5*x7*x8 + x4*x5*x7*x9 + x4*x5*x7*x10 + x4*x5*x8*x9 + x4*x5*x8*x10 + x4*x5*x9*x10 + x4*x6*x7*x8 + x4*x6*x7*x9 + x4*x6*x7*x10 + x4*x6*x8*x9 + x4*x6*x8*x10 + x4*x6*x9*x10 + x4*x7*x8*x9 + x4*x7*x8*x10 + x4*x7*x9*x10 + x4*x8*x9*x10 + x5*x6*x7*x8 + x5*x6*x7*x9 + x5*x6*x7*x10 + x5*x6*x8*x9 + x5*x6*x8*x10 + x5*x6*x9*x10 + x5*x7*x8*x9 + x5*x7*x8*x10 + x5*x7*x9*x10 + x5*x8*x9*x10 + x6*x7*x8*x9 + x6*x7*x8*x10 + x6*x7*x9*x10 + x6*x8*x9*x10 + x7*x8*x9*x10, x1*x2*x3*x4*x5 + x1*x2*x3*x4*x6 + x1*x2*x3*x4*x7 + x1*x2*x3*x4*x8 + x1*x2*x3*x4*x9 + x1*x2*x3*x4*x10 + x1*x2*x3*x5*x6 + x1*x2*x3*x5*x7 + x1*x2*x3*x5*x8 + x1*x2*x3*x5*x9 + x1*x2*x3*x5*x10 + x1*x2*x3*x6*x7 + x1*x2*x3*x6*x8 + x1*x2*x3*x6*x9 + x1*x2*x3*x6*x10 + x1*x2*x3*x7*x8 + x1*x2*x3*x7*x9 + x1*x2*x3*x7*x10 + x1*x2*x3*x8*x9 + x1*x2*x3*x8*x10 + x1*x2*x3*x9*x10 + x1*x2*x4*x5*x6 + x1*x2*x4*x5*x7 + x1*x2*x4*x5*x8 + x1*x2*x4*x5*x9 + x1*x2*x4*x5*x10 + x1*x2*x4*x6*x7 + x1*x2*x4*x6*x8 + x1*x2*x4*x6*x9 + x1*x2*x4*x6*x10 + x1*x2*x4*x7*x8 + x1*x2*x4*x7*x9 + x1*x2*x4*x7*x10 + x1*x2*x4*x8*x9 + x1*x2*x4*x8*x10 + x1*x2*x4*x9*x10 + x1*x2*x5*x6*x7 + x1*x2*x5*x6*x8 + x1*x2*x5*x6*x9 + x1*x2*x5*x6*x10 + x1*x2*x5*x7*x8 + x1*x2*x5*x7*x9 + x1*x2*x5*x7*x10 + x1*x2*x5*x8*x9 + x1*x2*x5*x8*x10 + x1*x2*x5*x9*x10 + x1*x2*x6*x7*x8 + x1*x2*x6*x7*x9 + x1*x2*x6*x7*x10 + x1*x2*x6*x8*x9 + x1*x2*x6*x8*x10 + x1*x2*x6*x9*x10 + x1*x2*x7*x8*x9 + x1*x2*x7*x8*x10 + x1*x2*x7*x9*x10 + x1*x2*x8*x9*x10 + x1*x3*x4*x5*x6 + x1*x3*x4*x5*x7 + x1*x3*x4*x5*x8 + x1*x3*x4*x5*x9 + x1*x3*x4*x5*x10 + x1*x3*x4*x6*x7 +\nx1*x3*x4*x6*x8 + x1*x3*x4*x6*x9 + x1*x3*x4*x6*x10 + x1*x3*x4*x7*x8 + x1*x3*x4*x7*x9 + x1*x3*x4*x7*x10 + x1*x3*x4*x8*x9 + x1*x3*x4*x8*x10 + x1*x3*x4*x9*x10 + x1*x3*x5*x6*x7 + x1*x3*x5*x6*x8 + x1*x3*x5*x6*x9 + x1*x3*x5*x6*x10 + x1*x3*x5*x7*x8 + x1*x3*x5*x7*x9 + x1*x3*x5*x7*x10 + x1*x3*x5*x8*x9 + x1*x3*x5*x8*x10 + x1*x3*x5*x9*x10 + x1*x3*x6*x7*x8 + x1*x3*x6*x7*x9 + x1*x3*x6*x7*x10 + x1*x3*x6*x8*x9 + x1*x3*x6*x8*x10 + x1*x3*x6*x9*x10 + x1*x3*x7*x8*x9 + x1*x3*x7*x8*x10 + x1*x3*x7*x9*x10 + x1*x3*x8*x9*x10 + x1*x4*x5*x6*x7 + x1*x4*x5*x6*x8 + x1*x4*x5*x6*x9 + x1*x4*x5*x6*x10 + x1*x4*x5*x7*x8 + x1*x4*x5*x7*x9 + x1*x4*x5*x7*x10 + x1*x4*x5*x8*x9 + x1*x4*x5*x8*x10 + x1*x4*x5*x9*x10 + x1*x4*x6*x7*x8 + x1*x4*x6*x7*x9 + x1*x4*x6*x7*x10 + x1*x4*x6*x8*x9 + x1*x4*x6*x8*x10 + x1*x4*x6*x9*x10 + x1*x4*x7*x8*x9 + x1*x4*x7*x8*x10 + x1*x4*x7*x9*x10 + x1*x4*x8*x9*x10 + x1*x5*x6*x7*x8 + x1*x5*x6*x7*x9 + x1*x5*x6*x7*x10 + x1*x5*x6*x8*x9 + x1*x5*x6*x8*x10 + x1*x5*x6*x9*x10 +\nx1*x5*x7*x8*x9 + x1*x5*x7*x8*x10 + x1*x5*x7*x9*x10 + x1*x5*x8*x9*x10 + x1*x6*x7*x8*x9 + x1*x6*x7*x8*x10 + x1*x6*x7*x9*x10 + x1*x6*x8*x9*x10 + x1*x7*x8*x9*x10 + x2*x3*x4*x5*x6 + x2*x3*x4*x5*x7 + x2*x3*x4*x5*x8 + x2*x3*x4*x5*x9 + x2*x3*x4*x5*x10 + x2*x3*x4*x6*x7 + x2*x3*x4*x6*x8 + x2*x3*x4*x6*x9 + x2*x3*x4*x6*x10 + x2*x3*x4*x7*x8 + x2*x3*x4*x7*x9 + x2*x3*x4*x7*x10 + x2*x3*x4*x8*x9 + x2*x3*x4*x8*x10 + x2*x3*x4*x9*x10 + x2*x3*x5*x6*x7 + x2*x3*x5*x6*x8 + x2*x3*x5*x6*x9 + x2*x3*x5*x6*x10 + x2*x3*x5*x7*x8 + x2*x3*x5*x7*x9 + x2*x3*x5*x7*x10 + x2*x3*x5*x8*x9 + x2*x3*x5*x8*x10 + x2*x3*x5*x9*x10\n+ x2*x3*x6*x7*x8 + x2*x3*x6*x7*x9 + x2*x3*x6*x7*x10 + x2*x3*x6*x8*x9 + x2*x3*x6*x8*x10 + x2*x3*x6*x9*x10 + x2*x3*x7*x8*x9 + x2*x3*x7*x8*x10 + x2*x3*x7*x9*x10 + x2*x3*x8*x9*x10 + x2*x4*x5*x6*x7 + x2*x4*x5*x6*x8 + x2*x4*x5*x6*x9 + x2*x4*x5*x6*x10 + x2*x4*x5*x7*x8 + x2*x4*x5*x7*x9 + x2*x4*x5*x7*x10 + x2*x4*x5*x8*x9 + x2*x4*x5*x8*x10 + x2*x4*x5*x9*x10 + x2*x4*x6*x7*x8 + x2*x4*x6*x7*x9 + x2*x4*x6*x7*x10 + x2*x4*x6*x8*x9 + x2*x4*x6*x8*x10 + x2*x4*x6*x9*x10 + x2*x4*x7*x8*x9 + x2*x4*x7*x8*x10 + x2*x4*x7*x9*x10 + x2*x4*x8*x9*x10 + x2*x5*x6*x7*x8 + x2*x5*x6*x7*x9 + x2*x5*x6*x7*x10 + x2*x5*x6*x8*x9 + x2*x5*x6*x8*x10 + x2*x5*x6*x9*x10 + x2*x5*x7*x8*x9 + x2*x5*x7*x8*x10\n+ x2*x5*x7*x9*x10 + x2*x5*x8*x9*x10 + x2*x6*x7*x8*x9 + x2*x6*x7*x8*x10 + x2*x6*x7*x9*x10 + x2*x6*x8*x9*x10 + x2*x7*x8*x9*x10 + x3*x4*x5*x6*x7 + x3*x4*x5*x6*x8 + x3*x4*x5*x6*x9 + x3*x4*x5*x6*x10 + x3*x4*x5*x7*x8 + x3*x4*x5*x7*x9 + x3*x4*x5*x7*x10 + x3*x4*x5*x8*x9 + x3*x4*x5*x8*x10 + x3*x4*x5*x9*x10 + x3*x4*x6*x7*x8 + x3*x4*x6*x7*x9 + x3*x4*x6*x7*x10 + x3*x4*x6*x8*x9 +\nx3*x4*x6*x8*x10 + x3*x4*x6*x9*x10 + x3*x4*x7*x8*x9 + x3*x4*x7*x8*x10 + x3*x4*x7*x9*x10 + x3*x4*x8*x9*x10 + x3*x5*x6*x7*x8 + x3*x5*x6*x7*x9 + x3*x5*x6*x7*x10 + x3*x5*x6*x8*x9 + x3*x5*x6*x8*x10 + x3*x5*x6*x9*x10 + x3*x5*x7*x8*x9 + x3*x5*x7*x8*x10 + x3*x5*x7*x9*x10 + x3*x5*x8*x9*x10 + x3*x6*x7*x8*x9 + x3*x6*x7*x8*x10 + x3*x6*x7*x9*x10 + x3*x6*x8*x9*x10 + x3*x7*x8*x9*x10\n+ x4*x5*x6*x7*x8 + x4*x5*x6*x7*x9 + x4*x5*x6*x7*x10 + x4*x5*x6*x8*x9 + x4*x5*x6*x8*x10 + x4*x5*x6*x9*x10 + x4*x5*x7*x8*x9 + x4*x5*x7*x8*x10 + x4*x5*x7*x9*x10 + x4*x5*x8*x9*x10 + x4*x6*x7*x8*x9 + x4*x6*x7*x8*x10 + x4*x6*x7*x9*x10 + x4*x6*x8*x9*x10 + x4*x7*x8*x9*x10 + x5*x6*x7*x8*x9 + x5*x6*x7*x8*x10 + x5*x6*x7*x9*x10 + x5*x6*x8*x9*x10 + x5*x7*x8*x9*x10 + x6*x7*x8*x9*x10, x1*x2*x3*x4*x5*x6 + x1*x2*x3*x4*x5*x7 + x1*x2*x3*x4*x5*x8 + x1*x2*x3*x4*x5*x9 + x1*x2*x3*x4*x5*x10 + x1*x2*x3*x4*x6*x7 + x1*x2*x3*x4*x6*x8 + x1*x2*x3*x4*x6*x9 + x1*x2*x3*x4*x6*x10 + x1*x2*x3*x4*x7*x8 + x1*x2*x3*x4*x7*x9 + x1*x2*x3*x4*x7*x10 + x1*x2*x3*x4*x8*x9 + x1*x2*x3*x4*x8*x10 + x1*x2*x3*x4*x9*x10 + x1*x2*x3*x5*x6*x7 + x1*x2*x3*x5*x6*x8 + x1*x2*x3*x5*x6*x9 + x1*x2*x3*x5*x6*x10 + x1*x2*x3*x5*x7*x8 + x1*x2*x3*x5*x7*x9 + x1*x2*x3*x5*x7*x10 + x1*x2*x3*x5*x8*x9 + x1*x2*x3*x5*x8*x10 + x1*x2*x3*x5*x9*x10 + x1*x2*x3*x6*x7*x8 + x1*x2*x3*x6*x7*x9 + x1*x2*x3*x6*x7*x10 + x1*x2*x3*x6*x8*x9 + x1*x2*x3*x6*x8*x10 + x1*x2*x3*x6*x9*x10 + x1*x2*x3*x7*x8*x9 + x1*x2*x3*x7*x8*x10 + x1*x2*x3*x7*x9*x10 + x1*x2*x3*x8*x9*x10 + x1*x2*x4*x5*x6*x7 + x1*x2*x4*x5*x6*x8 + x1*x2*x4*x5*x6*x9 + x1*x2*x4*x5*x6*x10 + x1*x2*x4*x5*x7*x8 + x1*x2*x4*x5*x7*x9 + x1*x2*x4*x5*x7*x10 + x1*x2*x4*x5*x8*x9 + x1*x2*x4*x5*x8*x10 + x1*x2*x4*x5*x9*x10 + x1*x2*x4*x6*x7*x8 + x1*x2*x4*x6*x7*x9 +\nx1*x2*x4*x6*x7*x10 + x1*x2*x4*x6*x8*x9 + x1*x2*x4*x6*x8*x10 + x1*x2*x4*x6*x9*x10 + x1*x2*x4*x7*x8*x9 + x1*x2*x4*x7*x8*x10 + x1*x2*x4*x7*x9*x10 + x1*x2*x4*x8*x9*x10 + x1*x2*x5*x6*x7*x8 + x1*x2*x5*x6*x7*x9 + x1*x2*x5*x6*x7*x10 + x1*x2*x5*x6*x8*x9 + x1*x2*x5*x6*x8*x10 + x1*x2*x5*x6*x9*x10 + x1*x2*x5*x7*x8*x9 + x1*x2*x5*x7*x8*x10 + x1*x2*x5*x7*x9*x10 + x1*x2*x5*x8*x9*x10\n+ x1*x2*x6*x7*x8*x9 + x1*x2*x6*x7*x8*x10 + x1*x2*x6*x7*x9*x10 + x1*x2*x6*x8*x9*x10 + x1*x2*x7*x8*x9*x10 + x1*x3*x4*x5*x6*x7 + x1*x3*x4*x5*x6*x8 + x1*x3*x4*x5*x6*x9 + x1*x3*x4*x5*x6*x10 + x1*x3*x4*x5*x7*x8 + x1*x3*x4*x5*x7*x9 + x1*x3*x4*x5*x7*x10 + x1*x3*x4*x5*x8*x9 + x1*x3*x4*x5*x8*x10 + x1*x3*x4*x5*x9*x10 + x1*x3*x4*x6*x7*x8 + x1*x3*x4*x6*x7*x9 + x1*x3*x4*x6*x7*x10 + x1*x3*x4*x6*x8*x9 + x1*x3*x4*x6*x8*x10 + x1*x3*x4*x6*x9*x10 + x1*x3*x4*x7*x8*x9 + x1*x3*x4*x7*x8*x10 + x1*x3*x4*x7*x9*x10 + x1*x3*x4*x8*x9*x10 + x1*x3*x5*x6*x7*x8 + x1*x3*x5*x6*x7*x9 + x1*x3*x5*x6*x7*x10 + x1*x3*x5*x6*x8*x9 + x1*x3*x5*x6*x8*x10 + x1*x3*x5*x6*x9*x10 + x1*x3*x5*x7*x8*x9 + x1*x3*x5*x7*x8*x10 + x1*x3*x5*x7*x9*x10 + x1*x3*x5*x8*x9*x10 + x1*x3*x6*x7*x8*x9\n+ x1*x3*x6*x7*x8*x10 + x1*x3*x6*x7*x9*x10 + x1*x3*x6*x8*x9*x10 + x1*x3*x7*x8*x9*x10 + x1*x4*x5*x6*x7*x8 + x1*x4*x5*x6*x7*x9 + x1*x4*x5*x6*x7*x10 + x1*x4*x5*x6*x8*x9 + x1*x4*x5*x6*x8*x10 + x1*x4*x5*x6*x9*x10 + x1*x4*x5*x7*x8*x9 + x1*x4*x5*x7*x8*x10 + x1*x4*x5*x7*x9*x10 + x1*x4*x5*x8*x9*x10 + x1*x4*x6*x7*x8*x9 + x1*x4*x6*x7*x8*x10 + x1*x4*x6*x7*x9*x10 + x1*x4*x6*x8*x9*x10 + x1*x4*x7*x8*x9*x10 + x1*x5*x6*x7*x8*x9 + x1*x5*x6*x7*x8*x10 + x1*x5*x6*x7*x9*x10 + x1*x5*x6*x8*x9*x10 + x1*x5*x7*x8*x9*x10 + x1*x6*x7*x8*x9*x10 + x2*x3*x4*x5*x6*x7 + x2*x3*x4*x5*x6*x8 + x2*x3*x4*x5*x6*x9 + x2*x3*x4*x5*x6*x10 + x2*x3*x4*x5*x7*x8 + x2*x3*x4*x5*x7*x9 + x2*x3*x4*x5*x7*x10 + x2*x3*x4*x5*x8*x9 + x2*x3*x4*x5*x8*x10 + x2*x3*x4*x5*x9*x10 + x2*x3*x4*x6*x7*x8 + x2*x3*x4*x6*x7*x9 + x2*x3*x4*x6*x7*x10 + x2*x3*x4*x6*x8*x9 + x2*x3*x4*x6*x8*x10 + x2*x3*x4*x6*x9*x10 + x2*x3*x4*x7*x8*x9 + x2*x3*x4*x7*x8*x10 + x2*x3*x4*x7*x9*x10 + x2*x3*x4*x8*x9*x10 + x2*x3*x5*x6*x7*x8 + x2*x3*x5*x6*x7*x9 + x2*x3*x5*x6*x7*x10 + x2*x3*x5*x6*x8*x9 + x2*x3*x5*x6*x8*x10 + x2*x3*x5*x6*x9*x10 + x2*x3*x5*x7*x8*x9 + x2*x3*x5*x7*x8*x10 + x2*x3*x5*x7*x9*x10 + x2*x3*x5*x8*x9*x10 + x2*x3*x6*x7*x8*x9 + x2*x3*x6*x7*x8*x10 + x2*x3*x6*x7*x9*x10 + x2*x3*x6*x8*x9*x10 + x2*x3*x7*x8*x9*x10 + x2*x4*x5*x6*x7*x8 + x2*x4*x5*x6*x7*x9 + x2*x4*x5*x6*x7*x10 + x2*x4*x5*x6*x8*x9 + x2*x4*x5*x6*x8*x10 + x2*x4*x5*x6*x9*x10 + x2*x4*x5*x7*x8*x9 + x2*x4*x5*x7*x8*x10 + x2*x4*x5*x7*x9*x10 + x2*x4*x5*x8*x9*x10 + x2*x4*x6*x7*x8*x9 + x2*x4*x6*x7*x8*x10 + x2*x4*x6*x7*x9*x10 + x2*x4*x6*x8*x9*x10 + x2*x4*x7*x8*x9*x10 + x2*x5*x6*x7*x8*x9 + x2*x5*x6*x7*x8*x10 + x2*x5*x6*x7*x9*x10 + x2*x5*x6*x8*x9*x10 + x2*x5*x7*x8*x9*x10 + x2*x6*x7*x8*x9*x10 + x3*x4*x5*x6*x7*x8 + x3*x4*x5*x6*x7*x9 + x3*x4*x5*x6*x7*x10 + x3*x4*x5*x6*x8*x9 + x3*x4*x5*x6*x8*x10\n+ x3*x4*x5*x6*x9*x10 + x3*x4*x5*x7*x8*x9 + x3*x4*x5*x7*x8*x10 + x3*x4*x5*x7*x9*x10 + x3*x4*x5*x8*x9*x10 + x3*x4*x6*x7*x8*x9 + x3*x4*x6*x7*x8*x10 + x3*x4*x6*x7*x9*x10 + x3*x4*x6*x8*x9*x10 + x3*x4*x7*x8*x9*x10 + x3*x5*x6*x7*x8*x9 + x3*x5*x6*x7*x8*x10 + x3*x5*x6*x7*x9*x10 + x3*x5*x6*x8*x9*x10 + x3*x5*x7*x8*x9*x10 + x3*x6*x7*x8*x9*x10 + x4*x5*x6*x7*x8*x9 + x4*x5*x6*x7*x8*x10 + x4*x5*x6*x7*x9*x10 + x4*x5*x6*x8*x9*x10 + x4*x5*x7*x8*x9*x10 + x4*x6*x7*x8*x9*x10 + x5*x6*x7*x8*x9*x10, x1*x2*x3*x4*x5*x6*x7 + x1*x2*x3*x4*x5*x6*x8 + x1*x2*x3*x4*x5*x6*x9 + x1*x2*x3*x4*x5*x6*x10 + x1*x2*x3*x4*x5*x7*x8 + x1*x2*x3*x4*x5*x7*x9 + x1*x2*x3*x4*x5*x7*x10 + x1*x2*x3*x4*x5*x8*x9 +\nx1*x2*x3*x4*x5*x8*x10 + x1*x2*x3*x4*x5*x9*x10 + x1*x2*x3*x4*x6*x7*x8 + x1*x2*x3*x4*x6*x7*x9 + x1*x2*x3*x4*x6*x7*x10 + x1*x2*x3*x4*x6*x8*x9 + x1*x2*x3*x4*x6*x8*x10 + x1*x2*x3*x4*x6*x9*x10 + x1*x2*x3*x4*x7*x8*x9 + x1*x2*x3*x4*x7*x8*x10 + x1*x2*x3*x4*x7*x9*x10 + x1*x2*x3*x4*x8*x9*x10 + x1*x2*x3*x5*x6*x7*x8 + x1*x2*x3*x5*x6*x7*x9 + x1*x2*x3*x5*x6*x7*x10 + x1*x2*x3*x5*x6*x8*x9 + x1*x2*x3*x5*x6*x8*x10 + x1*x2*x3*x5*x6*x9*x10 + x1*x2*x3*x5*x7*x8*x9 + x1*x2*x3*x5*x7*x8*x10 + x1*x2*x3*x5*x7*x9*x10 + x1*x2*x3*x5*x8*x9*x10\n+ x1*x2*x3*x6*x7*x8*x9 + x1*x2*x3*x6*x7*x8*x10 + x1*x2*x3*x6*x7*x9*x10 + x1*x2*x3*x6*x8*x9*x10 + x1*x2*x3*x7*x8*x9*x10 + x1*x2*x4*x5*x6*x7*x8 + x1*x2*x4*x5*x6*x7*x9 + x1*x2*x4*x5*x6*x7*x10 + x1*x2*x4*x5*x6*x8*x9 + x1*x2*x4*x5*x6*x8*x10 + x1*x2*x4*x5*x6*x9*x10 + x1*x2*x4*x5*x7*x8*x9 + x1*x2*x4*x5*x7*x8*x10 + x1*x2*x4*x5*x7*x9*x10 + x1*x2*x4*x5*x8*x9*x10 + x1*x2*x4*x6*x7*x8*x9 + x1*x2*x4*x6*x7*x8*x10 + x1*x2*x4*x6*x7*x9*x10 + x1*x2*x4*x6*x8*x9*x10 + x1*x2*x4*x7*x8*x9*x10 + x1*x2*x5*x6*x7*x8*x9 + x1*x2*x5*x6*x7*x8*x10 + x1*x2*x5*x6*x7*x9*x10 + x1*x2*x5*x6*x8*x9*x10 + x1*x2*x5*x7*x8*x9*x10 + x1*x2*x6*x7*x8*x9*x10 + x1*x3*x4*x5*x6*x7*x8 + x1*x3*x4*x5*x6*x7*x9 + x1*x3*x4*x5*x6*x7*x10 + x1*x3*x4*x5*x6*x8*x9 + x1*x3*x4*x5*x6*x8*x10 + x1*x3*x4*x5*x6*x9*x10 + x1*x3*x4*x5*x7*x8*x9 + x1*x3*x4*x5*x7*x8*x10 + x1*x3*x4*x5*x7*x9*x10 + x1*x3*x4*x5*x8*x9*x10 + x1*x3*x4*x6*x7*x8*x9 + x1*x3*x4*x6*x7*x8*x10 + x1*x3*x4*x6*x7*x9*x10 + x1*x3*x4*x6*x8*x9*x10 + x1*x3*x4*x7*x8*x9*x10 + x1*x3*x5*x6*x7*x8*x9 + x1*x3*x5*x6*x7*x8*x10 + x1*x3*x5*x6*x7*x9*x10 + x1*x3*x5*x6*x8*x9*x10 + x1*x3*x5*x7*x8*x9*x10 + x1*x3*x6*x7*x8*x9*x10 + x1*x4*x5*x6*x7*x8*x9 + x1*x4*x5*x6*x7*x8*x10 + x1*x4*x5*x6*x7*x9*x10 + x1*x4*x5*x6*x8*x9*x10 + x1*x4*x5*x7*x8*x9*x10 + x1*x4*x6*x7*x8*x9*x10\n+ x1*x5*x6*x7*x8*x9*x10 + x2*x3*x4*x5*x6*x7*x8 + x2*x3*x4*x5*x6*x7*x9 + x2*x3*x4*x5*x6*x7*x10 + x2*x3*x4*x5*x6*x8*x9 + x2*x3*x4*x5*x6*x8*x10 + x2*x3*x4*x5*x6*x9*x10 + x2*x3*x4*x5*x7*x8*x9 + x2*x3*x4*x5*x7*x8*x10 + x2*x3*x4*x5*x7*x9*x10 + x2*x3*x4*x5*x8*x9*x10 + x2*x3*x4*x6*x7*x8*x9 + x2*x3*x4*x6*x7*x8*x10 + x2*x3*x4*x6*x7*x9*x10 + x2*x3*x4*x6*x8*x9*x10 + x2*x3*x4*x7*x8*x9*x10 + x2*x3*x5*x6*x7*x8*x9 + x2*x3*x5*x6*x7*x8*x10 + x2*x3*x5*x6*x7*x9*x10 + x2*x3*x5*x6*x8*x9*x10 + x2*x3*x5*x7*x8*x9*x10 + x2*x3*x6*x7*x8*x9*x10 + x2*x4*x5*x6*x7*x8*x9 + x2*x4*x5*x6*x7*x8*x10 + x2*x4*x5*x6*x7*x9*x10 + x2*x4*x5*x6*x8*x9*x10 + x2*x4*x5*x7*x8*x9*x10 + x2*x4*x6*x7*x8*x9*x10 + x2*x5*x6*x7*x8*x9*x10 + x3*x4*x5*x6*x7*x8*x9 + x3*x4*x5*x6*x7*x8*x10 + x3*x4*x5*x6*x7*x9*x10 + x3*x4*x5*x6*x8*x9*x10 + x3*x4*x5*x7*x8*x9*x10 + x3*x4*x6*x7*x8*x9*x10 + x3*x5*x6*x7*x8*x9*x10 + x4*x5*x6*x7*x8*x9*x10, x1*x2*x3*x4*x5*x6*x7*x8 + x1*x2*x3*x4*x5*x6*x7*x9 + x1*x2*x3*x4*x5*x6*x7*x10 + x1*x2*x3*x4*x5*x6*x8*x9 + x1*x2*x3*x4*x5*x6*x8*x10 + x1*x2*x3*x4*x5*x6*x9*x10 + x1*x2*x3*x4*x5*x7*x8*x9 + x1*x2*x3*x4*x5*x7*x8*x10 + x1*x2*x3*x4*x5*x7*x9*x10 + x1*x2*x3*x4*x5*x8*x9*x10 + x1*x2*x3*x4*x6*x7*x8*x9 + x1*x2*x3*x4*x6*x7*x8*x10 + x1*x2*x3*x4*x6*x7*x9*x10 + x1*x2*x3*x4*x6*x8*x9*x10 + x1*x2*x3*x4*x7*x8*x9*x10 + x1*x2*x3*x5*x6*x7*x8*x9 + x1*x2*x3*x5*x6*x7*x8*x10\n+ x1*x2*x3*x5*x6*x7*x9*x10 + x1*x2*x3*x5*x6*x8*x9*x10 + x1*x2*x3*x5*x7*x8*x9*x10 + x1*x2*x3*x6*x7*x8*x9*x10 + x1*x2*x4*x5*x6*x7*x8*x9 + x1*x2*x4*x5*x6*x7*x8*x10 + x1*x2*x4*x5*x6*x7*x9*x10 + x1*x2*x4*x5*x6*x8*x9*x10 + x1*x2*x4*x5*x7*x8*x9*x10 + x1*x2*x4*x6*x7*x8*x9*x10 + x1*x2*x5*x6*x7*x8*x9*x10\n+ x1*x3*x4*x5*x6*x7*x8*x9 + x1*x3*x4*x5*x6*x7*x8*x10 + x1*x3*x4*x5*x6*x7*x9*x10 + x1*x3*x4*x5*x6*x8*x9*x10 + x1*x3*x4*x5*x7*x8*x9*x10 + x1*x3*x4*x6*x7*x8*x9*x10 + x1*x3*x5*x6*x7*x8*x9*x10 + x1*x4*x5*x6*x7*x8*x9*x10 + x2*x3*x4*x5*x6*x7*x8*x9 + x2*x3*x4*x5*x6*x7*x8*x10 + x2*x3*x4*x5*x6*x7*x9*x10 + x2*x3*x4*x5*x6*x8*x9*x10 + x2*x3*x4*x5*x7*x8*x9*x10 + x2*x3*x4*x6*x7*x8*x9*x10 + x2*x3*x5*x6*x7*x8*x9*x10 + x2*x4*x5*x6*x7*x8*x9*x10 + x3*x4*x5*x6*x7*x8*x9*x10, x1*x2*x3*x4*x5*x6*x7*x8*x9 + x1*x2*x3*x4*x5*x6*x7*x8*x10 + x1*x2*x3*x4*x5*x6*x7*x9*x10 + x1*x2*x3*x4*x5*x6*x8*x9*x10 + x1*x2*x3*x4*x5*x7*x8*x9*x10 + x1*x2*x3*x4*x6*x7*x8*x9*x10 + x1*x2*x3*x5*x6*x7*x8*x9*x10 + x1*x2*x4*x5*x6*x7*x8*x9*x10 + x1*x3*x4*x5*x6*x7*x8*x9*x10 + x2*x3*x4*x5*x6*x7*x8*x9*x10, x1*x2*x3*x4*x5*x6*x7*x8*x9*x10 + 1}):\n\nst := time[real]():\nBasis(J, tdeg(x1,x2,x3,x4,x5,x6,x7,x8,x9,x10)):\ntime[real]() - st;\n", "meta": {"hexsha": "02884aecfcda5ea2b56256d45599143ff4ee1a39", "size": 18067, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmark/maplescripts/cyclicsmall.mpl", "max_stars_repo_name": "sumiya11/FastGroebner.jl", "max_stars_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 7, "max_stars_repo_stars_event_min_datetime": "2022-01-22T20:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-14T02:22:21.000Z", "max_issues_repo_path": "benchmark/maplescripts/cyclicsmall.mpl", "max_issues_repo_name": "sumiya11/Groebner.jl", "max_issues_repo_head_hexsha": "0b0e354a9d84a5f84a11b3d4c72dcd991859c752", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 13, "max_issues_repo_issues_event_min_datetime": "2022-01-17T01:16:26.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T16:44:38.000Z", "max_forks_repo_path": "benchmark/maplescripts/cyclicsmall.mpl", "max_forks_repo_name": "sumiya11/FastGroebner.jl", "max_forks_repo_head_hexsha": "5d3f39cec61bac0a9da8c63d1f6fa6fbea03e962", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-22T18:30:38.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-22T18:30:38.000Z", "avg_line_length": 602.2333333333, "max_line_length": 2367, "alphanum_fraction": 0.6006531245, "num_tokens": 11338, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9099070060380482, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.5426986984194987}} {"text": "\n# Forward Kinematics for Robot based on MDH frames\n# Introduction\n# Direkte Kinematik basierend auf MDH-Parametern berechnen\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# tree -> Berechnung f\u00fcr eine beliebige Baumstruktur (ohne Schleifen)\n# floatb -> floating base wird durch base twist (Geschwindigkeit der Basis) oder vollst\u00e4ndige Orientierung (Euler-Winkel) ber\u00fccksichtigt\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# mdh_kinematics -> Berechnung der Vorw\u00e4rtskinematik mit modifizierten DH-Parametern nach [KhalilKle1986]\n# \n# Prinzip:\n# Berechne die direkte Kinematik.\n# Zus\u00e4tzlich k\u00f6nnen kinematische Zwangsbedingungen direkt ber\u00fccksichtigt werden. Diese sorgen daf\u00fcr, dass MDH-Winkel durch analytische Ausdr\u00fccke verallgemeinerter Koordinaten ersetzt werden.\n# Authors\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Sources\n# [KhalilKle1986] Khalil, W. & Kleinfinger, J.: A new geometric notation for open and closed-loop robots (1986)\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I\n# Initialization\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_debug := false:\ncodegen_opt := 2:\n# Code-Optimierung f\u00fcr die Kinematik (zusammenfassung paralleler Achsen).\n# Ist f\u00fcr einige Systeme vorteilhaft (serielle Ketten mit parallelen Achsen), f\u00fcr andere nicht (z.B. Baumstrukturen mit parallelen Achsen. Hier kann die Code-Optimierung mehr aus nicht trigonometrisch optimierten Termen herausholen).\n# Die Terme werden aber auf jeden Fall \u00fcbersichtlicher.\ncodegen_kinematics_opt := true:\n# Substitutionsreihenfolge von kinematischen Zwangsbedingungen (falls vorhanden) einstellen.\n# 1: Ersetzung bereits in Einzel-Transformationsmatrizen (dann ist die Zusammenfassung f\u00fcr mehrere Achsen aus codegen_kinematics_opt nicht mehr so leicht m\u00f6glich). Muss 1 sein f\u00fcr trigonometrische Ersetzung.\n# 2: Ersetzung erst nach der Zusammenfassung der Einzel-Transformationsmatrizen zu (kumulierten) Gesamt-Transformationsmatrizen\ncodegen_kinematics_subsorder := 1:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../helper/proc_combine2\":\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../transformation/proc_trotx\": \nread \"../transformation/proc_troty\": \nread \"../transformation/proc_trotz\": \nread \"../transformation/proc_transl\": \nread \"../transformation/proc_trafo_mdh\": \n# Funktionen aus Robotik-Repo\nread(\"../robotics_repo_path\"):\nread(sprintf(\"%s/transformation/maple/proc_eulxyz2r\", robotics_repo_path)):\n# Homogene Transformationsmatrix f\u00fcr Rotation aus XYZ-Euler-Winkel\neulxyztr := proc (alpha, beta, gamma) \n local T; \n T := Matrix(4,4,`<,>`(`<|>`(eulxyz2r(),`<,>`(0,0,0)),`<|>`(0,0,0,1)));\n return T \nend proc:\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"%s. Generiere Kinematik f\u00fcr %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nprintf(\"%s. Alle Daten geladen. Generiere Kinematik f\u00fcr %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name):\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(2)=-1 then\n use_simplify := 1: # standardm\u00e4\u00dfig simplify-Befehle anwenden. Sind meistens sinnvoll und in Ausnahmen nicht allzu sch\u00e4dlich\nelse\n use_simplify := simplify_options(2): # zweiter Eintrag ist f\u00fcr Kinematik\nend if:\n\n# Kinematische Zwangsbedingungen\n# Lade Ausdr\u00fccke f\u00fcr kinematische Zwangsbedingungen (Verkn\u00fcpfung von MDH-Gelenkwinkeln durch verallgemeinerte Koordinaten)\n# Lese Variablen: kintmp_subsexp, kintmp_qs, kintmp_qt\nkin_constraints_exist := false:\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nconstrfile := sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nif FileTools[Exists](constrfile) then\n read constrfile:\nend if:\nif kin_constraints_exist = true then:\n kintmp_qs := kintmp_qs: # gelesene Variable sonst nicht sichtbar\n kintmp_qt := kintmp_qt: # gelesene Variable sonst nicht sichtbar\n kintmp_subsexp := kintmp_subsexp:\n printf(\"%s. Kinematische Zwangsbedingungen gelesen.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nelse\n kintmp_qs := Matrix(1,1):\n kintmp_qt := Matrix(1,1):\n kintmp_subsexp := Matrix(1,2):\n kin_constraints_exist := false:\n # Zwangsbedingungen neu speichern, damit diese auch f\u00fcr andere Skripte verf\u00fcgbar sind (als dummy-Variablen).\n save kin_constraints_exist, kintmp_qs, kintmp_qt, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nend if:\n# Calculate Forward Kinematics (Single-Joint Transformation)\n# Trf is the Matrix of Transformation from i-1 to i\n# Trf_c is the cummulated Matrix of Transformation from 0 to i\nprintf(\"%s. Beginne Berechnung der Kinematik f\u00fcr einzelne Gelenk-Transformationen.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nTrf := Matrix(4, 4, NJ): # Diese Initialisierung bringt nichts (initialisiert nur 4x4-Matrix)\n;\nfor i from 1 to NJ do \n Trf(1 .. 4, 1 .. 4, i) := Matrix(4,4):\nend do:\nfor i from 1 to NJ do \n Trf(1 .. 4, 1 .. 4, i) := trafo_mdh_full(alpha[i,1], a[i,1], theta[i,1], d[i,1], beta[i,1], b[i,1]):\nend do:\n# Kinematische Zwangsbedingungen ersetzen (vor Berechnung der Gesamt-Transformation)\n# Substituiere allgemeine Ausdr\u00fccke der Winkel der Parallelstruktur mit kinematischen Zwangsbedingungen in Abh\u00e4ngigkeit der Haupt-Gelenkwinkel\nif kin_constraints_exist and codegen_kinematics_subsorder = 1 then\n for i from 1 to NJ do # Index \u00fcber Transformationsmatrizen aller K\u00f6rper\n for ix from 1 to 4 do # Index \u00fcber Zeilen der Transformationsmatrizen\n for iy from 1 to 4 do # Index \u00fcber Spalten der Transformationsmatrizen\n # Substituiere Zeitvariablen\n Trf(ix, iy, i) := convert_t_s( Trf(ix, iy, i) ):\n # Substituiere sin und cos der Winkel (einfachere Ausdr\u00fccke)\n Trf(ix, iy, i) := subs_kintmp_exp(Trf(ix, iy, i)):\n # Substituiere die verbleibenden Winkel direkt (einige Winkel sind nicht in den Ersetzungsausdr\u00fccken enthalten, da sie keine problematischen arctan-Ausdr\u00fccke enthalten.\n for jj from 1 to RowDimension(kintmp_qt) do # Index \u00fcber zu ersetzende Winkel\n Trf(ix, iy, i) := subs( { kintmp_s(jj, 1) = kintmp_qs(jj, 1) }, Trf(ix, iy, i) ): \n end do:\n Trf(ix, iy, i) := convert_s_t( Trf(ix, iy, i) ):\n end do:\n end do:\n if use_simplify>=1 then\n \t tmp_l1 := length(Trf(1 .. 4, 1 .. 4, i)): tmp_t1:=time():\n \t Trf(1 .. 4, 1 .. 4, i) := simplify2(Trf(1 .. 4, 1 .. 4, i)):\n \t tmp_l2 := length(Trf(1 .. 4, 1 .. 4, i)): tmp_t2:=time():\n \t printf(\"%s: Term f\u00fcr (Einzel-)Trafo-Matrix %d->%d vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n \t FormatTime(\"%Y-%m-%d %H:%M:%S\"), v(i), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\n end do:\n printf(\"%s. Ersetzungen der MDH-Parameter mit Ergebnissen der Parallelstruktur in verallgemeinerten Koordinaten erfolgreich (vor Berechnung der Gesamt-Transformation).\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n# Calculate Forward Kinematics (Multi-Joint Transformation)\nTrf_c := Matrix(4, 4, NJ+1): # Diese Initialisierung bringt nichts (initialisiert nur 4x4-Matrix)\nfor i from 1 to NJ+1 do \n Trf_c(1 .. 4, 1 .. 4, i) := Matrix(4,4): # Vollst\u00e4ndige Initialisierung\nend do:\n# Basis-Transformation: Unterschiedliche Darstellungsmethoden. F\u00fchren zu unterschiedlichen verallgemeinerten Koordinaten.\nif base_method_name = \"twist\" then:\n Trf_c(1 .. 4, 1 .. 4, 1) := transl(X_base_t[1..3,1]):\nend:\nif base_method_name = \"eulxyz\" then:\n Trf_c(1 .. 4, 1 .. 4, 1) := transl(X_base_t[1..3,1]) . eulxyztr(X_base_t[4,1], X_base_t[5,1], X_base_t[6,1]):\nend:\nprintf(\"%s. Beginne direkte Kinematik. Nutze die Methode %s f\u00fcr die Basis-Orientierung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), base_method_name):\n# Kinematik aller K\u00f6rper mit MDH-Ansatz Bestimmen. [KhalilKle1986].\n# Einfache Kinematik: Multiplikation an vorherige Transformationsmatrix\nif not(codegen_kinematics_opt) then\n printf(\"%s. Berechne Vorw\u00e4rts-Transformation der Kinematik ohne spezielle Optimierung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n for i from 1 to NJ do \n # Index des vorherigen Koordinatensystems\n j := v(i)+1:\n Trf_c(1 .. 4, 1 .. 4, i+1) := Multiply(Trf_c(1 .. 4, 1 .. 4, j), Trf(1 .. 4, 1 .. 4, i)):\n if use_simplify>=1 then\n \t tmp_l1 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t1:=time():\n \t Trf_c(1 .. 4, 1 .. 4, i+1) := simplify2(Trf_c(1 .. 4, 1 .. 4, i+1)):\n \t tmp_l2 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t2:=time():\n \t printf(\"%s: Term f\u00fcr (Gesamt-)Trafo-Matrix 0->%d vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n \t FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\n end do:\nend if:\n#Trf_c_orig := copy(Trf_c): # Debug-Ausdruck zum Vergleich der obigen mit der unteren Methode\n;\n# Optimierung der Terme: Summentheorem f\u00fcr Drehungen um aufeinanderfolgende Achsen.\n# Bei Verwendung dieser Optimierung funktioniert die Substitution mit trigonometrischen Ausdr\u00fccken von abh\u00e4ngigen Gelenken eventuell anders.\n# Die Funktionsweise kann mit aktivierten print-Befehlen nachvollzogen werden.\n\nif codegen_kinematics_opt then\n printf(\"%s. Beginne mit der Optimierung der Kinematik f\u00fcr parallele Gelenke.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n for i from 1 to NJ do\n #printf(\"----------------------\\ni=%d\\n\",i):\n # Bestimme Vorw\u00e4rtskinematik f\u00fcr das Koordinatensystem i (0=Basis)\n # Gehe solande r\u00fcckw\u00e4rts, wie die Gelenkachsen parallel sind\n j := i: # Lauf-Index \u00fcber Vorg\u00e4nger-Elemente (0=Basis)\n j2 := 0:# Index des Segmentes (0=Basis), das vor der Kette von parallelen Achsen ist\n Trf_tmp := IdentityMatrix(4,4); # Transformation von diesem Segment zum aktuellen\n Kette_akt := []:\n #printf(\"Trf_tmp neu initialisiert:\\n\"):\n #print(Trf_tmp);\n for k from 1 to NJ do # Schleife mit Dummy-L\u00e4nge. Wird abgebrochen, falls beendet.\n #printf(\"j=%d\\n\",j):\n Kette_akt := [j, op(Kette_akt)]:\n # Additionstheorem f\u00fcr Drehung um parallele Achsen (combine)\n # Pr\u00fcfe, welche Form rechentechnisch am g\u00fcnstigsten ist und w\u00e4hle diese (wrapper combine2)\n Trf_tmp := simplify2(combine2(Matrix(Trf(1 .. 4, 1 .. 4, j) . Trf_tmp))):\n #printf(\"Trf_tmp aktualisiert mit Trf %d. Aktuelle Kette: %s\\n\", j, convert(Kette_akt, string)):\n #print(Trf_tmp);\n if not(alpha(j) = 0) then\n # Die vorherige Achse ist nicht parallel zu dieser\n # Weitere Vereinfachungen ergeben keinen Sinn\n j2 := v(j):\n #printf(\"alpha ungleich null. Abbruch j2=%d.\\n\", j2):\n break:\n #else\n # printf(\"alpha ist Null. Vorherige Achse ist parallel\\n\"):\n end if:\n if v(j) = 0 then\n break: # Vorg\u00e4nger ist Basis. Keine weitere Untersuchung\n end if:\n #printf(\"v(%d)=%d\\n\", j, v(j)):\n j := v(j): # Nehme das Vorg\u00e4nger-Segment\n end do:\n Trf_c(1 .. 4, 1 .. 4, i+1) := Matrix(Trf_c(1 .. 4, 1 .. 4, j2+1)) . Trf_tmp:\n if use_simplify>=1 then\n \t tmp_l1 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t1:=time():\n \t Trf_c(1 .. 4, 1 .. 4, i+1) := simplify2(Trf_c(1 .. 4, 1 .. 4, i+1)):\n \t tmp_l2 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t2:=time():\n \t printf(\"%s: Term f\u00fcr (Gesamt-)Trafo-Matrix 0->%d vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs\\n\", \\\n \t FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\n #printf(\"Trf_tmp an Trf_c angeh\u00e4ngt (Eintrag zu K\u00f6rper %d. %d -> %d mit Kette %s)\\n\", i, j2, i, convert(Kette_akt, string)):\n #print(Trf_c(1 .. 4, 1 .. 4, i+1)):\n end do:\n printf(\"%s. Berechnung der direkten Kinematik mit Vereinfachungen f\u00fcr parallele Achsen erfolgreich.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\")\n):\nend if:\n# Kinematische Zwangsbedingungen ersetzen (nach Berechnung der Gesamt-Transformation)\n# Substituiere allgemeine Ausdr\u00fccke der Winkel der Parallelstruktur mit kinematischen Zwangsbedingungen in Abh\u00e4ngigkeit der Haupt-Gelenkwinkel\n# Da die Gesamt-Transformation Trf_c an dieser Stelle schon berechnet wurde, m\u00fcssen die Ausdr\u00fccke hier in Trf und Trf_c ersetzt werden.\nif kin_constraints_exist and codegen_kinematics_subsorder = 2 then\n printf(\"%s. Beginne Einsetzung der kinematischen Zwangsbedingungen in die direkte Kinematik (Gesamt-Transformation).\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n for i from 1 to NJ do # Index \u00fcber Transformationsmatrizen aller K\u00f6rper\n for ix from 1 to 4 do # Index \u00fcber Zeilen der Transformationsmatrizen\n for iy from 1 to 4 do # Index \u00fcber Spalten der Transformationsmatrizen\n # Substituiere Zeitvariablen\n Trf( ix, iy, i) := convert_t_s( Trf( ix, iy, i) ):\n Trf_c(ix, iy, i+1) := convert_t_s( Trf_c(ix, iy, i+1) ):\n # Substituiere sin und cos der Winkel (einfachere Ausdr\u00fccke)\n Trf(ix, iy, i) := subs_kintmp_exp(Trf( ix, iy, i)):\n Trf_c(ix, iy, i+1) := subs_kintmp_exp(Trf_c(ix, iy, i+1)):\n # Substituiere die verbleibenden Winkel direkt (einige Winkel sind nicht in den Ersetzungsausdr\u00fccken enthalten, da sie keine problematischen arctan-Ausdr\u00fccke enthalten.\n for jj from 1 to RowDimension(kintmp_qt) do # Index \u00fcber zu ersetzende Winkel\n Trf(ix, iy, i) := subs( { kintmp_s(jj, 1) = kintmp_qs(jj, 1) }, Trf( ix, iy, i) ):\n Trf_c(ix, iy, i+1) := subs( { kintmp_s(jj, 1) = kintmp_qs(jj, 1) }, Trf_c(ix, iy, i+1) ): \n end do:\n Trf(ix, iy, i) := convert_s_t( Trf( ix, iy, i) ):\n Trf_c(ix, iy, i+1) := convert_s_t( Trf_c(ix, iy, i+1) ):\n end do:\n end do:\n if use_simplify>=1 then\n \t tmp_l1 := length(Trf(1 .. 4, 1 .. 4, i)): tmp_t1:=time():\n \t Trf(1 .. 4, 1 .. 4, i) := simplify2(Trf(1 .. 4, 1 .. 4, i)):\n \t tmp_l2 := length(Trf(1 .. 4, 1 .. 4, i)): tmp_t2:=time():\n \t printf(\"%s. Term f\u00fcr Einzel-Trafo-Matrix %d->%d vereinfacht. L\u00e4nge: %d->%d Rechenzeit %1.1fs.\\n\", \\\n \t FormatTime(\"%Y-%m-%d %H:%M:%S\"), v(i), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n \t tmp_l1 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t1:=time():\n \t Trf_c(1 .. 4, 1 .. 4, i+1) := simplify2(Trf_c(1 .. 4, 1 .. 4, i+1)):\n \t tmp_l2 := length(Trf_c(1 .. 4, 1 .. 4, i+1)): tmp_t2:=time():\n \t printf(\"%s. Term f\u00fcr Gesamt-Trafo-Matrix 0->%d vereinfacht. L\u00e4nge: %d->%d Rechenzeit %1.1fs.\\n\", \\ \n \t FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end if:\n end do:\n printf(\"%s. Ersetzungen der MDH-Parameter mit Ergebnissen der Parallelstruktur in verallgemeinerten Koordinaten erfolgreich (nach Berechnung der Gesamt-Transformation).\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n# Export\nprintf(\"%s. Berechnung der Kinematik beendet. Beginne Matlab-Export.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n# Maple-Export\nsave Trf, Trf_c, sprintf(\"../codeexport/%s/tmp/kinematics_floatb_%s_rotmat_maple.m\", robot_name, base_method_name):\n\n# Export des symbolischen Ausdrucks f\u00fcr alle kumulierten Transformationsmatrizen auf einmal.\n# Export ohne letzte Zeile mit [0 0 0 1]\nTrf_c_Export := Matrix((NJ+1)*3, 4):\nfor i from 1 to NJ+1 do \n Trf_c_Export((i-1)*3+1 .. 3*i, 1..4) := Trf_c(1..3, 1..4, i):\nend do:\nif codegen_act then\n MatlabExport(convert_t_s(Trf_c_Export), sprintf(\"../codeexport/%s/tmp/fkine_mdh_floatb_%s_rotmat_matlab.m\", robot_name, base_method_name), codegen_opt):\nend if:\n\n# Export des symbolischen Ausdrucks f\u00fcr alle Gelenk-Transformationsmatrizen auf einmal.\n# Export ohne letzte Zeile mit [0 0 0 1]\nTrf_Export := Matrix((NJ)*3, 4):\nfor i from 1 to NJ do \n Trf_Export((i-1)*3+1 .. 3*i, 1..4) := Trf(1..3, 1..4, i):\nend do:\nif codegen_act then\n MatlabExport(convert_t_s(Trf_Export), sprintf(\"../codeexport/%s/tmp/joint_transformation_mdh_rotmat_matlab.m\", robot_name), codegen_opt):\nend if:\n\n# Export des symbolischen Ausdrucks f\u00fcr jede Transformationsmatrix einzeln\nfor i from 1 to NJ+1 do\n if codegen_act then\n MatlabExport(convert_t_s(Trf_c(1 .. 4, 1 .. 4, i)), sprintf(\"../codeexport/%s/tmp/fkine_%d_floatb_%s_rotmat_matlab.m\", robot_name, i-1, base_method_name), codegen_opt):\n end if:\nend do:\n\n\n", "meta": {"hexsha": "0690f87a4cef47b101cd9cd6f9c3fcec39a4bb3b", "size": 16457, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_kinematics/robot_tree_floatb_rotmat_mdh_kinematics.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_kinematics/robot_tree_floatb_rotmat_mdh_kinematics.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_kinematics/robot_tree_floatb_rotmat_mdh_kinematics.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 55.786440678, "max_line_length": 233, "alphanum_fraction": 0.6957525673, "num_tokens": 5663, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8459424295406088, "lm_q2_score": 0.6406358548398982, "lm_q1q2_score": 0.5419410514940882}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_x_r2scan_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_r2scan_params * )(p->params);\n*)\n\n$include \"mgga_x_rscan.mpl\"\n$include \"mgga_x_scan.mpl\"\n\n(* eqn S6 *)\nr2scan_alpha := (x, t) -> (t - x^2/8)/(K_FACTOR_C + params_a_eta*x^2/8):\n\n(* f(alpha) replaced with a polynomial for alpha in [0, 2.5], eqn S7 *)\nr2scan_f_alpha_neg := a -> exp(-params_a_c1*a/(1 - a)):\nr2scan_f_alpha := (a, ff) -> my_piecewise5(a <= 0, r2scan_f_alpha_neg(m_min(a, 0)), a <= 2.5, rscan_f_alpha_small(m_min(a, 2.5), ff), rscan_f_alpha_large(m_max(a, 2.5))):\n\n(* eqn S11 *)\nCn := 20/27 + params_a_eta*5/3:\n(* eqn S12 *)\nC2 := ff -> -add(i*ff[9-i], i=1..8) * (1-scan_h0x):\n\n(* eqn S10; this is analogous to scan_y *)\nr2scan_x := (p, ff) -> (Cn*C2(ff)*exp(-p^2/params_a_dp2^4)+MU_GE)*p:\n\nr2scan_f := (x, u, t) -> (scan_h1x(r2scan_x(scan_p(x), rscan_fx)) + r2scan_f_alpha(r2scan_alpha(x, t), rscan_fx) * (scan_h0x - scan_h1x(r2scan_x(scan_p(x), rscan_fx))))*scan_gx(x):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) -> mgga_exchange(r2scan_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "21b3c1ebf24cfde720aa9dd643b2a466ef6d33c5", "size": 1339, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_r2scan.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_r2scan.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_x_r2scan.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 35.2368421053, "max_line_length": 180, "alphanum_fraction": 0.644510829, "num_tokens": 533, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8459424295406088, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.5419410514940881}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_xc_1d_ehwlrg_params *params;\n\n assert(p->params != NULL);\n params = (lda_xc_1d_ehwlrg_params * )(p->params);\n*)\n\n$define xc_dimensions_1d\n\nf := (rs, zeta) -> \\\n (params_a_a1 + params_a_a2*n_total(rs) + params_a_a3*n_total(rs)^2) * n_total(rs)^params_a_alpha:\n", "meta": {"hexsha": "447f9ec01ca271aae4be0945903a4d56d122ad05", "size": 537, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_1d_ehwlrg.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_1d_ehwlrg.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_xc_1d_ehwlrg.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.5714285714, "max_line_length": 98, "alphanum_fraction": 0.6927374302, "num_tokens": 175, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.84594244507642, "lm_q2_score": 0.6406358411176238, "lm_q1q2_score": 0.5419410498386317}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_m05_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_m05_params * )(p->params);\n*)\n\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\n$include \"b97.mpl\"\n\n(* The parallel and perpendicular components of the energy *)\nm05_comp := (rs, z, spin, xs, t) ->\n + lda_stoll_par(f_pw, rs, z, 1)\n * b97_g(params_a_gamma_ss, params_a_css, xs)\n * Fermi_D_corrected(xs, t):\n\nm05_fpar := (rs, z, xs0, xs1, t0, t1) ->\n + m05_comp(rs, z, 1, xs0, t0)\n + m05_comp(rs, -z, -1, xs1, t1):\n\nm05_fperp := (rs, z, xs0, xs1, t0, t1) ->\n + lda_stoll_perp(f_pw, rs, z)\n * b97_g(params_a_gamma_ab, params_a_cab, sqrt(xs0^2 + xs1^2)):\n\nm05_f := (rs, z, xs0, xs1, t0, t1) ->\n + m05_fpar (rs, z, xs0, xs1, t0, t1)\n + m05_fperp(rs, z, xs0, xs1, t0, t1):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n m05_f(rs, z, xs0, xs1, t0, t1):\n\n", "meta": {"hexsha": "bd35885edcd7907cf39348e241f699ff6a3177b4", "size": 1146, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_m05.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_m05.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_m05.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.0454545455, "max_line_length": 68, "alphanum_fraction": 0.6326352531, "num_tokens": 462, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8652240756264638, "lm_q2_score": 0.6261241842048093, "lm_q1q2_score": 0.5417377185059798}} {"text": "# File: RigidMotionsParameterSpaceCommon.mpl \n#\n# Description:\n# This file contains functions used to obtain an arrangement 6 dimensional parameter space of 3D\n# digitized rigid motions.\n# This code has been written for research propose and its aim is to calculate a particular\n# arrangement of quadrics. Therefore, it can or it cannot be useful in study of generic\n# arrangements. The final output are sample points of full dimensional open cells.\n#\n# The code was written in relation with the paper: Kacper Pluta, Guillaume Moroz, Yukiko\n# Kenmochi, Pascal Romon, Quadric arrangement in classifying rigid motions of a 3D digital image,\n# 2016, https://hal.archives-ouvertes.fr/hal-01334257 referred late on as [Quadrics:2016].\n#\n# Author:\n# Kacper Pluta - kacper.pluta@esiee.fr\n# Laboratoire d'Informatique Gaspard-Monge - LIGM, A3SI, France\n# Guillaume Moroz - guillaume.moroz@inria.fr \n# INRIA Nancy, France\n#\n# Date:\n# 11/12/2015 \n#\n# License:\n# Simplified BSD License\n#\n# Copyright (c) 2015, Kacper Pluta, Guillaume Moroz\n# All rights reserved.\n\n# Redistribution and use in source and binary forms, with or without\n# modification, are permitted provided that the following conditions are met:\n# * Redistributions of source code must retain the above copyright\n# notice, this list of conditions and the following disclaimer.\n# * Redistributions in binary form must reproduce the above copyright\n# notice, this list of conditions and the following disclaimer in the\n# documentation and/or other materials provided with the distribution.\n#\n# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n# DISCLAIMED. IN NO EVENT SHALL Kacper Pluta and Guillaume Moroz BE LIABLE FOR ANY\n# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND\n# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n#\n#\n\nRigidMotionsParameterSpaceCommon := module() \n option package;\n uses RigidMotionsMaplePrimesCode;\n local EliminationResultant, RemoveExponants, OneVariableElimination, EliminationGroebner;\n export CayleyTransform, GetNeighborhood, AlgebraicSort, ReduceEvents, AdjustEvents, GenerateEvents,\n SerializeEvents, ReconstructEvents, UnivariatePolynomial;\n\n\n# Procedure: CayleyTransform\n# Compute Cayley transform for a 3x3 skew-symmetric matrix.\n#\n# Parameters:\n# vars - list of variables\n#\n# Output:\n# 3x3 (or 2x2) rotation matrix\n# \n# Links:\n# https://en.wikipedia.org/wiki/Cayley_transform\nCayleyTransform := proc( vars::list )\n local A::Matrix, QLSide::Matrix, QRSide::Matrix, dim:\n dim := nops(vars);\n if dim = 1 then\n A := Matrix( [ [ 0, vars[1] ], [ -vars[1], 0 ] ] ):\n elif dim = 2 then\n A := Matrix( [ [ 0, vars[2]/vars[1] ], [ -vars[2]/vars[1], 0 ] ] );\n elif dim = 3 then\n A := Matrix( [ [ 0, vars[1], vars[2] ], [ -vars[1], 0, vars[3] ], \n [ -vars[2], -vars[3], 0 ] ] ):\n else\n error \"Unsupported dimension! Check 1, 2 or 3\":\n end if:\n dim := upperbound(A)[1];\n QLSide := Matrix( dim, shape = identity ) - A:\n QRSide := LinearAlgebra:-MatrixInverse( Matrix( dim, shape = identity ) + A ):\n return simplify( QLSide . QRSide ):\nend proc:\n\n# Procedure: GetNeighborhood\n# Compute a neighborhood\n#\n# Parameters:\n# nType - size of neighborhood i.e. N1, N2, N3. \n#\n# Output:\n# List of vectors\nGetNeighborhood := proc( nType::string )\n local n6 := [[1, 0, 0], [0, 1, 0], [0, 0, 1], [-1, 0, 0], [0, -1, 0], [0, 0, -1], [0, 0, 0]]:\n local n18 := [[1, 1, 0], [1, 0, 1], [0, 1, 1], [-1, -1, 0], [-1, 0, -1], [0, -1, -1], \n [-1, 1, 0], [-1, 0, 1], [1, -1, 0], [1, 0, -1], [0, -1, 1], [0, 1, -1]]:\n local n26 := [[1, 1, 1], [-1, 1, 1], [1, -1, 1], [1, 1, -1], [-1, -1, 1], [-1, 1, -1], \n [-1, -1, -1], [1, -1, -1]]:\n\n if nType = \"N1\" then\n return n6:\n elif nType = \"N2\" then\n return( [ op( n6 ), op( n18 ) ] ):\n elif nType = \"N3\" then\n return( [ op( n6 ), op( n18 ), op(n26) ] ):\n else \n error \"Not supported type. Try N1, N2, N3.\":\n end if:\nend proc:\n\n\n# Procedure: EliminationGroebner\n# Computes univariate polynomial using Groebner basis and FGb library.\n#\n# Parameters:\n# S - a set of quadrics\n# vars - a list of variables\n#\n# Comments:\n# To use this procedure you need to install Jean-Charles Faug\u00e8re's FGb library\n# --http://www-polsys.lip6.fr/~jcf/FGb/FGb/index.html \n#\n# Output:\n# Univariate polynomial obtained from S.\n#\nEliminationGroebner := proc(S::list, vars::list)\n option cache;\n local univ := op(FGb:-fgb_gbasis_elim(S, 0, vars[2..], vars[1]));\n if univ = NULL then\n univ := 0;\n fi;\n return univ;\nend proc;\n\n# Procedure: EliminationResultant\n# Computes univariate polynomial.\n#\n# Parameters:\n# S - a set of polynomials in at least two variables\n# vars - variables to be eliminated\n#\n# Output:\n# Univariate polynomial obtained from S in the first variable.\nEliminationResultant := proc( S::list, vars::list )\n option cache;\n local p, var, res := S, permm;\n if nops(S) < 2 then\n error \"Wrong size of the input set: %1. Expected size is at least 2.\", S;\n fi;\n if not andmap(type, S, `polynom`) then\n error \"Wrong type of elements. Expected argument is a set of polynomials but received %1.\"; S; \n fi;\n if nops(vars) < 1 then\n error \"Wrong number of indeterminates. It should be at least 2.\";\n fi;\n if nops(vars) = 1 then\n permm := combinat:-permute(res, 2);\n res := [];\n for p in permm do\n res := [op(res), OneVariableElimination(p[1], p[2], vars[1])];\n od;\n return foldl( gcd, op(res) );\n fi;\n\n for var in vars[2..] do\n permm := combinat:-permute(res, 2);\n res := [];\n for p in permm do\n res := [op(res), OneVariableElimination(p[1], p[2], var)];\n od;\n od;\n\n return foldl( gcd, op(res) );\nend proc:\n\n# Procedure: RemoveExponants\n# Removes exponants in an expression\n#\n# Parameters:\n# r - expression, the expression to simplify\n#\n# Output:\n# An arithmetic expression that has the same square free part as r.\nRemoveExponants := proc(r)\n local remove_exponant, sqrr, result;\n remove_exponant := e -> if type(e,`^`) then op(1,e) else e end if;\n result := remove_exponant(r);\n if type(r,`*`) then\n result := map(remove_exponant, result);\n end if;\n return result;\nend proc;\n\nOneVariableElimination := proc( p, q, v)\n local r;\n if degree(p,v)>0 or degree(q,v)>0 then\n r := resultant(p, q, v); \n r := RemoveExponants(r);\n return r;\n elif nops(indets({p,q}))=1 then\n return gcd(p, q);\n else\n return p;\n end if;\nend proc;\n\n\n# Procedure: UnivariatePolynomial\n# Computes univariate polynomial.\n#\n# Parameters:\n# S - a set of quadrics\n# vars - a list of variables\n#\n# Comments:\n# If FGb is installed then fgb_gbasis_elim() is used and EliminationResultant, otherwise.\n# Note that, build-in solutions like Groebner:-UnivariatePolynomial are not used because of\n# potential memory explosion or other problems which make them practically useless.\n#\n# Output:\n# Univariate polynomial obtained from S.\n#\nUnivariatePolynomial := proc(S::list, vars::list)\n local output;\n if type(FGb, package) then\n return EliminationGroebner([op(S)], vars);\n else\n output := EliminationResultant([op(S)], vars);\n if output = 0 then\n return PolynomialIdeals:-UnivariatePolynomial(PolynomialIdeals:-PolynomialIdeal(S),vars[1]);\n fi;\n return output;\n fi;\nend proc;\n\n\n# Procedure: GenerateEvents\n# Generates events from a univariate polynomial (see EventType)\n#\n# Parameters:\n# x::polynom - a univariate polynomial\n# quads:: - a list of quadrics\n#\n# Output:\n# An Array of events generated from a given univariate polynomial.\nGenerateEvents := proc(x::polynom, quads::list)\n uses ArrayTools;\n local events := Array([]), factored, rootsF, sqrFree, rf;\n if nops(indets(x)) = 1 then\n factored := factors(x)[2,..,1];\n for sqrFree in factored do\n rootsF := RootFinding:-Isolate(sqrFree, output='interval');\n for rf in rootsF do\n Append(events, EventType(RealAlgebraicNumber(sqrFree, op(rf)[2][1], op(rf)[2][2]), quads));\n od;\n od;\n fi;\n return events;\nend proc;\n\n\n# Procedure: SerializeEvents\n# Changes (inplace) an Array of events into an Array of strings of unevaluated calls to\n# the constructor of EventType.\n#\n# Parameters:\n# events::Array - an Array of events (see EventType)\n#\n# Output:\n# An Array of strings to unevaluated calls of the constructor of EventType.\nSerializeEvents := proc(events::Array)\n return map[inplace](proc(x) sprintf(\"%a\", x) end proc, events);\nend proc;\n\n\n# Procedure: ReconstructEvents\n# Changes (inplace) an Array of strings of unevaluated calls to the constructor of EventType into\n# the proper objects.\n#\n# Parameters:\n# events::Array - an Array of events (see SerializeEvents)\n#\n# Output:\n# An Array of EventType.\nReconstructEvents := proc(events::Array)\n return map[inplace](proc(x) eval(parse(x)) end proc, events);\nend proc;\n\n\n# Procedure: ReduceEvents\n# Returns an array of events such that they are distinct. Each pair of events which are equal are\n# merged in such a way that a list of quadrics of the second on from a pair is merged with the\n# list of the first event.\n#\n# Parameters:\n# L::Array - an Array of events\n#\n# Output:\n# An Array of EventType.\nReduceEvents := proc(L::Array) \n local R, k, j, last, x; \n R := Array([]); k := 0; last := 1; \n for j from 2 to upperbound(L) do \n if Compare(L[j-1], L[j], _rest) <> 0 then \n k := k+1; \n R(k) := EventType(GetRealAlgebraicNumber(L[last]), \n ListTools:-MakeUnique([seq(op(GetQuadrics(x)) ,x=L[last .. j-1])]));\n last := j\n end if;\n end do;\n if last <> j then\n ArrayTools:-Append(R, EventType(GetRealAlgebraicNumber(L[last]), \n ListTools:-MakeUnique([seq(op(GetQuadrics(x)) ,x=L[last .. ()])])))\n fi;\n return R;\nend proc;\n\n\n# Procedure: AdjustEvents\n# Returns an array of events such that the first event will contains all the quadris and the last\n# event will be duplicated with changed interval of the underlaying real algebraic number.\n#\n# Parameters:\n# L::Array - an Array of events\n#\n# Output:\n# An Array of EventType.\nAdjustEvents := proc(events::Array, quadNum::integer, variables::list)\n local boundTmp, lastEvent;\n # assign all quadrics to the first even\n events[1] := EventType(GetRealAlgebraicNumber(events[1]), [seq(1..quadNum)]);\n # add the last slice twice but shifted to calculate correctly last quadrics\n boundTmp:= GetInterval(GetRealAlgebraicNumber(events[-1]))[2]+1;\n lastEvent := RealAlgebraicNumber(denom(boundTmp)*variables[1]-numer(boundTmp), boundTmp, boundTmp);\n ArrayTools:-Append(events, EventType(lastEvent, GetQuadrics(events[-1])), inplace=true)\nend proc;\n\n\n# Procedure: AlgebraicSort\n# Sorts [if possible in place] RealAlgebraicNumbers or Events. (see types: RealAlgebraicNumber \n# and EventType).\n#\n# Parameters:\n# events - a list or Array of RealAlgebraicNumbers or Events\n#\n# Output:\n# A increasingly sorted list or Array.\nAlgebraicSort :=proc(events)\n # In Maple <2016 there is a bug which causes: stack limit reached if sorting an empty Array\n if upperbound(events) <> 0 then\n return sort['inplace'](events, \n proc( l, r ) \n if Compare( l, r ) = -1 then\n return true:\n else \n return false:\n fi:\n end proc\n );\n fi;\n return events;\nend proc;\n\nend module;\n\n", "meta": {"hexsha": "43765cb22881f46f0b9988cd00b5d0fedf6a5395", "size": 12227, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "RigidMotionsParameterSpaceCommon.mpl", "max_stars_repo_name": "copyme/MapleTools", "max_stars_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "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": "RigidMotionsParameterSpaceCommon.mpl", "max_issues_repo_name": "copyme/MapleTools", "max_issues_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2016-04-14T11:48:04.000Z", "max_issues_repo_issues_event_max_datetime": "2016-05-13T13:48:01.000Z", "max_forks_repo_path": "RigidMotionsParameterSpaceCommon.mpl", "max_forks_repo_name": "copyme/MapleTools", "max_forks_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "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": 33.135501355, "max_line_length": 101, "alphanum_fraction": 0.6552711213, "num_tokens": 3524, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8267117940706734, "lm_q2_score": 0.6548947155710233, "lm_q1q2_score": 0.541409185237124}} {"text": "######################################################################\n\n`is_element/rel` := (A::set,B::set) -> proc(R)\n local AB,a,b;\n\n global reason;\n\n AB := [seq(seq([a,b],b in B),a in A)];\n\n if not type(R,set) then\n reason := [convert(procname,string),\"R is not a set\",R];\n return false;\n fi;\n\n if R minus {op(AB)} <> {} then\n reason := [convert(procname,string),\"R is not a subset of AxB\",R,A,B];\n return false;\n fi;\n\n return true;\nend;\n\n`is_equal/rel` := (A::set,B::set) -> proc(R,S)\n global reason;\n\n if R <> S then\n reason := [convert(procname,string),\"R <> S\",R,S];\n return false;\n fi;\n\n return true;\nend;\n\n`is_leq/rel` := (A::set,B::set) -> proc(R,S)\n global reason;\n\n if R minus S <> {} then\n reason := [convert(procname,string),\"R is not a subset of S\",R,S];\n return false;\n fi;\n\n return true;\nend;\n\n`bot/rel` := (A::set,B::set) -> {};\n`top/rel` := proc(A::set,B::set)\n local a,b;\n return {seq(seq([a,b],b in B),a in A)};\nend:\n\n`is_a_function/rel` := (A::set,B::set) -> proc(R)\n local r,N;\n\n r := `hash/rel`(A,B)(R);\n N := map(a -> nops(r[a]),A) minus {1};\n return evalb(N = {});\nend;\n\n`is_total/rel` := (A::set,B::set) -> (R) -> evalb(R = `top/rel`(A,B));\n\n`op/rel` := (A::set,B::set) -> (R) -> map(ab -> [ab[2],ab[1]],R);\n\n`hash/rel` := (A::set,B::set) -> proc(R)\n local r,a,b,ab;\n \n r := table();\n for a in A do r[a] := {}; od;\n for ab in R do\n a,b := op(ab);\n r[a] := {op(r[a]),b};\n od;\n\n return eval(r);\nend:\n\n`unhash/rel` := (A::set,B::set) -> proc(r)\n local a,b;\n {seq(seq([a,b],b in r[a]),a in A)};\nend;\n\n`id/rel` := proc(A::set)\n local a;\n return {seq([a,a],a in A)};\nend:\n\n`o/rel` := (A::set,B::set,C::set) -> proc(S,R)\n local r,s,sr,a;\n r := `hash/rel`(A,B)(R);\n s := `hash/rel`(B,C)(S);\n sr := table();\n for a in A do sr[a] := map(op,map(b -> s[b],r[a])); od;\n return `unhash/rel`(A,C)(sr);\nend;\n\n`list_elements/rel` := proc(A::set,B::set)\n local AB,a,b;\n AB := {seq(seq([a,b],b in B),a in A)};\n `list_elements/subsets`(AB);\nend:\n\n`count_elements/rel` := (A::set,B::set) -> 2^(nops(A)*nops(B));\n\n`random_element/rel` := (A::set,B::set) -> proc(p_)\n local AB,p,R,r,ab,a,b;\n p := `if`(nargs > 0,p_,0.5);\n r := rand(0..10^6-1);\n AB := {seq(seq([a,b],b in B),a in A)};\n R := NULL;\n for ab in AB do\n if r() < 10^6 * p then R := R,ab; fi;\n od:\n R := {R};\n return R;\nend:\n", "meta": {"hexsha": "18f163c1331d5536d3b47770defb89150873dfc2", "size": 2299, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/rel.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/rel.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/rel.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 19.9913043478, "max_line_length": 72, "alphanum_fraction": 0.5137016094, "num_tokens": 845, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.822189121808099, "lm_q2_score": 0.658417500561683, "lm_q1q2_score": 0.5413437065698937}} {"text": "######################################################################\n# pairs(A) is the set of all pairs (a,b) in A^2 with a <> b\n\n`is_element/pairs` := (A::set) -> proc(ab)\n type(ab,list) and nops(ab) = 2 and\n member(ab[1],A) and member(ab[2],A) and ab[1] <> ab[2];\nend;\n\n`is_equal/pairs` := (A::set) -> (ab,cd) -> evalb(ab = cd):\n\n`is_leq/pairs` := NULL;\n\n`random_element/pairs` := (A::set) -> proc()\n local n,r,i,j;\n n := nops(A);\n\n if n < 2 then return FAIL; fi;\n\n i := rand(1..n)(); \n j := rand(1..n-1)();\n if j >= i then j := j+1; fi;\n\n return [A[i],A[j]];\nend;\n\n`list_elements/pairs` := proc(A::set)\n local n,i,j;\n\n n := nops(A);\n\n [seq(op([seq([A[i],A[j]],j=1..i-1),seq([A[i],A[j]],j=i+1..n)]),i=1..n)];\nend:\n\n`count_elements/pairs` := (A::set) -> nops(A) * (nops(A)-1);\n", "meta": {"hexsha": "0668162161c504074e39401ed422d0e94b80309e", "size": 780, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/pairs.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/pairs.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/pairs.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 22.2857142857, "max_line_length": 73, "alphanum_fraction": 0.4794871795, "num_tokens": 290, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7431680086124811, "lm_q2_score": 0.7279754430043072, "lm_q1q2_score": 0.5410080602962997}} {"text": "(* type: mgga_exc *)\n(* prefix:\n mgga_c_ltapw_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_ltapw_params * )(p->params);\n*)\n\n$define lda_c_pw_params\n$include \"lda_c_pw.mpl\"\n\n(* kinetic energy density to electron density *)\nnt_tau := t -> (t/K_FACTOR_C)^(3*params_a_ltafrac/5):\n\n(* effective density *)\nn_eff_s := (rs, z, t) -> n_spin(rs, z) * nt_tau(t):\nn_eff := (rs, z, ts0, ts1) -> n_eff_s(rs, z, ts0) + n_eff_s(rs, -z, ts1):\n\n(* recompute rs and zeta *)\neff_rs := (rs, z, ts0, ts1) -> r_ws(n_eff(rs, z, ts0, ts1)):\neff_z := (rs, z, ts0, ts1) ->\n (n_eff_s(rs, z, ts0) - n_eff_s(rs, -z, ts1))/n_eff(rs, z, ts0, ts1):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n f_pw(eff_rs(rs, z, ts0, ts1), eff_z(rs, z, ts0, ts1)):\n\n", "meta": {"hexsha": "436109e8ebabbb9d410e3b695c78912116bec654", "size": 751, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_ltapw.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_ltapw.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_ltapw.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 27.8148148148, "max_line_length": 75, "alphanum_fraction": 0.5978695073, "num_tokens": 304, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8902942261220291, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5409990115292334}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n\n$define gga_x_pbe_tca_params\n$include \"gga_x_pbe.mpl\"\n\n$define gga_x_pw91_params\n$include \"gga_x_pw91.mpl\"\n\nmalpha := 1:\nmbeta := 19:\n\nfab := x -> 1/(1 + exp(-malpha*(x - mbeta))):\nf := x -> (1 - fab(x))*f_pbe(x) + fab(x)*f_pw91(x):", "meta": {"hexsha": "ddae7ca056eaa468a17e0e8b79495276128b603f", "size": 499, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_bpccac.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_x_bpccac.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_x_bpccac.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 23.7619047619, "max_line_length": 68, "alphanum_fraction": 0.6613226453, "num_tokens": 177, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127492339909, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.5408770937409673}} {"text": "with(combinat, cartprod): ss := [`$`(0 .. ORDER)]: \ncp := cartprod([ss, ss, ss, ss, ss, ss, ss]):\nret := []:\nwhile not cp[finished] do \n ret := [op(ret), cp[nextvalue]()] \nend do:\nvals := select(proc (x) options operator, arrow; convert(x, `+`) <= ORDER; end proc, ret):\nvalsm1 := vals:\nret := 'ret';\n# read \"../vals.mpl\":\n\nDLIST := [dL, dS, dR, dLS, dLR, dRS, dLRS]:\n\nxition := solve(\n [pLp=zLp + zLSp + zLRp + zLRSp,\n pSp=zSp + zLSp + zRSp + zLRSp,\n pRp=zRp + zLRp + zRSp + zLRSp,\n cLSp=(zLSp + zLRSp) - pLp*pSp,\n cLRp=(zLRp + zLRSp) - pLp*pRp,\n cRSp=(zRSp + zLRSp) - pSp*pRp,\n cLRSp=zLRSp - pLp*cRSp - pSp*cLRp - pRp*cLSp - pLp*pSp*pRp],\n [zLp, zSp, zRp, zLSp, zLRp, zRSp, zLRSp]\n)[1]:\n\n\npL := zL + zLS + zLR + zLRS;\npS := zS + zLS + zRS + zLRS;\npR := zR + zLR + zRS + zLRS;\ncLS := (zLS + zLRS) - pL*pS:\ncLR := (zLR + zLRS) - pL*pR:\ncRS := (zRS + zLRS) - pS*pR:\ncLRS := zLRS - pL*cRS - pS*cLR - pR*cLS - pL*pS*pR:\n\na_S_0 := s * (h + (1 - 2 * h) * pS) / (1 + s * pS * (2 * h + (1 - 2 * h) * pS)):\na_S_S := (1 - 2 * h) * s / (1 + s * pS * (2 * h + (1 - 2 * h) * pS)):\nqS := 1 - pS:\nqL := 1 - pL:\nqR := 1 - pR:\n\nrLRS := rLS_R + rRS_L + rLR_S:\n\n# Deltas\ndelta_pS := a_S_0 * pS * qS:\ndelta_pL := a_S_0 * cLS:\ndelta_pR := a_S_0 * cRS:\n\ng := (r) -> -r + a_S_0 * (1 - r) * (1 - 2 * pS) + a_S_S * r * pS * qS;\n\ndeltat_cLS := g(rLS) * cLS:\ndeltat_cRS := g(rRS) * cRS:\ndeltat_cLR := -rLR * cLR + a_S_0 * (1 - rLR) * cLRS + a_S_S * rLR * cLS * cRS:\ndeltat_cLRS := (-rLRS + a_S_0 * (1 - rLRS) * (1 - 2 * pS) + a_S_S * rLR_S * pS * qS) * cLRS -\n a_S_0 * (rLS_R + rRS_L) * pS * qS * cLR -\n (a_S_0 * (2 - rLS_R - rRS_L) - a_S_S * (1 - 2 * pS) * (rLS_R + rRS_L)) * cLS * cRS:\n\ndelta_cLS := deltat_cLS - a_S_0^2 * pS * qS * cLS:\ndelta_cRS := deltat_cRS - a_S_0^2 * pS * qS * cRS:\ndelta_cLR := deltat_cLR - a_S_0^2 * cLS * cRS:\ndelta_cLRS := deltat_cLRS - \n a_S_0 * (pS * qS * deltat_cLR + cLS * deltat_cRS + cRS * deltat_cLS) +\n 2 * a_S_0^3 * pS * qS * cLS * cRS:\n\nB := eval(xition, [pLp=pL + delta_pL, pSp=pS + delta_pS, pRp=pR + delta_pR, \n cLSp=cLS + delta_cLS, cLRp=cLR + delta_cLR, cRSp=cRS + delta_cRS, \n cLRSp=cLRS + delta_cLRS]\n):\n\nif ARG0 + ARG1 + ARG2 + ARG3 + ARG4 + ARG5 + ARG6 = 0 then\nCodeGeneration:-C(B, optimize=true, coercetypes=false, deducetypes=false, defaulttype=float, output=\"_transition.cii\"):\nend if:\n\nmgff := (p1*exp(t1)+p2*exp(t2)+p3*exp(t3)+p4*exp(t4)+p5*exp(t5)+p6*exp(t6)+p7*exp(t7)+(1-p1-p2-p3-p4-p5-p6-p7))^n:\nmultimgf := proc (i1, i2, i3, i4, i5, i6, i7) options operator, arrow; \n s := i1 + i2 + i3 + i4 + i5 + i6 + i7:\n if s = 0 then 1 \n else \n n^(-s)*simplify(subs(t1=0, t2=0, t3=0, t4=0, t5=0, t6=0, t7=0, \n diff(mgff, `$`(t1, i1), `$`(t2, i2), `$`(t3, i3),\n `$`(t4, i4), `$`(t5, i5), `$`(t6, i6), \n `$`(t7, i7))));\n end if;\nend proc:\n\nmgfsubs := proc (iL, iS, iR, iLS, iLR, iRS, iLRS) options operator, arrow;\n eval(multimgf(iL, iS, iR, iLS, iLR, iRS, iLRS),\n [p1=zLp, p2=zSp, p3=zRp, p4=zLSp, p5=zLRp, p6=zRSp, p7=zLRSp]);\n eval(%, B):\nend proc:\n\ndeltasubs := proc (iL, iS, iR, iLS, iLR, iRS, iLRS)\n ms := mgfsubs(iL, iS, iR, iLS, iLR, iRS, iLRS):\n eval(%, [zL=zL + dL, zS=zS + dS, zR=zR + dR,\n zLS=zLS + dLS, zLR=zLR + dLR, zRS=zRS + dRS,\n zLRS=zLRS + dLRS]):\nend proc:\n\n\nllhs := proc (aL, aS, aR, aLS, aLR, aRS, aLRS)\nrary := []:\nms := deltasubs(aL, aS, aR, aLS, aLR, aRS, aLRS):\nind := 1:\nfor vv in valsm1 do \n print(vv):\n coeftayl(ms, DLIST = [0, 0, 0, 0, 0, 0, 0], vv):\n cg := eval(%, [zL=dtL, zS=dtS, zR=dtR, zLS=dtLS, zLR=dtLR, zRS=dtRS, zLRS=dtLRS]):\n rary := [op(rary), ret[ind] = cg * Edelta_lhs(t - 1, p, vv[1], vv[2], vv[3], vv[4], vv[5], vv[6], vv[7])]:\n ind := ind + 1:\nend do:\nreturn rary:\nend proc:\n\nrrhs := proc(aL, aS, aR, aLS, aLR, aRS, aLRS)\n local e, c, xx; \n xx := expand(\n (dtL + dL)^aL *\n (dtS + dS)^aS *\n (dtR + dR)^aR *\n (dtLS + dLS)^aLS *\n (dtLR + dLR)^aLR *\n (dtRS + dRS)^aRS *\n (dtLRS + dLRS)^aLRS\n - dL^aL * dS^aS * dR^aR * dLS^aLS * dLR^aLR * dRS^aRS * dLRS^aLRS);\n c := coeffs(xx, DLIST, 'e'); \n convert(zip(proc (ee, cc) \n options operator, arrow; \n degs := map((term) -> degree(ee, term), DLIST):\n Edelta(t, p, degs[1], degs[2], degs[3], degs[4], degs[5], degs[6], degs[7])*cc;\n end proc, [e], [c]), `+`);\nend proc:\n\naL := ARG0;\naS := ARG1;\naR := ARG2;\naLS := ARG3;\naLR := ARG4;\naRS := ARG5;\naLRS := ARG6;\nprint(aL, aS, aR, aLS, aLR, aRS, aLRS);\nll := llhs(aL, aS, aR, aLS, aLR, aRS, aLRS):\noutl := cat(\"_lhs_\", aL, aS, aR, aLS, aLR, aRS, aLRS, \".cii\"):\nCodeGeneration:-C(ll, optimize=true, coercetypes=false, deducetypes=false, defaulttype=float, output=outl):\n\nrr := rrhs(aL, aS, aR, aLS, aLR, aRS, aLRS):\noutl := cat(\"_rhs_\", aL, aS, aR, aLS, aLR, aRS, aLRS, \".cii\"):\nCodeGeneration:-C([ret = rr], optimize=true, coercetypes=false, deducetypes=false, defaulttype=float, output=outl):\n\nmgfsubs(aL, aS, aR, aLS, aLR, aRS, aLRS):\nmm := eval(%, [zL=dtL, zS=dtS, zR=dtR, zLS=dtLS, zLR=dtLR, zRS=dtRS, zLRS=dtLRS]):\noutl := cat(\"_mgf_\", aL, aS, aR, aLS, aLR, aRS, aLRS, \".cii\"):\nCodeGeneration:-C([ret = mm], optimize=true, coercetypes=false, deducetypes=false, defaulttype=float, output=outl):\n", "meta": {"hexsha": "501a1dd7d0555d1dfe2903a8eaf1d250910a2a31", "size": 5376, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "threelocus/scripts/3l.mpl", "max_stars_repo_name": "terhorst/EandR-timeseries", "max_stars_repo_head_hexsha": "42391f902b867e4653d3d120e0be53c4251213f5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2015-08-21T21:52:47.000Z", "max_stars_repo_stars_event_max_datetime": "2015-08-21T21:52:47.000Z", "max_issues_repo_path": "threelocus/scripts/3l.mpl", "max_issues_repo_name": "terhorst/EandR-timeseries", "max_issues_repo_head_hexsha": "42391f902b867e4653d3d120e0be53c4251213f5", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2015-05-13T17:56:22.000Z", "max_issues_repo_issues_event_max_datetime": "2019-03-26T15:15:25.000Z", "max_forks_repo_path": "threelocus/scripts/3l.mpl", "max_forks_repo_name": "terhorst/EandR-timeseries", "max_forks_repo_head_hexsha": "42391f902b867e4653d3d120e0be53c4251213f5", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2016-08-19T06:14:37.000Z", "max_forks_repo_forks_event_max_datetime": "2016-08-19T06:14:37.000Z", "avg_line_length": 35.6026490066, "max_line_length": 119, "alphanum_fraction": 0.5342261905, "num_tokens": 2523, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8688267762381844, "lm_q2_score": 0.6224593452091672, "lm_q1q2_score": 0.540809346237412}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n\n(* This was checked against code kindly provided by Emil Proynov *)\n\n(* Equations (24) *)\na_24_i := [-113.693369789727190, 24.00502151278711440, 49.34131295839670750,\n -23.8242372168379302, 0.944080741695104794, 0.000293039144178338]:\nb_24_i := [-109.74263493216910, 16.2663129444242415, 54.4034331373908366,\n -25.154009904187990, 1.0]:\n\nf_r := rs -> add(a_24_i[i]*rs^(i-1), i=1..6)/add(b_24_i[i]*rs^(i-1), i=1..5):\n\n(* Equations (25) *)\nc_25_i := [-0.32481568604919886, 1.180131465463191050, -1.42693041498421640,\n 0.580344063812247980, -0.01099122367291440]:\nd_25_i := [-0.57786103193239430, 2.09708505883490736, -2.52188183586948180, 1.0]:\n\nf_s := z -> add(c_25_i[i]*z^(i-1), i=1..5)/add(d_25_i[i]*z^(i-1), i=1..4):\n\n(* Equation (23) *)\n(* The factor 1.28 is absent from the paper, but it is in the original code. See erratum *)\nss := (rs, z) -> f_r(rs)*f_s(z)*1.28:\n\n(* Equation (22) *)\nalpha_z := (rs, z) -> 2/(opz_pow_n(z,ss(rs, z)) + opz_pow_n(-z,ss(rs, z))):\n\n(* Equation (21) *)\neta6 := 0.41081146652128:\neta7 := 0.599343256903515:\neta8 := 1.70939476802168:\neta9 := 0.077123208419481:\neta10 := 0.46958449007619:\n\nalpha_n := rs ->\n + eta6\n + eta7*exp( -eta8*rs^(1/3))*rs^(2/3)\n + eta9*exp(-eta10*rs^(1/3))*rs^(1/3):\n\n(* Equation (20) *)\nalpha_eff := (rs, z) -> alpha_n(rs)*alpha_z(rs, z):\n\n(* Equation (19) *)\neta1 := 0.538074483500437:\neta2 := -2.226094990985190:\neta3 := 0.837303782322808:\neta4 := 2.619709858963178:\neta5 := 1.036657594643520:\n\nbeta_eff := rs ->\n + eta1\n + eta2*exp(-eta3*rs^(1/3))*rs^(1/4)\n + eta4*exp(-eta5*rs^(1/3))*rs^(1/3):\n\n(* Equation (15), see erratum *)\nax := (3*Pi^2)^(1/3):\nk_fs := (rs, z) -> ax*RS_FACTOR/rs * opz_pow_n(z,1/3):\n\n(* Equation (17) *)\nk_uu := (rs, z) -> alpha_eff(rs, z)*k_fs(rs, z):\nk_dd := (rs, z) -> alpha_eff(rs, -z)*k_fs(rs, -z):\n\n(* Equation (18) *)\nk_ud := (rs, z) -> beta_eff(rs)\n * 2*k_fs(rs, z)*k_fs(rs, -z)/(k_fs(rs, z) + k_fs(rs, -z)):\n\n(* Table III *)\na1 := 0.1846304394851914:\na2 := 5.93965654951900799:\na3 := 2.36958012866641818:\na4 := .51188865525958770e-1:\na5 := .9576892532004281e-1:\na6 := .283592616144882565e-1:\na7 := .226274169979695208e-1:\na8 := .531736155271654809e-2:\na9 := .1915378506400854:\na10 := .1473137771194929:\na11 := .1528250938350897:\na12 := 1.01508307543839117:\na13 := .7641254691754473e-1:\na14 := .898537460263473410:\na15 := .1795667349750801e-1:\na16 := .3461820740347690e-1:\na17 := .3591334699501599e-1:\na18 := .222017353476155799:\n\nc1 := 132.479090287794355:\nc2 := 32.4014708516771368:\nc3 := 22.5664453162503806:\nc4 := 11.2832226581251903:\nc5 := .401060523940960082:\nc6 := evalf(0.32):\nc7 := .751988482389300153e-1:\nc8 := 116.935042647480910:\nc9 := 29.6240023046901289:\nc10 := .482257181994472723:\nc11 := .246903981179097557:\nc12 := evalf(1/2):\nc13 := .410709696778185459:\nc14 := .105323524476768857:\nc15 := 14.5650971711659670:\nc16 := .781250000000000000:\nc17 := .623347313127238558:\nc18 := .146484374999999999:\nc19 := 111.811548105797788:\nc20 := .160041105570901272:\nc21 := evalf(.78125):\nc22 := .32086695060795739:\nc23 := 13.2844495072998436:\nc24 := .268418671319107341:\nc25 := .471060597934991862:\nc26 := evalf(1/4):\nc27 := .252882919616989509:\nc28 := .720485831127149779e-1:\nc29 := 42.6490544891031073:\n\n(* Definitions in the beginning of the appendix *)\nD_1 := k -> a6*k^2 + a7*k + a8:\nD_2 := k -> a1*k^2 + a10*k + a16:\nD_3 := k -> a5*k^2 + a13*k + a15:\nD_4 := k -> a9*k^2 + a11*k + a17:\nD_5 := k -> c5*k^2 + c6*k + c7:\nD_6 := k -> c12*k^2 + c13*k + c14:\nD_7 := k -> c16*k^2 + c17*k + c18:\nD_8 := k -> sqrt(c26*k^2 + c27*k + c28):\n\n(* Equation (10) *)\nQ_1ud := k -> 1/D_1(k) * (\n - arctan(a2*k + a3)*D_2(k)/k - log(D_1(k))*D_3(k)/k\n + log(k)*D_4(k)/k - a4*k + a12 + a14/k + a18/k^2\n):\n\n(* Equation (11) *)\nQ_2ud := k ->\n - c1/k - c2/k^2 - c3*log(k)/k + c4*log(D_5(k))/k\n + c8*arctan(a2*k + a3)/k + c9*log(k + c10)/k - c11/k*log(D_6(k)):\n\n(* Equation (12) *)\nQ_3ud := k ->\n + c19*arctan(c20/(c21*k + c22))/k - c23*arctanh((c24 + c25*k)/D_8(k))/k\n - c15*log(D_7(k))/k - c29*D_8(k)/k^2:\n\n(* Equation (9) *)\nec_opp := (rs, z) ->\n (1 - z^2)/4*(Q_1ud(k_ud(rs, z)) + Q_2ud(k_ud(rs, z)) + Q_3ud(k_ud(rs, z))):\n\n(* Equation (13) *)\nec_par := (rs, z) ->\n + opz_pow_n( z,2)/8*(Q_1ud(k_uu(rs, z)) + Q_2ud(k_uu(rs, z)) + Q_3ud(k_uu(rs, z)))\n + opz_pow_n(-z,2)/8*(Q_1ud(k_dd(rs, z)) + Q_2ud(k_dd(rs, z)) + Q_3ud(k_dd(rs, z))):\n\nf := (rs, z) -> n_total(rs)*(ec_opp(rs, z) + ec_par(rs, z)):\n", "meta": {"hexsha": "1264b143ae512464fe2343824cadce78c80e2869", "size": 4712, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pk09.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pk09.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_pk09.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 29.45, "max_line_length": 91, "alphanum_fraction": 0.6156621392, "num_tokens": 2109, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9343951552333004, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.5396088713993081}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\n$define gga_x_b86_mgc_params\n$include \"gga_x_b86.mpl\"\n\ncab := 0.63:\ncss := 0.96:\n\n(* Equation 50, same-spin correlation *)\nb88_css := (rs, z, xs, ts) ->\n - 0.01 * (1 + z)^(8/3) * 2^(-8/3) * n_total(rs)^(5/3) * (2*ts - xs^2/4)\n * b88_zss(css, b86_f, rs, z, xs)^4 * (\n 1 - 2*log(1 + b88_zss(css, b86_f, rs, z, xs)/2)\n / b88_zss(css, b86_f, rs, z, xs)\n ):\n\n(* Same-spin correlation overall *)\nb88_par := (rs, z, xs0, xs1, ts0, ts1) ->\n + my_piecewise3(screen_dens(rs, z), 0, b88_css(rs, z_thr( z), xs0, ts0))\n + my_piecewise3(screen_dens(rs, -z), 0, b88_css(rs, z_thr(-z), xs1, ts1)):\n\n(* Equation 49, opposite-spin correlation *)\nb88_cab := (rs, z, xs0, xs1) ->\n - 0.8 * (1 - z^2)/4 * n_total(rs)\n * b88_zab(cab, b86_f, rs, z, xs0, xs1) * (\n b88_zab(cab, b86_f, rs, z, xs0, xs1) - log(1 + b88_zab(cab, b86_f, rs, z, xs0, xs1))\n ):\n\n(* Whole functional *)\nb88_c_f := (rs, z, xs0, xs1, ts0, ts1) ->\n + b88_cab(rs, z, xs0, xs1)\n + b88_par(rs, z, xs0, xs1, ts0, ts1):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n b88_c_f(rs, z, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "234356720fa263cecc108fe7466c15c271c1718c", "size": 1338, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b88.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b88.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_b88.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 30.4090909091, "max_line_length": 90, "alphanum_fraction": 0.5859491779, "num_tokens": 583, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8856314828740729, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5381656341870634}} {"text": "######################################################################\n\n`is_element/cactus_planar_trees` := (A::set) -> proc(Js)\n global reason;\n local tag,J,s,sss,B,C,E,i0,i1,i2,e0,e1,e2,m,j,a;\n\n tag := \"is_element/cactus_planar_trees\";\n\n if A = {} then\n reason := [tag,\"A is empty\"];\n return false;\n fi;\n\n if not(type(Js,list) and nops(Js) = 2) then\n reason := [tag,\"Js is not a list of length 2\",Js];\n return false;\n fi;\n\n J,s := op(Js);\n\n if not(`is_element/cactus_trees`(A)(J)) then\n reason := [tag,\"J is not a pre cactus tree\",J,reason];\n fi;\n \n E := {seq(seq([a,j],a in j),j in J)};\n\n if not `is_element/cycord`(E)(s) then\n reason := [tag,\"s is not a cyclic ordering of E\",s,E];\n return false;\n fi;\n\n m := nops(s);\n sss := map(op,[s,s,s]);\n for i0 from 1 to m do\n e0 := s[i0];\n i1 := i0+1;\n while sss[i1][1] <> e0[1] do i1 := i1+1; od;\n e1 := sss[i1];\n i2 := i1+1;\n while sss[i2][2] <> e1[2] do i2 := i2+1; od;\n if sss[i2] <> e0 then\n reason := [tag,\"bad permutation structure\",s,i0,i1,i2];\n fi;\n od:\n return true;\nend:\n\n`is_equal/cactus_planar_trees` := (A::set) -> proc(Js0,Js1)\n local J0,J1,s0,s1,s2,n,i;\n\n J0,s0 := op(Js0);\n J1,s1 := op(Js1);\n\n if J0 <> J1 then return false; fi;\n if nops(s0) <> nops(s1) then return false; fi;\n\n n := nops(s0);\n if n = 0 then return true; fi;\n \n i := 1;\n while i <= n and s1[i] <> s0[1] do i := i+1; od;\n\n if i > n then return false; fi;\n s2 := [op(i..-1,s1),op(1..(i-1),s1)];\n\n return evalb (s0 = s2);\nend:\n\n######################################################################\n\n# There is a good partial order on this set, but we have not yet\n# written code for it.\n\n`is_leq/cactus_planar_trees` := NULL:\n\n######################################################################\n\n`glue_cycles/cactus_planar_trees` := (A::set) -> (J) -> proc(sA,sJ)\n local fA,fJ,a,j,m,n,i,u,v,s;\n\n fA := table():\n fJ := table():\n for a in A do\n m := nops(sA[a]);\n for i from 1 to m do\n fA[[a,sA[a][i]]] := [a,sA[a][`if`(i (J) -> proc(s)\n local sA,sJ,a,j;\n \n sA := table():\n sJ := table():\n for a in A do\n sA[a] := map(e -> e[2],select(e -> e[1] = a,s));\n od:\n for j in J do\n sJ[j] := map(e -> e[1],select(e -> e[2] = j,s));\n od:\n\n return [eval(sA),eval(sJ)];\nend:\n\n######################################################################\n\n`list_elements/cactus_planar_trees` := proc(A::set)\n local L,M,J,JJ,a,j,SA,SJ,sA,sJ,V,W,u,v,w;\n\n if nops(A) = 0 then\n return [];\n elif nops(A) = 1 then\n return [[{},[]]];\n fi;\n \n L := `list_elements/cactus_trees`(A);\n M := NULL;\n for J in L do\n JJ := table():\n for a in A do JJ[a] := select(j -> member(a,j),J); od:\n SA := [[]]:\n for a in A do\n V := `list_elements/cycord`(JJ[a]);\n SA := [seq(seq([op(u),a = v],u in SA),v in V)];\n od:\n SA := map(table,SA);\n SJ := [[]]:\n for j in J do\n W := `list_elements/cycord`(j);\n SJ := [seq(seq([op(u),j = w],u in SJ),w in W)];\n od:\n SJ := map(table,SJ);\n M := M,seq(seq([J,`glue_cycles/cactus_planar_trees`(A)(J)(sA,sJ)],sJ in SJ),sA in SA);\n od:\n return [M];\nend:\n\n######################################################################\n\n`count_elements/cactus_planar_trees` := NULL:\n\n######################################################################\n\n`random_element/cactus_planar_trees` := (A::set) -> proc()\n local J,sA,sJ,JJ,a,j,s;\n\n if nops(A) = 0 then\n return FAIL;\n elif nops(A) = 1 then\n return [{},[]];\n fi;\n \n J := `random_element/cactus_trees`(A)();\n sA := table();\n sJ := table();\n for a in A do\n JJ[a] := select(j -> member(a,j),J);\n sA[a] := `random_element/cycord`(JJ[a])();\n od;\n for j in J do\n sJ[j] := `random_element/cycord`(j)();\n od:\n s := `glue_cycles/cactus_planar_trees`(A)(J)(sA,sJ);\n return [J,s];\nend:\n", "meta": {"hexsha": "90b17640c12e143b98b5dfea06d71906534aa4ff", "size": 4043, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/cacti/cactus_planar_trees.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/cacti/cactus_planar_trees.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/cacti/cactus_planar_trees.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 21.972826087, "max_line_length": 88, "alphanum_fraction": 0.492703438, "num_tokens": 1442, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581000631542, "lm_q2_score": 0.6757645944891558, "lm_q1q2_score": 0.5376775733411896}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(x5(t), t) = k5*x6(t) + k4*x6(t) - k6*x5(t)*x3(t),\ndiff(x6(t), t) = -k5*x6(t) - k4*x6(t) + k6*x5(t)*x3(t),\ndiff(x4(t), t) = -k3*x4(t) - k2*x4(t) + k1*x1(t)*x2(t),\ndiff(x2(t), t) = k3*x4(t) + k2*x4(t) + k1*x1(t)*x2(t),\ndiff(x1(t), t) = k4*x6(t) + k2*x4(t) - k1*x1(t)*x2(t),\ndiff(x3(t), t) = k5*x6(t) + k3*x4(t) - k6*x5(t)*x3(t),\ny1(t) = x3(t),\ny2(t) = x2(t)\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "f09aad1757f76df75ff88d7954efa01a9ba33168", "size": 472, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/Chemical-reaction-network.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/Chemical-reaction-network.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/Chemical-reaction-network.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 36.3076923077, "max_line_length": 64, "alphanum_fraction": 0.5275423729, "num_tokens": 241, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9124361676202372, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.5373237416310134}} {"text": "######################################################################\n\n# General framework for geometric realisations of finite posets.\n\n`is_element/realisation/generic` :=\n (poset_name,el_test,leq_test) ->\nproc(x)\n local pn,C,t,u,i,j,m,a,b,c;\n global reason;\n\n pn := cat(\"is_element/realisation/\",poset_name);\n \n if not type(x,table) then\n reason := [pn,\"x is not a table\"];\n return false;\n fi;\n\n if map(nops,{indices(x)}) <> {1} then\n reason := [pn,\"x is not a unidimensional table\"];\n return false;\n fi;\n \n C := map(op,[indices(x)]);\n t := 0;\n for c in C do\n if not(el_test(c)) then\n reason := [pn,\"index c is not in the poset\",c];\n return false;\n fi;\n \n u := x[c];\n if not(`is_element/RR`(u) and u >= 0) then\n reason := [pn,\"x[c] is not in R_+\",c,x[c]];\n return false;\n fi;\n t := t+u;\n od;\n\n if t <> 1 then\n reason := [pn,\"sum of coordinates is not equal to 1\",t];\n return false;\n fi;\n\n m := nops(C);\n for i from 1 to m-1 do\n for j from i+1 to m do\n a := leq_test(C[i],C[j]);\n b := leq_test(C[j],C[i]);\n if not(a) and not(b) then\n reason := [pn,\"incomparable indices\",C[i],C[j]];\n return false;\n fi;\n if a and b then\n reason := [pn,\"equivalent but unequal indices\",C[i],C[j]];\n return false;\n fi;\n od;\n od;\n\n return true;\nend;\n\n`is_equal/realisation/generic` := \n (poset_name,eq_test) ->\nproc(x,y)\n local pn,C,D,t,u,i,j,m,a,b,c,d,dd;\n global reason;\n\n pn := cat(\"is_element/realisation/\",poset_name);\n\n C := map(op,[indices(x)]);\n C := select(c -> x[c] > 0,C);\n\n D := map(op,[indices(y)]);\n D := select(d -> y[d] > 0,D);\n\n if nops(C) <> nops(D) then\n reason := [pn,\"support sizes are different\",C,D];\n return false;\n fi;\n \n for c in C do\n dd := select(d -> eq_test(c,d),D);\n if nops(dd) = 0 then\n reason := [pn,\"index c in x unmatched\",c];\n return false;\n fi;\n if nops(dd) > 1 then\n reason := [pn,\"index c in x multiply matched\",c,dd];\n return false;\n fi;\n d := dd[1];\n if x[c] <> y[d] then\n reason := [pn,\"x[c] <> y[c]\",c,x[c],y[c]];\n return false;\n fi;\n od;\n\n return true;\nend;\n\n", "meta": {"hexsha": "124bb23c0502c626fc1720a705e8fbe7b4c2b084", "size": 2055, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/realisation.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/realisation.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/realisation.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 20.1470588235, "max_line_length": 70, "alphanum_fraction": 0.5581508516, "num_tokens": 677, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7931059511841119, "lm_q2_score": 0.6757645944891559, "lm_q1q2_score": 0.5359529214888676}} {"text": "# Collection of small procs to works with CRN\n# No documentation provided, they are self explanatory.\n\nwith(LinearAlgebra);\nwith(ListTools);\nwith(ArrayTools);\n\n## Suit of useful procs.\nequfy := proc(u)\nlocal i, v;\n v := copy(u);\n for i in seq(1..Size(v,1))\n do v[i] := v[i] = 0;\n end do;\n return v;\nend proc:\n\n\n## Angelica\nSignCoeffs := proc(p, var)\n return ListTools[MakeUnique](map(signum, [coeffs(collect(p, convert(var,set), distributed), var)]));\nend proc:\n\n## Angelica\nPolyToVector := proc(p, var)\nlocal i, j, thecoeffs, terms;\n thecoeffs := [coeffs(collect(p, var, distributed), var, 'terms')];\n return [seq([thecoeffs[j], seq(degree(terms[j], var[i]), i = 1 .. numelems(var))], j = 1 .. numelems([terms]))];\nend proc:\n\nSetFirstToOne := proc(l::list)::list;\nlocal i, t;\n t := Array(1 .. nops(l));\n for i to nops(l) do\n t[i] := l[i];\n t[i][1] := 1;\n end do;\n return convert(t, list);\nend proc:\n\nSearchAllPredicate := proc(f, L)\nlocal i, e, index;\n i := 0;\n index := Vector[row]();\n for e in L do\n i := i + 1;\n if f(e) then\n index := ;\n end if;\n end do;\n return index;\nend proc:\n\nPotentiallyNegCoeffs := proc(poly, parameters)\nlocal signcffs, index, negcffs, negexps;\n # polyvec := PolToVector(poly, vars);\n signcffs := map(X -> SignCoeffs(X, parameters), [seq(poly[i][1], i=1..nops(poly))]);\n print(signcffs);\n index := SearchAllPredicate(X -> (-1) in X, signcffs);\n negcffs := [seq(factor(poly[i][1]), i in index)];\n negexps := [seq(poly[i][2..], i in index)];\n print(Vector[column](negcffs));\n return (negcffs, negexps, index);\nend proc:\n\nkrelations := proc(poly, ks)\nlocal lc, facts, krel, fact;\n facts := factors(poly);\n krel := 1;\n for fact in facts[2] do\n if type(fact[2], odd) and (-1) in SignCoeffs(fact[1], {op(ks)}) then\n krel := krel*fact[1];\n end if;\n end do;\n return facts[1]*krel;\nend proc:\n\nSearchingMultistationarity := proc(sys, DJ, depenvars, xs, ks)\nlocal param, freevars, DJparam, polyA, vecpolyA, negcffA, negexpA, negA, krels;\n param := solve(convert(equfy(sys), set), convert(depenvars, set));\n freevars := [op(convert(xs, set) minus convert(depenvars, set))];\n DJparam := subs(param, DJ);\n polyA := numer(DJparam);\n print(\"Denominator of DJparam:(check that its sign just depends on the numerator)\");\n print(denom(DJparam));\n vecpolyA := PolyToVector(polyA, freevars);\n negcffA, negexpA, negA := PotentiallyNegCoeffs(vecpolyA, convert(ks, set));\n krels := map(X -> krelations(X, ks), negcffA);\n return (krels, negcffA, negexpA, negA, collect(polyA, freevars, 'distributed', factor), vecpolyA, param);\nend proc:\n\n## Angelica, Elisenda\nStabilityMatrix := proc(M::Matrix)\nlocal p, i, j, d, pol, m, k;\nglobal H;\n d := LinearAlgebra[Dimension](M)[1] - LinearAlgebra[Rank](M);\n p := simplify(LinearAlgebra[CharacteristicPolynomial](M, y)/y^d);\n H := HurwitzDet(degree(p, y));\n m := numelems(H);\n for i to m do H[i] := subs(seq(a[k] = coeff(p, y, k), k = 0 .. degree(p, y)), H[i]);\n end do;\n print(m*'expressions*will*be*studied');\n for j to m - 1 do print(['Hurwitz*determinant'*'H'[j], SignCoeffs(numer(H[j]), indets(numer(H[j]))), SignCoeffs(denom(H[j]), indets(denom(H[j])))]);\n end do;\n print([\"Lowest degree term\", SignCoeffs(numer(H[m]), indets(numer(H[m]))), SignCoeffs(denom(H[m]), indets(denom(H[m])))]);\nend proc:\n\n## Angelica, Elisenda\nHurwitzDet := proc(n::integer)::list;\nlocal s, t, H, M, i, j, k;\n M := Matrix(n);\n for i to n do\n for j to n do\n if (n - 2*i + j) in [seq(t, t = 0 .. n)] then M[i, j] := a[n - 2*i + j];\n end if;\n end do;\n end do;\n H := [];\n for i to n - 1 do H := [op(H), factor(LinearAlgebra[Determinant](LinearAlgebra[SubMatrix](M, [seq(k, k = 1 .. i)], [seq(k, k = 1 .. i)])))];\n end do;\n H := [op(H), a[0]];\n return H;\nend proc:\n\n# splitkrel := proc(krel, ks)\n# local poskrel, negkrel, terms, coefflist, i;\n# poskrel := 0;\n# negkrel := 0;\n# coefflist := coeffs(collect(krel, ks, distributed), ks, 'terms');\n# for i from 1 to numelems(coefflist) do\n# if coefflist[i] < 0 then\n# negkrel := negkrel - coefflist[i]*terms[i];\n# else\n# poskrel := poskrel + coefflist[i]*terms[i];\n# end if;\n# end do;\n# return [factor(negkrel), factor(poskrel)]\n# end proc:\n\nsplitkrel := proc(krel, ks)\nlocal poskrel, negkrel, terms, coefflist, ct;\n poskrel := 0;\n negkrel := 0;\n coefflist := coeffs(collect(krel, ks, distributed), ks, 'terms');\n for ct in zip(`[]`, [coefflist], [terms]) do\n if ct[1] < 0 then\n negkrel := negkrel - ct[1]*ct[2];\n else\n poskrel := poskrel + ct[1]*ct[2];\n end if;\n end do;\n return [factor(negkrel), factor(poskrel)]\nend proc:\n\nnicekrelstoLaTeX := proc(krel, ks)\nlocal skrel;\n skrel := splitkrel(krel, ks);\n return latex(skrel[2] pw91_f(xs):\n", "meta": {"hexsha": "cc410a00969188e515cf1b35bff1ba8863c77833", "size": 458, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pw91.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pw91.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pw91.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 24.1052631579, "max_line_length": 68, "alphanum_fraction": 0.6986899563, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920116079209, "lm_q2_score": 0.6688802669716107, "lm_q1q2_score": 0.5355670864863422}} {"text": "`is_element/EP/Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(x)\n global reason;\n local TT1,C,P,Q,T;\n\n TT1 := `big_sets/trees`(TT);\n if not is_table_on(TT1)(x) then\n reason := [convert(procname,string),\"x is not a table on TT1\",x,TT1];\n return false;\n fi;\n\n C := children_map(TT);\n for T in TT1 do\n Q := C[T];\n P := select(U -> nops(U) > 1,Q);\n if not `is_element/D/Fbar`(N)(P,Q)(x[T]) then\n reason := [convert(procname,string),\"x[T] is not in D/Fbar(N)(P,Q)\",x[T],P,Q,reason];\n return false;\n fi;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`is_equal/EP/Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(x,y)\n local TT1,C,P,Q,T,U;\n\n TT1 := `big_sets/trees`(TT);\n\n C := children_map(TT);\n for T in TT1 do\n Q := C[T];\n P := select(U -> nops(U) > 1,Q);\n if not `is_equal/E/Fbar`(N)(P,Q)(x[T],y[T]) then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`theta/EP/tree_Fbar_alt` := (N::posint) -> (A::set) -> (TT) -> proc(x)\n local TT1,C,P,Q,T,U,y;\n\n TT1 := `big_sets/trees`(TT);\n\n y := table();\n C := children_map(TT);\n for T in TT1 do\n Q := C[T];\n P := select(U -> nops(U) > 1,Q);\n y[T] := `theta/E/Fbar`(N)(P,Q)(x[T],y[T]);\n od;\n\n return eval(y);\nend:\n\n######################################################################\n\n`phi/EP/tree_Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(tpqx)\n local s,t,p,q,x,y,z,t0,x0,C,P,TT1,UU,VV,T,U,V,u,y0,n0,r;\n t := table();\n p := table();\n q := table();\n x := table();\n\n C := children_map(TT);\n P := parent_map(TT);\n TT1 := `big_sets/trees`(TT);\n\n for T in TT1 do \n t0[T],p[T],q[T],x0[T] := op(tpqx[T]);\n for U in C[T] do\n x[U] := x0[T][U];\n if nops(U) > 1 then t[U] := t0[T][U]; fi;\n od;\n od; \n\n s := table();\n\n for T in TT1 do\n UU := select(U -> (U minus T = {}),TT1);\n for U in UU do\n VV := select(V -> (U minus V = {}),UU);\n VV := sort([op(VV)],(V1,V2) -> evalb(nops(V1) < nops(V2)));\n r := nops(VV) - 1;\n s[T,U] := q[U] * mul(p[VV[i]],i=2..r+1) * mul(t[V[i]],i=1..r); \n od;\n od;\n\n y := table();\n for T in TT do\n y[T] := table();\n for u in A do y[T][u] := 0; od;\n for U in C[T] do\n for u in U do\n y[T][u] := x[T][U];\n od;\n od;\n y0 := `sum/vector_function`(N)(T)(y[T]) /~ nops(T);\n for u in T do y[T][u] := y[T][u] -~ y0; od;\n n0 := `norm/vector_functions`(y[T]);\n for u in T do y[T][u] := y[T][u] /~ n0; od;\n od;\n\n z := table();\n for T in TT1 do\n z[T] := table();\n for u in T do z[T][u] := [0$N]; od:\n\n UU := select(U -> (U minus T = {}),TT1);\n for U in UU do\n for u in U do\n z[T][u] := z[T][u] +~ s[T,U] *~ y[U][u];\n od;\n od;\n od;\n\n return eval(z);\nend:\n", "meta": {"hexsha": "4fe6ea61567432bd33fc3b3aecb74f9fafb0e5ba", "size": 2688, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/scratch/EP.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/scratch/EP.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/scratch/EP.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 21.6774193548, "max_line_length": 88, "alphanum_fraction": 0.4631696429, "num_tokens": 1018, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920116079209, "lm_q2_score": 0.6688802669716106, "lm_q1q2_score": 0.5355670864863421}} {"text": "lprint(\"ConRec(P,Q,n,k,x,t,Ls,shift,Pindex,Qindex), ConRecq(P,Q,n,k,x,t,Ls,shift,Pindex,Qindex,q)\");\r\n\r\n## Compute the recurrence relations of the connection coefficients\r\n## Input:\r\n## P,Q: two hypergeometric terms in k, degree index by n,\r\n## variable in x=x(t)\r\n##\r\n## shift: belonds to {`shiftP`,`shiftQ`},\r\n## recurrence relation involving shifts of the index of P or Q.\r\n##\t \r\n## Pindex, Qindex: the indices of P and Q\r\n##\r\n## Output:\r\n## ls: list of the coefficients of the recurrence relations\r\n## if length is 3, then\r\n## ls[1]c[m+1,n]+ls[2]c[m,n]+ls[3]c[m-1,n] = 0.\r\n## if length is 5, then\r\n## ls[1]c[m+2,n]+ls[2]c[m+1,n]+ls[3]c[m,n]+ls[4]c[m-1,n]+ls[5]c[m-2,n]=0.\r\n##\r\n## Example\r\n## P:=poch([la,2 la],n)/2^n*hyperterm([-n,n+2 la],[la+1/2],(1-s*x)/2,k);\r\n## Q:=2^(-n)*hyperterm([-n,n],[1/2],(1-x)/2,k);\r\n## L:=proc(f,x) diff(f,x); end proc:\r\n## ConRec(P,Q,n,k,x,x,L,`shiftP`,n,m); \r\n\r\nConRec:=proc(P,Q,n,k,x,t,Ls,shift,varm,varn)\r\nlocal L,Lp,lsp,lsq,lspp,lsqp,lsps,lsqs,re;\r\n\r\n ## Ls is either an operator L,\r\n ## or it is the list of two operators [L, Lp]\r\n \r\n if type(Ls,list) then\r\n L:=Ls[1]; Lp:=Ls[2];\r\n else\r\n L:=Ls; Lp:=0;\r\n fi;\r\n\r\n ## the 3-term recurrences of P and Q\r\n lsp:=tr_coe(P,x,n,k,t);\r\n lsq:=tr_coe(Q,x,n,k,t);\r\n\r\n ## the 3-term recurrences of LP and LQ\r\n lspp:=tr_coe(L(P,t),x,n,k,t);\r\n lsqp:=tr_coe(L(Q,t),x,n,k,t);\r\n\r\n if shift=`shiftP` then\r\n if Lp<>0 then\r\n re:=Ext_Zeil([Lp(P,t),subs(n=n+1,P),P,subs(n=n-1,P)],k,[t]);\r\n lsps:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n \r\n re:=Ext_Zeil([Lp(Q,t),subs(n=n+1,Q),Q,subs(n=n-1,Q)],k,[t]);\r\n lsqs:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n return(recgenM(lsp,lsq,lspp,lsqp,n,varm,varn,lsps,lsqs));\r\n else\r\n return(recgenM(lsp,lsq,lspp,lsqp,n,varm,varn));\r\n fi;\r\n else\r\n if Lp<>0 then\r\n re:=Ext_Zeil([Lp(P,t),subs(n=n+1,P),P,subs(n=n-1,P)],k,[t]);\r\n lsps:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n \r\n re:=Ext_Zeil([Lp(Q,t),subs(n=n+1,Q),Q,subs(n=n-1,Q)],k,[t]);\r\n lsqs:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n return(recgenN(lsp,lsq,lspp,lsqp,n,varm,varn,lsps,lsqs));\r\n else\r\n return(recgenN(lsp,lsq,lspp,lsqp,n,varm,varn));\r\n fi;\r\n fi; \r\n\r\nend proc:\r\n \r\n\r\n\r\n\r\n## Compute the recurrence relations of the connection coefficients / q-case\r\n## Input:\r\n## P,Q: two hypergeometric terms in k, degree index by n,\r\n## variable in x=x(t)\r\n##\r\n## shift: belonds to {`shiftP`,`shiftQ`},\r\n## recurrence relation involving shifts of the index of P or Q.\r\n##\t \r\n## Pindex, Qindex: the indices of P and Q\r\n##\r\n## Output:\r\n## ls: list of the coefficients of the recurrence relations\r\n## if length is 3, then\r\n## ls[1]c[m+1,n]+ls[2]c[m,n]+ls[3]c[m-1,n] = 0.\r\n## if length is 5, then\r\n## ls[1]c[m+2,n]+ls[2]c[m+1,n]+ls[3]c[m,n]+ls[4]c[m-1,n]+ls[5]c[m-2,n]=0.\r\n##\r\n## Example\r\n## P:=poch([la,2 la],n)/2^n*hyperterm([-n,n+2 la],[la+1/2],(1-s*x)/2,k);\r\n## Q:=2^(-n)*hyperterm([-n,n],[1/2],(1-x)/2,k);\r\n## L:=proc(f,x) diff(f,x); end proc:\r\n## ConRec(P,Q,n,k,x,x,L,`shiftP`,n,m); \r\n\r\nConRecq:=proc(P,Q,qn,k,x,t,Ls,shift,varm,varn,q)\r\nlocal L,Lp,lsp,lsq,lspp,lsqp,lsps,lsqs,re,R;\r\n\r\n ## Ls is either an operator L,\r\n ## or it is the list of two operators [L, Lp]\r\n \r\n if type(Ls,list) then\r\n L:=Ls[1]; Lp:=Ls[2];\r\n else\r\n L:=Ls; Lp:=0;\r\n fi;\r\n\r\n ## the 3-term recurrences of P and Q\r\n re:=qExt_Zeil([x*P,subs(qn=qn*q,P),P,subs(qn=qn/q,P)],k,q,[t]);\r\n lsp:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n re:=qExt_Zeil([x*Q,subs(qn=qn*q,Q),Q,subs(qn=qn/q,Q)],k,q,[t]);\r\n lsq:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n ## the 3-term recurrences of LP and LQ\r\n R:=qhyper_simp(L(P,t));\r\n re:=qExt_Zeil([x*R,subs(qn=qn*q,R),R,subs(qn=qn/q,R)],k,q,[t]);\r\n lspp:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n R:=qhyper_simp(L(Q,t));\r\n re:=qExt_Zeil([x*R,subs(qn=qn*q,R),R,subs(qn=qn/q,R)],k,q,[t]);\r\n lsqp:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n if shift=`shiftP` then\r\n if Lp<>0 then\r\n re:=qExt_Zeil([qhyper_simp(Lp(P,t)),subs(qn=qn*q,P),P,subs(qn=qn/q,P)],k,q,[t]);\r\n lsps:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n \r\n re:=qExt_Zeil([qhyper_simp(Lp(Q,t)),subs(qn=qn*q,Q),Q,subs(qn=qn/q,Q)],k,q,[t]);\r\n lsqs:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n return(recgenMq(lsp,lsq,lspp,lsqp,qn,varm,varn,lsps,lsqs,q));\r\n else\r\n return(recgenMq(lsp,lsq,lspp,lsqp,qn,varm,varn,q));\r\n fi;\r\n else\r\n if Lp<>0 then\r\n re:=qExt_Zeil([qhyper_simp(Lp(P,t)),subs(qn=qn*q,P),P,subs(qn=qn/q,P)],k,q,[t]);\r\n lsps:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n \r\n re:=qExt_Zeil([qhyper_simp(Lp(Q,t)),subs(qn=qn*q,Q),Q,subs(qn=qn/q,Q)],k,q,[t]);\r\n lsqs:=[-re[2]/re[1],-re[3]/re[1],-re[4]/re[1]];\r\n\r\n return(recgenNq(lsp,lsq,lspp,lsqp,qn,varm,varn,lsps,lsqs,q));\r\n else\r\n return(recgenNq(lsp,lsq,lspp,lsqp,qn,varm,varn,q));\r\n fi;\r\n fi; \r\n\r\nend proc:\r\n \r\n\r\n\r\n\r\n\r\n\r\n## compute the coefficients in the three-term relations\r\n## The input:\r\n## hypergeometric term 'P' on variable 'la' which is a polynomial in 'x'\r\n## the order of the polynomial is 'n', the summation index is 'k'\r\n## returen the recurrence\r\n## la*P_n(la) = c[1]*P_{n+1}(la) + c[2]*P_n(la) + c[3]*P_{n-1}(la)\r\n## \r\ntr_coe:=proc(P,la,n,k,x)\r\nlocal re;\r\n\r\n re:=Ext_Zeil([la*P, subs(n=n+1,P), P, subs(n=n-1, P)], k, [x]);\r\n return([-re[2]/re[1], -re[3]/re[1], -re[4]/re[1]]);\r\nend proc:\r\n\r\n\r\nrecgenM:=proc(recp,recq,recpp,recqp,var,m,n)\r\n\r\n local c11,c12,b1,c21,c22,b2,res,u,v,\r\n delta,xi,eta,deltap,xip,etap,detc,\r\n recps,recqs,c31,c32,b3;\r\n\r\n c11:=subs(var=n-1,recq[1]): # u_{n-1}\r\n c12:=subs(var=n+1,recq[3]): # w_{n+1}\r\n b1:=[subs(var=m,recp[1]), \r\n subs(var=m,recp[2])-subs(var=n,recq[2]),\r\n subs(var=m,recp[3])]; # right hand side of (2.3)\r\n\r\n c21:=subs(var=n-1,recqp[1]): # u'_{n-1}\r\n c22:=subs(var=n+1,recqp[3]): # w'_{n+1}\r\n b2:=[subs(var=m,recpp[1]), \r\n subs(var=m,recpp[2])-subs(var=n,recqp[2]),\r\n subs(var=m,recpp[3])]; # right hand side of (2.4)\r\n\r\n \r\n detc:=factor(c11*c22-c12*c21);\r\n if detc=0 then\r\n return([seq(c11*b2[k]-c21*b1[k],k=1..3)]);\r\n else\r\n u:=map(factor, [seq((c22*b1[k]-c12*b2[k])/detc,k=1..3)]); # (2.5)\r\n v:=map(factor, [seq((-c21*b1[k]+c11*b2[k])/detc,k=1..3)]); # (2.6)\r\n \r\n if nargs=7 then # no sigma(x)\r\n\r\n delta:=factor(u[1]): xi:=factor(u[2]):\r\n eta:=factor(u[3]):\r\n\r\n deltap:=factor(v[1]): xip:=factor(v[2]):\r\n etap:=factor(v[3]):\r\n\r\n return(map(factor,[subs(n=n+1,delta)*subs(m=m+1,deltap),\r\n subs(n=n+1,delta)*subs(m=m+1,xip)+subs(n=n+1,xi)*deltap,\r\n subs(n=n+1,delta)*subs(m=m+1,etap)+subs(n=n+1,xi)*xip\r\n +subs(n=n+1,eta)*subs(m=m-1,deltap)-1,\r\n subs(n=n+1,xi)*etap+subs(n=n+1,eta)*subs(m=m-1,xip),\r\n subs(n=n+1,eta)*subs(m=m-1,etap)]));\r\n\t \r\n elif nargs=9 then # with sigma(x)\r\n \r\n recps:=args[8]: recqs:=args[9]:\r\n c31:=subs(var=n-1,recqs[1]): # u''_{n-1}\r\n c32:=subs(var=n+1,recqs[3]): # w''_{n+1}\r\n b3:=[subs(var=m,recps[1]),\r\n subs(var=m,recps[2])-subs(var=n,recqs[2]),\r\n subs(var=m,recps[3])]; # right hand side of (2.8)\r\n\t \r\n return(map(factor,[seq(c31*u[k]+c32*v[k]-b3[k],k=1..3)]));\r\n fi;\r\n fi;\r\n\r\nend proc:\r\n\r\n\r\nrecgenN:=proc(recp,recq,recpp,recqp,var,m,n)\r\n\r\n local c11,c12,b1,c21,c22,b2,res,u,v,\r\n delta,xi,eta,deltap,xip,etap,detc,\r\n recps,recqs,c31,c32,b3;\r\n\r\n c11:=subs(var=m,recp[1]):\r\n c12:=subs(var=m,recp[3]):\r\n b1:=[subs(var=n-1,recq[1]),\r\n subs(var=n,recq[2])-subs(var=m,recp[2]),\r\n subs(var=n+1,recq[3])];\r\n\r\n c21:=subs(var=m,recpp[1]):\r\n c22:=subs(var=m,recpp[3]):\r\n b2:=[subs(var=n-1,recqp[1]),\r\n subs(var=n,recqp[2])-subs(var=m,recpp[2]),\r\n subs(var=n+1,recqp[3])];\r\n\r\n detc:=factor(c11*c22-c12*c21);\r\n if detc=0 then\r\n return([seq(c11*b2[k]-c21*b1[k],k=1..3)]);\r\n else\r\n u:=[seq((c22*b1[k]-c12*b2[k])/detc,k=1..3)];\r\n v:=[seq((-c21*b1[k]+c11*b2[k])/detc,k=1..3)];\r\n \r\n if nargs=7 then\r\n\r\n delta:=factor(u[1]): xi:=factor(u[2]):\r\n eta:=factor(u[3]):\r\n\r\n deltap:=factor(v[1]): xip:=factor(v[2]):\r\n etap:=factor(v[3]):\r\n\r\n return(map(factor,[subs(m=m-1,eta)*subs(n=n+1,etap),\r\n subs(m=m-1,xi)*etap+subs(m=m-1,eta)*subs(n=n+1,xip),\r\n subs(m=m-1,delta)*subs(n=n-1,etap)+subs(m=m-1,xi)*xip\r\n +subs(m=m-1,eta)*subs(n=n+1,deltap)-1,\r\n subs(m=m-1,delta)*subs(n=n-1,xip)+subs(m=m-1,xi)*deltap,\r\n subs(m=m-1,delta)*subs(n=n-1,deltap)]));\r\n \r\n elif nargs=9 then\r\n\r\n recps:=args[8]: recqs:=args[9]:\r\n\r\n c31:=subs(var=m,recps[1]):\r\n c32:=subs(var=m,recps[3]):\r\n b3:=[subs(var=n-1,recqs[1]),\r\n subs(var=n,recqs[2])-subs(var=m,recps[2]),\r\n subs(var=n+1,recqs[3])];\r\n\r\n return(map(factor,[seq(c31*u[4-k]+c32*v[4-k]-b3[4-k],k=1..3)]));\r\n fi;\r\n fi;\r\n\r\nend proc:\r\n\r\n\r\nrecgenMq:=proc(recp,recq,recpp,recqp,var,qm,qn,q)\r\n\r\n local c11,c12,b1,c21,c22,b2,res,u,v,\r\n delta,xi,eta,deltap,xip,etap,detc,\r\n recps,recqs,c31,c32,b3;\r\n\r\n c11:=subs(var=qn/q,recq[1]): # u_{n-1}\r\n c12:=subs(var=qn*q,recq[3]): # w_{n+1}\r\n b1:=[subs(var=qm,recp[1]), \r\n subs(var=qm,recp[2])-subs(var=qn,recq[2]),\r\n subs(var=qm,recp[3])]; # right hand side of (2.3)\r\n\r\n c21:=subs(var=qn/q,recqp[1]): # u'_{n-1}\r\n c22:=subs(var=qn*q,recqp[3]): # w'_{n+1}\r\n b2:=[subs(var=qm,recpp[1]), \r\n subs(var=qm,recpp[2])-subs(var=qn,recqp[2]),\r\n subs(var=qm,recpp[3])]; # right hand side of (2.4)\r\n\r\n \r\n detc:=factor(c11*c22-c12*c21);\r\n if detc=0 then\r\n print(\"D=0\");\r\n return([seq(c11*b2[k]-c21*b1[k],k=1..3)]);\r\n else\r\n u:=map(factor, [seq((c22*b1[k]-c12*b2[k])/detc,k=1..3)]); # (2.5)\r\n v:=map(factor, [seq((-c21*b1[k]+c11*b2[k])/detc,k=1..3)]); # (2.6)\r\n \r\n if nargs=8 then # no sigma(x)\r\n\r\n delta:=factor(u[1]): xi:=factor(u[2]):\r\n eta:=factor(u[3]):\r\n\r\n deltap:=factor(v[1]): xip:=factor(v[2]):\r\n etap:=factor(v[3]):\r\n\r\n return(map(factor,[subs(qn=qn*q,delta)*subs(qm=qm*q,deltap),\r\n subs(qn=qn*q,delta)*subs(qm=qm*q,xip)+subs(qn=qn*q,xi)*deltap,\r\n subs(qn=qn*q,delta)*subs(qm=qm*q,etap)+subs(qn=qn*q,xi)*xip\r\n +subs(qn=qn*q,eta)*subs(qm=qm/q,deltap)-1,\r\n subs(qn=qn*q,xi)*etap+subs(qn=qn*q,eta)*subs(qm=qm/q,xip),\r\n subs(qn=qn*q,eta)*subs(qm=qm/q,etap)]));\r\n\t \r\n elif nargs=10 then # with sigma(x)\r\n \r\n recps:=args[9]: recqs:=args[10]:\r\n c31:=subs(var=qn/q,recqs[1]): # u''_{n-1}\r\n c32:=subs(var=qn*q,recqs[3]): # w''_{n+1}\r\n b3:=[subs(var=qm,recps[1]),\r\n subs(var=qm,recps[2])-subs(var=qn,recqs[2]),\r\n subs(var=qm,recps[3])]; # right hand side of (2.8)\r\n\t \r\n return(map(factor,[seq(c31*u[k]+c32*v[k]-b3[k],k=1..3)]));\r\n fi;\r\n fi;\r\n\r\nend proc:\r\n\r\n\r\nrecgenNq:=proc(recp,recq,recpp,recqp,var,qm,qn,q)\r\n\r\n local c11,c12,b1,c21,c22,b2,res,u,v,\r\n delta,xi,eta,deltap,xip,etap,detc,\r\n recps,recqs,c31,c32,b3;\r\n\r\n c11:=subs(var=qm,recp[1]):\r\n c12:=subs(var=qm,recp[3]):\r\n b1:=[subs(var=qn/q,recq[1]),\r\n subs(var=qn,recq[2])-subs(var=qm,recp[2]),\r\n subs(var=qn*q,recq[3])];\r\n\r\n c21:=subs(var=qm,recpp[1]):\r\n c22:=subs(var=qm,recpp[3]):\r\n b2:=[subs(var=qn/q,recqp[1]),\r\n subs(var=qn,recqp[2])-subs(var=qm,recpp[2]),\r\n subs(var=qn*q,recqp[3])];\r\n\r\n detc:=factor(c11*c22-c12*c21);\r\n if detc=0 then\r\n return([seq(c11*b2[k]-c21*b1[k],k=1..3)]);\r\n else\r\n u:=[seq((c22*b1[k]-c12*b2[k])/detc,k=1..3)];\r\n v:=[seq((-c21*b1[k]+c11*b2[k])/detc,k=1..3)];\r\n \r\n if nargs=8 then\r\n\r\n delta:=factor(u[1]): xi:=factor(u[2]):\r\n eta:=factor(u[3]):\r\n\r\n deltap:=factor(v[1]): xip:=factor(v[2]):\r\n etap:=factor(v[3]):\r\n\r\n return(map(factor,[subs(qm=qm/q,eta)*subs(qn=qn*q,etap),\r\n subs(qm=qm/q,xi)*etap+subs(qm=qm/q,eta)*subs(qn=qn*q,xip),\r\n subs(qm=qm/q,delta)*subs(qn=qn/q,etap)+subs(qm=qm/q,xi)*xip\r\n +subs(qm=qm/q,eta)*subs(qn=qn*q,deltap)-1,\r\n subs(qm=qm/q,delta)*subs(qn=qn/q,xip)+subs(qm=qm/q,xi)*deltap,\r\n subs(qm=qm/q,delta)*subs(qn=qn/q,deltap)]));\r\n \r\n elif nargs=10 then\r\n\r\n recps:=args[9]: recqs:=args[10]:\r\n\r\n c31:=subs(var=qm,recps[1]):\r\n c32:=subs(var=qm,recps[3]):\r\n b3:=[subs(var=qn/q,recqs[1]),\r\n subs(var=qn,recqs[2])-subs(var=qm,recps[2]),\r\n subs(var=qn*q,recqs[3])];\r\n\r\n return(map(factor,[seq(c31*u[4-k]+c32*v[4-k]-b3[4-k],k=1..3)]));\r\n fi;\r\n fi;\r\n\r\nend proc:\r\n", "meta": {"hexsha": "bb033aceeb92d521f97af73265f0105b0b39251c", "size": 12689, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "ConRec.mpl", "max_stars_repo_name": "yanping76/Connection-Coefficients", "max_stars_repo_head_hexsha": "98144bff87b25811b85aee7df15f01789785a8fb", "max_stars_repo_licenses": ["Xnet", "X11"], "max_stars_count": null, "max_stars_repo_stars_event_min_datetime": null, "max_stars_repo_stars_event_max_datetime": null, "max_issues_repo_path": "ConRec.mpl", "max_issues_repo_name": "yanping76/Connection-Coefficients", "max_issues_repo_head_hexsha": "98144bff87b25811b85aee7df15f01789785a8fb", "max_issues_repo_licenses": ["Xnet", "X11"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "ConRec.mpl", "max_forks_repo_name": "yanping76/Connection-Coefficients", "max_forks_repo_head_hexsha": "98144bff87b25811b85aee7df15f01789785a8fb", "max_forks_repo_licenses": ["Xnet", "X11"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 31.4863523573, "max_line_length": 101, "alphanum_fraction": 0.5277799669, "num_tokens": 5319, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920020959544, "lm_q2_score": 0.6688802537704063, "lm_q1q2_score": 0.5355670695538767}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_c_lp96_params *params;\n\n assert(p->params != NULL);\n params = (lda_c_lp96_params * )(p->params);\n*)\n\nf := (rs, zeta) -> params_a_C1 + params_a_C2*n_total(rs)^(-1/3) + params_a_C3*n_total(rs)^(-2/3):\n\n", "meta": {"hexsha": "53e4085703ef78ccdd8492a94acd8103c40638e4", "size": 478, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_lp96.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_lp96.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_c_lp96.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.1578947368, "max_line_length": 97, "alphanum_fraction": 0.6652719665, "num_tokens": 152, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8175744939732856, "lm_q2_score": 0.6548947425132315, "lm_q1q2_score": 0.5354252377160205}} {"text": "(*\n Copyright (C) 2021 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_c_lypr_params *params;\n\n assert(p->params != NULL);\n params = (gga_c_lypr_params * )(p->params);\n*)\n\n$include \"gga_c_lyp.mpl\"\n\nlypr_eta := rr -> -2/(3*sqrt(Pi))*params_a_m2*params_a_omega\n * exp(-params_a_m2^2*params_a_omega^2*rr^2):\n\nlypr_t7 := (rr, z, xt, xs0, xs1) -> \n -rr * (1 - z^2)/4 * (\n + 7/6*(xt^2 - lyp_aux6*(xs0^2*opz_pow_n(z,8/3) + xs1^2*opz_pow_n(-z,8/3)))\n + (1 + (1 + z)/6)*xs0^2*lyp_aux6*opz_pow_n( z, 8/3)\n + (1 + (1 - z)/6)*xs1^2*lyp_aux6*opz_pow_n(-z, 8/3)\n ):\n\n(* This functional is very similar to gga_c_lyp. One adds the two erfc and\n the extra term proportinal to eta *)\nf_lypr_rr := (rr, z, xt, xs0, xs1) -> params_a_a*(\n + erfc(params_a_m1*params_a_omega*rr)*lyp_t1(rr, z)\n + erfc(params_a_m2*params_a_omega*rr)*lyp_omega(rr)*(\n + lyp_t2(rr, z, xt) + lyp_t3(z) + lyp_t4(rr, z, xs0, xs1)\n + lyp_t5(rr, z, xs0, xs1) + lyp_t6(z, xs0, xs1)\n )\n + lyp_omega(rr)*lypr_eta(rr)*lypr_t7(rr, z, xt, xs0, xs1)\n):\n\n(* rr = rs/RS_FACTOR is equal to n_total(rs)^(-1/3) *)\nf_lypr := (rs, z, xt, xs0, xs1) -> f_lypr_rr(rs/RS_FACTOR, z, xt, xs0, xs1):\n\nf := (rs, z, xt, xs0, xs1) -> f_lypr(rs, z, xt, xs0, xs1):\n\n", "meta": {"hexsha": "53b21b541612bf9230d1dd862a96d0c037d53e0d", "size": 1421, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_lypr.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_lypr.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_lypr.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 31.5777777778, "max_line_length": 78, "alphanum_fraction": 0.6213933849, "num_tokens": 608, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8807970811069351, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5352279462849987}} {"text": "StrongWolfe := module()\n\n description \"StrongWolfe linesearch\";\n\n # Module defined as a package (i.e.) collection of procedures\n option package, load = ModuleLoad, unload = ModuleUnLoad;\n\n export lines, linesearch, interpolate, zoom, esatta, AB_list, doplot, doplot2;\n \n local ModuleLoad,\n ModuleUnLoad,\n _debug,\n c_1_vec, c_2_vec, rho, max_iterations,\n Dphi_0, phi_0, A_list, B_list;\n\n uses LinearAlgebra;\n\n ModuleUnLoad := proc()\n printf(\"StrongWolfe unload\\n\");\n NULL;\n end proc:\n\n ModuleLoad := proc()\n printf(\"StrongWolfe load\\n\");\n _debug := true;\n c_1_vec := [0.1,0.01,1e-4]; # Armijo condition\n c_2_vec := [0.1,0.5,0.9]; # second (strong) Wolfe condition\n rho := 2; # bracket growth\n max_iterations := [5,5,10];\n NULL;\n end proc;\n \n # Explicitly call ModuleLoad here so the type is registered when this\n # code is cut&pasted in. ModuleLoad gets called when the module is\n # read from the repository, but the code used to define a module\n # (like the command below) is not called at library read time.\n ModuleLoad();\n\n AB_list := proc()\n A_list, B_list;\n end proc;\n\n lines := proc( f0, df0, L )\n [ [0,f0], [L,f0+L*rho*df0] ], [ [0,f0], [L,f0+L*sigma*df0] ];\n end proc;\n\n # a_lo = a_{i - 1}\n # a_hi = a_{i}\n interpolate := proc ( a_lo, a_hi, phi_lo, phi_hi, Dphi_lo, Dphi_hi )\n local d1, d2;\n d1 := Dphi_lo + Dphi_hi - 3 * (phi_lo - phi_hi) / (a_lo - a_hi);\n d2 := sqrt(d1 * d1 - Dphi_lo * Dphi_hi);\n return a_hi - (a_hi - a_lo) * ((Dphi_hi + d2 - d1) / (Dphi_hi - Dphi_lo + 2 * d2))\n end:\n\n zoom := proc( a_lo_in, a_hi_in, phi, Dphi )\n local kkk, iteration,\n c1_Dphi_0, c2_Dphi_0,\n a_lo, a_hi, a_j, \n phi_lo, phi_hi, phi_j, \n Dphi_lo, Dphi_hi, Dphi_j;\n\n a_lo := a_lo_in; phi_lo := phi(a_lo); Dphi_lo := Dphi(a_lo);\n a_hi := a_hi_in; phi_hi := phi(a_hi); Dphi_hi := Dphi(a_hi);\n\n # Shrink bracket\n for kkk from 1 to 3 do\n c1_Dphi_0 := c_1_vec[kkk]*Dphi_0;\n c2_Dphi_0 := c_2_vec[kkk]*Dphi_0;\n for iteration from 1 to max_iterations[kkk] do\n\n A_list := [ op(A_list), a_lo ];\n B_list := [ op(B_list), a_hi ];\n\n # Interpolate a_j\n if a_lo < a_hi then\n a_j := interpolate( a_lo, a_hi, phi_lo, phi_hi, Dphi_lo, Dphi_hi );\n else\n # TODO: Check if this is needed\n a_j := interpolate( a_hi, a_lo, phi_hi, phi_lo, Dphi_hi, Dphi_lo );\n end;\n\n # Evaluate phi(a_j)\n phi_j := phi(a_j);\n Dphi_j := Dphi(a_j);\n\n # Check Armijo\n if phi_j > phi_0 + a_j * c1_Dphi_0 or phi_j > phi_lo then\n a_hi := a_j;\n phi_hi := phi_j;\n Dphi_hi := Dphi_j;\n else\n\n if abs(Dphi_j) <= -c2_Dphi_0 then\n return a_j;\n end;\n\n if Dphi_j * (a_hi - a_lo) >= 0 then\n a_hi := a_lo;\n phi_hi := phi_lo;\n Dphi_hi := Dphi_lo; \n end;\n\n a_lo := a_j;\n phi_lo := phi_j;\n Dphi_lo := Dphi_j; \n end;\n end;\n end;\n\n # Quasi-error response\n return a_j;\n end;\n\n # `StrongWolfe`: This linesearch algorithm guarantees that \n # the step length satisfies the (strong) Wolfe conditions.\n # See Nocedal and Wright - Algorithms 3.5 and 3.6\n # This algorithm is mostly of theoretical interest,\n # users should most likely\n # `MoreThuente`, `HagerZhang` or `BackTracking`.\n\n linesearch := proc( phi, Dphi, alpha0 )\n local kkk, iteration, c1_Dphi_0, c2_Dphi_0,\n i, a_0, a_i, a_im1, phi_i, Dphi_i, phi_im1, a_star;\n\n phi_0 := phi(0);\n Dphi_0 := Dphi(0);\n\n A_list := [];\n B_list := [];\n\n # Step-sizes\n a_0 := 0;\n a_im1 := a_0;\n a_i := alpha0;\n phi_im1 := phi_0;\n\n for kkk from 1 to 3 do\n c1_Dphi_0 := c_1_vec[kkk]*Dphi_0;\n c2_Dphi_0 := c_2_vec[kkk]*Dphi_0;\n for iteration from 1 to max_iterations[kkk] do\n\n phi_i := phi(a_i);\n\n # Test Wolfe conditions\n if (phi_i > phi_0 + a_i * c1_Dphi_0) or\n (phi_i >= phi_im1 and (iteration > 1 or kkk > 1) ) then\n a_star := zoom( a_im1, a_i, phi, Dphi );\n return a_star, phi(a_star);\n end;\n\n Dphi_i := Dphi(a_i);\n\n # Check condition 2\n if abs(Dphi_i) <= -c2_Dphi_0 then\n return a_i, phi_i;\n end;\n\n # Check condition 3\n if Dphi_i >= 0 then # FIXME untested!\n a_star := zoom( a_i, a_im1, phi, Dphi );\n return a_star, phi(a_star);\n end;\n\n A_list := [ op(A_list), a_im1 ];\n B_list := [ op(B_list), a_i ];\n\n # Choose a_iplus1 from the interval (a_i, a_max)\n a_im1 := a_i;\n a_i := a_i * rho;\n\n # Update phi_im1\n phi_im1 := phi_i;\n end;\n end;\n\n # Quasi-error response TODO make this error instead\n printf(\"\\n\\nlinesearch failed!\\n\\n\");\n return a_im1, phi(a_im1);\n end:\n\n doplot := proc( f_in, df_in, alpha, amax)\n local f0, df0, x, AA, BB, CC, DD;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n display(AA,BB,CC,DD);\n end;\n\n doplot2 := proc( f_in, df_in, alpha, amax, A_list, B_list )\n local i, f0, df0, x, AA, BB, CC, DD, EE;\n f0 := evalf(f_in(0));\n df0 := evalf(df_in(0));\n\n AA := plot(f_in(x),x=0..amax);\n BB := plot([[0,f0],[amax,f0+amax*rho*df0]],color=\"LimeGreen\");\n CC := plot([[0,f0],[amax,f0+amax*sigma*df0]],color=\"blue\");\n DD := plot([[alpha,f_in(alpha)]],color=\"red\",style = point);\n EE := plot([seq([[A_list[i],-i/5],[B_list[i],-i/5]],i=1..nops(A_list))],color=\"black\");\n display(AA,BB,CC,DD,EE);\n end;\n\nend module:\n", "meta": {"hexsha": "eb58530f1cc6d7216e9941b39c1fd8fc4eaeaa5b", "size": 5929, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NL-StrongWolfe.mpl", "max_stars_repo_name": "ebertolazzi/NLtoolbox", "max_stars_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_stars_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-06-28T09:12:53.000Z", "max_stars_repo_stars_event_max_datetime": "2021-06-28T09:12:53.000Z", "max_issues_repo_path": "maple/NL-StrongWolfe.mpl", "max_issues_repo_name": "ebertolazzi/NLtoolbox", "max_issues_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_issues_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NL-StrongWolfe.mpl", "max_forks_repo_name": "ebertolazzi/NLtoolbox", "max_forks_repo_head_hexsha": "99e47bdc346f3ac7b4834f2a6b431327d00e5ab1", "max_forks_repo_licenses": ["BSD-2-Clause", "Unlicense"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 28.5048076923, "max_line_length": 91, "alphanum_fraction": 0.559284871, "num_tokens": 2014, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.737158174177441, "lm_q2_score": 0.7248702702332476, "lm_q1q2_score": 0.534344044920649}} {"text": "# 1 + 8 -> 9\nfunc $testSum (var %i i32) i32 {\n return (\n add i32(constval i32 1, constval i32 8))\n}\n\n# sqrt(4.0) -> 2.0\nfunc $testSqrt (var %i i32) f32 {\n return (\n sqrt f32(constval f32 4.0f))\n}\n\n# 5 + (5 + a) -> a + 10\nfunc &testConstVarFold00 (var %a i32) i32 {\n return (add i32 (\n constval i32 5,\n add i32 (constval i32 5, dread i32 %a)))\n}\n\n# 5 + (5 - a) -> 10 - a\nfunc &testConstVarFold01 (var %a i32) i32 {\n return (add i32 (\n constval i32 5,\n sub i32 (constval i32 5, dread i32 %a)))\n}\n\n# 5 + (a + 5) -> a + 10\nfunc &testConstVarFold02 (var %a i32) i32 {\n return (add i32 (\n constval i32 5,\n add i32 (dread i32 %a, constval i32 5)))\n}\n\n# 6 + (a - 5) -> a + 1\nfunc &testConstVarFold03 (var %a i32) i32 {\n return (add i32 (\n constval i32 6,\n sub i32 (dread i32 %a, constval i32 5)))\n}\n\n# 5 * (5 * a) -> 5 * (5 * a)\nfunc &testConstVarFold04 (var %a i32) i32 {\n return (mul i32 (\n constval i32 5,\n mul i32 (constval i32 5, dread i32 %a)))\n}\n\n# 5 * (a * 5) -> 5 * (a * 5)\nfunc &testConstVarFold05 (var %a i32) i32 {\n return (mul i32 (\n constval i32 5,\n mul i32 (dread i32 %a, constval i32 5)))\n}\n\n# 3 - (2 - a) -> a + 1\nfunc &testConstVarFold06 (var %a i32) i32 {\n return (sub i32 (\n constval i32 3,\n sub i32 (constval i32 2, dread i32 %a)))\n}\n\n# 3 - (2 + a) -> 1 - a\nfunc &testConstVarFold07 (var %a i32) i32 {\n return (sub i32 (\n constval i32 3,\n add i32 (constval i32 2, dread i32 %a)))\n}\n\n# 3 - (a + 2) -> 1 - a\nfunc &testConstVarFold08 (var %a i32) i32 {\n return (sub i32 (\n constval i32 3,\n add i32 (dread i32 %a, constval i32 2)))\n}\n\n# 3 - (a - 2) -> 5 - a\nfunc &testConstVarFold09 (var %a i32) i32 {\n return (sub i32 (\n constval i32 3,\n sub i32 (dread i32 %a, constval i32 2)))\n}\n\n# (2 + a) - 3 -> a - 1\nfunc &testConstVarFold10 (var %a i32) i32 {\n return (sub i32 (\n add i32 (constval i32 2, dread i32 %a),\n constval i32 3))\n}\n\n# (2 - a) - 3 -> -a - 1\nfunc &testConstVarFold11 (var %a i32) i32 {\n return (sub i32 (\n sub i32 (constval i32 2, dread i32 %a),\n constval i32 3))\n}\n\n# (a + 2) - 3 -> a - 1\nfunc &testConstVarFold12 (var %a i32) i32 {\n return (sub i32 (\n add i32 (dread i32 %a, constval i32 2),\n constval i32 3))\n}\n\n# (a - 2) - 3 -> a - 5\nfunc &testConstVarFold13 (var %a i32) i32 {\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 2),\n constval i32 3))\n}\n\n# 1 + (5 + ((5 - a) - 3)) -> 8 - a\nfunc &testConstVarFold15 (var %a i32) i32 {\n return (add i32 (\n constval i32 1,\n add i32 (\n constval i32 5,\n sub i32 (\n sub i32 (constval i32 5, dread i32 %a),\n constval i32 3))))\n}\n\n# 1 + (5 + ((5 - a) * 3)) -> ((5 - a) * 3) + 6\nfunc &testConstVarFold16 (var %a i32) i32 {\n return (add i32 (\n constval i32 1,\n add i32 (\n constval i32 5,\n mul i32 (\n sub i32 (constval i32 5, dread i32 %a),\n constval i32 3))))\n}\n\n# (-a) + b --> (-a) + b\nfunc &testConstantFoldAdd00 (var %a i32, var %b i32) i32 {\n return (add i32 (\n neg i32 (dread i32 %a),\n dread i32 %b))\n}\n\n# a + (-b) --> a + (-b)\nfunc &testConstantFoldAdd01 (var %a i32, var %b i32) i32 {\n return (add i32 (\n dread i32 %a,\n neg i32 (dread i32 %b)))\n}\n\n\n# 5.0f + (5 - a) -> same, no folding with floating point numbers\nfunc &testConstVarFold20 (var %a i32) i32 {\n return (add f32 (\n constval f32 5.0f,\n sub i32 (constval i32 5, dread i32 %a)))\n}\n\n\nfunc &testConstFold0 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a + 5) + ((2 + c) + (4 + 2))) -> ((a + c) + 13)\n return (add i32 (\n add i32 (dread i32 %a, constval i32 0x5),\n add i32 (\n add i32 (constval i32 0x2, dread i32 %c),\n add i32 (constval i32 0x4, constval i32 0x2))))\n}\n\nfunc &testConstFold1 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a + 5) + (2 + c)) -> ((a + c) + 7)\n return (add i32 (\n add i32 (dread i32 %a, constval i32 0x5),\n add i32 (constval i32 0x2, dread i32 %c)))\n}\n\nfunc &testConstFold2 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) - ((b - c) - (4 - 2))) -> ((a - (b - c)) - 3)\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n sub i32 (dread i32 %b, dread i32 %c),\n sub i32 (constval i32 0x4, constval i32 0x2))))\n}\n\nfunc &testConstFold3 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) + ((b - c) - (4 - 2))) -> ((a + (b - c)) - 7)\n return (add i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n sub i32 (dread i32 %b, dread i32 %c),\n sub i32 (constval i32 0x4, constval i32 0x2))))\n}\n\nfunc &testConstFold4 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) - ((4 - 2) - (4 - b))) -> ((a - b) - 3)\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n sub i32 (constval i32 0x4, constval i32 0x2),\n sub i32 (constval i32 0x4, dread i32 %b))))\n}\n\nfunc &testConstFold5 (var %a i32, var %b i32, var %c i32) i32 {\n # ((5 - a) - ((b - 4) - (4 - b))) -> (((-a) - (b - (-b))) + 13)\n return (sub i32 (\n sub i32 (constval i32 0x5, dread i32 %a),\n sub i32 (\n sub i32 (dread i32 %b, constval i32 0x4),\n sub i32 (constval i32 0x4, dread i32 %b))))\n}\n\nfunc &testConstFold6 (var %a i32, var %b i32, var %c i32) i32 {\n # ((5 - a) - ((4 - b) - (b - 4))) -> (((-a) - ((-b) - b)) - 3)\n return (sub i32 (\n sub i32 (constval i32 0x5, dread i32 %a),\n sub i32 (\n sub i32 (constval i32 0x4, dread i32 %b),\n sub i32 (dread i32 %b, constval i32 0x4))))\n}\n\nfunc &testConstFold7 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) - ((4 + 2) - (4 - (b - c)))) -> ((a - (b - c)) - 7)\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n sub i32 (\n constval i32 0x4,\n sub i32 (dread i32 %b, dread i32 %c)))))\n}\n\nfunc &testConstFold8 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) - ((4 + 2) - (4 * (b - c)))) -> ((a - (-(4 * (b - c)))) - 11)\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n mul i32 (\n constval i32 0x4,\n sub i32 (dread i32 %b, dread i32 %c)))))\n}\n\nfunc &testConstFold9 (var %a i32, var %b i32, var %c i32) i32 {\n # ((a - 5) - ((4 + 2) - (-(4 - (b - c))))) -> ((a - (-(b - c))) - 15)\n return (sub i32 (\n sub i32 (dread i32 %a, constval i32 0x5),\n sub i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n neg i32 (sub i32 (\n constval i32 0x4,\n sub i32 (dread i32 %b, dread i32 %c))))))\n}\n\nfunc &testConstFold10 (var %a i32, var %b i32, var %c i32) i32 {\n # ((4 + 2) * (-(4 - (3 - c)))) -> (6 * ((-c) - 1))\n return (mul i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n neg i32 (sub i32 (\n constval i32 0x4,\n sub i32 (constval i32 0x3, dread i32 %c)))))\n}\n\nfunc &testConstFold11 (var %a i32, var %b i32, var %c i32) i32 {\n # ((4 + 2) * (4 - (3 - c))) -> (6 * (c + 1))\n return (mul i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n sub i32 (\n constval i32 0x4,\n sub i32 (constval i32 0x3, dread i32 %c))))\n}\n\nfunc &testConstFold12 (var %a i32, var %b i32, var %c i32) i32 {\n # ((4 + 2) * (~(4 - (3 - c)))) -> (6 * (~(c + 1)))\n return (mul i32 (\n add i32 (constval i32 0x4, constval i32 0x2),\n bnot i32 (sub i32 (\n constval i32 0x4,\n sub i32 (constval i32 0x3, dread i32 %c)))))\n}\n\nfunc &testConstFold13 (var %a i32, var %b i32, var %c i32) i32 {\n # (5 * (((4 - 2) + (2 & 4)) - (4 - (c | 3)))) -> (5 * ((c | 3) - 2))\n return (mul i32 (\n constval i32 0x5,\n sub i32 (\n add i32 (\n sub i32 (constval i32 0x4, constval i32 0x2),\n band i32 (constval i32 0x2, constval i32 0x4)),\n sub i32 (\n constval i32 0x4,\n bior i32 (dread i32 %c, constval i32 0x3)))))\n}\n\nfunc &testConstFold14 (var %a i32, var %b i32, var %c i32) i32 {\n # (5 * (((4 - 2) + (2 & 4)) * (4 - (c | 3)))) -> (5 * (2 * (4 - (c | 3))))\n return (mul i32 (\n constval i32 0x5,\n mul i32 (\n add i32 (\n sub i32 (constval i32 0x4, constval i32 0x2),\n band i32 (constval i32 0x2, constval i32 0x4)),\n sub i32 (\n constval i32 0x4,\n bior i32 (dread i32 %c, constval i32 0x3)))))\n}\n\nfunc &testConstFold15 (var %a i32, var %b i32, var %c i32) i32 {\n # ((1 + 0) * (~(4 - (0 * c)))) -> (~4)\n return (mul i32 (\n add i32 (constval i32 0x1, constval i32 0x0),\n bnot i32 (sub i32 (\n constval i32 0x4,\n mul i32 (constval i32 0x0, dread i32 %c)))))\n}\n\nfunc &testConstFold16 (var %a i32, var %b i32, var %c i32) i32 {\n # ((~(4 - (c * 0))) * (1 + 0)) -> (~4)\n return (mul i32 (\n bnot i32 (sub i32 (\n constval i32 0x4,\n mul i32 (dread i32 %c, constval i32 0x0))),\n add i32 (constval i32 0x1, constval i32 0x0)))\n}\n\n\nfunc &testConstFoldDiv0 (var %a i32, var %b i32, var %c i32) i32 {\n # (5 / 0) * (1 + 1) -> 2\n return (mul i32 (\n div i32 (constval i32 0x5, constval i32 0x0),\n add i32 (constval i32 0x1, constval i32 0x1)))\n}\n\nfunc &testConstFoldFloor00 (var %a i32, var %b i32, var %c i32) i32 {\n # (floor(4.25) + c) * (1 + 1) -> (c + 4) * 2\n return (mul i32 (\n add i32 (floor i32 f32 (constval f32 4.25f), dread i32 %c),\n add i32 (constval i32 0x1, constval i32 0x1)))\n}\n\nfunc &testConstFoldFloor01 (var %a i32, var %b i32, var %c i32) i32 {\n # (floor(4.25) + 2) * (1 + 1) -> 12\n return (mul i32 (\n add i32 (floor i32 f32 (constval f32 4.25f), constval i32 0x2),\n add i32 (constval i32 0x1, constval i32 0x1)))\n}\n\nfunc &testConstFoldFloor02 (var %a i32, var %b i32, var %c i32) i32 {\n # floor((floor(4.25) + 1) + (1 + a)) -> floor(a + 6)\n return (floor i32 i32 (add i32 (\n add i32 (floor i32 f32 (constval f32 4.25f), constval i32 0x1),\n add i32 (constval i32 0x1, dread i32 %a))))\n}\n\nfunc &testConstFoldExtractbitsNode00 () i32 {\n # 487 = 00111100111\n # extractbits i32 6 5 (487) = 7 = 0111\n return (extractbits i32 6 5 (constval i32 487))\n}\n\nfunc &testConstFoldExtractbitsNode01 () i32 {\n # 487 = 00111100111\n # extractbits i32 4 5 (487) = -2 = 0xfffffffffffffffe\n return (extractbits i32 4 5 (constval i32 487))\n}\n\nfunc &testConstFoldExtractbitsNode02 (var %a i32, var %b i32, var %c i32) i32 {\n # 487 = 00111100111\n # extractbits i32 4 5 (487) = -2 = 0xfffffffffffffffe\n # extractbits((extractbits(487) + 1) + (1 + a)) -> extractbits(a)\n return (extractbits i32 4 5 (add i32 (\n add i32 (extractbits i32 4 5 (constval i32 487), constval i32 0x1),\n add i32 (constval i32 0x1, dread i32 %a))))\n}\n\nfunc &testConstFoldExtractbitsNode03 (var %a i32, var %b i32, var %c i32) i32 {\n # 487 = 00111100111\n # extractbits i32 6 5 (487) = 7 = 0111\n # extractbits((extractbits(487) + 1) + (1 + a)) -> extractbits(a + 9)\n return (extractbits i32 6 5 (add i32 (\n add i32 (extractbits i32 6 5 (constval i32 487), constval i32 0x1),\n add i32 (constval i32 0x1, dread i32 %a))))\n}\n\nfunc &testConstFoldCompareNode00 (var %a i32, var %b i32, var %c i32) i32 {\n # (ge(6, 2) + 1) + (1 + 2) -> 5\n return (add i32 (\n add i32 (\n ge i32 i32 (constval i32 6, constval i32 2),\n constval i32 1),\n add i32 (constval i32 1, constval i32 2)))\n}\n\nfunc &testConstFoldCompareNode01 (var %a i32, var %b i32, var %c i32) i32 {\n # ge((ge(6, 2) + 1), (1 + a)) -> ge(2, a + 1)\n return (ge i32 i32 (\n add i32 (\n ge i32 i32 (constval i32 6, constval i32 2),\n constval i32 1),\n add i32 (constval i32 1, dread i32 %a)))\n}\n\nfunc &testConstFoldTernaryNode00 (var %a i32, var %b i32, var %c i32) i32 {\n # (6 > 2 ? 5 : 0) + (1 + 2) -> 8\n return ( add i32 (\n select i32 (\n ge i32 i32 (constval i32 6, constval i32 2),\n constval i32 5,\n constval i32 0),\n add i32 (constval i32 1, constval i32 2)))\n}\n\nfunc &testConstFoldTernaryNode01 (var %a i32, var %b i32, var %c i32) i32 {\n # (6 > 10 ? 5 : 0) + (1 + a) -> (a + 1)\n return ( add i32 (\n select i32 (\n ge i32 i32 (constval i32 6, constval i32 10),\n constval i32 5,\n constval i32 0),\n add i32 (constval i32 1, dread i32 %a)))\n}\n\nfunc &testConstFoldTernaryNode02 (var %a i32, var %b i32, var %c i32) i32 {\n # 6 > a ? (1 + 6) + (1 + a) : 0 -> 6 > a ? a + 8 : 0\n return ( select i32 (\n ge i32 i32 (constval i32 6, dread i32 %a),\n add i32 (\n add i32 (constval i32 1, constval i32 6),\n add i32 (constval i32 1, dread i32 %a)),\n constval i32 0))\n}\n\ntype $Hello \n\ntype $Person ,\n @sex u1}>\n\n\nfunc &testConstFoldIassignNode00 (var %a i32) void {\n # this is equivalent to dassign %a 0 (constval i32 0x6)\n iassign <* i32> 0 (addrof ptr %a 0, add i32 (constval i32 1, constval i32 5))\n}\n\nfunc &testConstFoldIassignNode01 (var %a i32) void {\n var %bob $Person\n\n # this is equivalent to dassign %bob 5 (constval i32 0x6)\n iassign <* $Hello> 3 (addrof ptr %bob 2, add i32 (constval i32 1, constval i32 5))\n}\n\n\nfunc &testConstFoldIassignNode02 (var %a i32) void {\n # this is equivalent to dassign %a 0 (constval i32 0x6)\n iassign <* i32> 0 (\n iaddrof ptr <* i32> 0 (addrof ptr %a 0),\n add i32 (constval i32 1, constval i32 5))\n}\n\nfunc &testConstFoldIassignNode03 (var %a i32) void {\n\n var %bob $Person\n # this is equivalent to dassign %bob 5 (constval i32 0x6)\n iassign <* <$Hello>> 3 (\n iaddrof ptr <* <$Person>> 2 (addrof ptr %bob 0),\n add i32 (constval i32 1, constval i32 5))\n}\n\nfunc &testConstFoldIassignNode04 (var %a i32) void {\n\n var %bob $Person\n # this is equivalent to dassign %bob 5 (constval i32 0x6)\n iassign <* <$Hello>> 3 (\n iaddrof ptr <* <$Hello>> 0 (addrof ptr %bob 2),\n add i32 (constval i32 1, constval i32 5))\n}\n\n\nfunc &testConstFoldIassignNode05 (var %a i32) void {\n var %b <* i32>\n\n dassign %b (addrof ptr %a 0)\n\n # this is equivalent to iassign <* i32> 0 (dread ptr %a, constval i32 0x6)\n iassign <* i32> 0 (\n iaddrof ptr <* i32> 0 (dread ptr %a),\n add i32 (constval i32 1, constval i32 5))\n}\n\nfunc &testConstFoldIassignNode06 (var %a i32) void {\n var %bob $Person\n # this is equivalent to dassign %a 0 (dread i32 %bob 1)\n dassign %a 0 (iread agg <* <$Person>> 1 (addrof ptr %bob 0))\n}\n\nfunc &testConstFoldSwitchNode00 () void {\n # switch (1+4) ... -> goto @lab1\n switch ( add i32 (constval i32 1, constval i32 4)) @labdft {\n -2: goto @lab0\n 5: goto @lab1\n 8: goto @lab9 }\n\n @lab0\n return (constval i32 1)\n @labdft\n return (constval i32 2)\n @lab9\n return (constval i32 3)\n @lab1\n return (constval i32 4)\n}\n\nfunc &testConstFoldSwitchNode01 () void {\n # switch (1 + 10) ... -> goto @labdft\n switch ( add i32 (constval i32 1, constval i32 10)) @labdft {\n -2: goto @lab0\n 5: goto @lab1\n 8: goto @lab9 }\n\n @lab0\n return (constval i32 1)\n @labdft\n return (constval i32 2)\n @lab9\n return (constval i32 3)\n @lab1\n return (constval i32 4)\n}\n\nfunc &testConstFoldSwitchNode02 (var %a i32) void {\n # switch (5 + (5 - a)) ... -> switch (10 - a) ...\n switch (add i32 (\n constval i32 5,\n sub i32 (constval i32 5, dread i32 %a))) @labdft {\n -2: goto @lab0\n 5: goto @lab1\n 8: goto @lab9 }\n\n @lab0\n return (constval i32 1)\n @labdft\n return (constval i32 2)\n @lab9\n return (constval i32 3)\n @lab1\n return (constval i32 4)\n}\n\n\nfunc &testConstFoldArrayNode00 (var %x i32) void {\n var %a <* [15][15] i32>\n # fold indexes -> array ptr <* <[15][15] i32>> (constval i32 0x6, constval i32 0x4)\n dassign %x (\n iread i32 <* i32> (\n array 1 ptr <* [15][15] i32> (addrof ptr %a,\n add i32 (constval i32 1, constval i32 5),\n sub i32 (constval i32 5, constval i32 1))))\n}\n\nfunc &testDepositbitsNodeNode00 (var %a i32, var %c i32) i32 {\n return ( depositbits i32 1 23 (\n add i32 (\n add i32 (dread i32 %a, constval i32 0x5),\n add i32 (\n add i32 (constval i32 0x2, dread i32 %c),\n add i32 (constval i32 0x4, constval i32 0x2))),\n add i32 (constval i32 0x4, constval i32 0x8)))\n}\n\nfunc &testDepositbitsNodeNode01 () i32 {\n return ( depositbits i32 1 23 (\n add i32 (\n add i32 (constval i32 0x5, constval i32 0x5),\n add i32 (\n add i32 (constval i32 0x2, constval i32 0x2),\n add i32 (constval i32 0x4, constval i32 0x2))),\n add i32 (constval i32 0x4, constval i32 0x8)))\n}\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "d0b562cc934797ab3ecb9e62d007de68e85cb57c", "size": 16549, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0019-mapleall-irbuild-edge-constFoldTest/Main.mpl", "max_stars_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_stars_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 796, "max_stars_repo_stars_event_min_datetime": "2019-08-30T16:20:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-25T14:45:06.000Z", "max_issues_repo_path": "test/testsuite/irbuild_test/I0019-mapleall-irbuild-edge-constFoldTest/Main.mpl", "max_issues_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_issues_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 16, "max_issues_repo_issues_event_min_datetime": "2019-08-30T18:04:08.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-19T05:02:58.000Z", "max_forks_repo_path": "test/testsuite/irbuild_test/I0019-mapleall-irbuild-edge-constFoldTest/Main.mpl", "max_forks_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_forks_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 326, "max_forks_repo_forks_event_min_datetime": "2019-08-30T16:11:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-26T12:31:17.000Z", "avg_line_length": 28.3859348199, "max_line_length": 85, "alphanum_fraction": 0.5652305275, "num_tokens": 6969, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7905303186696747, "lm_q2_score": 0.6757646075489391, "lm_q1q2_score": 0.5342124105513505}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n\n$define gga_x_pbe_sol_params\n$include \"gga_x_pbe.mpl\"\n\ncc := 100:\nc1 := 0.5217:\n\nf1 := s -> f0_pbe(s)*(cc - s^4) + c1*s^3.5*(1 + s^2):\nf2 := s -> cc + s^6:\n\nf := x -> f1(X2S*x)/f2(X2S*x):", "meta": {"hexsha": "8835e45f7059850ce01d9cca7b183572b48c7ed9", "size": 451, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_x_q2d.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_x_q2d.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_x_q2d.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 22.55, "max_line_length": 68, "alphanum_fraction": 0.6274944568, "num_tokens": 174, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8670357666736772, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.5333031703790407}} {"text": "#sample\ntinput := \"5483143223\n2745854711\n5264556173\n6141336146\n6357385478\n4167524645\n2176841721\n6882881134\n4846848554\n5283751526\";\n\n#toy\ntinput := \"11111\n19991\n19191\n19991\n11111\";\n\ninput := FileTools:-Text:-ReadFile(\"AoC-2021-11-input.txt\" ):\n\nogrid := map((parse~),StringTools:-Explode~(StringTools:-Split(input)));\ngridw := nops(ogrid[1]); gridl := nops(ogrid);\n\nneighbors := proc(pt) # include diagonals\nlocal x, y, out;\nglobal gridw, gridl;\n out := NULL;\n (x,y) := pt[];\n if x > 1 then\n out := out, [x-1, y];\n if y > 1 then\n out := out, [x-1, y-1];\n end if;\n end if;\n if y > 1 then\n out := out, [x, y-1];\n if x< gridw then\n out := out, [x+1, y-1];\n end if;\n end if;\n if x < gridw then\n out := out, [x+1, y];\n if y < gridl then\n out := out, [x+1, y+1];\n end if;\n end if;\n if y < gridl then\n out := out, [x, y+1];\n if x > 1 then\n out := out, [x-1, y+1];\n end if;\n end if;\n return [out];\nend proc:\n \nflash := proc(x,y)\nlocal n, nb := neighbors([x,y]);\nglobal grid, flashed;\n if flashed[x,y] <> 0 then\n # flashed is a table to track that we flashed only once\n return;\n end if;\n flashed[x,y] := 1;\n for n in nb do\n # increment neighbors and maybe trigger their flashes \n grid[n[]] += 1;\n if grid[n[]] > 9 then\n flash(n[]);\n end if;\n end do;\nend proc: # flash\ntotalflashes := 0;\ngrid := Array(ogrid);\n\nfor dd from 1 to 1000 while add(grid) <> 0 do\n grid := grid +~ 1; # increment grid\n flashed := table(sparse=0); # clear flash tracking table\n # do the flashes - flash may trigger flashes earlier too\n for i from 1 to gridw do\n for j from 1 to gridl do\n if grid[i,j] > 9 then\n flash(i,j);\n end if;\n end do;\n end do;\n # count and reset flashed\n for i from 1 to gridw do\n for j from 1 to gridl do\n if grid[i,j] > 9 then\n grid[i,j] := 0;\n if i <= 100 then\n totalflashes+=1;\n end if;\n end if;\n end do;\n end do;\n\nend do: # days\n\nanswer1 := totalflashes;\nanswer2 := (dd-1);\n\n\n", "meta": {"hexsha": "cdb00087e71654010fb2eb5ac84ba006dc5699d7", "size": 2267, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day11/AoC11-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day11/AoC11-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day11/AoC11-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 21.5904761905, "max_line_length": 72, "alphanum_fraction": 0.5169827966, "num_tokens": 728, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7772998714925403, "lm_q2_score": 0.6859494550081926, "lm_q1q2_score": 0.5331884232282462}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\n$include \"mgga_c_scan.mpl\"\n\n(* Override definition of beta *)\nmbeta := (rs, t) -> 0.066725:\n\nrmggac_gamma1 := 0.08:\nrmggac_gamma2 := 0.3:\nrmggac_g := (alpha, s) ->\n (1 + rmggac_gamma1)*alpha/(rmggac_gamma1 + alpha + rmggac_gamma2*s^2):\n\nrmggac_f2 := (alpha, s) ->\n 3*rmggac_g(alpha, s)^3/(1 + rmggac_g(alpha, s)^3 + rmggac_g(alpha, s)^6):\nrmggac_f1 := (alpha, s) ->\n 1 - rmggac_f2(alpha, s):\n\nrmggac_gamma := 0.031091:\n(* from mmga_c_r2scan *)\nrmggac_w1 := (rs, z) -> exp(-f_pw(rs, z)/(rmggac_gamma*mphi(z)^3)) - 1:\nrmggac_H1 := (rs, z, t) -> rmggac_gamma*mphi(z)^3*log(1 + rmggac_w1(rs, z) * (1 - scan_e0_g(rs, z, t))):\n\nrmggac_eps1 := (rs, z, t) ->\n (f_pw(rs, z) + rmggac_H1(rs, z, t)):\n\nrmggac_alpha := (z, xt, ts0, ts1) ->\n (t_total(z, ts0, ts1) - xt^2/4)/(2**(1/3)*K_FACTOR_C):\n\nrmggac_f := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n + scan_e0(rs, z, X2S*2^(1/3)*xt)\n * rmggac_f1(rmggac_alpha(z, xt, ts0, ts1), X2S*2^(1/3)*xt)\n + rmggac_eps1(rs, z, tp(rs, z, xt))\n * rmggac_f2(rmggac_alpha(z, xt, ts0, ts1), X2S*2^(1/3)*xt):\n\n(* the functional is written for the other convention for tau *)\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n rmggac_f(rs, z, xt, xs0, xs1, 2*ts0, 2*ts1):\n", "meta": {"hexsha": "ace8941202d4585e605a48713a0da4de887ffe20", "size": 1465, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_rmggac.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_rmggac.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_rmggac.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 31.847826087, "max_line_length": 104, "alphanum_fraction": 0.6116040956, "num_tokens": 642, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8615382129861583, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.5331029891184765}} {"text": "#@ Not autoload\n\n# This file relates to the cubic with equation x[1]^3 + x[2]^3 + x[3]^3 = nu * x[1] * x[2] * x[3]\n\nom := exp( 2*Pi*I/3);\nob := exp(-2*Pi*I/3);\nR := [1,om,ob];\n\n# The group G acts on affine 3-space, preserving the above cubic.\n# The quotient G/Z acts on the projective plane, preserving our cubic curve\n\nid := IdentityMatrix(3);\nrho := <<0|0|1>,<1|0|0>,<0|1|0>>:\nzeta := DiagonalMatrix([1,om,ob]):\n\nZ := [id,om * id, ob * id];\nT := [seq(seq(DiagonalMatrix(rationalize(expand([om^i,om^j,om^(-i-j)]))),j=0..2),i=0..2)]:\nS := map(perm_matrix,combinat[permute](3)):\nG := [seq(seq(t.s,t in T),s in S)]:\n\n# rho and zeta commute in G/Z \nfor i from -1 to 1 do \n for j from -1 to 1 do \n g[i,j] := map(rationalize,rho^i . zeta^j);\n od;\nod:\n\n# We now define matrices U[i,j] = \n# Each e[i,j] generates a 1-dimensional summand in affine 3-space\n# On the complement of the locus where nu = 3 = 0, each pair \nU[0,0] := <<1|1|nu>,<-1|-nu-1|3>,<0|3|nu>>;\nfor i from -1 to 1 do\n for j from -1 to 1 do\n U[i,j] := map(expand,g[i,j] . U[0,0]);\n e[i,j] := convert(Column(U[i,j],1),list);\n u[i,j] := convert(Column(U[i,j],2),list);\n v[i,j] := convert(Column(U[i,j],3),list);\n od:\nod:\n\n", "meta": {"hexsha": "9bc06b784203378aabecbe48f651f88ce73f5255", "size": 1209, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/elliptic/fermat_cubic.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/elliptic/fermat_cubic.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/elliptic/fermat_cubic.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 29.487804878, "max_line_length": 97, "alphanum_fraction": 0.5839536807, "num_tokens": 484, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8175744939732855, "lm_q2_score": 0.6513548714339144, "lm_q1q2_score": 0.532531129409617}} {"text": "restart:\nDigits := 100:\nwith (numapprox):with(orthopoly):\nread \"common-procedures.mpl\";\nmkdir(\"TEMPATAN\");\n\n#First, quick phase\n#Approach for the first function:\n#atan(x) = atan(b(i)) + atan ( (x-bi) / (1+x*b(i) ) )\n#We try to have 64 correct bits\n\n\n\n#Constants\n\n\n#if (x >= xmax) : return arctan(x)/2)=neareast(Pi/2)\n\nlog[2](evalf(min(solve(arctan(x)=nearest(Pi/2),x)))):\nxmax:=2^54:\n\n\n#halfPi=Pi/2 (remark that maxvalue < Pi/2 so that atan(x) < Pi/2\n\nhalfPi:=nearest(Pi/2):\nhalfPi_to_plus_infinity:=nearest(nearest(Pi/2)*(1+2^(-53))):\n\n\n# invPi, for the atanpi function\n\ninvpih,invpil := hi_lo(1/Pi); \n\n\n\n# if (xmin simplify( solve( (x-bi) / (1+x*bi) = e ,x) ):\nminx := bi -> simplify(solve( (x-bi) /(1+x*bi)=-e ,x)):\n\nnextbi := proc (x) evalf( max(solve( minx(bi) = x ,bi) )*(1-marge)); end:\n\nallbi := proc (n)\n local xi,nbi,x,i,j;\n global b,a, nb_of_ai, nb_of_bi, value_for_dicho;\n x := e;\n nbi := 0;\n i := 0;\n while(i= 0) do\n nbi := nearest ( nextbi(x) );\n b[i] := evalf( nbi );\n a[i] := x;\n x := evalf(maxx(nbi));\n i:=i+1;\n od;\n j:=0;\n while ( 2^j < i ) do j:=j+1 od:\n nb_of_ai := i;\n nb_of_bi := i;\n b[i-1] := nearest(1/e+4):\n value_for_dicho := 2^j;\n return i,b[0],b[i-1];\nend:\n\nallbi(100);\n\n\n\n\n#The polynome and its size ( 4 because 4 terms : x^2/3, ...)\n\nQ9:= poly_exact(x-1/3*x^3+1/5*x^5 -1/7*x^7+1/9*x^9):\ndeg_poly := 4:\ncoef_poly[0]:=nearest (-1/3):\ncoef_poly[1]:=nearest (1/5):\ncoef_poly[2]:=nearest (-1/7):\ncoef_poly[3]:=nearest (1/9):\n\nQ := x^2 * coef_poly[0] + x^4*coef_poly[1] + x^6*coef_poly[2] + x^8 * coef_poly[3]:\n\nQprime := poly_exact( x * coef_poly[0] + x^2*coef_poly[1] + x^3*coef_poly[2] + x^4 * coef_poly[3]):\n\nlog[2] (infnorm( (arctan(x)-x*(1+Q) )/x,x=2^(-53)..e));\n# we can note that arctan(x) = sum((-1)^i*x^(2*i+1)/(2*i+1), i = (0 .. infinity))\n# so ( arctan(x) - Q9(x) ) / x = sum((-1)^i*x^(2*i)/(2*i+1), i = (5 .. infinity))\n# so abs ( (arctan(x) -Q9(x) )/x ) <= x^10 * sum((-1)^(i+1)*x^(2*i)/(2*i+1+10), i = (0 .. infinity))\n# <= x^10 * 1/11\n# <= 2^(-66) if x<2^(-6.3)\n\n\n\n\n\n\n\n\n\n#Conputation of the RN constant\n\n\n#Epsilon = relative error\n#Delta = absolute error\n#1st : Error about reduction:\n\nEpsilonXminusBi := 2^(-105):\n\n# 1 + x*b[i] :\nEpsilon1A22xbi := 2^(-104):\n\n\n# Xred = (x-b[i]) / ( 1 + x*b[i] )\n\nEpsilonXred := EpsilonXminusBi+Epsilon1A22xbi + 2^(-105):\n\nDeltaXred := EpsilonXred * e:\n\nlog2(EpsilonXred);\n\n#Polynomial evaluation :\n#atan ~= x - x^3/3 + x^5/5 - x^7/7 + x^9/9\n# ~= x * ( 1 + Q(x^2) )\n# = (xhi+xlo) * ( 1 + Q)\n# ~= xhi + (xhi*Q + xlo)\n\n# Warning : the approx about x !!\n\n#calc of Q:\n\nEpsilonXred2 := (1+2^(-53) + 2^(-105) )^2 * (1+2^(-53)) -1 :\n\nlog2(EpsilonXred2);\n\nerrlist:=errlist_quickphase_horner( degree( x^4 ),0,0,EpsilonXred2, 2**(-53)):\n\nrounding_error1:= compute_horner_rounding_error(Qprime,x,e,errlist,true):\n\nEpsilonQ := rounding_error1[1]:\nlog2(EpsilonQ);\n\n# Since q will be multiplied in x(1+q), its absolute error term is :\n\nQmax:=infnorm(Qprime,x=-e^2..e^2):\n\nDeltaQ := e*Qmax*EpsilonQ;\nlog2(DeltaQ);\n\n# calc of xi*Q + xlo + atan(b[i])lo\n\n#First the truncation of xredlo*q : at most half an ulp of xredhi*q\nDeltaTruncXredloQ := 2^(-53) * e * Qmax:\nlog2(DeltaTruncXredloQ);\n#then the sum of atanbilo and xredlo : the largest term is atanbilo\nDeltaAdd1 := 0.5*ulp(2^(-53)*(Pi/2 + e)):\nlog2(DeltaAdd1);\n\n#then compute xredhi*q\nDeltaXredhiQ := 0.5*ulp(e*Qmax):\nlog2(DeltaXredhiQ);\n\n# and the second addition\nDeltaAdd2 := 0.5*ulp(e*Qmax + 2^(-53)*(Pi/2 + e) ):\nlog2(DeltaAdd2);\n\nDeltaAtanlolo := DeltaTruncXredloQ + DeltaAdd1 + DeltaXredhiQ + DeltaAdd2:\nlog2(DeltaAtanlolo);\n\n# In the second reconstruction there is one more FP add which is\n# aligned to the previous:\nDeltaReconst := DeltaAtanlolo + DeltaAdd2 :\nlog2(DeltaReconst);\n\n\n\n# error due to the approx of atan by P : < e^11/11\nDeltaapprox := infnorm( (arctan(x)-x*(1+Q)), x=0..e):\n\nlog[2](Deltaapprox);\n\n\n\n\n\nDeltaTotal := Deltaapprox + DeltaQ + DeltaReconst :\nlog2(DeltaTotal);\nEpsilonTotal := evalf( DeltaTotal / arctan(xx) ):\n\nEpsilonFinal := infnorm( EpsilonTotal,xx=2^(-6.3)..1,'xmaxmax'):\nEpsilonFinal_i_10 := infnorm( EpsilonTotal,xx=a[10]..2^60,'xmaxmax'):\nlog2( EpsilonFinal );\nlog2( EpsilonFinal_i_10 );\n\n\n# Computation of e and e_i_30 (which is e when i>30 (ie x>1)\nE := evalf(compute_rn_constant(EpsilonFinal));\nE_i_10 := evalf(compute_rn_constant(EpsilonFinal_i_10));\n\n\n#An other Constant : when there is no reduction.\n#We compute the polynom and then atan(x) = x + x.Q\n\nEpsilonx2 := 2^(-53):\nerrlist:=errlist_quickphase_horner( degree( Qprime ),0,0,Epsilonx2, 2**(-53)):\nrounding_error:= compute_horner_rounding_error(Qprime,x,e,errlist,true):\n\nepsilon_Q := rounding_error[1]:\nlog[2](epsilon_Q);\n\nepsilon_x_Q := 2^(-52):\n\ndelta_final := 2^(-105)*x + epsilon_Q*x^3 + epsilon_x_Q*x^3 - arctan(x) + x*(1+Q):\nepsilon_final := infnorm(delta_final/x,x=2^(-10)..e):\nepsilon_final_m10 := infnorm(delta_final/x,x=2^(-24)..2^(-10)):\n\nlog[2](epsilon_final);\nE_no_reduction := evalf(compute_rn_constant(epsilon_final));\nE_no_reduction_m10 := evalf(compute_rn_constant(epsilon_final_m10));\n\n\n\n# Output\n\n\n#test\nfilename:=\"TEMPATAN/atan_fast.h\":\n\nfd:=fopen(filename, WRITE, TEXT):\nfprintf(fd, \"\\n/*File generated by maple/atan.mpl */\\n\"):\n\nfprintf(fd, \"#ifndef _ATAN_FAST_H\\n#define _ATAN_FAST_H\\n\\n\");\n\nfprintf(fd, \"#include \\\"crlibm.h\\\"\\n#include \\\"crlibm_private.h\\\"\\n\"):\n\nfprintf(fd,\"#ifdef WORDS_BIGENDIAN\\n\"):\nfprintf(fd, \"static const db_number HALFPI = {{0x3FF921FB,0x54442D18}};\"):\nfprintf(fd, \"static const db_number HALFPI_TO_PLUS_INFINITY = {{0x3FF921FB,0x54442D19}};\"):\nfprintf(fd,\"\\n#else\\n\"):\nfprintf(fd, \"static const db_number HALFPI = {{0x54442D18,0x3FF921FB}};\"):\nfprintf(fd, \"static const db_number HALFPI_TO_PLUS_INFINITY = {{0x54442D19,0x3FF921FB}};\"):\nfprintf(fd,\"\\n\"):\nfprintf(fd,\"#endif\\n\"):\n\nfprintf(fd, \"#define MIN_REDUCTION_NEEDED %1.50f\\n\",e):\n\nfprintf(fd, \"#define INVPIH %1.50f\\n\", invpih):\nfprintf(fd, \"#define INVPIL %1.50f\\n\", invpil):\n\nfprintf(fd,\"#define nb_of_ai %d\\n\",nb_of_ai):\nfprintf(fd,\"#define nb_of_bi %d\\n\",nb_of_bi):\n\n# we multiply by 2^(-20) in order to prevent from rounding\nfprintf(fd, \"static const double rncst[4] ={\\n\"):\nfprintf(fd, \"%1.50f , /* i<10 */ \\n\",E*(1+2^(-20))) :\nfprintf(fd, \"%1.50f , /* i>10 */ \\n\",E_i_10*(1+2^(-20))) :\nfprintf(fd, \"%1.50f , /* e > 2^-10 */ \\n\",E_no_reduction*(1+2^(-20))) :\nfprintf(fd, \"%1.50f , /* e < 2^-10 */ \\n };\\n\",E_no_reduction_m10*(1+2^(-20))) :\n\nfprintf(fd, \"static const double epsilon[4] ={\\n\"):\nfprintf(fd, \"%1.50e ,\\n\",EpsilonFinal *(1+2^(-20))) :\nfprintf(fd, \"%1.50e ,\\n\",EpsilonFinal_i_10*(1+2^(-20))) :\nfprintf(fd, \"%1.50e ,\\n\",epsilon_final*(1+2^(-20))) :\nfprintf(fd, \"%1.50e ,\\n };\\n\",epsilon_final_m10*(1+2^(-20))) :\n\nfprintf(fd, \"#define DEGREE %d\\n\", deg_poly):\nfprintf(fd, \"static double const coef_poly[%d] = \\n{\\n\",deg_poly):\n\nfor i from deg_poly-1 to 0 by -1 do\n fprintf(fd, \"/* coef for degree %d */ %1.50f, \\n\" , 2*i+3, coef_poly[i]):\nod:\nfprintf(fd,\" }; \\n\");\n\nfprintf(fd,\"#define A 0\\n\"):\nfprintf(fd,\"#define B 1\\n\"):\nfprintf(fd,\"#define ATAN_BHI 2\\n\"):\nfprintf(fd,\"#define ATAN_BLO 3\\n\"):\n\nfprintf(fd,\"\\n#ifdef WORDS_BIGENDIAN\\n \"):\n\nfor isbig from 1 to 0 by -1 do\n\n if(isbig=0) then\n fprintf(fd,\"#else\\n\");\n fi:\n\n if(not (nb_of_ai = nb_of_bi)) then\n printf(\"Warning : nb_of_ai != nb_of_bi, this should not work\");\n fi:\n\n fprintf(fd,\"\\n/* limits of the intervals [a[i],b[i]] */\\n\");\n fprintf(fd, \"static db_number const arctan_table[%d][4] = \\n{\\n\" , nb_of_ai );\n\n for i from 0 to nb_of_ai - 1 do\n fprintf(fd, \"{\\n/*a[%d] */ \",i);\n printendian(fd,a[i],isbig);\n fprintf(fd,\" ,\\n/*b[%d] : */ \",i):\n printendian(fd,b[i],isbig):\n fprintf(fd,\" ,\\n/*atan_b[%d]*/ \",i):\n printendian(fd, arctan(b[i]) ,isbig):\n fprintf(fd,\",\");\n printendian(fd, arctan(b[i])-nearest(arctan(b[i])) ,isbig);\n fprintf(fd,\" ,\\n}\\n,\");\n od;\n fprintf(fd,\"\\n};\\n\");\nod:\n\nfprintf(fd,\"\\n#endif\\n\\n\"):\n\nfprintf(fd, \"#endif /* def _ATAN_FAST_H */\\n\");\n\nfclose(fd);\n\n\n\n# Scs phase\n\n#Now we want a precision of 130 bits in order to have correct rounding in all cases.\nevalf(log[2](e^21/21));\n#Test about Rounding :\n#error on the polynom :\nP_scs := convert(series(arctan(x),x=0,21),polynom);\nevalf(log[2](e^21/21));\n#Intervals parameters\n#We choose the same e and the same intervals as in the quick phase.\n\n#We have the same b[i]s and a[i]s but we save atan[b[i]] on 4 doubles\n\n# Output\nfilename:=\"TEMPATAN/atan_accurate.h\":\nfd1:=fopen(filename, WRITE, TEXT):\n\nfprintf(fd1, \"#include \\\"crlibm.h\\\"\\n#include \\\"crlibm_private.h\\\" \\n#include \\\"atan_fast.h\\\"\\n\"):\nfprintf(fd1, \"\\n/*File generated by maple/atan.mpl */\\n\"):\n\nWrite_SCS_poly(fd1, \"constant_poly\", P_scs);\n\nfprintf(fd1,\"#define constant_poly_ptr (scs_ptr)&constant_poly\\n\");\n\n# The 1/Pi SCS constant\n fprintf(fd, \"static const scs InvPiSCS=\\n\"):\n WriteSCS(fd, evalf(1/Pi)):\n fprintf(fd, \";\\n#define InvPiSCS_ptr (scs_ptr)(& InvPiSCS)\\n\\n\"):\n\n\nfprintf(fd1,\"#ifdef WORDS_BIGENDIAN\\n\\n\"):\nfor isbig from 1 to 0 by -1 do\n if isbig = 0 then\n fprintf(fd1, \"\\n#else\\n\"):\n fi:\n\n fprintf(fd1,\"static const db_number atan_blolo[%d] = {\\n\",nb_of_ai);\n for i from 0 to nb_of_ai-1 do\n fprintf(fd1,\"/* %d */ \",i):\n temp0 := nearest(arctan(b[i]));\n temp := nearest( arctan(b[i]) - nearest(arctan(b[i])));\n temp1 := nearest( arctan(b[i]) - temp -temp0);\n printendian(fd1,temp1,isbig):\n fprintf(fd1,\", \\n\");\n od:\n\n fprintf(fd1,\"};\\n\"):\n\nod:\nfprintf(fd1,\"\\n#endif /* WORDS_BIGENDIAN */ \\n\");\n\nfclose(fd1);\n", "meta": {"hexsha": "fadf16031118a8bb10e604c950cca4cbe56b9724", "size": 9968, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "crlibm/maple/atan.mpl", "max_stars_repo_name": "squarePenguin/parvsl", "max_stars_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": "crlibm/maple/atan.mpl", "max_issues_repo_name": "squarePenguin/parvsl", "max_issues_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2019-03-25T17:02:38.000Z", "max_issues_repo_issues_event_max_datetime": "2019-03-25T17:02:38.000Z", "max_forks_repo_path": "crlibm/maple/atan.mpl", "max_forks_repo_name": "squarePenguin/parvsl", "max_forks_repo_head_hexsha": "0d502abe795540a3dfc99d43726d3fc29a5e6e5d", "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": 26.5813333333, "max_line_length": 108, "alphanum_fraction": 0.621388443, "num_tokens": 3693, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8031737963569014, "lm_q2_score": 0.6619228758499942, "lm_q1q2_score": 0.5316391090919178}} {"text": "with(Algebraic):\n\nfindElementaryIntegral := proc(maxint, maxdeg, raddeg, radexpt, x, ngoal)\n\n\tlocal ngiveup, nsincelast, totaltime, nfound, ntrials, nrepeats, num, den, rad, integrand, integral, radsqf, fac, r;\n\n\tSeed := randomize();\n\n\tngiveup := 2500;\n\n\trandinrange := rand(-maxint..maxint);\n\tnegrandinrange := rand(-maxint..-1);\n\tposrandinrange := rand(1..maxint);\n\trandf := rand(0.0..1.0);\n\n\tinterface(prettyprint=0);\n\n\tfound := [];\n\tnfound := 0;\n\tntrials := 0;\n\tnrepeats := 0;\n\tnsincelast := 0;\n\twhile (nfound < ngoal) do\n\n\t\tnum := [seq(randinrange()*x^k, k=0..maxdeg)];\n\t\tnum := convert(num, `+`);\n\t\tden := [seq(randinrange()*x^k, k=0..maxdeg)];\n\t\tden := convert(den, `+`);\n\t\trad := [seq(randinrange()*x^k, k=1..raddeg-1)];\n\t\trad := convert(rad, `+`);\n\t\tif randf() < 0.5 then\n\t\t\trad := x^raddeg + negrandinrange() + rad;\n\t\telse\n\t\t\trad := x^raddeg + posrandinrange() + rad;\n\t\tend if;\n\t\n\t\tif num*den*rad = 0 then next end if; \n\n\t\tradsqf := Squarefree(rad)[2];\n\t\tm := 1/radexpt;\n\n\t\tif nops(radsqf) = 1 then\n\t\t\tif degree(radsqf[1][1],x) = 1 then next end if;\n\t\tend if;\n\n\t\tbad := false;\n\t\tfor fac in radsqf do\n\t\t\tr := fac[2] mod m;\n\t\t\tif r = 0 then \n\t\t\t\tbad := true;\n\t\t\tend if;\n\t\tend do;\n\n\t\tif bad then next end if;\n\n\t\tintegrand := normal(num/den)/(rad)^radexpt; \n\n\t\tif evalb(integrand in found) then \n\t\t\tnrepeats += 1;\n\t\t\tif nrepeats > 4 then \n\t\t\t\tbreak\n\t\t\tend if;\n\t\t\tnext \n\t\tend if;\n\n\t\tntrials += 1;\n#\t\tprint (\"integrand = \", integrand);\n\t\tt0 := Now(ProcessClock);\n\t\tintegral := int(convert(integrand, RootOf), x);\n\t\tt1 := Now(ProcessClock);\n\t\ttotaltime := totaltime + t1 - t0;\n#\t\tprint(\"integral = \", integral);\n\n\t\tif not has(integral,[int,EllipticPi,EllipticE,EllipticF]) then\n\t\t\tnfound += 1;\n\t\t\tnsincelast := 0;\n\t\t\tfound := [op(found), integrand];\n\t\t\tprint(\"integrand = \", integrand);\n\t\t\tprint(\"integral = \", convert(integral, radical));\n\t\telse\n\t\t\tnsincelast += 1;\n\t\tend if;\n\n\t\tif nsincelast > ngiveup then break end if;\n\n\t\tif ntrials mod 100 = 0 then\n\t\t print(\"ntrials = \", ntrials, \", nfound = \", nfound, \", % elementary = \", evalf(100.0*nfound/ntrials));\n\t\tend if;\n\tend;\n\n\tprint(\"FINISHED! params = \", maxint, maxdeg, raddeg, radexpt, x, ngoal, \" ntrials = \", ntrials, \", nfound = \", nfound, \", % elementary = \", evalf(100.0*nfound/ntrials), \", mean time = \", evalf(totaltime/ntrials));\nend proc;\n\n", "meta": {"hexsha": "054d5e09e7a21e497ab5808afbf0b78cabde6882", "size": 2311, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple_search.mpl", "max_stars_repo_name": "stblake/algebraic_integration", "max_stars_repo_head_hexsha": "34599fb72b69d3e7814a441713ad1e7cbdc50435", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 6, "max_stars_repo_stars_event_min_datetime": "2021-04-06T05:05:18.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-03T18:09:32.000Z", "max_issues_repo_path": "maple_search.mpl", "max_issues_repo_name": "stblake/algebraic_integration", "max_issues_repo_head_hexsha": "34599fb72b69d3e7814a441713ad1e7cbdc50435", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2021-12-29T15:55:49.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-16T21:03:23.000Z", "max_forks_repo_path": "maple_search.mpl", "max_forks_repo_name": "stblake/algebraic_integration", "max_forks_repo_head_hexsha": "34599fb72b69d3e7814a441713ad1e7cbdc50435", "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": 24.585106383, "max_line_length": 214, "alphanum_fraction": 0.6101254868, "num_tokens": 847, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.82893881677331, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.5310479274935431}} {"text": " func $ceilf64toi32 (\n var %i f64\n ) i32 { \n return (\n ceil i32 f64(dread f64 %i))}\n\n func $ceilf64toi64 (\n var %i f64\n ) i64 { \n return (\n ceil i64 f64(dread f64 %i))}\n\n func $ceilf32toi32 (\n var %i f32\n ) i32 { \n return (\n ceil i32 f32(dread f32 %i))}\n\n\n func $ceilf32toi64 (\n var %i f32\n ) i64 { \n return (\n ceil i64 f32(dread f32 %i))}\n\n# todo float ceil\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "452853a54d985de2e3cdffec63b7965ff8661cf3", "size": 493, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0014-mapleall-irbuild-edge-ceil/Main.mpl", "max_stars_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_stars_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 796, "max_stars_repo_stars_event_min_datetime": "2019-08-30T16:20:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-25T14:45:06.000Z", "max_issues_repo_path": "test/testsuite/irbuild_test/I0014-mapleall-irbuild-edge-ceil/Main.mpl", "max_issues_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_issues_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 16, "max_issues_repo_issues_event_min_datetime": "2019-08-30T18:04:08.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-19T05:02:58.000Z", "max_forks_repo_path": "test/testsuite/irbuild_test/I0014-mapleall-irbuild-edge-ceil/Main.mpl", "max_forks_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_forks_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 326, "max_forks_repo_forks_event_min_datetime": "2019-08-30T16:11:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-26T12:31:17.000Z", "avg_line_length": 16.4333333333, "max_line_length": 43, "alphanum_fraction": 0.5801217039, "num_tokens": 197, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.766293653760418, "lm_q2_score": 0.6926419894793246, "lm_q1q2_score": 0.5307671608659967}} {"text": "kernelopts(assertlevel=2): # be strict on all assertions while testing\nkernelopts(opaquemodules=false): # allow testing of internal routines\nif not (NewSLO :: `module`) then\n WARNING(\"loading NewSLO failed\");\n `quit`(3);\nend if;\n\nwith(Hakaru):\nwith(NewSLO):\nwith(Partition):\n\n#####################################################################\n#\n# disintegration tests\n#\n#####################################################################\nd1 := Bind(Lebesgue(-infinity,infinity), x, Ret(Pair(-5*x,3/x))):\nd1r := {Weight(1/5,Ret(-15/t))}:\n\n# should try d2 with 1/c as well\nd2 := Bind(Lebesgue(-infinity,infinity), x, Ret(Pair((-1/7)*x-1,3))):\nd2r := {Weight(7, Ret(3))}:\n\n#The next two tests are simplified versions of the Borel-Kolmogorov paradox.\n#https://en.wikipedia.org/wiki/Borel-Kolmogorov_paradox\nd3 := Bind(Uniform(0,1), x, Bind(Uniform(0,1), y, Ret(Pair(x-y,f(x,y))))):\nd3r := {\n PARTITION([Piece(Or(t <= -1,1 < t)\n ,Msum())\n ,Piece(And(t <= 0, -1 < t)\n ,Weight(t+1,Bind(Uniform(-t,1),`y`,Ret(f(t+y,y)))))\n ,Piece(And(t <= 1, 0 < t)\n ,Weight(1-t,Bind(Uniform(0,1-t),`y`,Ret(f(t+y,y)))))\n ]) ,\n PARTITION([Piece(Or(t <= -1,1 < t)\n ,Msum())\n ,Piece(And(t <= 0, -1 < t)\n ,Weight(t+1,Bind(Uniform(0,t+1),`x`,Ret(f(x,-t+x)))))\n ,Piece(And(t <= 1, 0 < t)\n ,Weight(1-t,Bind(Uniform(t,1),`x`,Ret(f(x,-t+x)))))\n ]),\nPARTITION([Piece(Or(t <= -1,1 <= t),Msum())\n ,Piece(And(-1 < t,t <= 0),Weight(t+1,Bind(Uniform(0,t+1),x,Ret(f(x,-t+x)))))\n ,Piece(And(0 < t,t < 1),Weight(1-t,Bind(Uniform(t,1),x,Ret(f(x,-t+x)))))\n ])\n}:\n\nBUniform := proc(x,b,$) Bind(Uniform(0,1), x, b) end proc:\nd3_3 := BUniform(x, BUniform(y, BUniform(z, Ret(Pair(x+y+z,f(x,y,z)))))):\nd3_3_r := {}:\n\nd4 := Bind(Uniform(0,1), x, Bind(Uniform(0,1), y, Ret(Pair(x/y,x)))):\nd4r := {\n Weight(1/abs(t)^2,\n Bind(Uniform(0,1),x,\n piecewise(x < t,Weight(x,Ret(x)),Msum()))),\n piecewise(0 < t,\n Bind(Uniform(0,1),y,\n piecewise(t < 1/y,\n Weight(y,Ret(t*y)),\n Msum())),\n Msum()),\n PARTITION([Piece(t <= 0,Msum())\n , Piece(And(t <= 1, 0 < t),Weight(1/t,Bind(Uniform(0,t),x,Weight(x,Ret(x)))))\n , Piece(1 < t,Weight(1/2/t^2,BetaD(2,1)))]),\n PARTITION([Piece(t <= 0,Msum()), Piece(0 < t and t < 1,Weight(1/t,Bind(Uniform(0,t),x,Weight(x,Ret(x))))), Piece(1 <= t,Weight(1/2/t^2,BetaD(2,1)))])\n}:\n\n# like d3 but positive, and the entire parametric family.\nd3posfam := Bind(Uniform(0, 1), x, Bind(Uniform(0, 1), y, Ret(Pair(x+y+K_0, f(x, y))))):\nd3posfam_r := {\n PARTITION([ Piece(t <= K_0, Msum())\n , Piece(And(K_0 < t, t <= 1+K_0), Weight(t-K_0, Bind(Uniform(0, t-K_0), x, Ret(f(x, t-x-K_0)))))\n , Piece(And(t < 2+K_0, 1+K_0 < t), Weight(2-t+K_0, Bind(Uniform(-1+t-K_0, 1), x, Ret(f(x, t-x-K_0)))))\n , Piece(2+K_0 <= t, Msum())]) }:\nd3posfam_ctx := [K_0::real]:\n\nd5 := Bind(Gaussian(0,1), x, Bind(Gaussian(x,1), y, Ret(Pair(y,x)))):\nd5r := {Weight((1/2)*exp(-(1/4)*t^2)/Pi^(1/2), Gaussian((1/2)*t, (1/2)*2^(1/2)))}:\n\nd6 := Bind(Gaussian(0,1), x, Bind(Gaussian(x,1), y, Ret(Pair(x,y)))):\nd6r := {Weight(1/2*2^(1/2)/Pi^(1/2)*exp(-1/2*t^2),Gaussian(t,1))}:\n\n# note (y+y), which gives trouble for a syntactic approach\nnormalFB1 :=\n Bind(Gaussian(0,1), x,\n Bind(Gaussian(x,1), y,\n Ret(Pair((y+y)+x, _Unit)))):\n\nnormalFB1r := {Weight(1/26*exp(-1/26*t^2)/Pi^(1/2)*13^(1/2)*2^(1/2),Ret(_Unit))}:\n\n# tests taken from haskell/Tests/Disintegrate.hs\n# use same names, to be clearer\nnorm0a :=\n Bind(Gaussian(0,1), x,\n Bind(Gaussian(x,1), y,\n Ret(Pair(y, x)))):\n # note that the answer below is much nicer than the one expected in Haskell\nnorm0r := {Weight(1/2*exp(-1/4*t^2)/Pi^(1/2),Gaussian(t/2,sqrt(2)/2))}:\n\nnorm1a :=\n Bind(Gaussian(3,2), x,Ret(piecewise(x<0, Pair(-x, _Unit), Pair(x, _Unit)))):\nnorm1b :=\n Bind(Gaussian(3,2), x,piecewise(x<0, Ret(Pair(-x, _Unit)), Ret(Pair(x, _Unit)))):\n\n\nnorm1r_w := (1/4)*sqrt(2)*exp(-9/8)*((exp(t))^(3/4)/(exp(t^2))^(1/8)+1/((exp(t^2))^(1/8)*(exp(t))^(3/4)))/sqrt(Pi):\nnorm1r := {\n Weight( piecewise(t < 0 , 0\n ,0 <= t , norm1r_w\n )\n , Ret(_Unit)\n ) ,\n Weight( PARTITION([Piece(t < 0 , 0)\n ,Piece(0 <= t , norm1r_w)\n ])\n , Ret(_Unit)\n )\n}:\n\nassume(s::real, noiseT >= 3, noiseT <= 8, noiseE >= 1, noiseE <= 8);\neasyRoad:= [\n Bind(Uniform(3, 8), noiseT,\n Bind(Uniform(1, 4), noiseE,\n Bind(Gaussian(0, noiseT), x1,\n Bind(Gaussian(x1, noiseE), m1,\n Bind(Gaussian(x1, noiseT), x2,\n Bind(Gaussian(x2, noiseE), m2,\n Ret(Pair(Pair(m1,m2), Pair(noiseT,noiseE)))\n )))))),\n Pair(s,t)\n]:\n#The first expression below comes from the actual output of disint, hand-\n#simplified 1) to bring factors into the innnermost integral, 2) to combine\n#products of exps, and 3) to express the polynomial arg of exp in a logical way\n#by sub-factoring.\neasyRoadr:= {\n Weight( #Weight 1\n Pi/8,\n Bind( #Bind 1\n Uniform(3, 8), noiseT,\n Weight( #Weight 2\n 1/noiseT^2,\n Bind( #Bind 2\n Uniform(1, 4), noiseE,\n Weight( #Weight 3\n int( #Int 1\n int( #Int 2\n exp(\n -(x2^2/2 - x1*x2 + x1^2)/noiseT^2 -\n ((t-x2)^2 + (s-x1)^2)/noiseE^2\n )*2/Pi/noiseE,\n x2= -infinity..infinity\n ), #-Int 2\n x1= -infinity..infinity\n ), #-Int 1\n Ret(Pair(noiseT, noiseE))\n ) #-Weight 3\n ) #-Bind 2\n ) #-Weight 2\n ) #-Bind 1\n ), #-Weight 1\n\n #Hopefully, that's equivalent to...\n Bind(Uniform(3, 8), noiseT,\n Bind(Uniform(1, 4), noiseE,\n Bind(Gaussian(0, noiseT), x1,\n Bind(Weight(density[Gaussian](x1, noiseE)(s), Ret(_Unit)), _,\n Bind(Gaussian(x1, noiseT), x2,\n Weight(density[Gaussian](x2, noiseE)(t), Ret(Pair(noiseT, noiseE)))\n )))))\n}:\nhelloWorld:=\n Bind(Gaussian(0,1), mu,\n Bind(Plate(n, k, Gaussian(mu, 1)), nu,\n Ret(Pair(nu, mu))\n )):\nhelloWorldr:= {\n Bind(Gaussian(0,1), mu,\n Plate(n, i, Weight(density[Gaussian](mu, 1)(idx(t,i)), Ret(mu)))\n )\n}:\n\npair_x_x := Bind(Uniform(0, 1), x, Ret(Pair(x, x))):\npair_x_x_r := {\n PARTITION([Piece(t < 0, Msum()), Piece(And(0 <= t, t <= 1), Ret(t)),\n Piece(1 < t, Msum())]) }:\n\n#This first block of tests is to test the basic functionality of disint, and,\n#to some extent, the system as a whole. These tests may be meaningless to you,\n#the statistician and end user of this Hakaru product; they aren't meant to\n#have any statistical meaning.--Carl 2016Oct04\n\nTestDisint(\n [Ret(Pair(sqrt(Pi), x)), t &M Ret(7)],\n {Msum()},\n label= \"(d0_2) `Dirac` test 1\"\n);\n\nTestDisint(\n [Ret(Pair(sqrt(Pi), x^2)), t &M Ret(sqrt(Pi))],\n {Ret(x^2)},\n label= \"(d0_3) `Dirac` test 2\"\n);\n\nTestDisint(\n [Bind(Lebesgue((-1,1)*~infinity), x, Ret(Pair(sqrt(Pi), x^2))),\n t &M Ret(sqrt(Pi))\n ],\n {Bind(Lebesgue((-1,1)*~infinity), x1, Ret(x1^2))},\n label= \"(d0_4) `Dirac` test with `Bind`\"\n);\n\nTestDisint(d1, d1r, label = \"(d1) Disintegrate linear function\");\nTestDisint(d2, d2r, label = \"(d2) Disintegrate linear function II\");\nTestDisint(d5, d5r, label = \"(d5) Disintegrate N(0,1)*N(x,1), over y\");\nTestDisint(d6, d6r, label = \"(d6) Disintegrate N(0,1)*N(x,1), over x\");\nTestDisint(norm0a, norm0r,\n label = \"(norm0a) U(0,1) >>= \\x -> U(x,1) >>= \\y -> Ret(y,x)\"\n);\n\n## This one is kind of cosmetic; it would be 'fixed' properly if the\n## disintegration process did not use 'improve' to do \"domain information\n## discovery\", but rather had a specific function (and then improve could\n## indeed do this integral).\n# should work now\nTestDisint( normalFB1, normalFB1r,\n label = \"(d7_normalFB1) Disintegrate N(0,1)*N(x,1), over (y+y)+x\"\n );\n\nTestDisint(d3, d3r, label = \"(d3) Disintegrate U(0,1) twice, over x-y\");\n\n######################################################################\n#\n# These tests fail, and are expected to. Move them up when they\n# start passing (and are expected to).\n#\n# They are, however, roughly in order of what we'd like to have work.\n#\n\n# change of variables\nTestDisint(d4, d4r, label = \"(d4) Disintegrate U(0,1) twice, over x/y\");\n# funky piecewise\nTestDisint(norm1a, norm1r,\n label = \"(norm1a) U(0,1) into Ret of pw\"\n);\nTestDisint(norm1b, norm1r,\n label = \"(norm1b) U(0,1) into pw of Ret\"\n);\n#In this one the function in the inequality, x+x^3, is injective but nonlinear.\nTestDisint(\n Bind(Gaussian(0,1), x, Ret(Pair(x+x^3, f(x)))),\n {}, #I don't know what to expect.\n label= \"(d0_5) Injective nonlinear inequality\"\n);\n\nTestDisint(pair_x_x, pair_x_x_r, label=\"(pair_x_x) Disintegrate U(0,1) over Ret(x,x)\");\nTestDisint(d3_3, d3_3_r, [], 180\n , label = \"(d3_3) Disintegrate U(0,1) thrice, over x+y+z\");\nTestDisint(d3posfam, d3posfam_r, d3posfam_ctx\n , label = \"(d3posfam) Disintegrate U(0,1) twice, over x+y+K\");\n\n#This one is a basic test of the Counting wrt-var type.\n#This one gives the Weight(-1, ...) error\nTestDisint(\n [Bind(PoissonD(2), n, Ret(Pair(3,n))), n_wrt &M Counting((-1,1)*~infinity)],\n {}, #I don't know what to expect.\n label= \"(d0_1) `Counting` test; `Weight` bug (currently failing)\"\n);\n\nTestDisint(\n helloWorld, helloWorldr,\n [n::integer, n > 0],\n label= \"(helloWorld) Plate of Normals\"\n);\n\n# tests which take too long\nTestDisint(\n easyRoad, easyRoadr, [],\n 120, #takes 6 - 8 minutes to `improve` on an Intel i7\n label= \"(easyRoad) Combo of Normals with distinct Uniform noises\"\n);\n\n# Example from Chad (April 9, 2017)\nprog :=\n Bind(Gaussian(70,30), temp,\n Bind(Gaussian(temp, 10), withErr,\n Ret(Pair(min(withErr, 100), temp)))):\nTestDisint( prog, {}, label= \"censored temperature example\");\n", "meta": {"hexsha": "c98182620fd0e3b2abd05bf8f9f1c04cffc5ed8b", "size": 10075, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/DisintT.mpl", "max_stars_repo_name": "zaxtax/hakaru", "max_stars_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2015-02-07T17:57:04.000Z", "max_stars_repo_stars_event_max_datetime": "2016-01-29T19:40:24.000Z", "max_issues_repo_path": "maple/DisintT.mpl", "max_issues_repo_name": "zaxtax/hakaru", "max_issues_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/DisintT.mpl", "max_forks_repo_name": "zaxtax/hakaru", "max_forks_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "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": 34.7413793103, "max_line_length": 151, "alphanum_fraction": 0.552853598, "num_tokens": 3568, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7520125737597972, "lm_q2_score": 0.7057850340255386, "lm_q1q2_score": 0.5307592199586914}} {"text": "\n# Base Parameter Energy Regressor for Robot based on MDH frames\n# Einleitung\n# Erstellung einer parameterlinearen und -minimalen Regressorform\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# chain -> Berechnung f\u00fcr eine serielle Struktur (nicht: Baumstruktur)\n# fixb -> fixed base. Kein Floating base Modell. Dort ist diese Form der Minimalparameterform nicht m\u00f6glich.\n# energy -> Berechnung bezogen auf Energie\n# regressor -> Regressorform (parameterlinear)\n# linearsolve -> Nicht geometrischer Ansatz nach Khalil, sondern symbolischer Ansatz mit LinearSolve\n# Authors\n# Jonas Diekmeyer (Studienarbeit bei Elias Kn\u00f6chelmann)\n# Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2020-06\n# \n# (C) Institut fuer Mechatronische Systeme, Leibniz Universitaet Hannover\n# Quellen\n# [Diekmeyer2018_S678] Identifikation der inversen Dynamik eines seriellen Roboters im geschlossenen Regelkreis, Studienarbeit, imes, LUH, 2018\n# Initialisierung\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\ninterface(rtablesize=100): # Zur Anzeige von gr\u00f6\u00dferen Vektoren\n;\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name, base_method_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Absch\u00e4tzen der Komplexit\u00e4t\n;\n# Pr\u00fcfe, ob die symbolische Berechnung der Parameterminimierung berechnet werden sollte\nabort_this_worksheet := false:\n# Bestimme, ob es eine Baumstruktur ist. Wenn ja, funktioniert der andere Algorithmus nicht und dieser wird genommen.\ntree:=false:\nfor i from 1 to NJ do\n if not v(i) = i-1 then\n tree := true: break:\n end if:\nend do:\n\nif not (assigned(user_CoM) or assigned(user_M) or assigned(user_inertia) \\\n or kin_constraints_exist or tree) then\n # Es gibt keinen Sonderfall, diese Berechnung der Minimalparameter ist nicht notwendig.\n printf(\"Keine analytische Berechnung der Minimalparameter notwendig.\\n\"):\n abort_this_worksheet := true:\nend if:\n\nif assigned(dynpar_minimization_linsolve) and not dynpar_minimization_linsolve then\n printf(\"Analytische Berechnung der Minimalparameter manuell deaktiviert.\\n\"):\n abort_this_worksheet := true:\nend if:\n\nif assigned(dynpar_minimization_linsolve) and dynpar_minimization_linsolve then\n printf(\"Analytische Berechnung der Minimalparameter durch Option dynpar_minimization_linsolve verlangt.\\n\"):\n abort_this_worksheet := false:\nend if:\n\nif abort_this_worksheet then\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\nprintf(\"%s. Generiere Minimalparameterregressor der Energie f\u00fcr %s (symbolischer Ansatz)\\n\", \\ \n FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name, codegen_dynpar):\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(7)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardm\u00e4\u00dfig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # standardm\u00e4\u00dfig simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(7): # siebter Eintrag ist f\u00fcr Energie-Regressor\nend if:\n\n# Ergebnisse der Energie laden (aus robot_chain_fixb_rotmat_energy_regressor.mw)\nread sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_maple.m\", robot_name):\nt_ges := t_ges:\nread sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_maple.m\", robot_name):\nu_ges := u_ges:\n# Parameterminimierung\n# Siehe auch [Diekmeyer2018_S678] S. 19f. und 32ff.\n# Funktionen definieren\n\nsplitSummands := proc(input_expr)\n# Gibt eine Liste aller Summanden zur\u00fccachezur\u00fcck\n local expr, sub_expr:\n\n expr := expand(input_expr):\n \n if type(expr,'`+`') then\n sub_expr := op(expr):\n return sub_expr:\n else\n return expr:\n end if:\n \nend proc:\n\nsplitFactors := proc(input_expr)\n# Gibt eine Liste aller Faktoren zur\u00fcck\n local sub_expr:\n \n if type(input_expr,'`*`') then\n sub_expr := op(input_expr):\n return sub_expr:\n else\n return input_expr:\n end if:\n \nend proc:\n\nremoveEmptyRows := proc(h,G)\n local mh, mG, i, j, flag:\n \n flag := Vector[column](Size(G,1)):\n for i from 1 to Size(G,1) do\n flag(i) := 0:\n for j from 1 to Size(G,2) do\n if G(i,j) <> 0 then\n flag(i) := 1:\n end if:\n end do:\n end do:\n\n mh := Vector[column](Norm(flag,1)):\n mG := Matrix(Norm(flag,1),Size(G,2)):\n\n j := 1:\n for i from 1 to Size(G,1) do\n if flag(i) = 1 then\n mG(j,..) := G(i,..):\n mh(j) := h(i):\n j := j + 1:\n end if:\n end do:\n\n return mh, mG:\nend proc:\n\npermuteEmptyRows := proc(G)\n local Pb, Pd, i, j, k, flag:\n \n flag := Vector[column](Size(G,1)):\n for i from 1 to Size(G,1) do\n flag(i) := 0:\n for j from 1 to Size(G,2) do\n if G(i,j) <> 0 then\n flag(i) := 1:\n end if:\n end do:\n end do:\n\n Pb := Matrix(Norm(flag,1),Size(G,1)):\n Pd := Matrix(Size(G,1)-Norm(flag,1),Size(G,1)):\n\n j := 0:\n k := 0:\n for i from 1 to Size(G,1) do\n if flag(i) = 1 then\n j := j + 1:\n Pb(j,i) := 1:\n elif flag(i) = 0 then\n k := k + 1:\n Pd(k,i) := 1:\n end if:\n end do:\n\n return Pb, Pd:\nend proc:\n\nhasElement := proc(v, expr)\n# Gibt den Index des Vektorelements von \"v\" wieder, das dem Ausdruck \"expr\" entspricht.\n# Ist der Ausdruck nicht enthalten wird der h\u00f6chste Index um eins erh\u00f6ht wiedergegeben.\n local i:\n\n for i from 1 to NumElems(v) do\n if verify(v(i),expr) then\n return i:\n end if:\n end do:\n \n return NumElems(v)+1:\nend proc:\n\ntmp_tt1 := time(): tmp_timelastmessage := tmp_tt1:\n# Kinematikparameter, die als Argument von Sinus und Cosinus stehen ersetzen.\n# Ansonsten werden sie durch die Umwandlung in die Exponentialform mit ersetzt. Das ist aber nicht hilfreich.\nread sprintf(\"../codeexport/%s/tmp/parameter_kin\", robot_name):\npkin := pkin:\n\nlagrange := Vector[column](t_ges[1,..] - u_ges[1,..]):\n(*\n# TODO: Das scheint die Rechenzeit von LinearSolve in manchen F\u00e4llen stark zu verl\u00e4ngern\nfor j from 1 to RowDimension(pkin) do\n lagrange := subs(parse(sprintf(\"sin(%s)\", pkin(j,1)))=parse(sprintf(\"sin_%s\", pkin(j,1))), lagrange):\n lagrange := subs(parse(sprintf(\"cos(%s)\", pkin(j,1)))=parse(sprintf(\"cos_%s\", pkin(j,1))), lagrange):\nend do:\n*)\n\n# Parameter gruppieren. Siehe [Diekmeyer2018_S678] Gl. 3.27\n# Erstelle eine Matrix V, die die einzelnen Terme des Energie-Regressors gruppiert\n# Komponentenmatrix f\u00fcr jeden Eintrag des Lagrange-Regressors.\n# Initialisierung mit voller Dimension (notwendig f\u00fcr geschlossene kinematische Ketten;\n# in dem Fall sind die Eintr\u00e4ge der letzten Parameter Null/konstant. Bei rein seriellen Ketten nicht der Fall).\nV := Matrix(NumElems(lagrange),1):\nw := Vector[column](): # Hilfsvariable\nfor i from 1 to NumElems(lagrange) do # Parameter-Eintr\u00e4ge durchgehen\n if i=1 or time()-tmp_timelastmessage > 10.0 then # min. alle 10s Status ausgeben.\n printf(\"%s. Erstelle Komponentenmatrix f\u00fcr Lagrange-Regressor-Eintrag %d/%d\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, NumElems(lagrange)):\n tmp_timelastmessage := time():\n end if:\n lagrange_term := simplify(expand(lagrange(i))):\n # Umrechnung der Trigonometrische Funktion in Exponent-Darstellung.\n # Funktioniert nicht ganz wie erwartet, falls Parameter in sin/cos stehen. Dann treten Imagin\u00e4rteile auf.\n # Diese werden weiter unten wieder entfernt\n # Durch diesen Befehl wird die Spalten-Dimension der Matrix stark reduziert (ca. auf ein Drittel)\n lagrange_term := convert(lagrange_term,exp):\n lagrange_term := simplify(expand(lagrange_term),size):\n lagrange_summand := [splitSummands(lagrange_term)]:\n# print(lagrange_summand):\n for j from 1 to nops(lagrange_summand) do\n# printf(\"j=%d\\n\", j):\n # Konstante Ausdr\u00fccke werden nicht ber\u00fccksichtigt!\n if not has(lagrange_summand[j],t) then\n next:\n end if:\n lagrange_factor := [splitFactors(lagrange_summand[j])]:\n lagrange_timeVar := 1:\n lagrange_constant := 1:\n for k from 1 to nops(lagrange_factor) do\n# printf(\"k=%d\\n\", k):\n if has(lagrange_factor[k],t) then\n lagrange_timeVar := lagrange_timeVar * lagrange_factor[k]:\n else\n lagrange_constant := lagrange_constant * lagrange_factor[k]:\n end if\n end do:\n lagrange_timeVar := simplify(expand(lagrange_timeVar)):\n index_timeVar := hasElement(w,lagrange_timeVar):\n if index_timeVar > NumElems(w) then\n w(index_timeVar) := lagrange_timeVar:\n V(i,index_timeVar) := lagrange_constant:\n elif i > Size(V,1) then\n V(i,index_timeVar) := lagrange_constant:\n else\n V(i,index_timeVar) := V(i,index_timeVar) + lagrange_constant:\n end if:\n end do:\nend do:\n# Substitutierte sinus/cosinus-Terme der Kinematikparameter wieder zur\u00fcckersetzen\n\n(* Nicht notwendig, wenn oben auskommentiert.\nfor j from 1 to RowDimension(pkin) do\n V := subs(parse(sprintf(\"sin_%s\", pkin(j,1)))=parse(sprintf(\"sin(%s)\", pkin(j,1))), V):\n V := subs(parse(sprintf(\"cos_%s\", pkin(j,1)))=parse(sprintf(\"cos(%s)\", pkin(j,1))), V):\nend do:\n*)\n# \ntmp_tt2 := time():\nprintf(\"%s. Komponenten-Matrix des Energie-Regressors berechnet (%dx%d). Rechenzeit: %1.1fs\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), RowDimension(V), ColumnDimension(V), tmp_tt2-tmp_tt1):\nsave V, sprintf(\"../codeexport/%s/tmp/minimal_parameter_calculation_fixb_maple_linsolve_debug1.m\", robot_name):\n# Rang der Matrix pr\u00fcfen f\u00fcr Dimension des Parametervektors\ntmp_t1 := time():\nRankV := Rank(V):\ntmp_t2 := time():\nprintf(\"%s. Die Komponenten-Matrix des Energie-Regressors hat Rang %d. Rechenzeit: %1.1fs\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), RankV, tmp_t2-tmp_t1):\n# [Diekmeyer2018_S678] Gl. 3.27\ntmp_t1 := time():\nU := LinearSolve(Transpose(V),Transpose(V)):\ntmp_t2 := time():\nprintf(\"%s. Basis der Komponenten-Matrix mit LinearSolve gel\u00f6st. Resultat ist %dx%d. Rechenzeit: %1.1fs\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), RowDimension(U), ColumnDimension(U), tmp_t2-tmp_t1):\n# Freie Variablen (\"_t\") entfernen\nfor i from 1 to Size(V,1) - RankV do\n for j from 1 to Size(V,1) do\n # printf(\"subs %d,%d\\n\", i,j):\n U := subs([_t[i, j]=0],U):\n end do:\nend do:\n# [Diekmeyer2018_S678] Gl. 3.29\nPb, Pd :=permuteEmptyRows(U):\nP := Matrix([[Pb],[Pd]]):\nsave P, Pb, Pd, U, V, RankV, sprintf(\"../codeexport/%s/tmp/minimal_parameter_calculation_fixb_maple_linsolve_debug2.m\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/minimal_parameter_calculation_fixb_maple_linsolve_debug2.m\", robot_name):\n# [Diekmeyer2018_S678] Gl. 3.31 (links)\nParamvec2 := Pb.U.PV2_vec(11..,..):\n# Nachverarbeitung: Pr\u00fcfe ob Imagin\u00e4rteile aus Substitutionsalgorithmus vorhanden sind\ntmp_t1 := time():\n# Diese Pr\u00fcfung ist nur notwendig, wenn oben die Lagrange-Terme in Exponent-Form gebracht wurden\n# Dann ist es m\u00f6glich, dass imagin\u00e4re Ausdr\u00fccke im Parametervektor stehen.\nimagpart:=false:\nfor i from 1 to RowDimension(Paramvec2) do\n # Umrechnung der Exponentialform in trigonometrische Form\n Paramvec2(i,1) := simplify(convert(expand(Paramvec2(i,1)), trig));\n\n if not evalc(Im(Paramvec2[i,1])) = 0 then # m\u00fcssen eckige Klammern sein, damit evalc funktioniert.\n imagpart := true: # Imagin\u00e4rteil erkannt. Annahme: Auch nachfolgende Vereinfachung kann daran nichts \u00e4ndern.\n break:\n end if:\n if has(Paramvec2(i,1), I) then # Pr\u00fcfe auf Imagin\u00e4rteil durch Existenz der imagin\u00e4ren Einheit\n Paramvec2(i,1) := evalc(Re(Paramvec2[i,1])): # da Im() oben Null war, muss Re() den vollen Term enthalten.\n end if:\nend do:\nif imagpart then\n printf(\"Der Parametervektor hat trotz versuchter Substitution immer noch Imagin\u00e4rteile aus dem Algorithmus. Verwerfe L\u00f6sung und Abbruch.\\n\"):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\ntmp_t2 := time():\nParamvec2 := simplify2(Paramvec2): # nochmal vereinfachen\n;\nprintf(\"%s. Parameter-Vektor nachverarbeitet. Rechenzeit: %1.1fs\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_t2-tmp_t1):\n# Debug: Fertigen Parameter von anderem Durchlauf laden\n# read sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_maple_linsolve\", robot_name):\nprintf(\"%s. Dimension des Minimalparametervektors: %dx%d\\n\", \\ \n FormatTime(\"%Y-%m-%d %H:%M:%S\"), RowDimension(Paramvec2), ColumnDimension(Paramvec2)):\nParamvec2;\n# [Diekmeyer2018_S678] Gl. 3.31 (rechts)\nt_ges_minpar:=Transpose(Pb.Transpose(t_ges)):\nu_ges_minpar:=Transpose(Pb.Transpose(u_ges)):\nprintf(\"%s. Dimension der Regressormatrix: %dx%d\\n\", \\ \n FormatTime(\"%Y-%m-%d %H:%M:%S\"), RowDimension(t_ges_minpar), ColumnDimension(t_ges_minpar)):\n# Symbolischer Test des Erfolgs der Parameterminimierung: Ist konstant bzw. Null.\n# test_u := simplify2(u_ges_minpar.Paramvec2 - u_ges.PV2_vec(11..,..)):\n# test_t := simplify2(t_ges_minpar.Paramvec2 - t_ges.PV2_vec(11..,..)):\n# Code exportieren\nsave Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_maple\", robot_name):\nsave Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_maple_linsolve\", robot_name): # zum Testen gegen andere Implementierung\nif codegen_act then\n MatlabExport(Paramvec2, sprintf(\"../codeexport/%s/tmp/minimal_parameter_vector_fixb_matlab.m\", robot_name), codegen_opt):\nend if;\nsave t_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_minpar_maple.m\", robot_name):\nsave u_ges_minpar, sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_minpar_maple.m\", robot_name):\nif codegen_act then\n MatlabExport(convert_t_s(t_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_kinetic_fixb_regressor_minpar_matlab.m\", robot_name), codegen_opt):\nend if:\nif codegen_act then\n MatlabExport(convert_t_s(u_ges_minpar), sprintf(\"../codeexport/%s/tmp/energy_potential_fixb_regressor_minpar_matlab.m\", robot_name), codegen_opt):\nend if:\n\n\n", "meta": {"hexsha": "cd6532e5a18a84c795375af80af8cef7685d2148", "size": 14227, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_energy/robot_chain_fixb_energy_regressor_linearsolve.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_energy/robot_chain_fixb_energy_regressor_linearsolve.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_energy/robot_chain_fixb_energy_regressor_linearsolve.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 39.9634831461, "max_line_length": 148, "alphanum_fraction": 0.7243972728, "num_tokens": 4399, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718435083355187, "lm_q2_score": 0.6859494614282922, "lm_q1q2_score": 0.5294456388496727}} {"text": "da1 :=\n\n[\n [ #(1) boon ((1)-(43) are from http://homepages.math.uic.edu/~jan/demo.html)\n [s1**2+g1**2 - 1,\n s2**2+g2**2 - 1,\n C1*g1**3+C2*g2**3 - 6/5,\n C1*s1**3+C2*s2**3 - 6/5,\n C1*g1**2*s1+C2*g2**2*s2 - 7/10,\n C1*g1*s1**2+C2*g2*s2**2 - 7/10\n ],\n [s1,s2,g1,g2,C1,C2]\n ],\n [ #(2) eco6\n [(x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5)*x6 - 1,\n (x2 + x1*x3 + x2*x4 + x3*x5)*x6 - 2,\n (x3 + x1*x4 + x2*x5)*x6 - 3,\n (x4 + x1*x5)*x6 - 4,\n x5*x6 - 5,\n x1 + x2 + x3 + x4 + x5 + 1\n ],\n [x1,x2,x3,x4,x5,x6]\n ],\n [ #(3) mickey\n [ x**2 + 4*y**2 - 4,\n 2*y**2 - x\n ],\n [x, y]\n ],\n [ #(4) s9_1\n [ -d2*g - 2*d1*h1,\n 9*d2 + 4*b,\n -4*c*h1 - 2*d2*f - 3*d1*g,\n -7*c + 9*a - 8*f,\n -4*d1*f - 5*c*g - 6*h1 - 3*d2,\n -5*d1 - 6*c*f - 7*g + 9*b,\n 9*d1 + 6*a - 5*b,\n 9*c - 7*a + 8\n ],\n [a,b,c,d1,d2,f,g,h1]\n ],\n [ #(5) conform1\n [-9 - t2**2 - t3**2 - 3*t2**2*t3**2 + 8*t2*t3,\n -9 - t3**2 - t1**2 - 3*t3**2*t1**2 + 8*t3*t1,\n -9 - t1**2 - t2**2 - 3*t1**2*t2**2 + 8*t1*t2\n ],\n [t1, t2, t3]\n ],\n [ #(6) eco7\n [ (x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6)*x7 - 1,\n (x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6)*x7 - 2,\n (x3 + x1*x4 + x2*x5 + x3*x6)*x7 - 3,\n (x4 + x1*x5 + x2*x6)*x7 - 4,\n (x5 + x1*x6)*x7 - 5,\n x6*x7 - 6,\n x1 + x2 + x3 + x4 + x5 + x6 + 1\n ],\n [x1,x2,x3,x4,x5,x6,x7]\n ],\n [ #(7) geneig\n [-10*x1*x6^2+ 2*x2*x6^2-x3*x6^2+x4*x6^2+ 3*x5*x6^2+x1*x6+ 2*x2*x6+x3*x6+ 2*x4*\nx6+x5*x6+ 10*x1+ 2*x2-x3+ 2*x4-2*x5,\n 2*x1*x6^2-11*x2*x6^2+ 2*x3*x6^2-2*x4*x6^2+x5*x6^2+ 2*x1*x6+x2*x6+ 2*x3*x6+x4*\nx6+ 3*x5*x6+ 2*x1+ 9*x2+ 3*x3-x4-2*x5,\n-x1*x6^2+ 2*x2*x6^2-12*x3*x6^2-x4*x6^2+x5*x6^2+x1*x6+ 2*x2*x6-2*x4*x6-2*x5*x6-\nx1+ 3*x2+ 10*x3+ 2*x4-x5,\nx1*x6^2-2*x2*x6^2-x3*x6^2-10*x4*x6^2+ 2*x5*x6^2+ 2*x1*x6+x2*x6-2*x3*x6+ 2*x4*\nx6+ 3*x5*x6+ 2*x1-x2+ 2*x3+ 12*x4+x5,\n 3*x1*x6^2+x2*x6^2+x3*x6^2+ 2*x4*x6^2-11*x5*x6^2+x1*x6+ 3*x2*x6-2*x3*x6+ 3*x4*\nx6+ 3*x5*x6-2*x1-2*x2-x3+x4+ 10*x5,\nx1+x2+x3+x4+x5-1\n ],\n [x1, x2, x3, x4, x5, x6]\n ],\n [ #(8) noon3\n [x1*x2^2 + x1*x3^2 - 11/10*x1 + 1,\nx2*x1^2 + x2*x3^2 - 11/10*x2 + 1,\nx3*x1^2 + x3*x2^2 - 11/10*x3 + 1\n ],\n [x1, x2, x3]\n ], \n [ #(9) redcyc5\n [ 1 + y1 + y2 + y3 + y4,\n y1 + y1*y2 + y2*y3 + y3*y4 + y4,\n y1*y2 + y1*y2*y3 + y2*y3*y4 + y3*y4 + y4*y1,\n y1*y2*y3 + y1*y2*y3*y4 + y2*y3*y4 + y3*y4*y1 + y4*y1*y2,\n z0**5*y1*y2*y3*y4 - 1\n ],\n [y1,y2,y3,y4,z0]\n ],\n [ #(10) sendra\n [ -270*x**4*y**3 - 314*x*y**4 - 689*x*y**3 + 1428,\n36*x**7 + 417*x**6*y - 422*x**5*y**2 - 270*x**4*y**3 + 1428*x**3*y**4\n- 1475*x**2*y**5 + 510*x*y**6 - 200*x**6 - 174*x**5*y - 966*x**4*y**2\n+ 529*x**3*y**3 + 269*x**2*y**4 + 49*x*y**5 - 267*y**6 + 529*x**4*y\n+ 1303*x**2*y**3 - 314*x*y**4 + 262*y**5 + 36*x**4 - 788*x**2*y**2 \n- 689*x*y**3 + 177*y**4\n ],\n [x,y]\n ],\n [ #(11) cpdm5\n [4*x1^3+ 3*x1^2*x2+ 3*x1^2*x3+ 3*x1^2*x4+ 3*x1^2*x5+ 3*x1*x2^2+ 3*x1*x3^2+ 3*\nx1*x4^2+ 3*x1*x5^2+x2^3+x3^3+x4^3+x5^3+ 2*x1^2+ 3*x1*x2+ 3*x1*x3+ 3*x1*x4+ 3*\nx1*x5-x2^2-x3^2-x4^2-x5^2-6*x1,\nx1^3+ 3*x1^2*x2+ 3*x1*x2^2+ 4*x2^3+ 3*x2^2*x3+ 3*x2^2*x4+ 3*x2^2*x5+ 3*x2*\nx3^2+ 3*x2*x4^2+ 3*x2*x5^2+x3^3+x4^3+x5^3-x1^2+ 3*x1*x2+ 2*x2^2+ 3*x2*x3+ 3*\nx2*x4+ 3*x2*x5-x3^2-x4^2-x5^2-6*x2,\nx1^3+ 3*x1^2*x3+ 3*x1*x3^2+x2^3+ 3*x2^2*x3+ 3*x2*x3^2+ 4*x3^3+ 3*x3^2*x4+ 3*\nx3^2*x5+ 3*x3*x4^2+ 3*x3*x5^2+x4^3+x5^3-x1^2+ 3*x1*x3-x2^2+ 3*x2*x3+ 2*x3^2+\n 3*x3*x4+ 3*x3*x5-x4^2-x5^2-6*x3,\nx1^3+ 3*x1^2*x4+ 3*x1*x4^2+x2^3+ 3*x2^2*x4+ 3*x2*x4^2+x3^3+ 3*x3^2*x4+ 3*x3*\nx4^2+ 4*x4^3+ 3*x4^2*x5+ 3*x4*x5^2+x5^3-x1^2+ 3*x1*x4-x2^2+ 3*x2*x4-x3^2+ 3*\nx3*x4+ 2*x4^2+ 3*x4*x5-x5^2-6*x4,\nx1^3+ 3*x1^2*x5+ 3*x1*x5^2+x2^3+ 3*x2^2*x5+ 3*x2*x5^2+x3^3+ 3*x3^2*x5+ 3*x3*\nx5^2+x4^3+ 3*x4^2*x5+ 3*x4*x5^2+ 4*x5^3-x1^2+ 3*x1*x5-x2^2+ 3*x2*x5-x3^2+ 3*\nx3*x5-x4^2+ 3*x4*x5+ 2*x5^2-6*x5\n ],\n [x1, x2, x3, x4, x5]\n ],\n [ #(12) eco8\n [ (x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7)*x8 - 1,\n (x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6 + x5*x7)*x8 - 2,\n (x3 + x1*x4 + x2*x5 + x3*x6 + x4*x7)*x8 - 3,\n (x4 + x1*x5 + x2*x6 + x3*x7)*x8 - 4,\n (x5 + x1*x6 + x2*x7)*x8 - 5,\n (x6 + x1*x7)*x8 - 6,\n x7*x8 - 7,\n x1 + x2 + x3 + x4 + x5 + x6 + x7 + 1\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8]\n ], \n [ #(13) noon4\n [x1*x2^2 + x1*x3^2 + x1*x4^2 - 11/10*x1 + 1,\nx2*x1^2 + x2*x3^2 + x2*x4^2 - 11/10*x2 + 1,\nx3*x1^2 + x3*x2^2 + x3*x4^2 - 11/10*x3 + 1,\nx4*x1^2 + x4*x2^2 + x4*x3^2 - 11/10*x4 + 1\n ],\n [x1,x2,x3,x4]\n ],\n [ #(14) redcyc6\n [1 + y1 + y2 + y3 + y4 + y5,\n y1 + y1*y2 + y2*y3 + y3*y4 + y4*y5 + y5,\n y1*y2 + y1*y2*y3 + y2*y3*y4 + y3*y4*y5 + y4*y5 + y5*y1,\n y1*y2*y3 + y1*y2*y3*y4 + y2*y3*y4*y5 + y3*y4*y5 + y4*y5*y1 + y5*y1*y2,\n y1*y2*y3*y4 + y1*y2*y3*y4*y5 + y2*y3*y4*y5 + y3*y4*y5*y1\n + y4*y5*y1*y2 + y5*y1*y2*y3,\n z0**6*y1*y2*y3*y4*y5 - 1\n ],\n [y1,y2,y3,y4,y5,z0]\n ],\n [ #(15) solotarev\n [ 3*x**2-2*x-a,\n x**3-x**2-x*a+a-2*b-2,\n 3*y**2-2*y-a,\n y**3-y**2-y*a-a+2\n ],\n [x,y,a,b]\n ],\n [ #(16) noon5\n [x1*x2^2 + x1*x3^2 + x1*x4^2 + x1*x5^2 - 11/10*x1 + 1,\nx2*x1^2 + x2*x3^2 + x2*x4^2 + x2*x5^2 - 11/10*x2 + 1,\nx3*x1^2 + x3*x2^2 + x3*x4^2 + x3*x5^2 - 11/10*x3 + 1,\nx4*x1^2 + x4*x2^2 + x4*x3^2 + x4*x5^2 - 11/10*x4 + 1,\nx5*x1^2 + x5*x2^2 + x5*x3^2 + x5*x4^2 - 11/10*x5 + 1\n ],\n [x1,x2,x3,x4,x5]\n ], \n [ #(17) redcyc7\n [ 1 + y1 + y2 + y3 + y4 + y5 + y6,\n y1 + y1*y2 + y2*y3 + y3*y4 + y4*y5 + y5*y6 + y6,\n y1*y2 + y1*y2*y3 + y2*y3*y4 + y3*y4*y5 + y4*y5*y6 + y5*y6 + y6*y1,\n y1*y2*y3 + y1*y2*y3*y4 + y2*y3*y4*y5 + y3*y4*y5*y6 + y4*y5*y6\n+ y5*y6*y1 + y6*y1*y2,\n y1*y2*y3*y4 + y1*y2*y3*y4*y5 + y2*y3*y4*y5*y6 + y3*y4*y5*y6\n+ y4*y5*y6*y1 + y5*y6*y1*y2 + y6*y1*y2*y3,\n y1*y2*y3*y4*y5 + y1*y2*y3*y4*y5*y6 + y2*y3*y4*y5*y6 + y3*y4*y5*y6*y1\n+ y4*y5*y6*y1*y2 + y5*y6*y1*y2*y3 + y6*y1*y2*y3*y4,\n z0**7*y1*y2*y3*y4*y5*y6 - 1\n ],\n [y1,y2,y3,y4,y5,y6,z0]\n ],\n [ #(18) sparse5\n [x1**2*x2**2*x3**2*x4**2*x5**2 \n + 3*x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5,\n x1**2*x2**2*x3**2*x4**2*x5**2 \n + x1**2 + 3*x2**2 + x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5,\n x1**2*x2**2*x3**2*x4**2*x5**2 \n + x1**2 + x2**2 + 3*x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5,\n x1**2*x2**2*x3**2*x4**2*x5**2 \n + x1**2 + x2**2 + x3**2 + 3*x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5,\n x1**2*x2**2*x3**2*x4**2*x5**2 \n + x1**2 + x2**2 + x3**2 + x4**2 + 3*x5**2 + x1*x2*x3*x4*x5 + 5\n ],\n [x1,x2,x3,x4,x5]\n ],\n [ #(19) cyclic6\n [z0 + z1 + z2 + z3 + z4 + z5,\n z0*z1 + z1*z2 + z2*z3 + z3*z4 + z4*z5 + z5*z0,\n z0*z1*z2 + z1*z2*z3 + z2*z3*z4 + z3*z4*z5 + z4*z5*z0 + z5*z0*z1,\n z0*z1*z2*z3 + z1*z2*z3*z4 + z2*z3*z4*z5 + z3*z4*z5*z0 + z4*z5*z0*z1 \n + z5*z0*z1*z2,\n z0*z1*z2*z3*z4 + z1*z2*z3*z4*z5 + z2*z3*z4*z5*z0 + z3*z4*z5*z0*z1 \n + z4*z5*z0*z1*z2 + z5*z0*z1*z2*z3,\n z0*z1*z2*z3*z4*z5 - 1\n ],\n [z0,z1,z2,z3,z4,z5]\n ],\n [ #(20) extcyc6\n [ z0 + z1 + z2 + z3 + z4 + z5 - 1,\n z0*z1 + z1*z2 + z2*z3 + z3*z4 + z4*z5 + z5*z0 - 1,\n z0*z1*z2 + z1*z2*z3 + z2*z3*z4 + z3*z4*z5 + z4*z5*z0 + z5*z0*z1 - 1,\n z0*z1*z2*z3 + z1*z2*z3*z4 + z2*z3*z4*z5 + z3*z4*z5*z0 + z4*z5*z0*z1 \n + z5*z0*z1*z2 - 1,\n z0*z1*z2*z3*z4 + z1*z2*z3*z4*z5 + z2*z3*z4*z5*z0 + z3*z4*z5*z0*z1 \n + z4*z5*z0*z1*z2 + z5*z0*z1*z2*z3 - 1 ,\n z0*z1*z2*z3*z4*z5 - 1\n ],\n [z0,z1,z2,z3,z4,z5]\n ],\n [ #(21) cyclic7\n [z0 + z1 + z2 + z3 + z4 + z5 + z6,\n z0*z1 + z1*z2 + z2*z3 + z3*z4 + z4*z5 + z5*z6 + z6*z0,\n z0*z1*z2 + z1*z2*z3 + z2*z3*z4 + z3*z4*z5 + z4*z5*z6 + z5*z6*z0 + z6*z0*z1,\n z0*z1*z2*z3 + z1*z2*z3*z4 + z2*z3*z4*z5 + z3*z4*z5*z6 + z4*z5*z6*z0\n+ z5*z6*z0*z1 + z6*z0*z1*z2,\n z0*z1*z2*z3*z4 + z1*z2*z3*z4*z5 + z2*z3*z4*z5*z6 + z3*z4*z5*z6*z0 \n+ z4*z5*z6*z0*z1 + z5*z6*z0*z1*z2 + z6*z0*z1*z2*z3,\n z0*z1*z2*z3*z4*z5 + z1*z2*z3*z4*z5*z6 + z2*z3*z4*z5*z6*z0 + z3*z4*z5*z6*z0*z1\n+ z4*z5*z6*z0*z1*z2 + z5*z6*z0*z1*z2*z3 + z6*z0*z1*z2*z3*z4,\n z0*z1*z2*z3*z4*z5*z6 - 1\n ],\n [z0,z1,z2,z3,z4,z5,z6]\n ],\n [ #(22) puma\n [ x1^2 + x2^2 - 1,\n x3^2 + x4^2 - 1,\n x5^2 + x6^2 - 1,\n x7^2 + x8^2 - 1,\n 0004731/1000000*x1*x3 - 03578/10000*x2*x3 - 01238/10000*x1 - 0001637/1000000*x2 - 09338/10000*x4 + x7 \n- 03571/10000,\n 02238/10000*x1*x3 + 07623/10000*x2*x3 + 02638/10000*x1 - 007745/100000*x2 -06734/10000*x4 -06022/10000,\n x6*x8 + 03578/10000*x1 + 0004731/1000000*x2,\n -07623/10000*x1 + 02238/10000*x2 + 03461/10000\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8]\n ],\n [ #(23) redeco5\n [ x1 + x1*x2 + x2*x3 + x3*x4 - u5,\n x2 + x1*x3 + x2*x4 - 2*u5,\n x3 + x1*x4 - 3*u5,\n x4 - 4*u5,\n x1 + x2 + x3 + x4 + 1\n ],\n [x1,x2,x3,x4,u5]\n ],\n [ #(24) trink\n [ 45*y + 35*u - 165*v - 36,\n 35*y + 25*z + 40*t - 27*u,\n 25*y*u - 165*v**2 + 15*x - 18*z + 30*t,\n 15*y*z + 20*t*u - 9*x,\n -11*v**3 + x*y + 2*z*t,\n -11*u*v + 3*v**2 + 99*x\n ],\n [x,y,z,u,v,t]\n ],\n [ #(25) cassou\n [ 15*b**4*c*d1**2 + 6*b**4*c**3 + 21*b**4*c**2*d1 - 144*b**2*c\n - 8*b**2*c**2*d2\n - 28*b**2*c*d1*d2 - 648*b**2*d1 + 36*b**2*d1**2*d2 + 9*b**4*d1**3 - 120,\n 30*c**3*b**4*d1 - 32*d1*d2**2*c - 720*d1*b**2*c - 24*c**3*b**2*d2\n - 432*c**2*b**2 + 576*d2*c - 576*d1*d2 + 16*c*b**2*d1**2*d2\n + 16*d1**2*d2**2 + 16*d2**2*c**2 + 9*c**4*b**4 + 5184\n + 39*d1**2*b**4*c**2 + 18*d1**3*b**4*c - 432*d1**2*b**2 \n + 24*d1**3*b**2*d2 - 16*c**2*b**2*d1*d2 - 240*c,\n 216*d1*b**2*c - 162*d1**2*b**2 - 81*c**2*b**2 + 5184 + 1008*d2*c \n - 1008*d1*d2\n + 15*c**2*b**2*d1*d2 - 15*c**3*b**2*d2 - 80*d1*d2**2*c + 40*d1**2*d2**2 \n + 40*d2**2*c**2,\n 261 + 4*d1*b**2*c - 3*d1**2*b**2 - 4*c**2*b**2 + 22*d2*c - 22*d1*d2\n ],\n [b,c,d1,d2]\n ], \n [ #(26) katsura5\n [2*x**2+2*y**2+2*z**2+2*t**2+2*u**2+v**2-v,\n x*y+y*z+2*z*t+2*t*u+2*u*v-u,\n 2*x*z+2*y*t+2*z*u+u**2+2*t*v-t,\n 2*x*t+2*y*u+2*t*u+2*z*v-z,\n t**2+2*x*v+2*y*v+2*z*v-y,\n 2*x+2*y+2*z+2*t+2*u+v-1\n ],\n [x,y,z,u,v,t]\n ],\n [ #(27) quadfor2\n [ w1 + w2 - 1,\n w1*x1 + w2*x2,\n w1*x1**2 + w2*x2**2 - 2/3,\n w1*x1**3 + w2*x2**3\n ],\n [w1,w2,x1,x2]\n ],\n [ #(28) redeco6\n [ x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 - u6,\n x2 + x1*x3 + x2*x4 + x3*x5 - 2*u6,\n x3 + x1*x4 + x2*x5 - 3*u6,\n x4 + x1*x5 - 4*u6,\n x5 - 5*u6,\n x1 + x2 + x3 + x4 + x5 + 1\n ],\n [x1,x2,x3,x4,x5,u6]\n ],\n [ #(29) virasoro\n [8*x1^2+ 8*x1*x2+ 8*x1*x3+ 2*x1*x4+ 2*x1*x5+ 2*x1*x6+ 2*x1*x7-8*x2*x3-2*x4*x7\n-2*x5*x6-x1,\n 8*x1*x2-8*x1*x3+ 8*x2^2+ 8*x2*x3+ 2*x2*x4+ 2*x2*x5+ 2*x2*x6+ 2*x2*x7-2*x4*x6\n-2*x5*x7-x2,\n-8*x1*x2+ 8*x1*x3+ 8*x2*x3+ 8*x3^2+ 2*x3*x4+ 2*x3*x5+ 2*x3*x6+ 2*x3*x7-2*x4*\nx5-2*x6*x7-x3,\n 2*x1*x4-2*x1*x7+ 2*x2*x4-2*x2*x6+ 2*x3*x4-2*x3*x5+ 8*x4^2+ 8*x4*x5+ 2*x4*x6+\n 2*x4*x7+ 6*x4*x8-6*x5*x8-x4,\n 2*x1*x5-2*x1*x6+ 2*x2*x5-2*x2*x7-2*x3*x4+ 2*x3*x5+ 8*x4*x5-6*x4*x8+ 8*x5^2+\n 2*x5*x6+ 2*x5*x7+ 6*x5*x8-x5,\n-2*x1*x5+ 2*x1*x6-2*x2*x4+ 2*x2*x6+ 2*x3*x6-2*x3*x7+ 2*x4*x6+ 2*x5*x6+ 8*x6^2\n+ 8*x6*x7+ 6*x6*x8-6*x7*x8-x6,\n-2*x1*x4+ 2*x1*x7-2*x2*x5+ 2*x2*x7-2*x3*x6+ 2*x3*x7+ 2*x4*x7+ 2*x5*x7+ 8*x6*\nx7-6*x6*x8+ 8*x7^2+ 6*x7*x8-x7,\n-6*x4*x5+ 6*x4*x8+ 6*x5*x8-6*x6*x7+ 6*x6*x8+ 6*x7*x8+ 8*x8^2-x8\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8]\n ], \n [ #(30) d1\n [ x1**2 + x2**2 - 1,\n x3**2 + x4**2 - 1,\n x5**2 + x6**2 - 1,\n x7**2 + x8**2 - 1,\n x9**2 + x10**2 - 1,\n x11**2 + x12**2 - 1,\n 3*x3 + 2*x5 + x7 - 39701/10000,\n 3*x1*x4 + 2*x1*x6 + x1*x8 - 17172/10000,\n 3*x2*x4 + 2*x2*x6 + x2*x8 - 40616/10000,\n x3*x9 + x5*x9 + x7*x9 - 19791/10000,\n x2*x4*x9 + x2*x6*x9 + x2*x8*x9 + x1*x10 - 19115/10000,\n - x3*x10*x11 - x5*x10*x11 - x7*x10*x11 + x4*x12 + x6*x12 + x8*x12 - 04077/10000\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12]\n ],\n [ #(31) kin1\n [ s1**2 + c1**2 - 1,\n s2**2 + c2**2 - 1,\n s3**2 + c3**2 - 1,\n s4**2 + c4**2 - 1,\n s5**2 + c5**2 - 1,\n s6**2 + c6**2 - 1,\n s2*c5*s6 - s3*c5*s6 - s4*c5*s6 + c2*c6 + c3*c6 + c4*c6 - 04077/10000,\n c1*c2*s5 + c1*c3*s5 + c1*c4*s5 + s1*c5 - 19115/10000,\n s2*s5 + s3*s5 + s4*s5 - 19791/10000,\n c1*c2 + c1*c3 + c1*c4 + c1*c2 + c1*c3 + c1*c2 - 40616/10000,\n s1*c2 + s1*c3 + s1*c4 + s1*c2 + s1*c3 + s1*c2 - 17172/10000,\n s2 + s3 + s4 + s2 + s3 + s2 - 39701/10000\n ],\n [s1,c1,s2,c2,s3,c3,s4,c4,s5,c5,s6,c6]\n ],\n [ #(32) redeco7\n [ x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 - u7,\n x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6 - 2*u7,\n x3 + x1*x4 + x2*x5 + x3*x6 - 3*u7,\n x4 + x1*x5 + x2*x6 - 4*u7,\n x5 + x1*x6 - 5*u7,\n x6 - 6*u7,\n x1 + x2 + x3 + x4 + x5 + x6 + 1\n ],\n [x1,x2,x3,x4,x5,x6,u7]\n ],\n [ #(33) des18_3\n [6*a33*a10*a20 + 10*a22*a10*a31 + 8*a32*a10*a21 - 162*a10**2*a21\n+ 16*a21*a30 + 14*a31*a20 + 48*a10*a30,\n15*a33*a10*a21 - 162*a10**2*a22 - 312*a10*a20 + 24*a10*a30 + 27*a31*a21\n+ 24*a32*a20 + 18*a22*a10*a32 + 30*a22*a30 + 84*a31*a10, \n-240*a10 + 420*a33 - 64*a22 + 112*a32,\n180*a33*a10 - 284*a22*a10 - 162*a10**2 + 60*a22*a32 + 50*a32*a10 + 70*a30\n+ 55*a33*a21 + 260*a31 - 112*a20,\n66*a33*a10 + 336*a32 + 90*a31 + 78*a22*a33 - 1056*a10 - 90*a21,\n136*a33 - 136,\n4*a22*a10*a30 + 2*a32*a10*a20 + 6*a20*a30 - 162*a10**2*a20 + 3*a31*a21*a10,\n28*a22*a10*a33 + 192*a30 + 128*a32*a10 + 36*a31*a20 + 36*a33*a20 - 300*a10*a21 + 40*a32*a21 - 648*a10**2 + 44*a22*a31\n ],\n [a10,a20,a21,a22,a30,a31,a32,a33]\n ],\n [ #(34) kinema\n [z1**2 + z2**2 + z3**2 - 12*z1 - 68,\n z4**2 + z5**2 + z6**2 - 12*z5 - 68,\n z7**2 + z8**2 + z9**2 - 24*z8 - 12*z9 + 100,\n z1*z4 + z2*z5 + z3*z6 - 6*z1 - 6*z5 - 52,\n z1*z7 + z2*z8 + z3*z9 - 6*z1 - 12*z8 - 6*z9 + 64,\n z4*z7 + z5*z8 + z6*z9 - 6*z5 - 12*z8 - 6*z9 + 32,\n 2*z2 + 2*z3 - z4 - z5 - 2*z6 - z7 - z9 + 18,\n z1 + z2 + 2*z3 + 2*z4 + 2*z6 - 2*z7 + z8 - z9 - 38,\n z1 + z3 - 2*z4 + z5 - z6 + 2*z7 - 2*z8 + 8\n ],\n [z1,z2,z3,z4,z5,z6,z7,z8,z9]\n ], \n [ #(35) rabmo\n [x1 + x3 + x5 + 2*x7 - 1,\n x1*x2 + x3*x4 + 2*x5*x6 + 2*x7*x8 + 2*x7*x9 - 2/3,\n x1*x2^2 + x3*x4^2 + 2*x5*x6^2 + 2*x7*x8^2 + 2*x7*x9^2 - 2/5,\n x1*x2^3 + x3*x4^3 + 2*x5*x6^3 + 2*x7*x8^3 + 2*x7*x9^3 - 2/7,\n x1*x2^4 + x3*x4^4 + 2*x5*x6^4 + 2*x7*x8^4 + 2*x7*x9^4 - 2/9,\n x5*x6^2 + 2*x7*x8*x9 - 1/9,\n x5*x6^4 + 2*x7*x8^2*x9^2 - 1/25,\n x5*x6^3 + x7*x8*x9^2 + x7*x8^2*x9 - 1/15,\n x5*x6^4 + x7*x8*x9^3 + x7*x8^3*x9 - 1/21\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8,x9]\n ],\n [ #(36) redeco8\n [ x1 + x1*x2 + x2*x3 + x3*x4 + x4*x5 + x5*x6 + x6*x7 - 1*u8,\n x2 + x1*x3 + x2*x4 + x3*x5 + x4*x6 + x5*x7 - 2*u8,\n x3 + x1*x4 + x2*x5 + x3*x6 + x4*x7 - 3*u8,\n x4 + x1*x5 + x2*x6 + x3*x7 - 4*u8,\n x5 + x1*x6 + x2*x7 - 5*u8,\n x6 + x1*x7 - 6*u8,\n x7 - 7*u8,\n x1 + x2 + x3 + x4 + x5 + x6 + x7 + 1\n ],\n [x1,x2,x3,x4,x5,x6,x7,u8]\n ],\n [ #(37) wright\n [x1^2-x1+x2+x3+x4+x5-10,\nx2^2+x1-x2+x3+x4+x5-10,\nx3^2+x1+x2-x3+x4+x5-10,\nx4^2+x1+x2+x3-x4+x5-10,\nx5^2+x1+x2+x3+x4-x5-10\n ],\n [x1,x2,x3,x4,x5]\n ],\n [ #(38) des22_24\n [ 16*a20*a32 + 18*a21*a31 + 20*a22*a30,\n-80*a23 + 180*a34 + 855*a35,\n 7*a20*a31 + 8*a21*a30,\n 210*a35 - 210,\n 40*a20*a34 + 44*a21*a33 + 48*a22*a32 + 52*a23*a31 + 280*a30,\n 27*a20*a33 + 30*a21*a32 + 33*a22*a31 + 36*a23*a30,\n 55*a20*a35 + 60*a21*a34 + 65*a22*a33 + 70*a23*a32 + 80*a30 + 375*a31,\n 78*a21*a35 + 84*a22*a34 + 90*a23*a33 - 170*a20 + 102*a31 + 480*a32,\n136*a23*a35 - 114*a22 + 152*a33 + 720*a34,\n105*a22*a35 + 112*a23*a34 - 144*a21 + 126*a32 + 595*a33\n ],\n [a20,a21,a22,a23,a30,a31,a32,a33,a34,a35]\n ],\n [ #(39) ku10\n [ 5*x1*x2+ 5*x1+ 3*x2+ 55,\n 7*x2*x3+ 9*x2+ 9*x3+ 19,\n 3*x3*x4+ 6*x3+ 5*x4-4,\n 6*x4*x5+ 6*x4+ 7*x5+ 118,\nx5*x6+ 3*x5+ 9*x6+ 27,\n 6*x6*x7+ 7*x6+x7+ 72,\n 9*x7*x8+ 7*x7+x8+ 35,\n 4*x8*x9+ 4*x8+ 6*x9+ 16,\n 8*x9*x10+ 4*x9+ 3*x10-51,\n 3*x1*x10-6*x1+x10+ 5\n ],\n [x1,x2,x3,x4,x5,x6,x7,x8,x9,x10]\n ],\n [ #(40) lorentz\n [x1*x2-x1*x3-x4+ 1,\nx2*x3-x2*x4-x1+ 1,\n-x1*x3+x3*x4-x2+ 1,\nx1*x4-x2*x4-x3+ 1\n ],\n [x1,x2,x3,x4]\n ],\n [ #(41) rbpl24\n [62500*x1^2 + 62500*y1^2 + 62500*z1^2 -74529,\n625*x2^2 + 625*y2^2 + 625*z2^2 -1250*x2 -2624,\n12500*x3^2 + 12500*y3^2 + 12500*z3^2 + 2500*x3 -44975*y3 -10982,\n400000*x1*x2 + 400000*y1*y2 + 400000*z1*z2 -400000*x2 + 178837,\n1000000*x1*x3 + 1000000*y1*y3 + 1000000*z1*z3 + 100000*x3 -1799000*y3 -805427,\n2000000*x2*x3 + 2000000*y2*y3 + 2000000*z2*z3 -2000000*x2 + 200000*x3\n-3598000*y3 -1403,\n 113800000000000*x3*y2*z1\n-113800000000000*x2*y3*z1 -113800000000000*x3*y1*z2 +\n113800000000000*x1*y3*z2 + 113800000000000*x2*y1*z3\n-113800000000000*x1*y2*z3 -206888400000000*x2*y1 +\n206888400000000*x3*y1 + 206888400000000*x1*y2 -206888400000000*x3*y2\n-206888400000000*x1*y3 + 206888400000000*x2*y3 -2014260000000*x2*z1 +\n2014260000000*x3*z1 -61907200000000*y2*z1 + 61907200000000*y3*z1 +\n2014260000000*x1*z2 -2014260000000*x3*z2 + 61907200000000*y1*z2\n-61907200000000*y3*z2 -2014260000000*x1*z3 + 2014260000000*x2*z3\n-61907200000000*y1*z3 + 61907200000000*y2*z3 -362960716800000*x1 +\n38025201600000*x2 + 292548849600000*x3 + 11809567440000*y1 +\n1475978220000*y2 -825269402280000*y3 -1212982689600000*z1\n-151600474800000*z2 + 825859951200000*z3 -19295432410527,\n -777600000000*x3*y2*z1 + 777600000000*x2*y3*z1 +\n777600000000*x3*y1*z2 -777600000000*x1*y3*z2 -777600000000*x2*y1*z3 +\n777600000000*x1*y2*z3 -1409011200000*x2*y1 + 1409011200000*x3*y1 +\n1409011200000*x1*y2 -1409011200000*x3*y2 -1409011200000*x1*y3 +\n1409011200000*x2*y3 -1065312000000*x2*z1 + 1065312000000*x3*z1\n-805593600000*y2*z1 + 805593600000*y3*z1 + 1065312000000*x1*z2\n-1065312000000*x3*z2 + 805593600000*y1*z2 -805593600000*y3*z2\n-1065312000000*x1*z3 + 1065312000000*x2*z3 -805593600000*y1*z3 +\n805593600000*y2*z3 + 235685027200*x1 + 398417510400*x2 +\n158626915200*x3 -311668424000*y1 -268090368000*y2 + 72704002800*y3 +\n412221302400*z1 + 354583756800*z2 + 307085438400*z3 + 282499646407,\n3200*x2 + 1271\n ],\n [x1,y1,z1,x2,y2,z2,x3,y3,z3]\n ],\n [ #(42) reimer5\n [-1 + 2*x**2 - 2*y**2 + 2*z**2 - 2*t**2 + 2*u**2,\n-1 + 2*x**3 - 2*y**3 + 2*z**3 - 2*t**3 + 2*u**3,\n-1 + 2*x**4 - 2*y**4 + 2*z**4 - 2*t**4 + 2*u**4,\n-1 + 2*x**5 - 2*y**5 + 2*z**5 - 2*t**5 + 2*u**5,\n-1 + 2*x**6 - 2*y**6 + 2*z**6 - 2*t**6 + 2*u**6\n ],\n [x,y,z,t,u]\n ],\n [ #(43) eco5\n [ (x1 + x1*x2 + x2*x3 + x3*x4)*x5 - 1,\n (x2 + x1*x3 + x2*x4)*x5 - 2,\n (x3 + x1*x4)*x5 - 3,\n x4*x5 - 4,\n x1 + x2 + x3 + x4 + 1\n ],\n [x1,x2,x3,x4,x5]\n ]\n]:", "meta": {"hexsha": "cd8f1d7820bafcc2cc7cac35002e9696301fc38c", "size": 18788, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Examples/database1.mpl", "max_stars_repo_name": "lihaokun/StrongSfTriDec", "max_stars_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2022-03-21T11:48:40.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-21T11:50:26.000Z", "max_issues_repo_path": "Examples/database1.mpl", "max_issues_repo_name": "lihaokun/StrongSfTriDec", "max_issues_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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": "Examples/database1.mpl", "max_forks_repo_name": "lihaokun/StrongSfTriDec", "max_forks_repo_head_hexsha": "2c5c3bed0a07cb790820fd6ffc7567b5f6c524e4", "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": 35.7866666667, "max_line_length": 117, "alphanum_fraction": 0.481956568, "num_tokens": 10998, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.9334308147331957, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.5283391424621869}} {"text": "###############################################################################\n# Part 1: Algorithms for computation with subfields of rational functions\n###############################################################################\n\nwith(PolynomialIdeals):\n#------------------------------------------------------------------------------\n\nIdealsEq := proc(A, B)\n # Checks whether polynomial ideals are equal\n return evalb((A subset B) and (B subset A)):\nend:\n\n#------------------------------------------------------------------------------\n\nFieldToIdeal := proc(gens)\n # Input: generators of a subfield of the field of rational functions\n # Computes the MQS ideal of the field with the new variables of the form x_aux\n # See: https://mediatum.ub.tum.de/doc/685465/document.pdf Definition 2.16\n # https://doi.org/10.1016/j.jsc.2005.09.010 Lemma 2.1\n local all_vars, subs_dupl, all_dupl, common_denom, polys, f, gb:\n all_vars := indets(gens):\n subs_dupl := map(v -> v = cat(v, _aux), all_vars):\n all_dupl := map(v -> subs(subs_dupl, v), all_vars):\n common_denom := 1:\n polys := []:\n for f in gens do\n common_denom := lcm(common_denom, denom(f)):\n polys := [op(polys), numer(f) * subs(subs_dupl, denom(f)) - subs(subs_dupl, numer(f)) * denom(f)]:\n end do:\n #gb := Groebner[Basis]([op(polys), common_denom * t - 1], plex(t, op(all_dupl))):\n\n gb := Groebner[Basis]([op(polys), common_denom * t - 1], tdeg(t, op(all_dupl))):\n gb := Groebner[Walk](gb, tdeg(t, op(all_dupl)), lexdeg([t], [op(all_dupl)])):\n \n gb := select(p -> not (t in indets(p)), gb):\n return PolynomialIdeal(gb, variables=all_dupl):\nend proc:\n\n#------------------------------------------------------------------------------\n\nFieldCoefficientRestriction := proc(J, msq_for_subfield)\n # Input: J - a polynomial ideals over a field of rational functions\n # msq_for_subfield - the MQS ideal for a subfield E of coefficients (see FieldToIdeal)\n # Computes the radical of the restriction of the ideal to the subfield E \n # in the sense of https://doi.org/10.1016/j.jsc.2005.09.010 (MSQ-paper in what follows)\n #\n # NOTE: unlike the algorithm in the MQS-paper, we compute the radical, not the restriction itself\n # one can obtain the algorithm MQS-paper by replacing PrimeDecomposition with PrimaryDecomposition \n # in the code below\n local poly_vars, coeff_vars, subs_aux, coeff_aux, gens, subs_aux_msq, gens_msq, msq_ideal_aux, \n msq_components, J_ext, components, primes_to_keep, P, elim_P, comp, cleaned_ideal:\n\n poly_vars := IdealInfo[Variables](J):\n coeff_vars := IdealInfo[Parameters](J) union IdealInfo[Parameters](msq_for_subfield):\n subs_aux := map(v -> v = parse(cat(v, _aux_aux)), coeff_vars):\n coeff_aux := subs(subs_aux, coeff_vars):\n\n # list F of polynomials in the notation of the MSQ-paper, page 375\n gens := map(p -> subs(subs_aux, p * denom(p)), IdealInfo[Generators](J)):\n\n # Substitution to avoid names clashing between the aux variables in the msq ideal and the variables in J\n subs_aux_msq := map(v -> v = parse(cat(v, _aux)), IdealInfo[Variables](msq_for_subfield)):\n gens_msq := map(p -> subs(subs_aux_msq, p), IdealInfo[Generators](msq_for_subfield)):\n msq_ideal_aux := PolynomialIdeal(gens_msq, variables=map(s -> rhs(s), subs_aux_msq)):\n msq_components := [PrimeDecomposition(msq_ideal_aux)]:\n\n J_ext := PolynomialIdeal([op(gens), op(gens_msq)], variables=poly_vars union coeff_aux): \n components := [PrimeDecomposition(J_ext)]:\n \n # Selecting prime components as in Remark on page 377 in MSQ-paper\n primes_to_keep := []:\n for P in components do\n # Going through the prime decomposition of the MSQ-deal mimics the\n # working over the restricted field (which is what has been done in the MSQ-paper)\n elim_P := EliminationIdeal(P, coeff_aux):\n for comp in msq_components do\n if elim_P subset comp then\n primes_to_keep := [op(primes_to_keep), P]:\n end if:\n end do: \n end do:\n if nops(primes_to_keep) > 0 then\n cleaned_ideal := Intersect(op(primes_to_keep)):\n else\n cleaned_ideal := PolynomialIdeal([0], variables = poly_vars):\n end if:\n\n # Applying Lemma 2.2 from the MSQ-paper\n return EliminationIdeal(cleaned_ideal, poly_vars):\nend proc:\n\n#------------------------------------------------------------------------------\n\n\nFilterGenerators := proc(ideal)\n # Input: ideal over a rational function field\n # Computes a simplified set of generators of the field of definition\n local gb, gens, p, cf, lc, gsorted, result, big_ideal, cur_ideal, g, new_ideal:\n gb := Groebner[Basis](ideal, tdeg(op(IdealInfo[Variables](ideal)))):\n gens := {}:\n for p in gb do\n cf := sort([coeffs(p, IdealInfo[Variables](ideal))], (a, b) -> length(convert(a, string)) < length(convert(b, string))):\n lc := cf[1]:\n cf := map(c -> c / lc, cf):\n gens := {op(gens), op(cf[2..nops(cf)])}:\n end do:\n gsorted := sort([op(gens)], (a, b) -> length(convert(a, string)) < length(convert(b, string)));\n result := {}:\n big_ideal := FieldToIdeal(gens):\n cur_ideal := FieldToIdeal(result):\n for g in gsorted do\n if big_ideal = cur_ideal then\n return result:\n end if:\n new_ideal := FieldToIdeal({op(result), g}):\n if new_ideal <> cur_ideal then\n \t # a dirty hack to transform -1/a to a\n if convert(g, string)[1] = \"-\" then\n g := -g:\n end:\n if convert(g, string)[1] = \"1\" then\n g := 1 / g:\n end:\n result := {op(result), g}:\n cur_ideal := new_ideal:\n end if:\n end do:\n return result:\nend proc:\n\n#------------------------------------------------------------------------------\n\nFieldIntersection := proc(gens_left, gens_right)\n # Input: gens_left and gens_right - generators of a subfields E and F of a field of rational functions\n # If terminates, resturns an ideal with field of definition being the intersection of generators of E and F\n # Is guaranteed to terminate if at least one of E and F is algebraically closed in rational functions (see REF)\n # Implementation below is a version of Algorithm 2.38 from https://mediatum.ub.tum.de/doc/685465/document.pdf\n local msq_left, msq_right, poly_vars, coeff_vars, Ii, Ji, gb, result, p, cf, lc;\n\n msq_left := FieldToIdeal(gens_left):\n msq_right := FieldToIdeal(gens_right):\n poly_vars := IdealInfo[Variables](msq_left) union IdealInfo[Variables](msq_right):\n coeff_vars := IdealInfo[Parameters](msq_left) union IdealInfo[Parameters](msq_right):\n\n Ii := PolynomialIdeal([1], variables=poly_vars):\n Ji := msq_left:\n\n while not IdealsEq(Ii, Ji) do\n Ii := FieldCoefficientRestriction(Ji, msq_right):\n Ji := FieldCoefficientRestriction(Ii, msq_left):\n end do:\n\n return Ji:\nend proc:\n\n#------------------------------------------------------------------------------\n\nCompareFields := proc(gens_l, gens_r)\n # Checks whether gens_l and gens_r generate the same subfield of rational functions\n return IdealsEq(FieldToIdeal(gens_l), FieldToIdeal(gens_r)):\nend proc:\n\n\n#------------------------------------------------------------------------------\n\n###############################################################################\n# Part 2: Algorithm for computing identifiable functions\n###############################################################################\n\nwith(DifferentialAlgebra):\n\n#===============================================================================\n\nExtractDenominator := proc(model)\n # Input: model a list of rational functions\n # returns the function multiplied by their denominators and \n # an inequality corresponding to the LCM of the denominators\n local common_denom, r;\n common_denom := 1:\n for r in model do\n common_denom := lcm(common_denom, denom(r)):\n end do:\n return [op(map(p -> denom(p) * p, model)), common_denom <> 0]:\nend proc:\n\n#===============================================================================\nCheckReducibilitySet := proc(polys, charset)\n # Input: polys - list of differential polynomials\n # charset - a characteristic set\n # Returns true iff all the polynomials are reduced to zero wrt to the charset\n local result, e:\n result := true:\n for e in polys do\n if NormalForm(e, charset) <> 0 then\n result := false:\n break:\n end if:\n end do:\n return result:\nend proc:\n#===============================================================================\n\nGetIOEquations := proc(model, states, inputs, outputs, params, use_brackets, infolevel, target)\n # Input: model - list of differential polynomials defining the model\n # states, ios, params - list of names of state variables, input-output variables\n # and parameter, respectively\n # Computes a list of input-output equations of the model\n local Relim, Rorig, charsets, chset_orig, general_comps, general, c, e, gen_comp, io_eqs:\n Relim := DifferentialRing(blocks = [[op(states)], [op(outputs)], [op(inputs)]], derivations = [t], arbitrary = params):\n if not use_brackets then\n Relim := DifferentialRing(blocks = [[op(states)], op(outputs), [op(inputs)]], derivations = [t], arbitrary = params):\n end if:\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n \n \n if infolevel > 0 then\n LogText(sprintf(\" Computing the characteristic set (singsol = none)\\n\"), target):\n end if:\n charsets := RosenfeldGroebner(model, Relim, singsol = none):\n if CheckReducibilitySet(Equations(charsets[1]), chset_orig) then \n gen_comp := charsets[1]:\n else\n if infolevel > 0 then\n LogText(sprintf(\" Did not pick the right component. Using singsol = all\\n\"), target):\n end if:\n charsets := RosenfeldGroebner(model, Relim):\n if infolevel > 0 then\n LogText(sprint(\" Selecting the general component\\n\"), target):\n end if:\n general_comps := []:\n for c in charsets do\n general := true:\n for e in Equations(c) do\n if NormalForm(e, chset_orig) <> 0 then\n general := false:\n break:\n end if:\n end do:\n if general then\n general_comps := [op(general_comps), c]:\n end if:\n end do:\n if nops(general_comps) > 1 then\n LogText(sprintf(\"More than one component is considered general!\", general_comps), target):\n end if:\n gen_comp := general_comps[1]:\n end if:\n io_eqs := Equations(gen_comp, leader < parse(cat(states[-1], \"(t)\"))):\n return io_eqs:\nend proc:\n\n#===============================================================================\n\n# Adapted from \n# https://www.mapleprimes.com/questions/36772-Extract-Specific-Coefficients-Of-A-Multivariate\n# by Kitonum 15364\ncoefff:=proc(P, t)\n local L, H, i, k:\n L:=[coeffs(P, indets(P), 'h_aux_for_coef')]: H:=[h_aux_for_coef]: k:=0:\n for i from 1 to nops(H) do\n if H[i]=t then k:=L[i] fi:\n end do:\n return k;\nend proc:\n\n#===============================================================================\n\nDecomposePolynomial := proc(p, vars_main, vars_coef, infolevel, target)\n # Input: p - polynomial in two groups of variables: vars_main and vars_coef\n # Computes a decomposition of minimal length of p as a linear combination \n # of products A * B, where A is a polynomial in vars_main and B \n # is a polynomial in vars_coef return two lists: list of A's and list of B's\n local cf, monoms, result_cf, result_monom, i, c, m, j, lc, lm, coeff_in_c:\n cf := [coeffs(collect(p, vars_main, 'distributed'), vars_main, 'monoms')]:\n monoms := [monoms]:\n result_cf := []:\n result_monom := Array([]):\n if infolevel > 0 then\n LogText(sprintf(\" Number of monomials: %a\\n\", nops(cf)), target):\n end:\n for i from 1 to nops(cf) do\n c := cf[i]:\n m := monoms[i]:\n for j from 1 to nops(result_cf) do\n lc, lm := Groebner[LeadingTerm](result_cf[j], plex(op(vars_coef))):\n coeff_in_c := coefff(c, lm):\n c := c - coeff_in_c / lc * result_cf[j]:\n result_monom[j] := result_monom[j] + coeff_in_c / lc * m:\n end do:\n if c <> 0 then\n result_cf := [op(result_cf), c]:\n ArrayTools[Append](result_monom, m):\n end if:\n end do:\n if infolevel > 0 then\n LogText(sprintf(\" Reduced to: %a\\n\", nops(result_cf)), target):\n end:\n return [result_cf, convert(result_monom, list)]:\nend proc:\n\n#===============================================================================\n\nConstructWronskian := proc(io_eq, model, states, inputs, outputs, params, state_space, infolevel, target)\n # Input - the same as for GetIOEquations + one IO-equation + flag subs_param\n # Computes the Wronskian for this equation using the representation\n # given by DecomposePolynomial. Return a pair of the Wronskian\n # reduced modulo the original system and a list of coefficients\n # of the compressed io_eq\n local getNormalForm, diff_to_ord, v, vt, h, v_ord, vd, p, decomp, diff_polys, Rorig, chset_orig,\n M, yus, yus_reduced, yus_list, M_sub, roll, params_sub, ios, ps_sol, ps, i:\n\n diff_to_ord := {}:\n ios := [op(inputs), op(outputs)]:\n for v in ios do\n vt := parse(cat(v, \"(t)\")):\n diff_to_ord := {op(diff_to_ord), vt = v}:\n for h from 1 to nops(states) + 1 do\n v_ord := parse(cat(v, \"_\", h)):\n vd := diff(vt, t$h):\n diff_to_ord := {op(diff_to_ord), vd = v_ord}:\n end do:\n end do:\n p := subs(diff_to_ord, io_eq):\n if infolevel > 0 then\n LogText(sprintf(\" Combining monomials to reduce the dimension\\n\"), target):\n end if:\n decomp := DecomposePolynomial(p, map(e -> rhs(e), diff_to_ord), params, infolevel, target):\n diff_polys := map(p -> subs(map(e -> rhs(e) = lhs(e), diff_to_ord), p), decomp[2]):\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n \n if infolevel > 0 then\n LogText(sprintf(\" Computing the Wronskian\\n\"), target):\n end if:\n M := VectorCalculus[Wronskian](diff_polys, t):\n yus := indets(M) minus {t}:\n\n if infolevel > 0 then\n LogText(sprintf(\" Reducing the Wronskian\\n\"), target):\n end if:\n if state_space <> [] then\n ps_sol := GetPSSolution(state_space, nops(yus)):\n yus_reduced := []:\n for v in ios do\n vt := parse(cat(v, \"(t)\")):\n ps := subs(ps_sol, v(t)):\n for i from 0 to nops(yus) - 1 do\n yus_reduced := [op(yus_reduced), vt = subs({t = 0}, ps)]:\n vt := diff(vt, t):\n ps := diff(ps, t):\n end do:\n end do:\n else\n getNormalForm := proc (p, chset_orig)\n return p=DifferentialAlgebra:-NormalForm(p, chset_orig):\n end proc:\n Rorig := DifferentialRing(blocks = [[op(outputs)], [op(states)], [op(inputs)]], derivations = [t], arbitrary = params):\n # DifferentialRing(blocks = [[op(inputs)], [op(outputs)], [op(states)]], derivations = [t], arbitrary = params):\n chset_orig := RosenfeldGroebner(model, Rorig)[1]:\n yus_list := convert(yus, list):\n yus_reduced:=Threads:-Seq[tasksize=nops(yus_list)](getNormalForm(yus_list[i], chset_orig), i =1..nops(yus_list)):\n # yus_reduced := map(p -> p = NormalForm(p, chset_orig), yus):\n end if:\n \n # iofun:=map(y->parse(cat(convert(y, string), \"(t)\")), ios):\n # derivative_orders:=table([seq(p=0, p in iofun)]):\n # for each in yus_list do\n # indets_ := indets(each) minus {t}: # get indets of derivative to compute order\n # function_ := op(indets_ intersect {op(iofun)}): # for which function?\n # order:=numelems(indets_): # compute order\n # if derivative_orders[function_] parse(cat(x, \"(t)\")) = x, states), M_sub):\n return [M_sub, decomp[1]]:\nend proc:\n\n#===============================================================================\n\nSingleExperimentIdentifiableFunctions := proc(model, output_targets, {infolevel := 1})\n # Input: model - ODE model represented as a list of differential polynomials\n # Computes generators of the field of single-identifiable functions\n local result, start, finish, states, inputs, outputs, model_eq, ios, params, io_eqs, si_gens, eq, wrnsk, echelon_form, model_denomfree, target: \t\n states, inputs, outputs, params, model_eq := op(ParseInput_(model)): # states, ios, params := op(ParseInput_(model)):\n ios := [op(inputs), op(outputs)]:\n\n # Step 1\n if infolevel > 0 then\n LogText(sprintf(\"SE Step 1: Computing input-output equations\\n\"), output_targets[log]):\n end if:\n model_denomfree := ExtractDenominator(model_eq):\n io_eqs := GetIOEquations(model_denomfree, states, inputs, outputs, params, false, infolevel, output_targets[log]):\n if infolevel > 0 then\n LogText(sprintf(\"SE Total number of io-equations: %a\\n\", nops(io_eqs)), output_targets[log]):\n end if:\n\n \t si_gens := {}:\n\t for eq in io_eqs do\n\t # Step 2\n\t if infolevel > 0 then\n\t LogText(sprintf(\"SE Step 2: Constructing the Wronskian\\n\"), output_targets[log]):\n\t end if:\n\t wrnsk := ConstructWronskian(eq, model_denomfree, states, inputs, outputs, params, [], infolevel, output_targets[log])[1]:\n\t # Step 3\n\t if infolevel > 0 then\n\t LogText(sprintf(\"SE Step 3: Computing the reduced row echelon form of the Wronskian\\n\"), output_targets[log]):\n\t end if:\n\t echelon_form := LinearAlgebra[ReducedRowEchelonForm](wrnsk):\n\t si_gens := {op(si_gens), op(select(x -> not type(x, numeric), convert(echelon_form, list)))}:\n\t end do:\n\n # Step 4\n if infolevel > 0 then\n LogText(sprintf(\"SE Step 4: restricting to the field of parameters\"), output_targets[log]):\n end if:\n \tresult:=map(simplify, convert(FilterGenerators(FieldIntersection(si_gens, params)), list)):\n\tDocumentTools:-SetProperty(output_targets[single], expression, result, 'refresh'):\n\treturn result:\nend proc:\n\n#===============================================================================\n# Adapted from https://github.com/pogudingleb/SIAN\nFunctionToVariable_ := proc(f):\n convert(convert(f, string)[1..-4], symbol):\nend proc:\n\nParseInput_ := proc(model)\n local all_symbols, x_functions, io_functions, params, states, ios, diff_polys, lhss, out_functions, in_functions, inputs, outputs:\n diff_polys := map(eq -> lhs(eq) - rhs(eq), model):\n all_symbols := foldl(`union`, op( map(e -> indets(e), diff_polys) )) minus {t}:\n x_functions := map(f -> int(f, t), select( f -> type(int(f, t), function(name)), all_symbols )):\n io_functions := select( f -> not type(int(f, t), function(name)) and type(f, function(name)) and not f in x_functions, all_symbols ):\n lhss := map(eq -> lhs(eq), model):\n out_functions := select(f -> f in lhss, io_functions):\n in_functions := select(f -> not (f in lhss), io_functions):\n params := [op(select(f -> not type(f, function(name)) and not type(int(f, t), function(name)), all_symbols))]:\n states := [op(map(FunctionToVariable_, x_functions))]:\n inputs := [op(map(FunctionToVariable_, in_functions))]:\n outputs := [op(map(FunctionToVariable_, out_functions))]:\n return [states, inputs, outputs, params, diff_polys]:\nend proc:\n\n#===============================================================================\n\nMultiExperimentIdentifiableFunctions := proc(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets): # {simplified_generators := false, no_bound := false})\n # Input: model - ODE model in the state-space form\n # Computes the bound from Theorem REF. Returns a list containing\n # 1. the bound\n # 2. the list of lists of coefficients of the IO-equations (after compression)\n # 3. (optional) simplified set of generators of the field of multi-experiment identifiable functions\n #\n # Optional keyword arguments:\n # 1. simplified_generators - if False, then just the coefficients of the IO-equations are returned.\n # if True, they are being simplified (maybe be a substantial simplification)\n # but this takes time\n # 2. no_bound - if True, then bound for the number of experiments is not computed (may save a lot of time)\n\n local states, inputs, outputs, ios, params, model_eqs, io_eqs, io_coeffs, io_coef, wrnsk, s, roll, wrnsk_sub, r, bound, \n generators, i, eq, result, model_denomfree, target, start, finish, infolevel, use_brackets, output_permutations, \n outputs_, io_coeffs_sb, io_eqs_sb, bound_sb, skip_simplify, result_sb, best_output_ordering, returned_generators, idx, old_bound:\n\n states, inputs, outputs, params, model_eqs := op(ParseInput_(model)):\n use_brackets:=false:\n output_permutations := combinat[permute](outputs):\n output_permutations:= output_permutations[..min(nops(output_permutations),max_perms)];\n \n infolevel := 1:\n model_denomfree := ExtractDenominator(model_eqs):\n skip_simplify := false:\n old_bound := 10: # this will be replaced by a smaller boud every time\n idx:=0:\n for use_brackets in [true, false] do\n for outputs in output_permutations do\n \tLogText(sprintf(\"Permutation:\\t%a\\n\", outputs), output_targets[log]):\n \t# the first iteration is default permutation\n\t \t LogText(sprintf(\"Use Brackets?\\t%a\\n\", use_brackets), output_targets[log]):\n\t if infolevel > 0 then\n\t LogText(sprintf(\"ME Computing input-output equations\\n\"), output_targets[log]):\n\t \t end if:\n\t \t io_eqs := GetIOEquations(model_denomfree, states, inputs, outputs, params, use_brackets, infolevel, output_targets[log]):\n\t \t if infolevel > 0 then\n\t LogText(sprintf(\"ME Total number of io-equations: %a\\n\", nops(io_eqs)), output_targets[log]):\n\t end if:\n\t io_coeffs := []:\n\t \n\t for eq in io_eqs do\n\t io_coef := DecomposePolynomial(eq, indets(eq) minus {op(params)}, params, infolevel, output_targets[log])[1]:\n\t io_coeffs := [op(io_coeffs), io_coef]:\n\t end do:\n\n\t generators := {}:\n \t for io_coef in io_coeffs do\n io_coef := sort(io_coef, (a, b) -> length(convert(a, string)) < length(convert(b, string)));\n for i from 2 to nops(io_coef) do\n generators := {op(generators), io_coef[i] / io_coef[1]}:\n end do:\n end do:\n bound := 0:\n\t\t if no_bound = false then\n for eq in io_eqs do\n if infolevel > 0 then\n LogText(sprintf(\"ME Constructing the Wronskian\\n\"), output_targets[log]):\n end if:\n wrnsk, io_coef := op(ConstructWronskian(eq, model_denomfree, states, inputs, outputs, params, model, infolevel, output_targets[log])):\n # in the notation of the theorem\n s := nops(io_coef) - 1:\n # substitution does not increase the rank, so the resulting bound will be correct\n roll := rand(1..15):\n wrnsk_sub := map(v -> v = roll(), indets(wrnsk)):\n r := LinearAlgebra[Rank](subs(wrnsk_sub, wrnsk)):\n bound := max(bound, s - r + 1):\n end do:\n end if:\n if bound 0 then\n\t\t LogText(sprintf(\"ME WARNING: Entering simplification of generators! if this takes too long, try unchecking \\\"Simplified Generators\\\"\\n\"), output_targets[log]):\n end if:\n result := [op(result), FilterGenerators(FieldToIdeal(generators))]:\n DocumentTools:-SetProperty(output_targets[multi], expression, map(simplify, convert(result[3], list)), 'refresh'):\n returned_generators := result[3]:\n else\n DocumentTools:-SetProperty(output_targets[multi], expression, map(simplify, convert(result[2], list)), 'refresh'):\n returned_generators := result[2]:\n end if:\n if old_bound > 0 then\n \t DocumentTools:-SetProperty(output_targets[bound_], expression, old_bound, 'refresh'):\n \t if old_bound=1 then\n \t \t skip_simplify := true:\n \t \t if simplify_bound then\n \t \t\t LogText(sprintf(\"Bound on the number of experiments = 1, \\\"Try to refine bound\\\" was selected but it will be skipped\"), output_targets[log]):\n \t \t end if:\n\t \t if simplified_generators then\n \t\t DocumentTools:-SetProperty(output_targets[single], expression, map(simplify, convert(result[3], list)), 'refresh'):\n \t\t else\n \t \t\t DocumentTools:-SetProperty(output_targets[single], expression, map(simplify, convert(result[2], list)), 'refresh'):\n \t\t end if:\n \t end if:\n else\n\t DocumentTools:-SetProperty(output_targets[bound_], expression, \"\",'refresh'):\n end if:\n if skip_simplify or not simplify_bound then\n \tbreak:\n \telse\n \t\tDocumentTools:-SetProperty(\"being_refined\", caption, \"being refined\", 'refresh'):\n end if:\n end do: # loop over outputs\n if skip_simplify or not simplify_bound then\n # only breaks if we do not simplify. the code runs at most once\n break:\n end if:\n end do:\n DocumentTools:-SetProperty(\"being_refined\", caption, \"\", 'refresh'):\n return [bound, returned_generators];#table([bd=bound]):\nend proc:\n\nGetPSSolution := proc(model, ord)\n # Input: model and integer ord\n # Output: a truncated power series solution with random parameter values\n # and initial conditions of order ord\n local roll, states, inputs, outputs, params, model_eqs, model_sub,\n x_funcs, x_sols, x_eqs, cur_ord, i, rhs_eval, total_sub, y_funcs, y_sols,\n params_subs, input_subs:\n roll := rand(1..15):\n states, inputs, outputs, params, model_eqs := op(ParseInput_(model)):\n params_subs := map(p -> p = roll(), params):\n input_subs := map(u -> parse(cat(u, \"(t)\")) = add([seq(roll() * t^i, i=0..ord)]), inputs):\n model_sub := subs(params_subs, model):\n model_sub := subs(input_subs, model_sub):\n x_funcs := map(x -> parse(cat(x, \"(t)\")), states):\n x_sols := map(x -> x = roll(), x_funcs):\n x_eqs := map(x -> subs(model_sub, diff(x, t)), x_funcs):\n \n for cur_ord from 1 to ord do\n for i from 1 to nops(x_funcs) do\n rhs_eval := series(subs(x_sols, x_eqs[i]), t, ord + 1):\n x_sols[i] := (lhs(x_sols[i]) = (rhs(x_sols[i]) + t^cur_ord * coeff(rhs_eval, t, cur_ord - 1) / cur_ord)):\n end do:\n end do:\n \n total_sub := [op(x_sols), op(params_subs), op(input_subs)]:\n y_funcs := map(y -> parse(cat(y, \"(t)\")), outputs):\n y_sols := map(y -> y = subs(total_sub, subs(model_sub, y)), y_funcs):\n \n return [op(y_sols), op(input_subs), op(params_subs), op(x_sols)]:\nend proc:\n\n", "meta": {"hexsha": "b04d1daf0697e780bee9255e89d2f0e58d087a76", "size": 29287, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "src/ComputeIdentifiableFunctions.mpl", "max_stars_repo_name": "iliailmer/sian-web-app", "max_stars_repo_head_hexsha": "0c5f8afceba45fd23391e7fd670c14b6fd469305", "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": "src/ComputeIdentifiableFunctions.mpl", "max_issues_repo_name": "iliailmer/sian-web-app", "max_issues_repo_head_hexsha": "0c5f8afceba45fd23391e7fd670c14b6fd469305", "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": "src/ComputeIdentifiableFunctions.mpl", "max_forks_repo_name": "iliailmer/sian-web-app", "max_forks_repo_head_hexsha": "0c5f8afceba45fd23391e7fd670c14b6fd469305", "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": 47.4667747164, "max_line_length": 183, "alphanum_fraction": 0.5863010892, "num_tokens": 7378, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7981867777396212, "lm_q2_score": 0.6619228625116081, "lm_q1q2_score": 0.5283380767403268}} {"text": "`is_element/shellings` := (A::set) -> (R) -> proc(S)\n global reason;\n local S0,S1,d,n,i,j,k,c,N,K;\n\n if A = {} then\n reason := [\"is_element/shellings\",\"A is empty\"];\n return false;\n fi;\n\n if not type(S,list) then\n reason := [\"is_element/shellings\",\"S is not a list\",S];\n return false;\n fi;\n\n S0 := `maximal_chains/partord`(A)(R);\n\n if {op(S)} <> S0 then\n reason := [\"is_element/shellings\",\"S is not an enumeration of the maximal simplices\",S,S0];\n return false;\n fi;\n\n if nops(map(nops,S0)) <> 1 then\n reason := [\"is_element/shellings\",\"The maximal simplices are not all of the same dimension\",S0];\n return false;\n fi;\n\n d := nops(S0[1]) - 1;\n n := nops(S);\n S1 := map(c -> {op(c)},S);\n N := table();\n\n for i from 2 to n do\n N[i] := select(j -> nops(S1[j] intersect S1[i]) = d,{seq(k,k=1..i-1)});\n if N[i] = {} then\n reason := [\"is_element/shellings\",\"The initial shelling condition fails for i\",S,i];\n return false;\n fi;\n od:\n\n for i from 1 to n-1 do\n for j from i+1 to n do\n c := S1[i] intersect S1[j];\n K := select(k -> c minus S1[k] = {} ,N[j]);\n if K = {} then\n reason := [\"is_element/shellings\",\"The shelling condition fails for (i,j)\",S,i,j];\n return false;\n fi;\n od;\n od; \n\n return true;\nend:\n\n######################################################################\n\n`is_element/edge_lex_labellings` := (A::set) -> (R) -> proc(l)\n global reason;\n local H,C,d,l0,cut,inc,cmp,R0,C0,C1,c0,c1,ab,a,b,u,i;\n\n if `bottom_element/partord`(A)(R) = FAIL then\n reason := [\"is_element/edge_lex_labellings\",\"There is no bottom element\",A,R];\n return false;\n fi;\n\n if `top_element/partord`(A)(R) = FAIL then\n reason := [\"is_element/edge_lex_labellings\",\"There is no top element\",A,R];\n return false;\n fi;\n\n H := `hasse_diagram/partord`(A)(R);\n\n if not(is_table_on(H)(l)) then\n reason := [\"is_element/edge_lex_labellings\",\n \"l is not a table indexed by the edges of the Hasse diagram\",l,H];\n return false;\n fi;\n\n C := `maximal_chains/partord`(A)(R);\n if nops(map(nops,C)) <> 1 then\n reason := [\"is_element/shellings\",\"The maximal simplices are not all of the same dimension\",C];\n return false;\n fi;\n\n d := nops(C[1]) - 1;\n\n l0 := (c) -> [seq(l[[c[i],c[i+1]]],i=1..nops(c)-1)];\n cmp := proc(c,d)\n local u;\n\n u := select(x -> x <> 0,l0(d) -~ l0(c));\n return evalb(u <> [] and u[1] > 0);\n end:\n \n cut := proc(c,a,b)\n local i,c0;\n\n i := 1;\n while c[i] <> a do i := i+1; od;\n c0 := NULL;\n while c[i] <> b do \n c0 := c0,c[i];\n i := i+1;\n od;\n c0 := [c0,b];\n return c0;\n end:\n\n inc := proc(c)\n local u,v,m;\n u := l0(c);\n v := [op(u),u[-1]] -~ [u[1],op(u)];\n m := min(op(v));\n return evalb(m >= 0); \n end:\n\n R0 := select(ab -> ab[1] <> ab[2],R);\n for ab in R0 do\n a,b := op(ab);\n C0 := select(c -> member(a,c) and member(b,c),C);\n C0 := map(cut,C0,a,b);\n C1 := select(inc,C0);\n\n if nops(C1) <> 1 then\n reason := \n [\"is_element/shellings\",\n \"The interval [a,b] does not have a unique increasing maximal chain\",\n ab,C0,C1];\n return false;\n fi;\n\n c1 := op(C1);\n for c0 in C0 minus C1 do\n if not cmp(c1,c0) then\n reason := \n [\"is_element/shellings\",\n \"In the interval [a,b], the increasing chain is not lex-smallest\",\n ab,c0,c1];\n return false;\n fi;\n od;\n od:\n\n return true;\nend:\n", "meta": {"hexsha": "10d0383a8f4e29259059c90c65a74050a34684e8", "size": 3279, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/shelling.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/shelling.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/shelling.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 22.6137931034, "max_line_length": 98, "alphanum_fraction": 0.5638914303, "num_tokens": 1125, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8152324803738429, "lm_q2_score": 0.647798211152541, "lm_q1q2_score": 0.5281061424596244}} {"text": "make_tetrahedron_complex := proc()\n global tetrahedron_complex;\n \n local T,V,E,F,v,f,P2,P3,g,s,x,eqs,sol;\n \n V := [seq(i,i=1..4)];\n E := [seq(seq([i,j],j=i+1..4),i=1..4)];\n F := [seq(seq(seq([i,j,k],k=j+1..4),j=i+1..4),i=1..4)];\n\n T := table([]);\n\n T[\"vertices\"] := V;\n T[\"edges\"] := E;\n T[\"coedges\"] := E;\n T[\"faces\"] := F;\n T[\"max_simplices\"] := F;\n\n T[\"edge_index\"] := make_index(T[\"edges\"]):\n T[\"face_index\"] := make_index(T[\"faces\"]):\n\n T[\"simplices\"] := [map(v -> [v],V),op(E),op(F)];\n\n T[\"embedding_dim\"] := 3;\n T[\"embedding\"] := table([\n 1 = [ 1, 1, 1], 2 = [ 1,-1,-1], 3 = [-1, 1,-1], 4 = [-1,-1, 1]\n ]);\n \n T[\"axial_embedding\"] :=\n table([1 = simplex_embedding([1,0,0,0]),\n 2 = simplex_embedding([0,1,0,0]),\n\t 3 = simplex_embedding([0,0,1,0]),\n\t 4 = simplex_embedding([0,0,0,1])]);\n\n v := eval(T[\"embedding\"]);\n\n T[\"normalised_embedding\"] :=\n table([seq(i = v[i] *~ (sqrt(3)/3), i = 1..4)]);\n \n T[\"dual_embedding\"] := table([seq(i = -~ v[i],i = 1..4)]);\n \n `plot/simplicial_complex`(T);\n\n T[\"edge_centres\"] :=\n map(e -> (v[e[1]] +~ v[e[2]]) /~ 2,T[\"edges\"]);\n\n T[\"face_centres\"] :=\n map(f -> (v[f[1]] +~ v[f[2]] +~ v[f[3]]) /~ 3, T[\"faces\"]);\n\n f := u -> combine(simplify(rationalize(u /~ sqrt(add(u[i]^2,i=1..3)))));\n P2 := [seq(seq(f(v[i] +~ v[j]),j=i+1..4),i=1..3)];\n P3 := [seq(f(v[i]),i=1..4),seq(f(-~ v[i]),i=1..4)];\n\n T[\"poles\"] := table([2 = P2, 3 = P3]);\n\n T[\"planes\"] := [\n seq(seq(f(v[i] -~ v[j]),j=i+1..4),i=1..3),\n seq(seq(f(v[j] -~ v[i]),j=i+1..4),i=1..3)\n ];\n\n T[\"pole_plots\"] := table([\n 2 = map(u -> line(1.2 *~ u, -1.2 *~ u,color=green,thickness=4),T[\"poles\"][2]),\n 3 = map(u -> line(1.2 *~ u, -1.2 *~ u,color=red ,thickness=4),T[\"poles\"][3])\n ]);\n\n T[\"all_poles_plot\"] := display(\n op(T[\"pole_plots\"][2]),op(T[\"pole_plots\"][3]),\n scaling=constrained,axes=none\n );\n \n T[\"symmetry_group\"] := combinat[permute](4);\n T[\"rotation_group\"] :=\n select(s -> mul(mul(s[j] - s[i],j=i+1..4),i=1..3) > 0, T[\"symmetry_group\"]);\n\n T[\"symmetry_matrix\"] := table():\n\n for s in T[\"symmetry_group\"] do\n g := Matrix(3,3,[seq(x[i],i=1..9)]);\n eqs := map(op,[seq(convert(g . Vector(v[i]) - Vector(v[s[i]]),list),i = 1..4)]);\n sol := solve(eqs);\n T[\"symmetry_matrix\"][s] := simplify(rationalize(subs(sol,convert(g,listlist))));\n od:\n\n tetrahedron_complex := eval(T);\n return eval(T);\nend:\n\nmake_tetrahedron_complex():\n", "meta": {"hexsha": "5c8c9b96d9d0447dc211c3ebae3972f135f1a3f5", "size": 2354, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial_complexes/tetrahedron_complex.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/tetrahedron_complex.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial_complexes/tetrahedron_complex.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 26.75, "max_line_length": 82, "alphanum_fraction": 0.5186915888, "num_tokens": 941, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8175744761936438, "lm_q2_score": 0.6442251201477016, "lm_q1q2_score": 0.5267020151555444}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_c *)\n(* prefix:\n mgga_x_m11_l_params *params;\n\n assert(p->params != NULL);\n params = (mgga_x_m11_l_params * ) (p->params);\n*)\n\n$include \"mgga_x_m08.mpl\"\n$include \"lda_x_erf.mpl\"\n\nf_spin := (rs, z, x, t) ->\n lda_x_ax*(1 + z)^(4/3)/rs * (\n + attenuation_erf(a_cnst*rs/(1 + z)^(1/3)) * m08_f(params_a_a, params_a_b, x, t)\n + (1 - attenuation_erf(a_cnst*rs/(1 + z)^(1/3))) * m08_f(params_a_c, params_a_d, x, t)\n ):\n\n\nf_m11_l := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n f_spin(rs, z, xs0, ts0) + f_spin(rs, -z, xs1, ts1):\n\nf := (rs, z, xt, xs0, xs1, ts0, ts1, us0, us1) ->\n f_m11_l(rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "2ae584d2fddfe848900f17e471232234ba7880a5", "size": 875, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_m11_l.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_x_m11_l.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_x_m11_l.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 27.34375, "max_line_length": 90, "alphanum_fraction": 0.616, "num_tokens": 351, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8459424295406088, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.5265647589271194}} {"text": "with(LinearAlgebra):\nwith(VectorCalculus):\nwith(plottools);\n\nNALU := proc(w1,w2,ghat1,ghat2,x,t,epsilon)\n\tlocal g1, g2, z1, z2, L, i;\n\tg1 := 1/~(1 +~ exp~(-ghat1));\n\tz1 := g1 *~ (w1.x) +~ (1 -~ g1) *~ exp~(w1.log~(abs(x) +~ epsilon));\n\n\tg2 := 1/~(1 +~ exp~(-ghat2));\n\tz2 := g2 *~ (w2.z1) +~ (1 -~ g2) *~ exp~(w2.log~(abs(z1) +~ epsilon));\n\n\tL := (z2 -~ t)^~2;\n\treturn add(L[i],i=1..numelems(L));\nend proc:\n\nNALUsafe := proc(w1,w2,ghat1,ghat2,x,t)\n\tlocal g1, g2, z1, z2, L, i;\n\tg1 := 1/~(1 +~ exp~(-ghat1));\n\tz1 := g1 *~ (w1.x) +~ (1 -~ g1) *~ exp~(w1.log~(abs(x -~ 1) +~ 1));\n\n\tg2 := 1/~(1 +~ exp~(-ghat2));\n\tz2 := g2 *~ (w2.z1) +~ (1 -~ g2) *~ exp~(w2.log~(abs(z1 -~ 1) +~ 1));\n\n\tL := (z2 -~ t)^~2;\n\treturn add(L[i],i=1..numelems(L));\nend proc:\n\n\nNALU(<, >, <>, , , , t, epsilon);\n\nP := plot3d(\n\tNALU(<, >, <>, , , <2, 2>, 8, 10^(-8)),\n\tw = -1.5..1.5, g = -3..3,\n\tview = [-1.5..1.5, -3..3, 0..300],\n\taxes=boxed):\nP;\n\nP := plot3d(\n\tNALU(<, >, <>, , , <2, 2>, 16, 10^(-8)),\n\tw = -1.5..1.5, g = -3..3,\n\tview = [-1.5..1.5, -3..3, 0..300],\n\taxes=boxed):\nP;\n\nNALUsafe(<, >, <>, , , , t, epsilon);\n\nP := plot3d(\n\tNALUsafe(<, >, <>, , , <2, 2>, 8),\n\tw = -1.5..1.5, g = -3..3,\n\tview = [-1.5..1.5, -3..3, 0..300],\n\taxes=boxed):\nP;\n\nP := plot3d(\n\tNALUsafe(<, >, <>, , , <2, 2>, 16),\n\tw = -1.5..1.5, g = -3..3,\n\tview = [-1.5..1.5, -3..3, 0..300],\n\taxes=boxed):\nP;\n\nsolveNALUsafe := proc(x, t)\n\tlocal i, v, w, g, eq, sol1, sol2, sols;\n\n\teq := NALUsafe(<, >, <>, , , x, t);\n\tsols := [];\n for v from -3 to 3 by 0.1 do\n sol1 := fsolve(eval(eq, g=v) = 0, w);\n sol2 := fsolve(eval(eq, g=v) = 0, w, avoid={{w = sol1}});\n sols := [op(sols), [sol1, v], [sol2, v]];\n end do;\n\n\treturn sols;\nend proc:\n\nsolveNALU := proc(x, t, epsilon)\n\tlocal i, v, w, g, eq, sols, sol1, sol2, sol3, sol4;\n\n\teq := NALU(<, >, <>, , , x, t, epsilon);\n\tsols := [];\n for v from -3 to 3 by 0.1 do\n sol1 := fsolve(eval(eq, g=v) = 0, w);\n sol2 := fsolve(eval(eq, g=v) = 0, w, avoid={{w = sol1}});\n if v < 0.9 and v >= 0 then\n sol3 := fsolve(eval(eq, g=v) = 0, w, avoid={{w = sol1}, {w = sol2}});\n sols := [op(sols), [sol1, v], [sol2, v], [sol3, v]];\n elif v < 0 then\n sol3 := fsolve(eval(eq, g=v) = 0, w, avoid={{w = sol1}, {w = sol2}});\n sol4 := fsolve(eval(eq, g=v) = 0, w, avoid={{w = sol1}, {w = sol2}, {w = sol3}});\n sols := [op(sols), [sol1, v], [sol2, v], [sol3, v], [sol4, v]];\n else\n sols := [op(sols), [sol1, v], [sol2, v]];\n end if;\n end do;\n\n\treturn sols;\nend proc:\n\nNALUsols := solveNALU(<2, 2>, 8, 10^(-8));\nP := plot(NALUsols, style = 'point', view = [-1.5..1.5, -3..3]):\nP;\n\nNALUsafesols := solveNALUsafe(<2, 2>, 8);\nP := plot(NALUsafesols, style = 'point', view = [-1.5..1.5, -3..3]):\nP;\n", "meta": {"hexsha": "433883f4c2111488a5ad35cc4e8879f253df37e2", "size": 3040, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "notes/loss-curvature.mpl", "max_stars_repo_name": "wlm2019/Neural-Arithmetic-Units", "max_stars_repo_head_hexsha": "f9de9d004bb2dc2ee28577cd1760d0a00c185836", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 147, "max_stars_repo_stars_event_min_datetime": "2019-10-07T11:01:54.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-16T02:51:18.000Z", "max_issues_repo_path": "notes/loss-curvature.mpl", "max_issues_repo_name": "wlm2019/Neural-Arithmetic-Units", "max_issues_repo_head_hexsha": "f9de9d004bb2dc2ee28577cd1760d0a00c185836", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1, "max_issues_repo_issues_event_min_datetime": "2019-12-03T12:40:21.000Z", "max_issues_repo_issues_event_max_datetime": "2019-12-03T12:40:21.000Z", "max_forks_repo_path": "notes/loss-curvature.mpl", "max_forks_repo_name": "wlm2019/Neural-Arithmetic-Units", "max_forks_repo_head_hexsha": "f9de9d004bb2dc2ee28577cd1760d0a00c185836", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 19, "max_forks_repo_forks_event_min_datetime": "2019-12-21T15:58:44.000Z", "max_forks_repo_forks_event_max_datetime": "2021-09-03T08:32:38.000Z", "avg_line_length": 28.679245283, "max_line_length": 90, "alphanum_fraction": 0.4414473684, "num_tokens": 1449, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7826624688140728, "lm_q2_score": 0.6723316860482763, "lm_q1q2_score": 0.526208777264472}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\nparams_a_kappa := 4.8827323:\nparams_a_mu := 0.3511128:\n$include \"gga_x_pbe.mpl\"\n\ndldf_a := [1, -0.1637571, -0.1880028, -0.4490609, -0.0082359]:\ndldf_csi_HF := 1 - 0.6144129:\n\ndldf_f := (x, u, t) ->\n + dldf_csi_HF*pbe_f(x)*mgga_series_w(dldf_a, 5, t):\n\nf := (rs, z, xt, xs0, xs1, u0, u1, t0, t1) ->\n mgga_exchange(dldf_f, rs, z, xs0, xs1, u0, u1, t0, t1):\n", "meta": {"hexsha": "b6febb8810d1b7272a993e8f9aaf37dcc6fdf5f7", "size": 621, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_dldf.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_dldf.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/hyb_mgga_x_dldf.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 27.0, "max_line_length": 68, "alphanum_fraction": 0.6489533011, "num_tokens": 265, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8933094088947399, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.5260602013107492}} {"text": "N := 3;\nA := {1,2,3,4,5,6};\nTT := `random_element/trees`(A)();\n\ncheck_map_generic(\"phi/nonempty_subsets/prime_simplex\",\"nonempty_subsets\",\"prime_simplex\",[[A]]);\ncheck_map_generic(\"centres/cubes\",\"cubes\",\"F\",[[N],[A]]);\ncheck_map_generic(\"fatten/F\",\"F\",\"cubes\",[[N],[A]]);\ncheck_map_generic(\"inc/F/Fbar\",\"F\",\"Fbar\",[[N],[A]]);\ncheck_map_generic(\"extend/tree_height_functions\",\"tree_height_functions\",\"height_functions\",\n [[A],[TT]],[[A],[TT]],[[A]]);\ncheck_map_generic(\"critical_tree/Fbar\",\"Fbar\",\"full_trees\",[[N],[A]],[[N],[A]],[[A]]);\n\nN := 2;\nA := {1,2,3,4,5};\n\ncheck_map_generic(\"phi/SEM/SCQ\",\"SEM\",\"SCQ\",[[N],[A]]);\ncheck_map_generic(\"psi/SCQ/SEM\",\"SCQ\",\"SEM\",[[N],[A]]);\ncheck_map_generic(\"sigma/SEM/F\",\"SEM\",\"F\",[[N],[A]]);\ncheck_map_generic(\"mu/F/SEM\",\"F\",\"SEM\",[[N],[A]]);\ncheck_map_generic(\"phi2/Fbar/P2\",\"Fbar\",\"P2\",[[N],[A]]);\ncheck_map_generic(\"psi/Fbar/Q\",\"Fbar\",\"Q\",[[N],[A]],[[N],[A]],[[A]]);\n", "meta": {"hexsha": "430eba2fd043f8af6cf6ed0681f59030f8992bfd", "size": 927, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib_checks/check_all_maps.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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_checks/check_all_maps.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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_checks/check_all_maps.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 42.1363636364, "max_line_length": 97, "alphanum_fraction": 0.6030204962, "num_tokens": 323, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8499711794579723, "lm_q2_score": 0.6187804267137442, "lm_q1q2_score": 0.5259455291193885}} {"text": "$ifndef _TCON_REFINE_\n$define _TCON_REFINE_\n\n$include \"Condition.mpl\"\n$include \"Utils.mpl\"\n\n# \u7b80\u5316\u53d8\u6362\u65b9\u7a0b\u7684\u7ea6\u675f\u6761\u4ef6\ntconRefine:=proc(s::TeqSol)\n s:-tcons:=[map[2](singleRefine,s:-rsol,s:-tcons[1]),\n map[2](singleRefine,s:-rsol,s:-tcons[2])];\n # s:-tcons:=map(x->epDeal~(x),s:-tcons);\n return s;\nend proc:\n\n# \u5bf9\u4e8e v[k] \u5220\u53bb a[k]>0 \u548c a[k]<0 \u7ea6\u675f\nsingleRefine:=proc(rsol,con)\n local ind,n,rep,vs;\n n:=numelems(rsol);\n rep:=add(rsol[i]*v[i],i=1..n);\n vs:=indets(rep,name);\n if numelems(vs)<>1 then\n return con;\n else\n vs:=op([1,1],vs);\n return con minus {a[vs]>0,a[vs]<0};\n end if;\nend proc:\n\n# \u5904\u7406\u6bcf\u4e2a\u53ef\u80fd\u60c5\u51b5\u7684\u7ea6\u675f\u6761\u4ef6\nepDeal:=proc(s::set)\n local ca,ce,r;\n ce,ca:=selectremove(has,s,epsilon);\n ce:=ceDeal~(ce);\n r:=ce union ca;\n r:=classifySolve(r);\n return r;\nend proc:\n\n# \u5355\u4e2a\u5173\u4e8eepsilon\u7684\u6761\u4ef6\u5904\u7406\nceDeal:=proc(e)\n local rs;\n # \u6709\u7684\u65f6\u5019solve\u4f1a\u62bd\uff0c\u5bf9\u4e8e\u8fd9\u79cd\u60c5\u51b5\u4e0d\u505a\u5904\u7406\n try\n rs:=conSolve(e);\n catch :\n return e;\n end try;\n if numelems(rs)=0 then\n # \u65e0\u89e3\u5219\u539f\u6837\u8fd4\u56de\n return e;\n elif numelems(rs)=1 then\n # \u53ea\u6709\u4e00\u4e2a\u89e3\uff0c\u5219\u4e0d\u8bba\u6709\u591a\u5c11\u6761\u4ef6\u90fd\u53ef\u4ee5\n return rs[][];\n else\n return e;\n end if;\nend proc:\n\n# \u6c42\u89e3\u4e0d\u7b49\u5f0f\uff0c\n# \u5728\u89e3\u4e2d\u5220\u9664\u81ea\u7531\u53d8\u91cf\n# \u5220\u9664\u548cepsilon\u6709\u5173\u7684\u7ea6\u675f\nconSolve:=proc(c)\n local r;\n r:=[RealDomain:-solve(c)];\n r:=map(x->remove(t->evalb(lhs(t)=rhs(t)),x),r);\n r:=map(x->remove(has,x,epsilon),r);\n r:=[{r[]}[]];# \u53bb\u91cd\n return r;\nend proc:\n\n$endif", "meta": {"hexsha": "b45f4bd3e989b488fc03e177ef0999f827ee1072", "size": 1417, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/TConRefine.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-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": "InvClassify/TConRefine.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "InvClassify/TConRefine.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 19.9577464789, "max_line_length": 57, "alphanum_fraction": 0.5688073394, "num_tokens": 573, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.798186787341014, "lm_q2_score": 0.6584175139669997, "lm_q1q2_score": 0.5255401602023767}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_k_pg_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_pg_params * )(p->params);\n*)\n\npg_f0 := s -> 5/3*s^2 + exp(-params_a_pg_mu * s^2):\npg_f := x -> pg_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) -> gga_kinetic(pg_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "4544624636b21583f4b36c005432daef568737e5", "size": 519, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "external/libxc-5.1.6/maple/gga_exc/gga_k_pg.mpl", "max_stars_repo_name": "pmu2022/lsms", "max_stars_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-01-27T14:45:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-27T14:45:51.000Z", "max_issues_repo_path": "external/libxc-5.1.6/maple/gga_exc/gga_k_pg.mpl", "max_issues_repo_name": "pmu2022/lsms", "max_issues_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 3, "max_issues_repo_issues_event_min_datetime": "2021-09-14T01:30:26.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-25T14:05:10.000Z", "max_forks_repo_path": "external/libxc-5.1.6/maple/gga_exc/gga_k_pg.mpl", "max_forks_repo_name": "pmu2022/lsms", "max_forks_repo_head_hexsha": "3c5f266812cad0b6d570bef9f5abb590d044ef92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2022-01-03T18:16:26.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-03T18:16:26.000Z", "avg_line_length": 24.7142857143, "max_line_length": 68, "alphanum_fraction": 0.6396917148, "num_tokens": 183, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8198933359135361, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.5252530681305039}} {"text": "\n# Velocity Calculation for the Robot based on MDH frames\n# Introduction\n# Berechnung der Geschwindigkeit von Koordinatensystemen und Schwerpunkten\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# tree -> Berechnung f\u00fcr eine beliebige Baumstruktur (ohne Schleifen)\n# velocity_mdh_angles -> Berechnung der Geschwindigkeit der MDH-Koordinaten (Drehung und Verschiebung in z-Richtung. Diese k\u00f6nnen zeitabh\u00e4ngig sein.\n# Authors\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# \n# Sources\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I (WS 2014/15)\n# [Ott2008] Cartesian Impedance Control of Redundant and Flexible-Joint Robots\n# Initialization\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\ncodegen_act := true:\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"%s. Generiere Geschwindigkeit f\u00fcr %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name):\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\n# Lade Ausdr\u00fccke f\u00fcr kinematische Zwangsbedingungen (Verkn\u00fcpfung von MDH-Gelenkwinkeln durch verallgemeinerte Koordinaten)\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nkintmp_qt := kintmp_qt:\nkintmp_qt := kintmp_qt:\nkin_constraints_exist := kin_constraints_exist:\nkintmp_subsexp := kintmp_subsexp:\n# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(4)=-1 then # Standard-Einstellungen:\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardm\u00e4\u00dfig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # standardm\u00e4\u00dfig simplify-Befehle anwenden\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(4): # vierter Eintrag ist f\u00fcr Geschwindigkeit\nend if:\n\n# Zeitableitung der Drehwinkel berechnen\n# Ersetze die MDH-Winkel durch verallgemeinerte Koordinaten\n# Falls die Gelenkwinkel nicht direkt mit verallgemeinerten Koordinaten \u00fcberstimmen (bei Kopplungen, kinematischen Schleifen) steht hier eine l\u00e4ngere Berechnung. Ansonsten reicht das triviale Einsetzen:\n# thetaD := qJD_t:\n# Ersetze die MDH-Drehung und Verschiebung entlang der z-Achse durch verallgemeinerte Koordinaten\ntheta_qt := theta:\nd_qt := d:\nfor ii from 1 to NJ do\n for jj from 1 to RowDimension(kintmp_qt) do\n theta_qt(ii, 1) := subs( { kintmp_t(jj, 1) = kintmp_qt(jj, 1) }, theta_qt(ii, 1) ):\n d_qt(ii, 1) := subs( { kintmp_t(jj, 1) = kintmp_qt(jj, 1) }, d_qt(ii, 1) ): \n end do:\nend do:\n# Zeitableitung der MDH-Drehung und Verschiebung entlang der z-Achse in Abh\u00e4ngigkeit der verallgemeinerten Koordinaten\nthetaD := Matrix(NJ, 1):\ndD := Matrix(NJ, 1):\n\nfor i from 1 to NJ do\n thetaD(i,1) := diff(theta_qt(i,1), t):\n dD(i,1) := diff(d_qt(i,1), t):\nend do:\nif kin_constraints_exist then # ist nur rechenaufw\u00e4ndig, wenn ZB vorliegen\n printf(\"%s. Zeitableitung der MDH-Winkel gebildet.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\nend if:\n# Terme vereinfachen\n\nif use_simplify>=1 and kin_constraints_exist then # ist nur sinnvoll, wenn ZB vorliegen\n tmp_t0 := time():\n tmp_l0 := length(thetaD)+length(dD):\n printf(\"%s: Vereinfache MDH-Geschwindigkeiten. L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l0):\n for i from 1 to NJ do\n tmp_t1 := time():\n tmp_l1 := length(thetaD(i,1)) + length(dD(i,1)): # es kann sowieso nur einer der beiden Informationen enthalten\n printf(\"%s: Vereinfache MDH-Geschw. %d. L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1):\n thetaD(i,1) := simplify2(thetaD(i,1)):\n dD(i,1) := simplify2(dD(i,1)):\n tmp_t2 := time():\n tmp_l2 := length(thetaD(i,1)) + length(dD(i,1)):\n printf(\"%s: MDH-Geschw. %d vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), i, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end do:\n tmp_l3 := length(thetaD)+length(dD):\n printf(\"%s: MDH-Geschwindigkeiten vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l0, tmp_l3, tmp_t2-tmp_t0):\nend if:\n\n# Ausdruck f\u00fcr Zeitableitungen der MDH-Winkel exportieren\nif codegen_act then\n MatlabExport(convert_t_s(thetaD), sprintf(\"../codeexport/%s/tmp/velocity_mdh_angles_matlab.m\", robot_name), codegen_opt):\n MatlabExport(convert_t_s(dD), sprintf(\"../codeexport/%s/tmp/velocity_mdh_deltaz_matlab.m\", robot_name), codegen_opt):\nend if:\n# Ausdruck f\u00fcr Maple speichern\nsave thetaD, dD, sprintf(\"../codeexport/%s/tmp/velocity_mdh_angles_maple.m\", robot_name):\n\n\n\n", "meta": {"hexsha": "5b3c5ea917a5b9b1ff4024610c7b1f031ff15938", "size": 5079, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_kinematics/robot_tree_velocity_mdh_angles.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_kinematics/robot_tree_velocity_mdh_angles.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_kinematics/robot_tree_velocity_mdh_angles.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 45.3482142857, "max_line_length": 202, "alphanum_fraction": 0.7361685371, "num_tokens": 1663, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8244619220634456, "lm_q2_score": 0.6370308082623217, "lm_q1q2_score": 0.525207644593584}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-10-input.txt\" ):\n\nlines := StringTools:-Split(input):\nmatchlookup := table( [ \"]\"=\"[\", \"}\"=\"{\", \">\"=\"<\", \")\"=\"(\",\n \"[\"=\"]\", \"{\"=\"}\", \"<\"=\">\", \"(\"=\")\" ] );\nscores := table( [ \"]\"=57, \"}\"=1197, \">\"=25137, \")\"=3 ] ):\nscores2 := table( [\"(\"=1, \"[\"=2, \"{\"=3, \"<\"=4] ):\n\npoints := 0:\nbadlines := NULL:\nfor j to nops(lines) do\n\n bracestack := DEQueue();\n for i to length(lines[j]) do \n if lines[j][i] in { \"[\", \"{\", \"<\", \"(\" } then \n push_back(bracestack, lines[j][i]);\n elif lines[j][i] in { \"]\", \"}\", \">\", \")\" } then\n c := pop_back(bracestack); \n if not c = matchlookup[lines[j][i]] then\n printf(\"Expected %a, but found %a instead.\\n\",\n matchlookup[c], lines[j][i] );\n points += scores[lines[j][i]];\n badlines := badlines, j;\n break;\n end if;\n end if;\n end do;\n\n acscore[j] := 0;\n while not empty(bracestack) do\n c := pop_back(bracestack);\n acscore[j] := 5*acscore[j] + scores2[c];\n end do;\nend do:\n\nanswer1 := points;\nanswer2 := round(Statistics:-Median([seq( acscore[i],\n i in ({ seq(1..nops(lines)) } minus {badlines}))] ));\n\n\n\n", "meta": {"hexsha": "acf483dd233727c9caadf7510c946e8ce42ae628", "size": 1269, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day10/AoC10-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day10/AoC10-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day10/AoC10-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 30.2142857143, "max_line_length": 62, "alphanum_fraction": 0.4554767533, "num_tokens": 380, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8056321889812553, "lm_q2_score": 0.6513548646660542, "lm_q1q2_score": 0.5247524454245026}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_bc95_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_bc95_params * )(p->params);\n*)\n\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\n(* The B97 function g *)\nbc95_gpar := (xs, ts) -> ts*Fermi_D(xs, ts)/(K_FACTOR_C*(1 + params_a_css*xs^2)^2):\nbc95_gperp := (xs0, xs1) -> 1/(1 + params_a_copp*(xs0^2 + xs1^2)):\n\n(* The parallel and perpendicular components of the energy *)\nbc95_fpar := (rs, z, xs0, xs1, ts0, ts1) ->\n + lda_stoll_par(f_pw, rs, z, 1) * bc95_gpar(xs0, ts0)\n + lda_stoll_par(f_pw, rs, -z, -1) * bc95_gpar(xs1, ts1):\n\nbc95_fperp := (rs, z, xs0, xs1) ->\n lda_stoll_perp(f_pw, rs, z) * bc95_gperp(xs0, xs1):\n\nf_bc95 := (rs, z, xs0, xs1, ts0, ts1) ->\n + bc95_fpar (rs, z, xs0, xs1, ts0, ts1)\n + bc95_fperp(rs, z, xs0, xs1):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n f_bc95(rs, z, xs0, xs1, ts0, ts1):\n\n", "meta": {"hexsha": "d465bfe17f86d3ff8573e72e966c3cc1b1872a49", "size": 1161, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_bc95.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_bc95.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_bc95.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 29.025, "max_line_length": 84, "alphanum_fraction": 0.6408268734, "num_tokens": 461, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8688267626522814, "lm_q2_score": 0.6039318337259583, "lm_q1q2_score": 0.5247121399587802}} {"text": " func $foo6 (\n var %i f64\n ) f64 { \n return (\n recip f64(dread f64 %i))}\n\n func $foo7 (\n var %i f32\n ) f32 { \n return (\n recip f32(dread f32 %i))}\n\n func $foo8 (\n var %i f64\n ) f64 { \n return (\n recip f64(constval f64 -1.24))}\n\n func $foo9 (\n var %i f32\n ) f32 { \n return (\n recip f32(constval f32 -1.24f))}\n# todo float recip\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "e1f91e8403cba11e0be313b1778910f20a6976ae", "size": 461, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0064-mapleall-irbuild-edge-recip/Main.mpl", "max_stars_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_stars_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 796, "max_stars_repo_stars_event_min_datetime": "2019-08-30T16:20:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-25T14:45:06.000Z", "max_issues_repo_path": "test/testsuite/irbuild_test/I0064-mapleall-irbuild-edge-recip/Main.mpl", "max_issues_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_issues_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 16, "max_issues_repo_issues_event_min_datetime": "2019-08-30T18:04:08.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-19T05:02:58.000Z", "max_forks_repo_path": "test/testsuite/irbuild_test/I0064-mapleall-irbuild-edge-recip/Main.mpl", "max_forks_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_forks_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 326, "max_forks_repo_forks_event_min_datetime": "2019-08-30T16:11:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-26T12:31:17.000Z", "avg_line_length": 16.4642857143, "max_line_length": 43, "alphanum_fraction": 0.5596529284, "num_tokens": 181, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7799928900257126, "lm_q2_score": 0.6723317057447908, "lm_q1q2_score": 0.5244139502197964}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: lda_exc *)\n(* prefix:\n lda_x_params *params;\n\n assert(p->params != NULL);\n params = (lda_x_params * )(p->params);\n*)\n\n$ifdef lda_x_params\nparams_a_alpha := 1:\n$endif\n\nf_lda_x := (rs, z) ->\n + params_a_alpha*my_piecewise3(screen_dens(rs, z), 0, lda_x_spin(rs, z))\n + params_a_alpha*my_piecewise3(screen_dens(rs, -z), 0, lda_x_spin(rs, -z)):\nf := (rs, z) -> f_lda_x(rs, z):\n", "meta": {"hexsha": "ede071968314fd504dee29fa03e5ae1f5cb8f723", "size": 633, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/lda_exc/lda_x.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.32, "max_line_length": 77, "alphanum_fraction": 0.6587677725, "num_tokens": 209, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8459424528443251, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.523452637893348}} {"text": "# This makes the formal group law for integral Morava K-theory\n# We truncate powers d+1 and higher\n\nmake_fgl_Morava := proc(p,n,d)\n local T,ld,x,y,u,i;\n\n T := table();\n T[\"p\"] := p;\n T[\"n\"] := n;\n T[\"d\"] := d;\n T[\"height\"] := n;\n T[\"degree\"] := d;\n T[\"modulus\"] := 0;\n\n ld := 0;\n while p^ld <= d/p do ld := ld+1; od;\n T[\"log_degree\"] := ld;\n \n T[\"log\"] := unapply(add(x^(p^(n*i))/p^i,i=0..ld),x);\n T[\"p_series\"] := unapply(x^(p^n),x);\n\n Order := d+2;\n \n T[\"exp\"] :=\n unapply(\n convert(\n solve(x = series(T[\"log\"](y) + sin(y)^(d+1),y=0,d+1),y),\n polynom,x\n ),\n x\n );\n\n T[\"p_series\"] := \n unapply(expand(convert(series(T[\"exp\"](p*T[\"log\"](x)),x=0,d+1),polynom,x)),x);\n\n T[\"sum\"] :=\n unapply(\n subs(u=1,expand(convert(series(T[\"exp\"](T[\"log\"](u*x)+T[\"log\"](u*y)),u=0,d+1),polynom,u))),\n x,y\n ):\n\n T[\"sum0\"] := unapply(mods(T[\"sum\"](x,y),p),x,y);\n T[\"p_series0\"] := unapply(mods(T[\"p_series\"](x),p),x);\n\n return eval(T);\nend:\n", "meta": {"hexsha": "9cbe5762f46cc18fb556ddcb1a225a66873c05cb", "size": 943, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/morava/fgl.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/morava/fgl.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/morava/fgl.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 20.0638297872, "max_line_length": 94, "alphanum_fraction": 0.5185577943, "num_tokens": 366, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8991213826762113, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.52266203861407}} {"text": "# # Weyl group related operations on weyl word\n# # by Shizuo Kaji\n# requires coxeter and weyl package by J.Stembridge\n# http://www.math.lsa.umich.edu/~jrs/maple.html\n#\n# global variables:\n# R: Lie type\n# B: the set of simple roots\n\nWeylOps := module() option package;\n export `.`,inv,descent,minrep,PReducedWd,WeylFunc,e,c,symmetric,e2w,e2a,a2e,a2w,w2a,deg_X,dimr,relative_roots,e2ref,action,oneline;\n # inverse of weyl word\n inv := proc (weyl::list);\n\treturn ListTools[Reverse](weyl);\n end proc;\n\n # operator '.' as product\n `.` := overload(\n [\n proc(a::list, b::list) option overload(callseq_only); global R;\n return(reduce([op(a),op(b)],R));\n end,\n proc(a::indexed, b::indexed) option overload(callseq_only);\n if op(0,a)=`s` and op(0,b)=`s` then\n return(s[op(1,a).op(1,b)]);\n else\n return(a*b);\n end if;\n end,\n proc(a::`+`, b::anything) option overload(callseq_only);\n return map(`.`,a,b);\n end,\n proc(a::anything, b::`+`) option overload(callseq_only);\n return map2(`.`,a,b);\n end,\n proc(a::`*`, b::anything) option overload(callseq_only);\n return op(1,a)*((a/op(1,a)).b);\n end,\n proc(a::anything, b::`*`) option overload(callseq_only);\n return op(1,b)*(a.(b/op(1,b)));\n end\n ]\n):\n\n# descent set of the weyl word \"weyl\"\ndescent := proc(weyl::list) local i, V; global R;\n\tV := {};\n\tfor i from 1 to rank(R) do\n\t if nops(weyl.[i]) < nops(weyl) then\n \t\tV := {op(V), i};\n\t end if;\n end do:\n\treturn V;\nend proc;\n\n# minimal coset representative of \"weyl\" according to \"roots\"\nminrep := proc(weyl::list, roots::set) local i,temp; global R;\n for i in roots do\n temp:=weyl.[i]:\n if nops(temp) < nops(weyl) then return(procname(temp, roots)); end if:\n end do:\n return(weyl):\nend proc:\n\n# enumerate all reduced words (minimal coset representatives) of \"R\" upto length \"len\"\nPReducedWd := proc (R, roots::set:={}, maxlen::integer:=nops(longest_elt(R)))\n local B, r, v, i, j, len, newvects, newwords, words, oldvects;\n B := base(R); r := rank(B);\n\tnewvects := [add(weights(R)[i], i={$1..r} minus roots)];\n words := Array(0..maxlen); words[0]:=[[]];\n for len from 1 to maxlen do;\n oldvects := newvects;\n newvects := []; newwords := NULL;\n for j to nops(oldvects) do\n for i to r do\n if 0 < iprod(B[i], oldvects[j]) then\n v := reflect(B[i], oldvects[j]);\n if not member(v, newvects) then\n newvects := [op(newvects), v];\n newwords := newwords, reduce([i,op(words[len-1][j])],R);\n end if\n end if\n end do\n end do;\n if newwords=NULL then break; end if;\n words[len] := [newwords];\n end do;\n return convert(words[1..len-1],list);\nend proc;\n\n# iterative application of a function of simple roots for a weyl word poly\nWeylFunc := proc(weyl, f::polynom, func::procedure) local i,temp;\n\ttemp := f;\n if type(weyl,'numeric') then\n return weyl*f;\n elif type(weyl,'list') then\n for i from nops(weyl) to 1 by -1 do\n temp := func(weyl[i], temp);\n end do;\n return temp;\n elif type(weyl, 'indexed') then\n if op(0,weyl)=`s` then\n return procname(op(1,weyl), f, func);\n else\n return weyl*f;\n end if;\n elif type(weyl, linear) then\n\t return add(coeff(weyl,ind)*procname(ind, f, func), ind=indets(weyl));\n else\n print(\"error in WeylFunc:\",weyl);\n end if;\nend proc:\n\n## Utility Functions\n# coordinate variables\ne := proc (j::integer);\n return cat('e', j);\nend proc;\n\n# elementary symmetric function \"c(i)\" of \"t[1..r]\"\nc := proc (deg::integer,sym::symbol := `t`) global R;\n return symmetric(deg, [seq(sym[i], i = 1 .. rank(R))])\nend proc;\n\n# elementary symmetric function of degree \"deg\" in \"vars\"\nsymmetric := proc (deg::integer, vars::list) local T;\n return sort(expand(coeff(mul(T+i, i=vars), T, nops(vars)-deg)));\nend proc;\n\n# convert vector in \"e\" into weights \"w[1..r]\"\ne2w := proc (el::linear) global R;\n return add(weight_coords(el, R)[i]*w[i], i=1..rank(R));\nend proc;\n\n# convert vector in \"e\" into simple roots \"a[1..r]\"\ne2a := proc (el::{polynom, list}) global R;\n if type(el, rational) then\n\t return el;\n elif type(el, linear) then\n return add(root_coords(el, R)[i]*a[i], i=1..rank(R));\n elif type(el, `*`) or type(el, list) then\n\t return map(procname, el);\n elif type(el, `^`) then\n\t return procname(op(1,el))^op(2,el);\n else\n print(\"error in e2a:\",el);\n return infinity;\n end if;\nend proc;\n\n# convert vector in \"e\" into simple roots \"a[1..r]\"\na2e := proc (apol::{polynom, list}) global B;\n return eval(apol,[seq(a[i]=B[i],i=1..nops(B))]);\nend proc:\n\n# convert a-poly into w-poly\na2w := proc (apol::polynom) global R,B;\n return eval(apol, [seq(a[j]=add(weight_coords(B[j], R)[i]*w[i], i=1..nops(B)), j=1..nops(B))]);\nend proc;\n\n# convert w-poly into a-poly\nw2a := proc (wpol::polynom) global R,B;\n return eval(wpol, [seq(w[j]=add(root_coords(weights(R)[j], R)[i]*a[i], i=1..nops(B)), j=1..nops(B))]);\nend proc;\n\n# degree of a polynomial in X[]\ndeg_X := proc(f::polynom) local d,max_d,term,temp,x,y;\n if type(f,`+`) then\n max_d:=0;\n for term in f do\n d := procname(term);\n if d>max_d then max_d:=d; end if;\n end do;\n return max_d;\n elif type(f,`^`) then\n procname(op(1,f))*op(2,f);\n else\n temp := f;\n for x in indets(f) do\n temp := eval(temp, x=y^(nops(op(1,x))));\n end do;\n return degree(temp);\n end if;\nend proc:\n\n# dimension of the standard representation of R\ndimr := proc(R) local lie_type; option remember;\n\tlie_type := name_of(R);\n if lie_type = cat('A',rank(R)) then\n return rank(R)+1;\n elif lie_type = G2 then\n return 3;\n elif lie_type = E6 or lie_type = E7 then\n return 8;\n else\n return rank(R);\n end if;\nend proc:\n\n# positive roots relative to a parabolic subgroup\nrelative_roots := proc(R,roots::set) local L;\n L:={seq(base(R)[i],i=roots)};\n L:=orbit(L,R);\n return {op(pos_roots(R))} minus {op(L)};\nend proc:\n\n# vector to reflection\ne2ref:=proc(el) local i,w; global R;\n vec2fc(reflect(el,interior_pt(R)),R,'w');\n return w;\nend proc:\n\n# action of a reduced word on a linear sum of ei\naction:=proc(w::list,el::polynom) global B;\n return reflect(seq(B[i],i=w),el);\nend proc:\n\n# one line notation of elements in classical groups\noneline:=proc(weyl::list) local deg, lie_type, L, i; global R,pg;\n\tlie_type := name_of(R);\n if lie_type = cat('A',rank(R)) then\n deg := rank(R)+1;\n elif lie_type = cat('B',rank(R)) or lie_type = cat('C',rank(R)) or lie_type = cat('D',rank(R)) then\n deg := 2*rank(R);\n else\n return -infinity;\n end if;\n L:=convert(multperm(weyl,pg), 'permlist', deg);\n if lie_type = cat('B',rank(R)) or lie_type = cat('C',rank(R)) or lie_type = cat('D',rank(R)) then\n L:=L[-rank(R)..-1];\n for i from 1 to nops(L) do;\n if L[i]<=rank(R) then\n L[i]:=L[i]-rank(R)-1;\n else\n L[i]:=L[i]-rank(R);\n end if;\n end do;\n end if;\n return convert(L,array);\nend proc:\n\n\nend module:\n", "meta": {"hexsha": "db254735be9c4eda9c17c70e3ebabc8c0361a021", "size": 7394, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "WeylOps.mpl", "max_stars_repo_name": "shizuo-kaji/WeylGroup", "max_stars_repo_head_hexsha": "f22a71f9e0c1765d472dd51053680a65bee5304c", "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": "WeylOps.mpl", "max_issues_repo_name": "shizuo-kaji/WeylGroup", "max_issues_repo_head_hexsha": "f22a71f9e0c1765d472dd51053680a65bee5304c", "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": "WeylOps.mpl", "max_forks_repo_name": "shizuo-kaji/WeylGroup", "max_forks_repo_head_hexsha": "f22a71f9e0c1765d472dd51053680a65bee5304c", "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": 30.3032786885, "max_line_length": 133, "alphanum_fraction": 0.5760075737, "num_tokens": 2326, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8244619177503205, "lm_q2_score": 0.6334102775181399, "lm_q1q2_score": 0.5222226521253683}} {"text": "// A COMMEnt\n/* Another\n comment */\nvar X : int := 4 + (6 * 2);\nprint X;\nprint \"\\n\";\n", "meta": {"hexsha": "96279f4a2d1d5316995ec3fdf0e41c55de8e1c98", "size": 87, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/p4.mpl", "max_stars_repo_name": "nicohi/mini-pl-interpreter", "max_stars_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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/p4.mpl", "max_issues_repo_name": "nicohi/mini-pl-interpreter", "max_issues_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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/p4.mpl", "max_forks_repo_name": "nicohi/mini-pl-interpreter", "max_forks_repo_head_hexsha": "432cd0713046fba10fdf3668b9ce8d04f0412cc6", "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": 12.4285714286, "max_line_length": 27, "alphanum_fraction": 0.5057471264, "num_tokens": 32, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7490872131147276, "lm_q2_score": 0.6959583313396339, "lm_q1q2_score": 0.5213334868671825}} {"text": "######################################################################\n\n`eta/stasheff_trees` := proc(A::set)\n if nops(A) = 1 then \n return [`eta/ord`(A),`eta/trees`(A)];\n else\n return FAIL;\n fi;\nend;\n\n`gamma/stasheff_trees` := (A::set,B::set) -> (p) -> proc(Y,XX)\n local R,TT,SS,UUUU,b;\n\n R,TT := op(Y);\n\n SS := table();\n UUUU := table();\n\n for b in B do\n SS[b],UUUU[b] := op(XX[b]);\n od;\n\n return [`gamma/ord`(A,B)(p)(R,SS),\n `gamma/trees`(A,B)(p)(TT,UUUU)];\nend;\n", "meta": {"hexsha": "55b40df7c24e239d7352ba7454773201eb15528a", "size": 476, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/stasheff_trees.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/stasheff_trees.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/stasheff_trees.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 18.3076923077, "max_line_length": 70, "alphanum_fraction": 0.4537815126, "num_tokens": 163, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8459424373085146, "lm_q2_score": 0.6150878555160665, "lm_q1q2_score": 0.5203289196541288}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_x *)\n\na1 := 3*Pi/X_FACTOR_C:\n\nf := (rs, x, t, u) -> a1/(2*t - u/4):", "meta": {"hexsha": "3d2d147da82fd46aab01694929058606662bca85", "size": 325, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_x_mk00.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_x_mk00.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_x_mk00.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.0, "max_line_length": 68, "alphanum_fraction": 0.6492307692, "num_tokens": 111, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8615382094310355, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.5203103506466641}} {"text": "# File: RigidMotionsParameterSpaceDecompostion.mpl \n#\n# Description:\n# This file contains functions used to obtain an arrangement 6 dimensional parameter space of 3D\n# digitized rigid motions.\n# This code has been written for research propose and its aim is to calculate a particular\n# arrangement of quadrics. Therefore, it can or it cannot be useful in study of generic\n# arrangements. The final output are sample points of full dimensional open cells.\n#\n# The code was written in relation with the paper: Kacper Pluta, Guillaume Moroz, Yukiko\n# Kenmochi, Pascal Romon, Quadric arrangement in classifying rigid motions of a 3D digital image,\n# 2016, https://hal.archives-ouvertes.fr/hal-01334257 referred late on as [Quadrics:2016].\n#\n# Author:\n# Kacper Pluta - kacper.pluta@esiee.fr\n# Laboratoire d'Informatique Gaspard-Monge - LIGM, A3SI, France\n#\n# Date:\n# 11/12/2015 \n#\n# License:\n# Simplified BSD License\n#\n# Copyright (c) 2015, Kacper Pluta\n# All rights reserved.\n\n# Redistribution and use in source and binary forms, with or without\n# modification, are permitted provided that the following conditions are met:\n# * Redistributions of source code must retain the above copyright\n# notice, this list of conditions and the following disclaimer.\n# * Redistributions in binary form must reproduce the above copyright\n# notice, this list of conditions and the following disclaimer in the\n# documentation and/or other materials provided with the distribution.\n#\n# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\" AND\n# ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED\n# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\n# DISCLAIMED. IN NO EVENT SHALL Kacper Pluta BE LIABLE FOR ANY\n# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES\n# (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;\n# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND\n# ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT\n# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS\n# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n#\n#\n\nRigidMotionsParameterSpaceDecompostion := module() \n option package;\n uses RigidMotionsParameterSpaceDecompostionRecursive, RigidMotionsParameterSpaceCommon;\n\n local GetQuadric, IsMonotonic, ComputeSetOfQuadrics,\n ComputeEventsATypeGrid, ComputeEventsBTypeGrid, ComputeEventsCTypeGrid,\n ComputeAsymptoticABEventsGrid, ComputeAsymptoticAAEvents, \n ComputeEventsFromAlgebraicNumbers, IsAsymptotic;\n \n # Only the procedures with prefix Launch* should be called! Other are exported only for \n # the grid framework.\n export IsAsymptoticIntersection, ComputeSamplePoints, ParallelComputeSamplePoints,\n LaunchComputeEvents, LaunchComputeSamplePoints; \n\n #Variables shared by grid nodes;\n global Q, events, vars, dbPath, skipped;\n\n# Procedure: GetQuadric\n# Compute a quadric.\n#\n# Parameters:\n# R - a 3x3 rotation matrix obtained from Cayley transform\n# neighbor - a vector which points on a neighbor\n# hGridPlane - a half-grid plane i.e. k_dim + 1/2\n# axis - a given row of R matrix\n# \n# Output:\n# Multivariate polynomial of degree 2 related to the changed of configuration of image patch and\n# given in [Quadrics:2016] as equation (7).\nGetQuadric := proc(R::~Matrix, neighbor::~Vector, hGridPlane::~Vector, axis::integer)\n local r := R . neighbor - hGridPlane;\n if axis > 0 and axis < 4 then\n return simplify( ( 2 * denom( R[1][1] ) ) * r[axis] );\n else\n error \"Wrong dimension: dim must be in [1,3].\";\n end if:\nend proc:\n\n\n# Procedure: IsMonotonic\n# Check if given polynomial of degree 2 is non-positive or non-negative\n#\n# Parameters:\n# x - a polynomial\n#\n# Output:\n# true if polynomial of degree 2 is non-positive and false otherwise\nIsMonotonic := proc( x::~polynom )\n local homo, hessian, signmap, clean:\n homo := Groebner:-Homogenize( x, v ):\n hessian := 1 / 2 * VectorCalculus:-Hessian( homo, [ op( indets( x ) ), v ] ):\n signmap := map( signum, LinearAlgebra:-Eigenvalues( hessian ) ):\n signmap := convert( signmap, list ):\n clean := remove( `=`, signmap , 0 ):\n return ( andmap( `=`, clean, 1 ) or andmap( `=`, clean, -1 ) ):\nend proc:\n\n\n# Procedure: ComputeSetOfQuadrics\n# Compute a set of quadrics which are reduced by duplicated and these ones\n# which are strictly positive or negative.\n#\n# Parameters:\n# R - a rotation matrix obtained from Cayley transform\n# nType - size of neighborhood i.e. N_1, N_2, N_3. \n# axis - a given axis i.e. 1 = x, 2 = y and 3 = z \n# kRange - a range of planes to consider\n#\n# Output:\n# List of quadrics of form f - g reduced by duplicated---up to constant\n# factor---and these ones which are strictly positive or negative.\nComputeSetOfQuadrics := proc( R::~Matrix,\n nType::string,\n axis::~integer,\n kRange::~list )\n local neighborhood := GetNeighborhood( nType ):\n local quadrics := Array([]):\n local f::polynom, g::polynom, quadric::polynom:\n local indexes := []:\n local T := combinat:-cartprod( [ neighborhood, neighborhood, kRange, kRange ] ):\n\n if LinearAlgebra:-Determinant(R) <> 1 or [upperbound(R)] <> [3,3] or nops(indets(R)) = 0 then\n error \"Used matrix is not a correct 3 x 3 rotation matrix!\";\n fi;\n\n if axis < 1 or axis > 3 then\n error \"Axis is not from range [1,3].\";\n fi:\n\n while not T[ finished ] do\n indexes := T[ nextvalue ]():\n f := GetQuadric( R, Vector( indexes[1] ), Vector( 3, indexes[3] + 1/2 ), axis ):\n g := GetQuadric( R, Vector( indexes[2] ), Vector( 3, indexes[4] + 1/2 ), axis ):\n quadric := f - g:\n if not type(quadric, constant) then\n quadric := quadric / lcoeff( quadric ):\n ArrayTools:-Append(quadrics,quadric):\n end if:\n end do:\n quadrics := convert(quadrics,set):\n quadrics := remove( IsMonotonic, quadrics ):\n quadrics := Threads:-Map(proc(x) normal(x) * denom(x) end proc, quadrics):\n return quadrics:\nend proc:\n\n\n# Procedure: IsAsymptotic\n# Checks if given quadric has an asymptotic critical value. For this moment a direction is fixed\n# to a.\n#\n# Parameters:\n# x - a quadric in three variables\n# vars - a list of variables\n#\n# Output:\n# List of solution for which partial derivatives in vars[2] and vars[3] are collinear.\nIsAsymptotic := proc(x::polynom, vars::list)\n local vec, Vb, Vc, VV, sols;\n if nops(vars) < 3 then\n error \"Expected at least three variables!\";\n fi;\n vec := VectorCalculus:-Gradient(x, vars);\n Vb := Vector(3, [coeff(vec[2],vars[2]),coeff(vec[2],vars[3]),eval(vec[2],[vars[-2]=0,vars[-1]=0])]);\n Vc := Vector(3, [coeff(vec[3],vars[2]),coeff(vec[3],vars[3]),eval(vec[3],[vars[-2]=0,vars[-1]=0])]);\n VV := LinearAlgebra:-CrossProduct(Vb, Vc);\n if norm(VV,1) = 0 then\n return {{vars[1]=0}};\n fi;\n sols := solve({VV[1] = 0, VV[2] = 0,VV[3] = 0,vars[1]>=0}, [vars[1]]);\n if sols = NULL then\n return {};\n else\n return sols;\n fi;\nend proc:\n\n\n# Procedure: IsAsymptoticIntersection\n# Checks if intersection of two quadrics has an asymptotic critical value. For this moment a\n# direction is fixed to a.\n#\n# Parameters:\n# p - a quadric in three variables\n# q - a quadric in three variables\n# vars - a list of variables\n#\n# Output:\n# List of solution for which intersection of p and q has an asymptotic intersection\n# Comment:\n# - Since Groebner package seems to have memory leak I should rather replace \n# PolynomialIdeals:-EliminationIdeal by resultant elimination similarly to what I did with\n# univariate polynomials.\n# TODO:\n# - Allow user to chose a direction. \n# - if there is no intersection between quadrics then skip it.\nIsAsymptoticIntersection := proc( p::polynom, q::polynom, vars::list )\n local J := PolynomialIdeals:-`<,>`(p,q);\n local Pb, Pc, Cb, Cc, sols, univ;\n if nops(vars) < 3 then\n error \"Expected at least three variables!\";\n fi;\n Pb := PolynomialIdeals:-EliminationIdeal(J,{op(vars[1..2])}):\n Pb := PolynomialIdeals:-IdealInfo:-Generators(Pb)[1];\n Pc := PolynomialIdeals:-EliminationIdeal(J,{op(vars[[1,3]])});\n Pc := PolynomialIdeals:-IdealInfo:-Generators(Pc)[1];\n Cb := lcoeff(Pb, vars[2]);\n Cc := lcoeff(Pc, vars[3]);\n return lcm(Cb,Cc);\nend proc:\n\n\n# Procedure: ComputeEventsATypeGrid\n# Compute events such that a sweep plane is tangent to a quadric. \n#\n# Parameters:\n# Q - a set of quadrics or conics\n# dim - a list of indexes of variables used to calculate partial derivatives\n# vars - a list of variables\n#\n# Output:\n# List of ranges which contains roots of a system(q, d/db q, d/dc q).\n#\n# Comment:\n# - only the first direction is supported\nComputeEventsATypeGrid := proc( Q, dim::list, vars::list )\n local s, result := Array([]);\n if nops(vars) < 3 then\n error \"Expected at least three variables!\";\n fi;\n s := proc(i::integer, vars::list)\n local sys, univ;\n local q := Q[i];\n sys := [q, diff( q, vars[ dim[1] ] ), diff( q, vars[ dim[2] ] )];\n univ := UnivariatePolynomial(sys, vars);\n return SerializeEvents(GenerateEvents(univ, [i]));\n end proc:\n map[inplace](proc(x) ArrayTools:-Extend(result, x, inplace=true) end proc, \n [Grid:-Seq(s(i, vars), i=1..nops(Q))]);\n return ReconstructEvents(result);\nend proc:\n\n\n# Procedure: ComputeEventsBType\n# Compute events such that intersection of two quadrics is tangent to sweeping plane.\n#\n# Parameters:\n# dir - a direction of a gradient product it should\n# be the same as director of sweep \n# Q - a set of conics\n# vars - a list of variables\n#\n# Output:\n# Indexes of quadrics which intersect and a component of a vector product of \n# their gradients in given direction have a common root.\nComputeEventsBTypeGrid := proc( Q, dir::integer, vars::list )\n local s, result := Array([]);\n if nops(vars) < 3 then\n error \"Expected at least three a variables!\";\n fi;\n s := proc(i, j, vars::list)\n local p, prod, univ, sys:\n prod := LinearAlgebra:-CrossProduct( VectorCalculus:-Gradient( Q[i], vars ),\n VectorCalculus:-Gradient( Q[j], vars ) )[dir]:\n sys := [Q[i], Q[j], prod];\n univ := UnivariatePolynomial(sys, vars);\n return SerializeEvents(GenerateEvents(univ, [i, j]));\n end proc:\n map[inplace](proc(x) ArrayTools:-Extend(result, x, inplace=true) end proc, \n [Grid:-Seq(seq(s(i, j, vars), j=i+1..nops(Q)), i=1..nops(Q))]);\n return ReconstructEvents(result);\nend proc;\n\n\n# Procedure: ComputeEventsCTypeGrid\n# Compute events such that three quadrics intersects in a point. \n#\n# Parameters:\n# Q - a set of quadrics\n# vars - a list of variables\n#\n# Output:\n# Indexes of quadrics which intersect in a point.\nComputeEventsCTypeGrid := proc( Q, vars::list )\n uses ArrayTools;\n local result := Array([]), s;\n if nops(vars) < 3 then\n error \"Expected at least three a variables!\";\n fi;\n s := proc (i, j, k, vars::list)\n local univ, sys;\n sys := [Q[i], Q[j], Q[k]];\n univ := UnivariatePolynomial(sys, vars);\n return SerializeEvents(GenerateEvents(univ, [i, j, k]));\n end proc;\n map[inplace](proc(x) Extend(result, x, inplace=true) end proc, [Grid:-Seq(seq(seq(s(i, j, k, vars), \n k=j+1..nops(Q)),j=i+1..nops(Q)),i=1..nops(Q))]);\n return ReconstructEvents(result);\nend proc:\n\n\n# Procedure: ComputeAsymptoticAAEvents\n# Compute real algebraic numbers which corresponds to \n# asymptotic cases given by one quadrics.\n#\n# Parameters:\n# Q - a set of quadrics\n# vars - a list of variables\n#\n# Output:\n# A list of real algebraic numbers and indexes of quadrics -- events.\nComputeAsymptoticAAEvents:=proc(Q, vars::list)\n uses ArrayTools;\n local result := Array([]), s;\n if nops(vars) < 3 then\n error \"Expected at least three a variables!\";\n fi;\n s:=proc(i::integer, vars::list)\n local events := Array([]), sol, rootsF, tmp:\n rootsF := IsAsymptotic(Q[i], vars):\n for sol in rootsF do\n sol := op(sol);\n if not type(rhs(sol), rational) then\n error \"Irrational asymptotic case! Are you sure the input is a set of quadrics?\"\n fi:\n ArrayTools:-Append(events, EventType(RealAlgebraicNumber(lhs(sol) * denom(rhs(sol)) -\n numer(rhs(sol)), rhs(sol), rhs(sol)), [i]));\n od:\n return events;\n end proc;\n map[inplace](proc(x) Extend(result, x, inplace=true) end proc, [seq(s(i, vars), i=1..nops(Q))]);\n return result;\nend proc;\n\n\n# Procedure: ComputeAsymptoticABEvents\n# Compute real algebraic numbers which corresponds to \n# asymptotic cases given by one quadrics.\n#\n# Parameters:\n# Q - a set of quadrics\n# vars - a list of variables\n#\n# Output:\n# A list of real algebraic numbers and indexes of quadrics -- events.\nComputeAsymptoticABEventsGrid:=proc(Q, vars::list)\n uses ArrayTools;\n local result := Array([]), s;\n if nops(vars) < 3 then\n error \"Expected at least three a variables!\";\n fi;\n s:=proc(i::integer, j::integer, vars::list)\n local poly;\n poly := RigidMotionsParameterSpaceDecompostion:-IsAsymptoticIntersection(Q[i], Q[j], vars);\n if poly = NULL or nops(poly) = 0 then\n return [];\n fi;\n return SerializeEvents(GenerateEvents(poly, [i, j]));\n end proc;\n map[inplace](proc(x) Extend(result, x, inplace=true) end proc, [Grid:-Seq(seq(s(i, j, vars),\n j=i+1..nops(Q)), i=1..nops(Q))]);\n return ReconstructEvents(result);\nend proc;\n\n\n# Procedure: ComputeEventsFromAlgebraicNumbers\n# Compute and sort events\n#\n# Parameters:\n# Q - set of quadrics or conics\n# vars - a list of variables\n# Output:\n# Sorted set of events\nComputeEventsFromAlgebraicNumbers := proc( Q, vars::list )\n local events := Array([]);\n ArrayTools:-Extend(events, ComputeEventsATypeGrid( Q, [2, 3], vars ), inplace=true);\n ArrayTools:-Extend(events, ComputeEventsBTypeGrid( Q, 1, vars ), inplace=true);\n ArrayTools:-Extend(events, ComputeEventsCTypeGrid( Q, vars ), inplace=true);\n ArrayTools:-Extend(events, ComputeAsymptoticAAEvents(Q, vars), inplace=true);\n ArrayTools:-Extend(events, ComputeAsymptoticABEventsGrid(Q, vars), inplace=true);\n return AlgebraicSort(events);\nend proc:\n\n\n# Procedure: LaunchComputeEvents\n# Computes sorted list of events for rotational part of rigid motions using the grid framework\n#\n#\n# Parameters:\n# variables - list of variables in which the problem is expressed\n# databasePath - a path to a copy of the database CompRegister.db\n# nType - neighborhood type: N1, N2 or N3.\n# kRange - range of grid lines passed as a list\n# Output:\n# It populates a database given by databasePath.\nLaunchComputeEvents := proc(variables::list, databasePath::string, nType::string, kRange::list) \n local Q, Q1, Q2, Q3, R, i, db := Object(ComputationRegister, databasePath);\n vars := variables;\n dbPath:=databasePath;\n R := CayleyTransform(variables);\n Q1 := ComputeSetOfQuadrics(R, nType, 1, kRange); \n Q2 := map2(subs, [a = b, b = c, c = a], Q1);\n Q3 := map2(subs, [a = b, b = c, c = a], Q2);\n Q := [op(Q1), op(Q2), op(Q3), op(variables)];\n for i from 1 to nops(Q) do\n InsertQuadric(db, i, Q[i]);\n od;\n SynchronizeQuadrics(db);\n events := ComputeEventsFromAlgebraicNumbers(Q, variables);\n events := select[flatten](proc(x) evalb(GetInterval(GetRealAlgebraicNumber(x))[2] >= 0) end proc,\n events);\n events := ReduceEvents(events);\n AdjustEvents(events, upperbound(Q), variables);\n #Insert events into the register\n for i from 1 to upperbound(events) do\n InsertEvent(db, i, events[i]);\n od;\n SynchronizeEvents(db);\n Close(db);\nend proc:\n\n\n# Procedure: ComputeSamplePoints\n# Computes sample points for rotational part of rigid motions\n#\n#\n# Parameters:\n# Q - list of quadrics\n# events - an array of events\n# first - integer value which indicates a first event to proceed.\n# last - integer value which indicates a last event to proceed.\n# vars - list of variables in which conics are expressed\n# db - an instance of the class ComputationRegister\n# skipped - a list of the events' indices to be skipped\n#\n# Output:\n# It populates a database, given by databasePath, with sample points.\nComputeSamplePoints := proc (Q, events::Array, first::integer, last::integer, \n vars::list, db::ComputationRegister, skipped::list:=[]) \nlocal i, midpoint, sys, samplePoints, disjointEvent:=[], ranumI, ranumJ;\n if first < 0 or last < 0 or last < first or upperbound(events) <= last then \n error \"Bounds of the list of the events range are incorrect.\": \n end if:\n for i from first to last do \n if i in skipped then\n next;\n fi:\n sys := Q[GetQuadrics(events[i])];\n ranumI := GetRealAlgebraicNumber(events[i]);\n ranumJ := GetRealAlgebraicNumber(events[i+1]);\n disjointEvent:=DisjointRanges(ranumI, ranumJ);\n midpoint := (GetInterval(disjointEvent[1])[2] + GetInterval(disjointEvent[2])[1])/2:\n # never call eval with sets!!\n sys := eval(sys, vars[1] = midpoint);\n LaunchComputeSamplePoints2D(sys, midpoint, 1, false, vars[2..], db);\n SynchronizeSamplePoints(db);\n InsertComputedNumber(db, i);\n end do;\nend proc:\n\n\n# Procedure: ParallelComputeSamplePoints\n# Computes sample points for rotational part of rigid motions. It should be call via Grid\n# framework.\nParallelComputeSamplePoints := proc()\n local me, n, events, skipped, first, last, offset, noEvents;\n local db:=Object(ComputationRegister, dbPath);\n me := Grid:-MyNode();\n skipped := FetchComputedNumbers(db);\n offset := FetchLowerEventID(db) - 1;\n noEvents := NumberOfEvents(db);\n # events-1 because the last event is a copy of events[-2]\n n := trunc((noEvents-1) / Grid:-NumNodes());\n first := offset + me * n + 1; last := offset + (me + 1) * n;\n if me = Grid:-NumNodes() - 1 then\n last := last + ((noEvents + offset) - (last + 1));\n fi;\n # recreate events\n events := FetchEvents(db, first, last + 1); \n RigidMotionsParameterSpaceDecompostion:-ComputeSamplePoints(Q, events, first , last, vars, db, skipped);\n Close(db);\n Grid:-Barrier();\nend proc:\n\n# Procedure: LaunchComputeSamplePoints\n# Resumes computations of sample points for rotational part of rigid motions using\n# the grid framework.\n#\n#\n# Parameters:\n# variables - list of variables in which the problem is expressed\n# databasePath - a path to a database file. If file does not exist it will be crated.\n# nType - neighborhood type: N1, N2 or N3.\n# nodes - number of nodes used in the parallel computations\n# Output:\n# It populates a database given by databasePath.\nLaunchComputeSamplePoints := proc(variables::list, databasePath::string, nType::string, \n nodes:=kernelopts(numcpus))\n local db:=Object(ComputationRegister, databasePath);\n vars:=variables;\n dbPath:=databasePath;\n Q := FetchQuadrics(db);\n Close(db);\n Grid:-Setup(\"local\");\n Grid:-Launch(RigidMotionsParameterSpaceDecompostion:-ParallelComputeSamplePoints, \n imports=['Q', 'vars', 'dbPath'], numnodes=nodes, allexternal=false);\nend proc;\n\nend module:\n", "meta": {"hexsha": "47e7a630d2b9103635b3b04438310870fc5bdea0", "size": 19623, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "RigidMotionsParameterSpaceDecomposition.mpl", "max_stars_repo_name": "copyme/MapleTools", "max_stars_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "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": "RigidMotionsParameterSpaceDecomposition.mpl", "max_issues_repo_name": "copyme/MapleTools", "max_issues_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 9, "max_issues_repo_issues_event_min_datetime": "2016-04-14T11:48:04.000Z", "max_issues_repo_issues_event_max_datetime": "2016-05-13T13:48:01.000Z", "max_forks_repo_path": "RigidMotionsParameterSpaceDecomposition.mpl", "max_forks_repo_name": "copyme/MapleTools", "max_forks_repo_head_hexsha": "7491d0d2cab715e2dd984ce7ba0fb8db46cbe73f", "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": 38.0290697674, "max_line_length": 106, "alphanum_fraction": 0.6669214697, "num_tokens": 5418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8244619177503206, "lm_q2_score": 0.6297746213017459, "lm_q1q2_score": 0.5192251920289194}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_x *)\n(* prefix:\n gga_k_dk_params *params;\n \n assert(p->params != NULL);\n params = (gga_k_dk_params * )(p->params);\n*)\n\nf := x -> \n add(1*params_a_aa[i]*x^(2*(i-1)), i=1..5) /\n add(1*params_a_bb[i]*x^(2*(i-1)), i=1..5):", "meta": {"hexsha": "1f4f53dae7f2bf2817aaf6901e1f3efc6f8e5392", "size": 480, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_k_dk.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_k_dk.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_k_dk.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.2631578947, "max_line_length": 68, "alphanum_fraction": 0.63125, "num_tokens": 170, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8289388083214156, "lm_q2_score": 0.6261241772283034, "lm_q1q2_score": 0.5190186293328567}} {"text": "######################################################################\n\n`eta/partitions` := (A::set) -> `if`(nops(A)=1,{A},FAIL);\n\n`gamma/partitions` := (A::set,B::set) -> (p) -> proc(pi,omega)\n local F,rho,u,v,b;\n\n F := fibres(A,B)(p);\n\n rho := NULL;\n for u in pi do\n if nops(u) = 1 then\n b := op(u);\n rho := rho,op(omega[b]);\n else\n rho := rho,`union`(seq(F[b],b in u));\n fi;\n od;\n\n rho := {rho};\n return rho;\nend;\n", "meta": {"hexsha": "51435e242e40252c8c3d73d5cda38463577b2378", "size": 426, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/partitions.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/partitions.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/partitions.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 18.5217391304, "max_line_length": 70, "alphanum_fraction": 0.4225352113, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718434978390747, "lm_q2_score": 0.6688802537704064, "lm_q1q2_score": 0.5162708747056384}} {"text": "Q := [b*c+a, a*c-b, b*c-2*c^2+a-2, b*c-c^2+a-1, b*c+c^2+a+1, b*c+2*c^2+a+2, 2*\nb*c-c^2+2*a-1, 2*b*c+c^2+2*a+1, a*c-2*c^2-b-2, a*c-c^2-b-1, a*c+c^2-b+1, a*c+2\n*c^2-b+2, 2*a*c-c^2-2*b-1, 2*a*c+c^2-2*b+1, a*c-2*b*c-2*a-b, a*c-b*c-a-b, a*c+\nb*c+a-b, a*c+2*b*c+2*a-b, 2*a*c-b*c-a-2*b, 2*a*c+b*c+a-2*b, a^2+b^2-3*c^2-3, a\n^2+b^2-c^2-1, 3*a^2+3*b^2-c^2-1, a^2+b^2-2*b*c-2*a, a^2+b^2-b*c-a, a^2+b^2+b*c\n+a, a^2+b^2+2*b*c+2*a, 2*a^2+2*b^2-b*c-a, 2*a^2+2*b^2+b*c+a, a^2-2*a*c+b^2+2*b\n, a^2-a*c+b^2+b, a^2+a*c+b^2-b, a^2+2*a*c+b^2-2*b, 2*a^2-a*c+2*b^2+b, 2*a^2+a*\nc+2*b^2-b, a*c-2*b*c-c^2-2*a-b-1, a*c-2*b*c+c^2-2*a-b+1, a*c-b*c-2*c^2-a-b-2,\na*c-b*c-c^2-a-b-1, a*c-b*c+c^2-a-b+1, a*c-b*c+2*c^2-a-b+2, a*c+b*c-2*c^2+a-b-2\n, a*c+b*c-c^2+a-b-1, a*c+b*c+c^2+a-b+1, a*c+b*c+2*c^2+a-b+2, a*c+2*b*c-c^2+2*a\n-b-1, a*c+2*b*c+c^2+2*a-b+1, 2*a*c-b*c-c^2-a-2*b-1, 2*a*c-b*c+c^2-a-2*b+1, 2*a\n*c+b*c-c^2+a-2*b-1, 2*a*c+b*c+c^2+a-2*b+1, a^2+b^2-4*b*c-3*c^2-4*a-3, a^2+b^2-\\\n4*b*c-c^2-4*a-1, a^2+b^2-4*b*c+c^2-4*a+1, a^2+b^2-4*b*c+3*c^2-4*a+3, a^2+b^2-2\n*b*c-3*c^2-2*a-3, a^2+b^2-2*b*c-c^2-2*a-1, a^2+b^2-b*c-c^2-a-1, a^2+b^2+b*c-c^\n2+a-1, a^2+b^2+2*b*c-3*c^2+2*a-3, a^2+b^2+2*b*c-c^2+2*a-1, a^2+b^2+4*b*c-3*c^2\n+4*a-3, a^2+b^2+4*b*c-c^2+4*a-1, a^2+b^2+4*b*c+c^2+4*a+1, a^2+b^2+4*b*c+3*c^2+\n4*a+3, 3*a^2+3*b^2-4*b*c-c^2-4*a-1, 3*a^2+3*b^2-4*b*c+c^2-4*a+1, 3*a^2+3*b^2-2\n*b*c-c^2-2*a-1, 3*a^2+3*b^2+2*b*c-c^2+2*a-1, 3*a^2+3*b^2+4*b*c-c^2+4*a-1, 3*a^\n2+3*b^2+4*b*c+c^2+4*a+1, a^2-4*a*c+b^2-3*c^2+4*b-3, a^2-4*a*c+b^2-c^2+4*b-1, a\n^2-4*a*c+b^2+c^2+4*b+1, a^2-4*a*c+b^2+3*c^2+4*b+3, a^2-2*a*c+b^2-3*c^2+2*b-3,\na^2-2*a*c+b^2-c^2+2*b-1, a^2-a*c+b^2-c^2+b-1, a^2+a*c+b^2-c^2-b-1, a^2+2*a*c+b\n^2-3*c^2-2*b-3, a^2+2*a*c+b^2-c^2-2*b-1, a^2+4*a*c+b^2-3*c^2-4*b-3, a^2+4*a*c+\nb^2-c^2-4*b-1, a^2+4*a*c+b^2+c^2-4*b+1, a^2+4*a*c+b^2+3*c^2-4*b+3, 3*a^2-4*a*c\n+3*b^2-c^2+4*b-1, 3*a^2-4*a*c+3*b^2+c^2+4*b+1, 3*a^2-2*a*c+3*b^2-c^2+2*b-1, 3*\na^2+2*a*c+3*b^2-c^2-2*b-1, 3*a^2+4*a*c+3*b^2-c^2-4*b-1, 3*a^2+4*a*c+3*b^2+c^2-\\\n4*b+1, a^2-2*a*c+b^2-b*c-a+2*b, a^2-2*a*c+b^2+b*c+a+2*b, a^2-a*c+b^2-2*b*c-2*a\n+b, a^2-a*c+b^2-b*c-a+b, a^2-a*c+b^2+b*c+a+b, a^2-a*c+b^2+2*b*c+2*a+b, a^2+a*c\n+b^2-2*b*c-2*a-b, a^2+a*c+b^2-b*c-a-b, a^2+a*c+b^2+b*c+a-b, a^2+a*c+b^2+2*b*c+\n2*a-b, a^2+2*a*c+b^2-b*c-a-2*b, a^2+2*a*c+b^2+b*c+a-2*b, 2*a^2-a*c+2*b^2-b*c-a\n+b, 2*a^2-a*c+2*b^2+b*c+a+b, 2*a^2+a*c+2*b^2-b*c-a-b, 2*a^2+a*c+2*b^2+b*c+a-b,\na^2-4*a*c+b^2-4*b*c+c^2-4*a+4*b+1, a^2-4*a*c+b^2-2*b*c-c^2-2*a+4*b-1, a^2-4*a*\nc+b^2-2*b*c+c^2-2*a+4*b+1, a^2-4*a*c+b^2-2*b*c+3*c^2-2*a+4*b+3, a^2-4*a*c+b^2+\n2*b*c-c^2+2*a+4*b-1, a^2-4*a*c+b^2+2*b*c+c^2+2*a+4*b+1, a^2-4*a*c+b^2+2*b*c+3*\nc^2+2*a+4*b+3, a^2-4*a*c+b^2+4*b*c+c^2+4*a+4*b+1, a^2-2*a*c+b^2-4*b*c-c^2-4*a+\n2*b-1, a^2-2*a*c+b^2-4*b*c+c^2-4*a+2*b+1, a^2-2*a*c+b^2-4*b*c+3*c^2-4*a+2*b+3,\na^2-2*a*c+b^2-2*b*c-3*c^2-2*a+2*b-3, a^2-2*a*c+b^2-2*b*c-c^2-2*a+2*b-1, a^2-2*\na*c+b^2-2*b*c+c^2-2*a+2*b+1, a^2-2*a*c+b^2-b*c+c^2-a+2*b+1, a^2-2*a*c+b^2+b*c+\nc^2+a+2*b+1, a^2-2*a*c+b^2+2*b*c-3*c^2+2*a+2*b-3, a^2-2*a*c+b^2+2*b*c-c^2+2*a+\n2*b-1, a^2-2*a*c+b^2+2*b*c+c^2+2*a+2*b+1, a^2-2*a*c+b^2+4*b*c-c^2+4*a+2*b-1, a\n^2-2*a*c+b^2+4*b*c+c^2+4*a+2*b+1, a^2-2*a*c+b^2+4*b*c+3*c^2+4*a+2*b+3, a^2-a*c\n+b^2-2*b*c+c^2-2*a+b+1, a^2-a*c+b^2-b*c-c^2-a+b-1, a^2-a*c+b^2+b*c-c^2+a+b-1,\na^2-a*c+b^2+2*b*c+c^2+2*a+b+1, a^2+a*c+b^2-2*b*c+c^2-2*a-b+1, a^2+a*c+b^2-b*c-\nc^2-a-b-1, a^2+a*c+b^2+b*c-c^2+a-b-1, a^2+a*c+b^2+2*b*c+c^2+2*a-b+1, a^2+2*a*c\n+b^2-4*b*c-c^2-4*a-2*b-1, a^2+2*a*c+b^2-4*b*c+c^2-4*a-2*b+1, a^2+2*a*c+b^2-4*b\n*c+3*c^2-4*a-2*b+3, a^2+2*a*c+b^2-2*b*c-3*c^2-2*a-2*b-3, a^2+2*a*c+b^2-2*b*c-c\n^2-2*a-2*b-1, a^2+2*a*c+b^2-2*b*c+c^2-2*a-2*b+1, a^2+2*a*c+b^2-b*c+c^2-a-2*b+1\n, a^2+2*a*c+b^2+b*c+c^2+a-2*b+1, a^2+2*a*c+b^2+2*b*c-3*c^2+2*a-2*b-3, a^2+2*a*\nc+b^2+2*b*c-c^2+2*a-2*b-1, a^2+2*a*c+b^2+2*b*c+c^2+2*a-2*b+1, a^2+2*a*c+b^2+4*\nb*c-c^2+4*a-2*b-1, a^2+2*a*c+b^2+4*b*c+c^2+4*a-2*b+1, a^2+2*a*c+b^2+4*b*c+3*c^\n2+4*a-2*b+3, a^2+4*a*c+b^2-4*b*c+c^2-4*a-4*b+1, a^2+4*a*c+b^2-2*b*c-c^2-2*a-4*\nb-1, a^2+4*a*c+b^2-2*b*c+c^2-2*a-4*b+1, a^2+4*a*c+b^2-2*b*c+3*c^2-2*a-4*b+3, a\n^2+4*a*c+b^2+2*b*c-c^2+2*a-4*b-1, a^2+4*a*c+b^2+2*b*c+c^2+2*a-4*b+1, a^2+4*a*c\n+b^2+2*b*c+3*c^2+2*a-4*b+3, a^2+4*a*c+b^2+4*b*c+c^2+4*a-4*b+1, 3*a^2-4*a*c+3*b\n^2-2*b*c+c^2-2*a+4*b+1, 3*a^2-4*a*c+3*b^2+2*b*c+c^2+2*a+4*b+1, 3*a^2-2*a*c+3*b\n^2-4*b*c+c^2-4*a+2*b+1, 3*a^2-2*a*c+3*b^2-2*b*c-c^2-2*a+2*b-1, 3*a^2-2*a*c+3*b\n^2+2*b*c-c^2+2*a+2*b-1, 3*a^2-2*a*c+3*b^2+4*b*c+c^2+4*a+2*b+1, 3*a^2+2*a*c+3*b\n^2-4*b*c+c^2-4*a-2*b+1, 3*a^2+2*a*c+3*b^2-2*b*c-c^2-2*a-2*b-1, 3*a^2+2*a*c+3*b\n^2+2*b*c-c^2+2*a-2*b-1, 3*a^2+2*a*c+3*b^2+4*b*c+c^2+4*a-2*b+1, 3*a^2+4*a*c+3*b\n^2-2*b*c+c^2-2*a-4*b+1, 3*a^2+4*a*c+3*b^2+2*b*c+c^2+2*a-4*b+1, -b*c+a, a*b+c,\n-2*b^2-b*c+a-2, -b^2-2*b*c+2*a-1, -b^2-b*c+a-1, b^2-2*b*c+2*a+1, b^2-b*c+a+1,\n2*b^2-b*c+a+2, a*b-2*b*c+2*a+c, a*b-b*c+a+c, a*b+b*c-a+c, a*b+2*b*c-2*a+c, 2*a\n*b-b*c+a+2*c, 2*a*b+b*c-a+2*c, a*b-2*b^2+c-2, a*b-b^2+c-1, a*b+b^2+c+1, a*b+2*\nb^2+c+2, 2*a*b-b^2+2*c-1, 2*a*b+b^2+2*c+1, a^2-2*b*c+c^2+2*a, a^2-b*c+c^2+a, a\n^2+b*c+c^2-a, a^2+2*b*c+c^2-2*a, 2*a^2-b*c+2*c^2+a, 2*a^2+b*c+2*c^2-a, a^2-3*b\n^2+c^2-3, a^2-b^2+c^2-1, 3*a^2-b^2+3*c^2-1, a^2-2*a*b+c^2-2*c, a^2-a*b+c^2-c,\na^2+a*b+c^2+c, a^2+2*a*b+c^2+2*c, 2*a^2-a*b+2*c^2-c, 2*a^2+a*b+2*c^2+c, a*b-2*\nb^2-b*c+a+c-2, a*b-2*b^2+b*c-a+c-2, a*b-b^2-2*b*c+2*a+c-1, a*b-b^2-b*c+a+c-1,\na*b-b^2+b*c-a+c-1, a*b-b^2+2*b*c-2*a+c-1, a*b+b^2-2*b*c+2*a+c+1, a*b+b^2-b*c+a\n+c+1, a*b+b^2+b*c-a+c+1, a*b+b^2+2*b*c-2*a+c+1, a*b+2*b^2-b*c+a+c+2, a*b+2*b^2\n+b*c-a+c+2, 2*a*b-b^2-b*c+a+2*c-1, 2*a*b-b^2+b*c-a+2*c-1, 2*a*b+b^2-b*c+a+2*c+\n1, 2*a*b+b^2+b*c-a+2*c+1, a^2-3*b^2-4*b*c+c^2+4*a-3, a^2-3*b^2-2*b*c+c^2+2*a-3\n, a^2-3*b^2+2*b*c+c^2-2*a-3, a^2-3*b^2+4*b*c+c^2-4*a-3, a^2-b^2-4*b*c+c^2+4*a-\\\n1, a^2-b^2-2*b*c+c^2+2*a-1, a^2-b^2-b*c+c^2+a-1, a^2-b^2+b*c+c^2-a-1, a^2-b^2+\n2*b*c+c^2-2*a-1, a^2-b^2+4*b*c+c^2-4*a-1, a^2+b^2-4*b*c+c^2+4*a+1, a^2+b^2+4*b\n*c+c^2-4*a+1, a^2+3*b^2-4*b*c+c^2+4*a+3, a^2+3*b^2+4*b*c+c^2-4*a+3, 3*a^2-b^2-\\\n4*b*c+3*c^2+4*a-1, 3*a^2-b^2-2*b*c+3*c^2+2*a-1, 3*a^2-b^2+2*b*c+3*c^2-2*a-1, 3\n*a^2-b^2+4*b*c+3*c^2-4*a-1, 3*a^2+b^2-4*b*c+3*c^2+4*a+1, 3*a^2+b^2+4*b*c+3*c^2\n-4*a+1, a^2-2*a*b-b*c+c^2+a-2*c, a^2-2*a*b+b*c+c^2-a-2*c, a^2-a*b-2*b*c+c^2+2*\na-c, a^2-a*b-b*c+c^2+a-c, a^2-a*b+b*c+c^2-a-c, a^2-a*b+2*b*c+c^2-2*a-c, a^2+a*\nb-2*b*c+c^2+2*a+c, a^2+a*b-b*c+c^2+a+c, a^2+a*b+b*c+c^2-a+c, a^2+a*b+2*b*c+c^2\n-2*a+c, a^2+2*a*b-b*c+c^2+a+2*c, a^2+2*a*b+b*c+c^2-a+2*c, 2*a^2-a*b-b*c+2*c^2+\na-c, 2*a^2-a*b+b*c+2*c^2-a-c, 2*a^2+a*b-b*c+2*c^2+a+c, 2*a^2+a*b+b*c+2*c^2-a+c\n, a^2-4*a*b-3*b^2+c^2-4*c-3, a^2-4*a*b-b^2+c^2-4*c-1, a^2-4*a*b+b^2+c^2-4*c+1,\na^2-4*a*b+3*b^2+c^2-4*c+3, a^2-2*a*b-3*b^2+c^2-2*c-3, a^2-2*a*b-b^2+c^2-2*c-1,\na^2-a*b-b^2+c^2-c-1, a^2+a*b-b^2+c^2+c-1, a^2+2*a*b-3*b^2+c^2+2*c-3, a^2+2*a*b\n-b^2+c^2+2*c-1, a^2+4*a*b-3*b^2+c^2+4*c-3, a^2+4*a*b-b^2+c^2+4*c-1, a^2+4*a*b+\nb^2+c^2+4*c+1, a^2+4*a*b+3*b^2+c^2+4*c+3, 3*a^2-4*a*b-b^2+3*c^2-4*c-1, 3*a^2-4\n*a*b+b^2+3*c^2-4*c+1, 3*a^2-2*a*b-b^2+3*c^2-2*c-1, 3*a^2+2*a*b-b^2+3*c^2+2*c-1\n, 3*a^2+4*a*b-b^2+3*c^2+4*c-1, 3*a^2+4*a*b+b^2+3*c^2+4*c+1, a^2-4*a*b-b^2-2*b*\nc+c^2+2*a-4*c-1, a^2-4*a*b-b^2+2*b*c+c^2-2*a-4*c-1, a^2-4*a*b+b^2-4*b*c+c^2+4*\na-4*c+1, a^2-4*a*b+b^2-2*b*c+c^2+2*a-4*c+1, a^2-4*a*b+b^2+2*b*c+c^2-2*a-4*c+1,\na^2-4*a*b+b^2+4*b*c+c^2-4*a-4*c+1, a^2-4*a*b+3*b^2-2*b*c+c^2+2*a-4*c+3, a^2-4*\na*b+3*b^2+2*b*c+c^2-2*a-4*c+3, a^2-2*a*b-3*b^2-2*b*c+c^2+2*a-2*c-3, a^2-2*a*b-\\\n3*b^2+2*b*c+c^2-2*a-2*c-3, a^2-2*a*b-b^2-4*b*c+c^2+4*a-2*c-1, a^2-2*a*b-b^2-2*\nb*c+c^2+2*a-2*c-1, a^2-2*a*b-b^2+2*b*c+c^2-2*a-2*c-1, a^2-2*a*b-b^2+4*b*c+c^2-\\\n4*a-2*c-1, a^2-2*a*b+b^2-4*b*c+c^2+4*a-2*c+1, a^2-2*a*b+b^2-2*b*c+c^2+2*a-2*c+\n1, a^2-2*a*b+b^2-b*c+c^2+a-2*c+1, a^2-2*a*b+b^2+b*c+c^2-a-2*c+1, a^2-2*a*b+b^2\n+2*b*c+c^2-2*a-2*c+1, a^2-2*a*b+b^2+4*b*c+c^2-4*a-2*c+1, a^2-2*a*b+3*b^2-4*b*c\n+c^2+4*a-2*c+3, a^2-2*a*b+3*b^2+4*b*c+c^2-4*a-2*c+3, a^2-a*b-b^2-b*c+c^2+a-c-1\n, a^2-a*b-b^2+b*c+c^2-a-c-1, a^2-a*b+b^2-2*b*c+c^2+2*a-c+1, a^2-a*b+b^2+2*b*c+\nc^2-2*a-c+1, a^2+a*b-b^2-b*c+c^2+a+c-1, a^2+a*b-b^2+b*c+c^2-a+c-1, a^2+a*b+b^2\n-2*b*c+c^2+2*a+c+1, a^2+a*b+b^2+2*b*c+c^2-2*a+c+1, a^2+2*a*b-3*b^2-2*b*c+c^2+2\n*a+2*c-3, a^2+2*a*b-3*b^2+2*b*c+c^2-2*a+2*c-3, a^2+2*a*b-b^2-4*b*c+c^2+4*a+2*c\n-1, a^2+2*a*b-b^2-2*b*c+c^2+2*a+2*c-1, a^2+2*a*b-b^2+2*b*c+c^2-2*a+2*c-1, a^2+\n2*a*b-b^2+4*b*c+c^2-4*a+2*c-1, a^2+2*a*b+b^2-4*b*c+c^2+4*a+2*c+1, a^2+2*a*b+b^\n2-2*b*c+c^2+2*a+2*c+1, a^2+2*a*b+b^2-b*c+c^2+a+2*c+1, a^2+2*a*b+b^2+b*c+c^2-a+\n2*c+1, a^2+2*a*b+b^2+2*b*c+c^2-2*a+2*c+1, a^2+2*a*b+b^2+4*b*c+c^2-4*a+2*c+1, a\n^2+2*a*b+3*b^2-4*b*c+c^2+4*a+2*c+3, a^2+2*a*b+3*b^2+4*b*c+c^2-4*a+2*c+3, a^2+4\n*a*b-b^2-2*b*c+c^2+2*a+4*c-1, a^2+4*a*b-b^2+2*b*c+c^2-2*a+4*c-1, a^2+4*a*b+b^2\n-4*b*c+c^2+4*a+4*c+1, a^2+4*a*b+b^2-2*b*c+c^2+2*a+4*c+1, a^2+4*a*b+b^2+2*b*c+c\n^2-2*a+4*c+1, a^2+4*a*b+b^2+4*b*c+c^2-4*a+4*c+1, a^2+4*a*b+3*b^2-2*b*c+c^2+2*a\n+4*c+3, a^2+4*a*b+3*b^2+2*b*c+c^2-2*a+4*c+3, 3*a^2-4*a*b+b^2-2*b*c+3*c^2+2*a-4\n*c+1, 3*a^2-4*a*b+b^2+2*b*c+3*c^2-2*a-4*c+1, 3*a^2-2*a*b-b^2-2*b*c+3*c^2+2*a-2\n*c-1, 3*a^2-2*a*b-b^2+2*b*c+3*c^2-2*a-2*c-1, 3*a^2-2*a*b+b^2-4*b*c+3*c^2+4*a-2\n*c+1, 3*a^2-2*a*b+b^2+4*b*c+3*c^2-4*a-2*c+1, 3*a^2+2*a*b-b^2-2*b*c+3*c^2+2*a+2\n*c-1, 3*a^2+2*a*b-b^2+2*b*c+3*c^2-2*a+2*c-1, 3*a^2+2*a*b+b^2-4*b*c+3*c^2+4*a+2\n*c+1, 3*a^2+2*a*b+b^2+4*b*c+3*c^2-4*a+2*c+1, 3*a^2+4*a*b+b^2-2*b*c+3*c^2+2*a+4\n*c+1, 3*a^2+4*a*b+b^2+2*b*c+3*c^2-2*a+4*c+1, a*c+b, a*b-c, a*c-2*b^2-2*c^2+b,\na*c-b^2-c^2+b, a*c+b^2+c^2+b, a*c+2*b^2+2*c^2+b, 2*a*c-b^2-c^2+2*b, 2*a*c+b^2+\nc^2+2*b, a*b-2*b^2-2*c^2-c, a*b-b^2-c^2-c, a*b+b^2+c^2-c, a*b+2*b^2+2*c^2-c, 2\n*a*b-b^2-c^2-2*c, 2*a*b+b^2+c^2-2*c, a*b-2*a*c-2*b-c, a*b-a*c-b-c, a*b+a*c+b-c\n, a*b+2*a*c+2*b-c, 2*a*b-a*c-b-2*c, 2*a*b+a*c+b-2*c, a^2-3*b^2-3*c^2+1, a^2-b^\n2-c^2+1, 3*a^2-b^2-c^2+3, a^2-2*a*c-2*b+1, a^2-a*c-b+1, a^2+a*c+b+1, a^2+2*a*c\n+2*b+1, 2*a^2-a*c-b+2, 2*a^2+a*c+b+2, a^2-2*a*b+2*c+1, a^2-a*b+c+1, a^2+a*b-c+\n1, a^2+2*a*b-2*c+1, 2*a^2-a*b+c+2, 2*a^2+a*b-c+2, a*b-2*a*c-b^2-c^2-2*b-c, a*b\n-2*a*c+b^2+c^2-2*b-c, a*b-a*c-2*b^2-2*c^2-b-c, a*b-a*c-b^2-c^2-b-c, a*b-a*c+b^\n2+c^2-b-c, a*b-a*c+2*b^2+2*c^2-b-c, a*b+a*c-2*b^2-2*c^2+b-c, a*b+a*c-b^2-c^2+b\n-c, a*b+a*c+b^2+c^2+b-c, a*b+a*c+2*b^2+2*c^2+b-c, a*b+2*a*c-b^2-c^2+2*b-c, a*b\n+2*a*c+b^2+c^2+2*b-c, 2*a*b-a*c-b^2-c^2-b-2*c, 2*a*b-a*c+b^2+c^2-b-2*c, 2*a*b+\na*c-b^2-c^2+b-2*c, 2*a*b+a*c+b^2+c^2+b-2*c, a^2-4*a*c-3*b^2-3*c^2-4*b+1, a^2-4\n*a*c-b^2-c^2-4*b+1, a^2-4*a*c+b^2+c^2-4*b+1, a^2-4*a*c+3*b^2+3*c^2-4*b+1, a^2-\\\n2*a*c-3*b^2-3*c^2-2*b+1, a^2-2*a*c-b^2-c^2-2*b+1, a^2-a*c-b^2-c^2-b+1, a^2+a*c\n-b^2-c^2+b+1, a^2+2*a*c-3*b^2-3*c^2+2*b+1, a^2+2*a*c-b^2-c^2+2*b+1, a^2+4*a*c-\\\n3*b^2-3*c^2+4*b+1, a^2+4*a*c-b^2-c^2+4*b+1, a^2+4*a*c+b^2+c^2+4*b+1, a^2+4*a*c\n+3*b^2+3*c^2+4*b+1, 3*a^2-4*a*c-b^2-c^2-4*b+3, 3*a^2-4*a*c+b^2+c^2-4*b+3, 3*a^\n2-2*a*c-b^2-c^2-2*b+3, 3*a^2+2*a*c-b^2-c^2+2*b+3, 3*a^2+4*a*c-b^2-c^2+4*b+3, 3\n*a^2+4*a*c+b^2+c^2+4*b+3, a^2-4*a*b-3*b^2-3*c^2+4*c+1, a^2-4*a*b-b^2-c^2+4*c+1\n, a^2-4*a*b+b^2+c^2+4*c+1, a^2-4*a*b+3*b^2+3*c^2+4*c+1, a^2-2*a*b-3*b^2-3*c^2+\n2*c+1, a^2-2*a*b-b^2-c^2+2*c+1, a^2-a*b-b^2-c^2+c+1, a^2+a*b-b^2-c^2-c+1, a^2+\n2*a*b-3*b^2-3*c^2-2*c+1, a^2+2*a*b-b^2-c^2-2*c+1, a^2+4*a*b-3*b^2-3*c^2-4*c+1,\na^2+4*a*b-b^2-c^2-4*c+1, a^2+4*a*b+b^2+c^2-4*c+1, a^2+4*a*b+3*b^2+3*c^2-4*c+1,\n3*a^2-4*a*b-b^2-c^2+4*c+3, 3*a^2-4*a*b+b^2+c^2+4*c+3, 3*a^2-2*a*b-b^2-c^2+2*c+\n3, 3*a^2+2*a*b-b^2-c^2-2*c+3, 3*a^2+4*a*b-b^2-c^2-4*c+3, 3*a^2+4*a*b+b^2+c^2-4\n*c+3, a^2-2*a*b-a*c-b+2*c+1, a^2-2*a*b+a*c+b+2*c+1, a^2-a*b-2*a*c-2*b+c+1, a^2\n-a*b-a*c-b+c+1, a^2-a*b+a*c+b+c+1, a^2-a*b+2*a*c+2*b+c+1, a^2+a*b-2*a*c-2*b-c+\n1, a^2+a*b-a*c-b-c+1, a^2+a*b+a*c+b-c+1, a^2+a*b+2*a*c+2*b-c+1, a^2+2*a*b-a*c-\nb-2*c+1, a^2+2*a*b+a*c+b-2*c+1, 2*a^2-a*b-a*c-b+c+2, 2*a^2-a*b+a*c+b+c+2, 2*a^\n2+a*b-a*c-b-c+2, 2*a^2+a*b+a*c+b-c+2, a^2-4*a*b-4*a*c+b^2+c^2-4*b+4*c+1, a^2-4\n*a*b-2*a*c-b^2-c^2-2*b+4*c+1, a^2-4*a*b-2*a*c+b^2+c^2-2*b+4*c+1, a^2-4*a*b-2*a\n*c+3*b^2+3*c^2-2*b+4*c+1, a^2-4*a*b+2*a*c-b^2-c^2+2*b+4*c+1, a^2-4*a*b+2*a*c+b\n^2+c^2+2*b+4*c+1, a^2-4*a*b+2*a*c+3*b^2+3*c^2+2*b+4*c+1, a^2-4*a*b+4*a*c+b^2+c\n^2+4*b+4*c+1, a^2-2*a*b-4*a*c-b^2-c^2-4*b+2*c+1, a^2-2*a*b-4*a*c+b^2+c^2-4*b+2\n*c+1, a^2-2*a*b-4*a*c+3*b^2+3*c^2-4*b+2*c+1, a^2-2*a*b-2*a*c-3*b^2-3*c^2-2*b+2\n*c+1, a^2-2*a*b-2*a*c-b^2-c^2-2*b+2*c+1, a^2-2*a*b-2*a*c+b^2+c^2-2*b+2*c+1, a^\n2-2*a*b-a*c+b^2+c^2-b+2*c+1, a^2-2*a*b+a*c+b^2+c^2+b+2*c+1, a^2-2*a*b+2*a*c-3*\nb^2-3*c^2+2*b+2*c+1, a^2-2*a*b+2*a*c-b^2-c^2+2*b+2*c+1, a^2-2*a*b+2*a*c+b^2+c^\n2+2*b+2*c+1, a^2-2*a*b+4*a*c-b^2-c^2+4*b+2*c+1, a^2-2*a*b+4*a*c+b^2+c^2+4*b+2*\nc+1, a^2-2*a*b+4*a*c+3*b^2+3*c^2+4*b+2*c+1, a^2-a*b-2*a*c+b^2+c^2-2*b+c+1, a^2\n-a*b-a*c-b^2-c^2-b+c+1, a^2-a*b+a*c-b^2-c^2+b+c+1, a^2-a*b+2*a*c+b^2+c^2+2*b+c\n+1, a^2+a*b-2*a*c+b^2+c^2-2*b-c+1, a^2+a*b-a*c-b^2-c^2-b-c+1, a^2+a*b+a*c-b^2-\nc^2+b-c+1, a^2+a*b+2*a*c+b^2+c^2+2*b-c+1, a^2+2*a*b-4*a*c-b^2-c^2-4*b-2*c+1, a\n^2+2*a*b-4*a*c+b^2+c^2-4*b-2*c+1, a^2+2*a*b-4*a*c+3*b^2+3*c^2-4*b-2*c+1, a^2+2\n*a*b-2*a*c-3*b^2-3*c^2-2*b-2*c+1, a^2+2*a*b-2*a*c-b^2-c^2-2*b-2*c+1, a^2+2*a*b\n-2*a*c+b^2+c^2-2*b-2*c+1, a^2+2*a*b-a*c+b^2+c^2-b-2*c+1, a^2+2*a*b+a*c+b^2+c^2\n+b-2*c+1, a^2+2*a*b+2*a*c-3*b^2-3*c^2+2*b-2*c+1, a^2+2*a*b+2*a*c-b^2-c^2+2*b-2\n*c+1, a^2+2*a*b+2*a*c+b^2+c^2+2*b-2*c+1, a^2+2*a*b+4*a*c-b^2-c^2+4*b-2*c+1, a^\n2+2*a*b+4*a*c+b^2+c^2+4*b-2*c+1, a^2+2*a*b+4*a*c+3*b^2+3*c^2+4*b-2*c+1, a^2+4*\na*b-4*a*c+b^2+c^2-4*b-4*c+1, a^2+4*a*b-2*a*c-b^2-c^2-2*b-4*c+1, a^2+4*a*b-2*a*\nc+b^2+c^2-2*b-4*c+1, a^2+4*a*b-2*a*c+3*b^2+3*c^2-2*b-4*c+1, a^2+4*a*b+2*a*c-b^\n2-c^2+2*b-4*c+1, a^2+4*a*b+2*a*c+b^2+c^2+2*b-4*c+1, a^2+4*a*b+2*a*c+3*b^2+3*c^\n2+2*b-4*c+1, a^2+4*a*b+4*a*c+b^2+c^2+4*b-4*c+1, 3*a^2-4*a*b-2*a*c+b^2+c^2-2*b+\n4*c+3, 3*a^2-4*a*b+2*a*c+b^2+c^2+2*b+4*c+3, 3*a^2-2*a*b-4*a*c+b^2+c^2-4*b+2*c+\n3, 3*a^2-2*a*b-2*a*c-b^2-c^2-2*b+2*c+3, 3*a^2-2*a*b+2*a*c-b^2-c^2+2*b+2*c+3, 3\n*a^2-2*a*b+4*a*c+b^2+c^2+4*b+2*c+3, 3*a^2+2*a*b-4*a*c+b^2+c^2-4*b-2*c+3, 3*a^2\n+2*a*b-2*a*c-b^2-c^2-2*b-2*c+3, 3*a^2+2*a*b+2*a*c-b^2-c^2+2*b-2*c+3, 3*a^2+2*a\n*b+4*a*c+b^2+c^2+4*b-2*c+3, 3*a^2+4*a*b-2*a*c+b^2+c^2-2*b-4*c+3, 3*a^2+4*a*b+2\n*a*c+b^2+c^2+2*b-4*c+3];\n", "meta": {"hexsha": "9806325fe99abfccc9147956af958e5b19c72c67", "size": 13929, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "files/quadrics_N2.mpl", "max_stars_repo_name": "copyme/copyme.github.io", "max_stars_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": "files/quadrics_N2.mpl", "max_issues_repo_name": "copyme/copyme.github.io", "max_issues_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": "files/quadrics_N2.mpl", "max_forks_repo_name": "copyme/copyme.github.io", "max_forks_repo_head_hexsha": "112c2a9eac8ca155224d86d390d5cf701e16db6b", "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": 78.2528089888, "max_line_length": 79, "alphanum_fraction": 0.475195635, "num_tokens": 10252, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8757869981319863, "lm_q2_score": 0.588889130767832, "lm_q1q2_score": 0.5157414440677144}} {"text": "################################################################\n# Utility function for irregular term extraction\n# Usage:\n#\n# gencoeffs(a/x+c+b*x+a*x^3,x);\n# \n# Returns ->> [-1, a], [0, c], [1, b], [2, 0], [3, a]\n#\n# (i.e. it returns a list of powers of x and their coefficients\n################################################################\n\ngencoeffs := proc(expr::algebraic, var::name)\n local i;\n if (expr <> 0 ) then\n return seq([i,frontend(coeff,[expr,var,i])],\n i=frontend(ldegree,[expr,var]) .. frontend(degree,[expr,var]));\n else \n return [0,0];\n end if;\nend proc;\n\n\n#######################################################\n# List of grid functions symbols defined in the problem\n# See BSSN_Spher.mw or BSSN_Spher.mpl\n#######################################################\n\ngrid_functions:={alpha,K,beta,phi,Axx,Athth,A,B,metxx,metthetatheta,DDLxx,DDLthetatheta,rho,TS,Lamx,em4phi,RRxx,RRthetatheta,JSxx,JSthth,Uxx,Pxx,Uthetatheta,Pthetatheta,C5s,C1s,psi,Sx,PI2,PHI2,U,rPI,iPI,rPHI,iPHI,a1,rpsi,ipsi,rPIb2,iPIb2,b1,a2,rpsidot,ipsidot,C5psi,divbeta};\n\n\n################################################################\n# List of tensors, will be used for getting the RHS of equations\n# and looping over all of the equations\n################################################################\n\nall_tensors:=[ \n [EMPH,0,dn],\n [DPH,0,dn] , [dg,2,dn] , \n [met,2,dn], [DDL,2,dn],\n [DB,0,dn],\n [DTK,0,dn],\n [RR,2,dn], [U,2,dn] , [P,2,dn],\n [DAA,2,dn],\n [DLAM,1,up],\n [C1,0,dn],\n [C5,0,dn],\n [HS,0,dn],\n [HS3,0,dn],\n [MK,1,up]\n ];\n\n# List of coordinates used: (x is r in spherical coordinate here)\ncoord:=[x,theta,phi];\n\n######################################################################\n# The coordiante coefficients that are defined \n# in the definition of the generic 3-metric in curvilinear coordinate.\n######################################################################\n\ncoordcoef:=[1,x^2,x^2*sin(theta)^2];\n\n\n####################################################################\n# Initiating a table for the diff expression of tensors\n# tt[A][all][x] will store the x compononent of tensor A\n# tt[A][sep][x] will store the x component of tensor A in seperated\n# powers of 'r' \n# tt[A][reg][x] will store the regular part of above\n# tt[A][dis][x] will become the finite difference approximation of\n# the above. All in all, 'tt' is our working table of everything!\n####################################################################\n\ntt:=table([]):\n\n\n\n#########################################\n# All of the following atomic variables\n# will be used for indexing in table 'tt' \n# and shall not be assigned anythin\n#########################################\n\nunassign('all');\nunassign('sep');\nunassign('tres');\nunassign('reg');\nunassign('dis');\nunassign('disreg');\nunassign('disinf');\nunassign('inf');\n\n####### IMPORTANT NOTE: ###############################\n# Never use i,j,k as indexing as when working with FD as\n# they are protected by default to be used as indexing \n# of coordinates x, y , z\n########################################################\n\n\nfor jj from 1 to nops(all_tensors) do\n\n\n # Tensor name \n nm:= all_tensors[jj][1]:\n\n # Tensor rank\n rank := all_tensors[jj][2]:\n\n # Tensor type\n tp := all_tensors[jj][3]:\n\n # rank-1 tensors\n if rank = 1 then\n tt[nm][all] := table( [ seq( coord[ii] = expand(grcomponent(nm(tp),[coord[ii]])/coordcoef[ii]) ,ii=1..nops(coord)) ] ):\n end if;\n\n #Assuming rank-2 tensors are all diagnoal (it is the case in spherical symmetry)\n if rank = 2 then\n tt[nm][all] := table( [ seq( coord[ii] = expand(grcomponent(nm(tp,tp),[coord[ii],coord[ii]])/coordcoef[ii]) ,ii=1..nops(coord)) ] ):\n end if;\n\n if rank = 0 then\n tt[nm][all] := grcomponent(nm):\n end if;\n\n #Breaking down the expressions to regular and irregular parts\n\n if rank <> 0 then\n tt[nm][sep] := table ( [ seq( coord[ii] = [ gencoeffs(tt[nm][all][coord[ii]],'x') ] , ii=1..nops(coord) ) ] ) ;\n \n end if;\n\n if rank = 0 then\n tt[nm][sep] := [gencoeffs(tt[nm][all],'x')]; \n end if;\nend do:\n\n# Reading EOM for matter and adding it to tt table\nread(\"eq_evol_matter.mpl\");\n\nevol_matters := [ [EQRPIb2,0,dn] , [EQIPIb2,0,dn] , [EQRPSI,0,dn] ,[EQIPSI,0,dn], [DRPSI,0,dn], [DIPSI,0,dn] ]:\n\ntt[EQRPIb2][all] := rhs( eq_evol_rPIb2 ):\ntt[EQIPIb2][all] := rhs( eq_evol_iPIb2 ):\ntt[EQRPSI][all] := rhs(eq_evol_rpsi):\ntt[EQIPSI][all] := rhs(eq_evol_ipsi):\ntt[DRPSI][all] := diff(rpsi(t,x),x)+myzero*x:\ntt[DIPSI][all] := diff(ipsi(t,x),x)+myzero*x:\n\n\nfor jj from 1 to nops(evol_matters) do\n nm:= evol_matters[jj][1]:\n #Breaking down the expressions to regular and irregular parts\n tt[nm][sep] := [gencoeffs(tt[nm][all],'x')]; \nend do:\n\n\n\n# Updating all_tensors with newly added tensors:\n\nall_tensors:=[ \n [EMPH,0,dn],\n [DPH,0,dn] , [dg,2,dn] , \n [met,2,dn], [DDL,2,dn],\n [DB,0,dn],\n [DTK,0,dn],\n [RR,2,dn], [U,2,dn] , [P,2,dn],\n [DAA,2,dn],\n [DLAM,1,up],\n [C1,0,dn],\n [C5,0,dn],\n [HS,0,dn], \n [HS3,0,dn], \n [MK,1,up],\n [EQRPIb2,0,dn], \n [EQIPIb2,0,dn],\n [EQIPSI,0,dn],\n [EQRPSI,0,dn],\n [DRPSI,0,dn],\n [DIPSI,0,dn]\n ];\n\n\n#Checking that gencoeffs generated coefficients correctly:\ncheck_res := true;\nif (check_res) then\n\n\t\tfor jj from 1 to nops(all_tensors) do\n\t\t nm:= all_tensors[jj][1]:\n\t\t rank := all_tensors[jj][2]:\n\t\t tp := all_tensors[jj][3]:\n\t\t if rank <> 0 then \n\t\t\ttt[nm][tres] := table ( [ seq ( coord[ii] = simplify(expand( tt[nm][all][coord[ii]] - sum(x^tt[nm][sep][coord[ii]][k][1]*tt[nm][sep][coord[ii]][k][2],k=1..nops(tt[nm][sep][coord[ii]]) ) )) ,ii=1..nops(coord) ) ] );\n\t\t else \n\t\t\ttt[nm][tres] := simplify(expand( tt[nm][all] - sum(x^tt[nm][sep][k][1]*tt[nm][sep][k][2],k=1..nops(tt[nm][sep]) ) ))\n\t\t end if;\n\t\tend do:\n\n\n\n\t\tfor jj from 1 to nops(all_tensors) do\n\t\t nm:= all_tensors[jj][1]:\n\t\t rank := all_tensors[jj][2]:\n\t\t tp := all_tensors[jj][3]:\n\t\t if rank <> 0 then\n\t\t\t for ii from 1 to nops(coord) do\n\t\t\t print(tt[nm][tres][coord[ii]]);\n\t\t\t end do\n\t\t else \n\t\t\t print(tt[nm][tres]);\n\t\t end if;\n\t\t \n\t\tend do:\nend if;\n\n\nfor jj from 1 to nops(all_tensors) do\n nm:= all_tensors[jj][1]:\n rank := all_tensors[jj][2]:\n tp := all_tensors[jj][3]:\n if rank <> 0 then\n for ii from 1 to nops(coord) do\n if tt[nm][sep][coord[ii]][1][1] >= 0 then\n print(nm + comp + coord[ii] + reg );\n else\n print( nm + comp + coord[ii] + ireg);\n kk := 1;\n while ( tt[nm][sep][coord[ii]][kk][1] < 0 ) do\n print( tt[nm][sep][coord[ii]][kk][2]*x^tt[nm][sep][coord[ii]][kk][1] );\n kk := kk + 1;\n end do\n end if;\n end do;\n else \n if tt[nm][sep][1][1] >= 0 then \n print(nm + comp + reg);\n else\n print(nm + comp + ireg);\n kk := 1;\n while ( tt[nm][sep][kk][1] < 0 ) do\n print( tt[nm][sep][kk][2]*x^tt[nm][sep][kk][1] );\n kk := kk + 1;\n end do\n end if;\n end if;\n \nend do:\n\n# End of residual check\n\n\n#### NOTE: ############################################\n# Below was effectively disabled by setting all to 0\n# i.e. we decided to leave the expressions as they are\n#######################################################\n\n# Table to regularize the negative powers of see the following\nreg_tbl:= table( [ \n [dg,theta,-1] = 0 , \n [dg,phi,-1] = 0 ,\n [DDL,theta,-1] = 0 ,\n [DDL,phi,-1] = 0 , \n [RR,x,-2] = 0 ,\n [RR,x,-1] = 0,\n [RR,theta,-2] = 0,\n [RR,theta,-1] = 0,\n [RR,phi,-2] = 0,\n [RR,phi,-1] = 0,\n [P,theta,-1] = 0,\n [P,phi,-1] = 0,\n [DLAM,x,-2] = 0,\n [DLAM,x,-1] = 0,\n [C1,-1] = 0, \n [HS,-1] = 0,\n [HS3,-1] = 0,\n [EQRPIb2,-1] = 0 ,\n [EQIPIb2,-1] = 0,\n [MK,x,-1] = 0,\n [DB,-1] = 0\n] );\n\n\n#################################################\n# Building list of regular terms in expressions:\n# Irregular term replacement was disabled\n#################################################\nfor ii from 1 to nops(all_tensors) do\n nm:= all_tensors[ii][1]:\n rank := all_tensors[ii][2]:\n tp := all_tensors[ii][3]:\n if rank <> 0 then \n for jj from 1 to nops(coord) do\n if tt[nm][sep][coord[jj]][1][1] >= 0 then\n tt[nm][reg][coord[jj]] := tt[nm][all][coord[jj]];\n else\n acm := 0;\n for kk from 1 to nops( tt[nm][sep][coord[jj]] ) do\n ord := tt[nm][sep][coord[jj]][kk][1];\n trm := tt[nm][sep][coord[jj]][kk][2]; \n if ord < 0 then\n if not(assigned(reg_tbl[ [nm,coord[jj],ord] ] ) ) then\n print(\"uncomplete reg table for:\");\n print(nm + coord[jj] + ord);\n error(\"quiting...\");\n else\n acm := acm + reg_tbl[ [nm,coord[jj],ord] ];\n end if;\n else\n acm := acm + trm*x^ord;\n end if;\n end do;\n tt[nm][reg][coord[jj]] := acm;\n end if\n end do;\n else\n\n if tt[nm][sep][1][1] >= 0 then\n tt[nm][reg] := tt[nm][all];\n else\n acm := 0;\n for kk from 1 to nops( tt[nm][sep] ) do\n ord := tt[nm][sep][kk][1];\n trm := tt[nm][sep][kk][2]; \n if ord < 0 then\n if not(assigned(reg_tbl[ [nm,ord] ] ) ) then\n print(\"uncomplete reg table for:\");\n print(nm + ord);\n error(\"quitting...\");\n else\n acm := acm + reg_tbl[ [nm,ord] ];\n end if;\n else\n acm := acm + trm*x^ord;\n end if;\n end do;\n tt[nm][reg]:= acm;\n end if\n\n end if;\nend do:\n\n\n# Treating 3-Reimmenn tensor seperately\n\nnot_all_tensors:=[\n [RR,2,dn]\n ];\n\nR_rest := table([]);\nR_ireg := table([]);\n\nfor ii from 1 to nops(not_all_tensors) do\n nm:= not_all_tensors[ii][1]:\n rank := not_all_tensors[ii][2]:\n tp := not_all_tensors[ii][3]:\n if rank <> 0 then\n for jj from 1 to nops(coord) do\n rr_ireg := 0;\n rr_rest := 0;\n for kk from 1 to nops( tt[nm][sep][coord[jj]] ) do\n ord := tt[nm][sep][coord[jj]][kk][1];\n trm := tt[nm][sep][coord[jj]][kk][2];\n if ord < 0 then\n rr_ireg:= rr_ireg + trm*x^ord;\n else\n rr_rest := rr_rest + trm*x^ord;\n end if;\n end do;\n R_ireg[coord[jj]] := rr_ireg;\n R_rest[coord[jj]] := rr_rest;\n end do;\n end if;\nend do:\n\ncheck := true;\n\n#############################################\n# Following will print the difference \n# between all and reg aka the irregular terms\n# in the tensor components\n#############################################\n\nif check then\n for ii from 1 to nops(all_tensors) do\n nm:= all_tensors[ii][1]:\n rank := all_tensors[ii][2]:\n tp := all_tensors[ii][3]:\n if rank <> 0 then\n for jj from 1 to nops(coord) do \n print(nm + coord[jj] );\n ress:=simplify(expand(tt[nm][all][coord[jj]] - tt[nm][reg][coord[jj]]));\n print(expand(ress));\n end do:\n else\n print(nm);\n ress:=simplify(expand(tt[nm][all] - tt[nm][reg]));\n print(expand(ress));\n end if;\n\n end do; \n\nend if;\n", "meta": {"hexsha": "b9b0c43fb448d69bce56f94a8645242fbd83d0ea", "size": 11340, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "built_eqns.mpl", "max_stars_repo_name": "rmanak/bssn_spher", "max_stars_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "built_eqns.mpl", "max_issues_repo_name": "rmanak/bssn_spher", "max_issues_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": "built_eqns.mpl", "max_forks_repo_name": "rmanak/bssn_spher", "max_forks_repo_head_hexsha": "b91104fd6b9b7cf1ba08e35efd65ff219ab7a5a9", "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": 28.2089552239, "max_line_length": 275, "alphanum_fraction": 0.4869488536, "num_tokens": 3602, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7745833737577158, "lm_q2_score": 0.6654105454764747, "lm_q1q2_score": 0.5154159452491297}} {"text": "\n# Definitions for Robot Dynamics Code Generation\n# Init\n# Erstelle Definitionen f\u00fcr die Maple-Skripte zur Berechnung von Kinematik und Dynamik des Roboters\n# \n# Quellen:\n# [1] Sousa, C. D. and Cortesao, R.: Physical feasibility of robot base inertial parameter identification: A linear matrix inequality approach (2014)\n# [2] Ayusawa, K. and Venture, G. and Nakamura, Y.: Identifiability and identification of inertial parameters using the underactuated base-link dynamics for legged multibody systems (2013)\n# [3] Fujimoto, Y. and Obata, S. and Kawamura, A.: Robust biped walking with active interaction control between foot and ground (1998)\n# [4] Khalil, W. and Kleinfinger, J.-F.: Minimum operations and minimum parameters of the dynamic models of tree structure robots (1987)\n# \n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_convert_t_s\":\nread \"../helper/proc_vec2skew\":\ncodegen_act := true:\n# Lese Umgebungsvariable f\u00fcr Codegenerierung.\nread \"../robot_codegen_definitions/robot_env\":\nprintf(\"Generiere Parameter f\u00fcr %s\\n\",robot_name):\n# Robotics Definitions\n# Joint Angles, Velocities and Accelerations in time depending and substitution form.\n# Time Depending form is for time differentiation.\n# Substitution Form is for partial differentiation and code export.\nqJ_t := Matrix(NQJ, 1):\nqJ_s := Matrix(NQJ, 1):\nqJD_s := Matrix(NQJ, 1):\nqJDD_s := Matrix(NQJ, 1):\nfor i from 1 to NQJ do\n qJ_t(i,1):=parse(sprintf(\"qJ%d(t)\", i)):\n qJ_s(i,1):=parse(sprintf(\"qJ%ds\", i)):\n qJD_s(i,1):=parse(sprintf(\"qJD%ds\", i)):\n qJDD_s(i,1):=parse(sprintf(\"qJDD%ds\", i)):\nend do:\nqJD_t := diff~(qJ_t, t):\nqJDD_t := diff~(qJD_t, t):\n# Gravity vector in world frame\nif not assigned(g_world) then\n g_world := Matrix(3, 1):\n g_world(1 .. 3, 1) := :\nend if:\n# Position und Orientierung der Basis. Die Orientierung ist mit XYZ-Euler-Winkeln definiert, die aber nicht im weiteren Algorithmus verwendet werden (nur Platzhalter).\n# Eine Invertierung der Orientierungsdarstellung sollte nicht notwendig werden, von daher kein Problem mit Orientierungsrepr\u00e4sentationssingularit\u00e4t.\n# gem. [2], S. 4 X_base_t SE(3): Position und Orientierung.\nNQB := 6:\nX_base_t:=Matrix(6, 1, [rx_base(t),ry_base(t),rz_base(t),alphax_base(t), betay_base(t), gammaz_base(t)]):\nX_base_s:=Matrix(6, 1, [rxs_base,rys_base,rzs_base,alphaxs_base, betays_base, gammazs_base]):\n# Geschwindigkeit der Basis (pelvis)\n# Twist: Verallgemeinerte Geschwindigkeit. Diese Darstellung ist nicht konsistent (Ableitung der Position stimmt nicht mit Ausdruck der Geschwindigkeit \u00fcberein)\nV_base_t:=Matrix(6, 1, [diff~(rx_base(t),t),diff~(ry_base(t),t),diff~(rz_base(t),t),omegax_base(t), omegay_base(t), omegaz_base(t)]):\nV_base_s:=Matrix(6, 1, [vxs_base,vys_base,vzs_base,omegaxs_base, omegays_base, omegazs_base]):\n# Zeitableitung davon\nVD_base_t:=diff~(V_base_t,t):\nVD_base_s:=Matrix(6, 1, [vDxs_base,vDys_base,vDzs_base,omegaDxs_base, omegaDys_base, omegaDzs_base]):\n# Name der Methode f\u00fcr die Orientierungsdarstellung der Basis\nbase_method_name := \"twist\":\n# Umrechnung von der Ableitung der Basis-Orientierung zu Winkelgeschwindigkeiten:\n# Wird hier nicht weiter beachtet (physikalisch falsch f\u00fcr eine Betrachtung der Dynamik der Basis).\n# Erm\u00f6glicht eine einfachere Berechnung f\u00fcr Mechanismen, wo die R\u00fcckwirkung auf die Basis nicht in der Vorw\u00e4rtsdynamik simuliert werden muss.\nT_basevel := IdentityMatrix(3, 3):\n# Verallgemeinerte Koordinaten, gem [2], S. 4, [3], S.1\nNQ:=NQJ+NQB:\nq_t := Matrix(NQ,1, ):\nq_s := Matrix(NQ,1, ):\nqD_t:= Matrix(NQ,1, ):\nqD_s:= Matrix(NQ,1, ):\nqDD_t:= Matrix(NQ,1, ):\nqDD_s:= Matrix(NQ,1, ):\n# MDH-Gelenkwinkel neu speichern (Definition der verallg. Koordinaten war dort noch nicht bekannt\ntheta := value(theta):\n# Standard-Werte festlegen\n# Anzahl der K\u00f6rper (Number of Links):\nif not assigned(NL) then\n NL := NJ + 1:\n printf(\"Variable NL ist nicht gegeben. Insgesamt %d Gelenke. Nehme an, dass jedes Gelenk einem K\u00f6rper zugeordnet ist (keine Schleifen)\\n\", NJ):\nelse\n NVJ := NJ - (NL - 1):\n printf(\"Variable NL=%d ist gegeben. Insgesamt %d Gelenke. Davon sind die ersten %d einem K\u00f6rper zugeordnet und die letzten %d virtuell.\\n\", NL, NJ, NJ-NVJ, NVJ):\nend if:\n# Gelenktyp (0=Revolute, 1=Prismatic, 2=Static). Sollte in der Definition festgelegt sein. Falls nicht, wird alles auf Revolute gesetzt\nif not assigned(sigma) then\n sigma := Matrix(NJ,1):\n printf(\"Variable sigma ist nicht gegeben. Setze alle Gelenke als Drehgelenk (sigma=1)\\n\"):\nend if:\n# Aktuierung (1=aktiv, 0=passiv). Sollte in der Definition festgelegt sein. Falls nicht, wird alles auf Aktiv gesetzt\nif not assigned(mu) then\n mu := Matrix(NJ,1,1):\n printf(\"Variable mu ist nicht gegeben. Setze alle Gelenke als aktiv (mu=1)\\n\"):\nend if:\n# Segmentreihenfolge der Roboterstruktur. Sollte in der Definition festgelegt sein. Falls nicht, wird eine serielle Kette angenommen\nif not assigned(v) then\n v := Matrix(NL-1,1,i->i-1):\n printf(\"Variable v ist nicht gegeben. Setze serielle Kette (0,1,2,...)\\n\"):\nend if:\n# Parameter f\u00fcr Baumstruktur. Sollte in der Definition festgelegt sein. Falls nicht, wird eine serielle Kette angenommen\nif not assigned(b) then\n b := Matrix(NJ,1):\n printf(\"Variable b ist nicht gegeben. zus\u00e4tzliche Verschiebung auf Null\\n\"):\nend if:\nif not assigned(beta) then\n beta := Matrix(NJ,1):\n printf(\"Variable beta ist nicht gegeben. zus\u00e4tzliche Verschiebung auf Null\\n\"):\nend if:\n# Eingabe pr\u00fcfen\n# Validit\u00e4t der Vorg\u00e4nger-Indizes. Konvention: Vorg\u00e4nger hat kleineren Index. Siehe Khalil-Publikationen (dort evtl nur implizit so verwendet).\nfor i from 1 to NJ do\n if v(i) >= i then\n printf(\"v(%d)=%d. Verletzt die Regel, dass die Vorg\u00e4nger-Nummer kleiner sein muss als die aktuelle Nummer.\\n\", i, v(i)):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\n end if:\nend do:\n\n# Dynamics Parameters\n# Mass of each link\nM_generic := Matrix(NL, 1):\nfor i from 1 to NL do\n M_generic[i,1]:=parse(sprintf(\"M%d\", i-1)):\nend do:\nM := copy(M_generic):\nif assigned(user_M) then\n if not RowDimension(user_M) = NL then\n printf(\"Input user_M is not of size %dx1. Error.\\n\", NL):\n end if:\n # Mass parameter given by user. Some entries can be zero or equal\n for i from 1 to NL do\n if user_M[i,1]<>M_generic[i,1] and user_M[i,1]<>0 then # check input\n printf(\"User input for mass %d should be either \\\"%s\\\" or zero. Not \\\"%s\\\". Continue anyway. \\n\", i-1, M_generic[i,1], user_M[i,1]):\n end if:\n M[i,1]:=user_M[i,1]:\n end do:\n printf(\"Masseparameter von Benutzer gesetzt. Eingabe f\u00fcr M:\\n\"):\n print(M);\nend if:\n# Center of Mass of each link (in link frame)\nr_i_i_Si := Matrix(3, NL):\nr_i_i_Si_generic := Matrix(3, NL):\nfor i from 1 to NL do\n r_i_i_Si_generic[1,i]:=parse(sprintf(\"SX%d\", i-1)):\n r_i_i_Si_generic[2,i]:=parse(sprintf(\"SY%d\", i-1)):\n r_i_i_Si_generic[3,i]:=parse(sprintf(\"SZ%d\", i-1)):\nend do:\nif not assigned(user_CoM) then\n r_i_i_Si := r_i_i_Si_generic:\nelse\n if RowDimension(user_CoM) <> 3 or ColumnDimension(user_CoM) <> NL then\n printf(\"Input user_CoM is not of size 3x%d. Error.\\n\", NL):\n end if:\n for i from 1 to NL do\n for j from 1 to 3 do\n if user_CoM[j,i]<>r_i_i_Si_generic[j,i] and user_CoM[j,i]<>0 then # check input\n printf(\"User input for CoM %d,%d should be either \\\"%s\\\" or zero. Not \\\"%s\\\". Continue anyway. \\n\", j, i-1, r_i_i_Si_generic[j,i], convert(user_CoM[j,i],string)):\n end if:\n end do:\n r_i_i_Si[1..3,i]:=user_CoM[1..3,i]:\n end do:\n printf(\"Schwerpunktsparameter von Benutzer gesetzt. Eingabe f\u00fcr r_i_i_Si:\\n\"):\n print(r_i_i_Si);\nend if:\n\n# First Moment (mass and center of mass)\nmr_i_i_Si := Matrix(3, NL):\nmr_i_i_Si_generic := Matrix(3, NL):\nxyzstrings := [\"X\", \"Y\", \"Z\"]:\nfor i from 1 to NL do\n for j from 1 to 3 do # loop over x-, y-, z-coordinates of the CoM\n mr_i_i_Si_generic[j,i]:= parse(sprintf(\"M%s%d\", xyzstrings[j], i-1)):\n end do:\n if M[i,1] = 0 then next; end if: # Zero Mass can be set by the user. Then the first moment stays zero\n for j from 1 to 3 do # loop over x-, y-, z-coordinates of the CoM\n if r_i_i_Si[j,i] = parse(sprintf(\"S%s%d\", xyzstrings[j], i-1)) then\n \t # default value for CoM is set (not overwritten by user input).\n \t # Set default value for first moment\n mr_i_i_Si[j,i]:= parse(sprintf(\"M%s%d\", xyzstrings[j], i-1)):\n else\n # CoM is written by the user. Put this assumption also in the first moment to reduce dynamics parameters\n \t mr_i_i_Si[j,i] := M[i,1]*r_i_i_Si[j,i]:\n end if:\n end do:\nend do:\n\n# Inertia of each link (about the center of mass, in link frame)\nI_i_Si := Matrix(6, NL):\nI_i_Si_generic := Matrix(6, NL):\nfor i from 1 to NL do\n if M[i,1] = 0 then next; end if: # Zero Mass can be set by the user. Then the inertia stays zero\n I_i_Si_generic[1,i]:=parse(sprintf(\"XXC%d\", i-1)):\n I_i_Si_generic[2,i]:=parse(sprintf(\"XYC%d\", i-1)):\n I_i_Si_generic[3,i]:=parse(sprintf(\"XZC%d\", i-1)):\n I_i_Si_generic[4,i]:=parse(sprintf(\"YYC%d\", i-1)):\n I_i_Si_generic[5,i]:=parse(sprintf(\"YZC%d\", i-1)):\n I_i_Si_generic[6,i]:=parse(sprintf(\"ZZC%d\", i-1)):\nend do:\nif not assigned(user_inertia) then\n I_i_Si := I_i_Si_generic:\nelse\n if RowDimension(user_inertia) <> 6 or ColumnDimension(user_inertia) <> NL then\n printf(\"Input user_inertia is not of size 6x%d. Error.\\n\", NL):\n end if:\n for i from 1 to NL do\n for j from 1 to 6 do\n if user_inertia[j,i]<>I_i_Si_generic[j,i] and user_inertia[j,i]<>0 then # check input\n printf(\"User input for inertia %d,%d should be either \\\"%s\\\" or zero. Not \\\"%s\\\". Continue anyway. \\n\", j, i-1, convert(I_i_Si_generic[j,i],string), convert(user_inertia[j,i],string)):\n end if:\n end do:\n I_i_Si[1..6,i]:=user_inertia[1..6,i]:\n end do:\n printf(\"Tr\u00e4gheitsparameter von Benutzer gesetzt. Eingabe f\u00fcr I_i_Si:\\n\"):\n print(I_i_Si);\nend if:\n\n# Inertia of each link (about the origin of body frame, in link frame)\n# Berechne die Inertial-Tr\u00e4gheitsmomente mit dem Steinerschen Verschiebungssatz\nI_i_i_calc := Matrix(6, NL):\nfor i from 1 to NL do\n # Tr\u00e4gheitstensor (3x3) um den K\u00f6rperschwerpunkt in K\u00f6rper-KS\n I_i_Si_Tensor := Matrix([[I_i_Si[1, i], I_i_Si[2, i], I_i_Si[3, i]], [I_i_Si[2, i], I_i_Si[4, i], I_i_Si[5, i]], [I_i_Si[3, i], I_i_Si[5, i], I_i_Si[6, i]]]):\n # Steinerschen Satz anwenden\n I_i_i_Tensor := I_i_Si_Tensor + M[i,1]*Transpose(vec2skew(r_i_i_Si[1..3,i])) . vec2skew(r_i_i_Si[1..3,i]):\n # Wieder als Matrix abspeichern\n I_i_i_calc[..,i] := :\nend do:\n\n# Allgemeine Form des Tr\u00e4gheitstensors (Eintr\u00e4ge sind unabh\u00e4ngige Parameter)\nI_i_i_generic := Matrix(6, NL):\nfor i from 1 to NL do\n I_i_i_generic[1,i]:=parse(sprintf(\"XX%d\", i-1)):\n I_i_i_generic[2,i]:=parse(sprintf(\"XY%d\", i-1)):\n I_i_i_generic[3,i]:=parse(sprintf(\"XZ%d\", i-1)):\n I_i_i_generic[4,i]:=parse(sprintf(\"YY%d\", i-1)):\n I_i_i_generic[5,i]:=parse(sprintf(\"YZ%d\", i-1)):\n I_i_i_generic[6,i]:=parse(sprintf(\"ZZ%d\", i-1)):\nend do:\n\n# Pr\u00fcfe, welche Eintr\u00e4ge des Tr\u00e4gheitstensors noch Schwerpunkts-Parameter enthalten. Diese m\u00fcssen wieder auf die Standard-Werte mit unabh\u00e4ngigen Parametern gesetzt werden\nI_i_i := Matrix(6, NL):\ncompstrings := [\"XX\", \"XY\", \"XZ\", \"YY\", \"YZ\", \"ZZ\"]:\nfor i from 1 to NL do\n if M[i,1] = 0 then next; end if: # Zero Mass can be set by the user. Then the inertia stays zero\n for j from 1 to 6 do # Alle Komponenten des Tensors\n # Nicht Null. Setze erstmal allgemeinen Eintrag:\n I_i_i[j,i] := I_i_i_generic[j,i]:\n # Pr\u00fcfe, ob Schwerpunktsparameter vorkommt (durch Verschiebungssatz s.o.)\n IhasCoM := false:\n for k from 1 to 3 do\n if has(I_i_i_calc[j,i], r_i_i_Si_generic[k,i]) then\n \t IhasCoM := true: # Der Eintrag enth\u00e4lt die Schwerpunktskoordinaten. Nicht zul\u00e4ssig f\u00fcr weitere Rechnung.\n \t break:\n end if:\n end do:\n if has(I_i_i_calc[j,i], I_i_Si_generic[j,i]) then\n \t IhasCoM := true: # Es steht der Schwerpunktsbezogene Tr\u00e4gheitsterm drin. Weitere Rechnung damit nicht m\u00f6glich.\n end if:\n if IhasCoM = true then\n next: # Es kommt ein Schwerpunktsparameter vor. Belasse Parameter auf allgemeinem Wert.\n end if:\n I_i_i[j,i] := I_i_i_calc[j,i]:\n end do:\nend do:\n\n# Vector of stacked dynamics parameters for regressor form\n# Matrix of link inertial parameters, stacked link parameter vectors.\n# Diese Parameter-Matrix wird nur benutzt, um f\u00fcr die Generierung der Regressorform danach abzuleiten.\n# Hier stehen also die allgemeinen (\"generic\") Parameter drin. Es ist egal, ob diese bereits durch den Benutzer zu Null gesetzt sind.\n# Dann w\u00fcrden die allgemeinen Parameter nicht in der Dynamik vorkommen und die Ableitung w\u00e4re Null.\nPV2_mat := Matrix(NL, 10):\nfor i to NL do \n PV2_mat[i, 1 .. 6] := I_i_i_generic[1 .. 6, i]:\n PV2_mat[i, 7 .. 9] := mr_i_i_Si_generic[1 .. 3, i]:\n PV2_mat[i, 10] := M_generic[i, 1]:\nend do:\n\n# Parameter-Vektor Erstellen: vector of link inertial parameters (delta in [1]).\n# Gleiche \u00dcberlegung wie f\u00fcr Parameter-Matrix\nPV2_vec := Matrix(10*(NL), 1):\nfor i to NL do \n for j to 10 do \n PV2_vec[10*(i-1)+j] := PV2_mat[i, j]:\n end do:\nend do:\n# Kinematische Zwangsbedingungen\n# Pr\u00fcfe, ob kinematische Zwangsbedingungen in der Roboterkonfiguration genannt sind durch Pr\u00fcfung der Existenz der entsprechenden Variablen.\nif type( kintmp_t, 'Matrix') = false then\n kintmp_t := Matrix(1,1): # Dummy-Werte damit sp\u00e4ter alles funktioniert\n kintmp_s := Matrix(1,1):\nend if:\n# Export\nsave q_t, q_s, qD_t, qD_s, qDD_t, qDD_s, qJ_t, qJ_s, qJD_t, qJD_s, qJDD_t, qJDD_s, g_world, X_base_t, X_base_s, V_base_t, V_base_s, VD_base_t, VD_base_s, qoffset, theta, alpha, d, a,v,b,beta, sigma,mu,M, r_i_i_Si, mr_i_i_Si, I_i_i, I_i_Si, PV2_vec, PV2_mat, robot_name, NQ,NQB,NQJ,NJ,NL, base_method_name, T_basevel, kintmp_t, kintmp_s, sprintf(\"../codeexport/%s/tmp/tree_floatb_twist_definitions\", robot_name):\nsave q_t, q_s, qD_t, qD_s, qDD_t, qDD_s, qJ_t, qJ_s, qJD_t, qJD_s, qJDD_t, qJDD_s, g_world, X_base_t, X_base_s, V_base_t, V_base_s, VD_base_t, VD_base_s, qoffset, theta, alpha, d, a,v,b,beta, sigma,mu,M, r_i_i_Si, mr_i_i_Si, I_i_i, I_i_Si, PV2_vec, PV2_mat, robot_name, NQ,NQB,NQJ,NJ,NL, base_method_name, T_basevel, kintmp_t, kintmp_s, sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\n# Einzelne DH-Parameter als Matlab-Code exportieren. Damit l\u00e4sst sich in Matlab ein passender Parametersatz generieren.\n# Die folgenden Dateien m\u00fcssen immer generiert werden, wenn die Bash-Skripte zur Funktionszusammensetzung fehlerfrei laufen sollen.\n# Benutze die Funktion convert_t_s, um eventuelle Substitutionsvariablen f\u00fcr konstante Gelenkwinkel zu verwenden, da die Matlab-Terme auch mit substituierten Ausdr\u00fccken generiert werden.\n# Zur Kennzeichnung von zeitabh\u00e4ngigen und konstanten Ausdr\u00fccken kann \"delta1(t)\", \"delta1\" und \"delta1s\" verwendet werden.\nMatlabExport(v, sprintf(\"../codeexport/%s/tmp/parameters_mdh_v_matlab.m\", robot_name), 2):\nMatlabExport(convert_t_s(a), sprintf(\"../codeexport/%s/tmp/parameters_mdh_a_matlab.m\", robot_name), 2):\nd_export := d *~ (1-~sigma):\nMatlabExport(convert_t_s(d_export), sprintf(\"../codeexport/%s/tmp/parameters_mdh_d_matlab.m\", robot_name), 2):\ntheta_export := theta *~ sigma:\nMatlabExport(convert_t_s(theta_export), sprintf(\"../codeexport/%s/tmp/parameters_mdh_theta_matlab.m\", robot_name), 2):\nMatlabExport(convert_t_s(b), sprintf(\"../codeexport/%s/tmp/parameters_mdh_b_matlab.m\", robot_name), 2):\nMatlabExport(convert_t_s(alpha), sprintf(\"../codeexport/%s/tmp/parameters_mdh_alpha_matlab.m\", robot_name), 2):\nMatlabExport(convert_t_s(beta), sprintf(\"../codeexport/%s/tmp/parameters_mdh_beta_matlab.m\", robot_name), 2):\nMatlabExport(convert_t_s(qoffset), sprintf(\"../codeexport/%s/tmp/parameters_mdh_qoffset_matlab.m\", robot_name), 2):\nMatlabExport(sigma, sprintf(\"../codeexport/%s/tmp/parameters_mdh_sigma_matlab.m\", robot_name), 2):\nMatlabExport(mu, sprintf(\"../codeexport/%s/tmp/parameters_mdh_mu_matlab.m\", robot_name), 2):\n\n# Einzelne Dynamikparameter als Matlab-Code exportieren. Wenn die Parameter durch Benutzereingaben ver\u00e4ndert wurden, l\u00e4sst sich diese Information so weiter benutzen.\n# (z.B. in der Definition von Eingabeparametern in den Testskripten).\n# In den Maple-Variablen ist die Spalte der Index der K\u00f6rper und die Zeilen sind die Indizes f\u00fcr die xyz-Komponenten (einfacherer Aufruf der Variablen)\n# In Matlab ist es umgekehrt (f\u00fchrt zu konsistenterem Code in Matlab): Die Zeilen entsprechen dem K\u00f6rper-Index. Daher hier Transponierung.\n# Zus\u00e4tzlich ist die Reihenfolge der Komponenten der Tr\u00e4gheitstensoren in Matlab und Maple unterschiedlich (daher die Indizierung).\n# Matlab: xx, yy, zz, xy, xz, yz (erst Hauptmomente, dann Deviationsmomente)\n# Maple: xx, xy, xz, yy, yz, zz (Dreiecksform)\nMatlabExport(M, sprintf(\"../codeexport/%s/tmp/parameters_dyn_mges_matlab.m\", robot_name), 2):\nMatlabExport(Transpose(r_i_i_Si), sprintf(\"../codeexport/%s/tmp/parameters_dyn_rSges_matlab.m\", robot_name), 2):\nMatlabExport(Transpose(I_i_Si([1,4,6,2,3,5],..)), sprintf(\"../codeexport/%s/tmp/parameters_dyn_Icges_matlab.m\", robot_name), 2):\nMatlabExport(Transpose(mr_i_i_Si), sprintf(\"../codeexport/%s/tmp/parameters_dyn_mrSges_matlab.m\", robot_name), 2):\nMatlabExport(Transpose(I_i_i([1,4,6,2,3,5],..)), sprintf(\"../codeexport/%s/tmp/parameters_dyn_Ifges_matlab.m\", robot_name), 2):\n\n", "meta": {"hexsha": "a60a49cc08d70da7215fabbeb77519bbd01d22cb", "size": 17780, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_definitions/robot_tree_floatb_twist_definitions.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_definitions/robot_tree_floatb_twist_definitions.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_definitions/robot_tree_floatb_twist_definitions.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 54.8765432099, "max_line_length": 411, "alphanum_fraction": 0.7254780652, "num_tokens": 5912, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8418256393148981, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5146770205339527}} {"text": "input := FileTools:-Text:-ReadFile(\"AoC-2021-6-input.txt\" ):\ntally := table(sparse=0,Statistics:-Tally(\n StringTools:-Split(input,\",\")));\nlanternfish := Array(0..8, [tally[\"0\"],tally[\"1\"],tally[\"2\"],tally[\"3\"],\n tally[\"4\"],tally[\"5\"],0,0,0]);\n\nto 256 do\n day0 := lanternfish[0];\n lanternfish[0..7] := lanternfish[1..8];\n lanternfish[8] := day0;\n lanternfish[6] := lanternfish[6] + day0;\nend do:\n\nanswer2 := add(lanternfish);\n", "meta": {"hexsha": "4453d4962ac479545065a5e4fc291650d469d42e", "size": 443, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Day6/AoC6-Maple.mpl", "max_stars_repo_name": "johnpmay/AdventOfCode2021", "max_stars_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2021-12-04T18:24:03.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-04T18:24:03.000Z", "max_issues_repo_path": "Day6/AoC6-Maple.mpl", "max_issues_repo_name": "johnpmay/AdventOfCode2021", "max_issues_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "Day6/AoC6-Maple.mpl", "max_forks_repo_name": "johnpmay/AdventOfCode2021", "max_forks_repo_head_hexsha": "b51756bcebea662333072cf518cf040a962ef8b7", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 29.5333333333, "max_line_length": 72, "alphanum_fraction": 0.611738149, "num_tokens": 159, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8267117769928211, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.5145944598036482}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_vsxc_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_vsxc_params * )(p->params);\n*)\n\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\n$include \"gvt4.mpl\"\n\nvsxc_comp := (rs, z, spin, xs, ts) ->\n + lda_stoll_par(f_pw, rs, z, 1)\n * gtv4(params_a_alpha_ss, params_a_dss, xs, 2*(ts - K_FACTOR_C))\n * Fermi_D(xs, ts):\n\n(* The parallel and perpendicular components of the energy *)\nvsxc_fpar := (rs, z, xs0, xs1, ts0, ts1) ->\n + vsxc_comp(rs, z, 1, xs0, ts0)\n + vsxc_comp(rs, -z, -1, xs1, ts1):\n\nvsxc_fperp := (rs, z, xs0, xs1, ts0, ts1) ->\n + lda_stoll_perp(f_pw, rs, z)\n * gtv4(params_a_alpha_ab, params_a_dab, sqrt(xs0^2 + xs1^2), 2*(ts0 + ts1 - 2*K_FACTOR_C)):\n\nvsxc_f := (rs, z, xs0, xs1, ts0, ts1) ->\n + vsxc_fpar (rs, z, xs0, xs1, ts0, ts1)\n + vsxc_fperp(rs, z, xs0, xs1, ts0, ts1):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n vsxc_f(rs, z, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "9fb82693cb915d0262169c40bd45499bc44fc048", "size": 1216, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_vsxc.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_vsxc.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_vsxc.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 28.2790697674, "max_line_length": 93, "alphanum_fraction": 0.6381578947, "num_tokens": 486, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8791467738423874, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5143897920892279}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_gga_c *)\n\n$include \"gga_c_pw91.mpl\"\n\nc1 := 1.1015:\nc2 := 0.6625:\n\nf := (rs, z, xt, xs0, xs1) ->\n + c1*f_pw91(rs, z, xt, xs0, xs1) + (c2 - c1)*(\n + f_pw91(rs*(2*(1 + z))^(1/3), 1, xs0, xs0, 0)\n + f_pw91(rs*(2*(1 - z))^(1/3), -1, xs1, 0, xs1)\n):", "meta": {"hexsha": "d4513bf5d3a1b102e25d20eacf9800e24bc145fc", "size": 507, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/gga_c_optc.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/gga_c_optc.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/gga_c_optc.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.35, "max_line_length": 68, "alphanum_fraction": 0.5798816568, "num_tokens": 215, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.8615382094310357, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.5138499448781445}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n\n$include \"mgga_c_scan.mpl\"\n\n(* we need to redefine two functions *)\nscan_e0_g := (rs, z, t) -> (1 + 8*A(rs, z, t)*t^2)^(-1/4)/2\n + (1 + 80*A(rs, z, t)^2*t^4)^(-1/8)/2:\nscan_g_infty := s -> (1 + 4*scan_chi_infty*s^2)^(-1/4)/2\n + (1 + 80*scan_chi_infty^2*s^4)^(1/8)/2:\n\n(* and the new parameters *)\nscan_b1c := 0.030197:\nscan_b2c := -0.06623:\nscan_b3c := 0.16672:\n\n(* set parameters of f_alpha *)\nparams_a_c1 := 1.131:\nparams_a_c2 := 1.7:\nparams_a_d := 1.37:\n", "meta": {"hexsha": "ab5f1292622e8620a894bac8f712eb9e409666bc", "size": 733, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_revscan.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_revscan.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_revscan.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.1785714286, "max_line_length": 68, "alphanum_fraction": 0.6152796726, "num_tokens": 287, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8652240791017535, "lm_q2_score": 0.5926665999540698, "lm_q1q2_score": 0.5127894131596273}} {"text": "make_GL3_2 := proc()\n global GL3_2;\n local G,L,E,f,n,i,j,k,g,h;\n \n G := table():\n\n L := [[]]:\n for i from 1 to 9 do\n L := [seq(seq([op(u),j],j=0..1),u in L)];\n od:\n\n # Strange order ensures that 1 comes first, followed by other\n # upper unitriangular matrices.\n f := (u) -> Matrix([[u[7],u[5],u[6]],\n [u[1],u[8],u[4]],\n\t\t [u[3],u[2],u[9]]]);\n L := select(u -> mods(Determinant(f(u)),2) <> 0,L);\n n := nops(L);\n E := map(f,L);\n \n G[\"elements\"] := E;\n \n G[\"index\"] := table():\n for i from 1 to n do G[\"index\"][convert(E[i],listlist)] := i; od:\n \n G[\"id\"] := IdentityMatrix(3);\n G[\"o\"] := (u,v) -> map(mods,u . v,2);\n G[\"inv\"] := (u) -> map(mods,1 / u,2);\n\n G[\"o_table\"] := table();\n G[\"inv_table\"] := table();\n\n for i from 1 to n do\n g := G[\"elements\"][i];\n G[\"inv_table\"][i] := G[\"index\"][convert(G[\"inv\"](g),listlist)];\n\n for j from 1 to n do\n h := G[\"elements\"][j];\n G[\"o_table\"][i,j] := G[\"index\"][convert(G[\"o\"](g,h),listlist)];\n od:\n od:\n\n G[\"ee\"] := convert(IdentityMatrix(n),listlist);\n\n G[\"ring_id\"] := G[\"ee\"][1];\n \n G[\"antipode\"] := proc(u)\n local n,M,w,i,j;\n n := 168;\n M := eval(GL3_2[\"inv_table\"]);\n w := [seq(u[M[i]],i=1..n)];\n return w;\n end:\n \n G[\"convolve\"] := proc(u,v)\n local n,J,M,w,i,j,ii;\n n := 168;\n J := eval(GL3_2[\"inv_table\"]);\n M := eval(GL3_2[\"o_table\"]);\n w := [0$n];\n for i from 1 to n do\n if u[i] <> 0 then\n ii := J[i];\n w := w +~ [seq(u[i] * v[M[ii,j]],j=1..n)];\n fi;\n od;\n\n return w;\n end:\n\n G[\"borel_elements\"] :=\n [seq(seq(seq(Matrix([[1,i,j],[0,1,k],[0,0,1]]),i=0..1),j=0..1),k=0..1)]:\n G[\"borel_indices\"] :=\n map(b -> G[\"index\"][convert(b,listlist)],G[\"borel_elements\"]);\n G[\"borel_sum\"] := [0$168]:\n for i in G[\"borel_indices\"] do\n G[\"borel_sum\"] := G[\"borel_sum\"] +~ G[\"ee\"][i]:\n od:\n\n G[\"coxeter_elements\"] := map(permutation_matrix,combinat[permute](3)):\n G[\"coxeter_indices\"] := map(w -> G[\"index\"][convert(w,listlist)],G[\"coxeter_elements\"]):\n G[\"signed_coxeter_sum\"] := [0$168]:\n for i in G[\"coxeter_indices\"] do\n G[\"signed_coxeter_sum\"] := G[\"signed_coxeter_sum\"] +~ Determinant(E[i]) *~ G[\"ee\"][i]:\n od:\n\n G[\"steinberg_idempotent\"] :=\n G[\"convolve\"](G[\"signed_coxeter_sum\"], G[\"borel_sum\"]) / 21;\n \n GL3_2 := eval(G);\n return(eval(G));\nend:\n\n", "meta": {"hexsha": "d2bf39f3038e079b8fa36d2f25252706f71b9073", "size": 2252, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/groups/GL3_2.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/groups/GL3_2.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/groups/GL3_2.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 23.9574468085, "max_line_length": 89, "alphanum_fraction": 0.5284191829, "num_tokens": 854, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956580903722561, "lm_q2_score": 0.6442251064863697, "lm_q1q2_score": 0.5125829179968082}} {"text": "\n# Lagrange Formalis for Robot based on MDH frames\n# Einleitung\n# Berechnung des Lagrange-Formalismus\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# tree -> Berechnung f\u00fcr eine beliebige Baumstruktur (ohne Schleifen)\n# floatb -> floating base wird durch base twist (Geschwindigkeit der Basis) oder vollst\u00e4ndige Orientierung (Euler-Winkel) ber\u00fccksichtigt\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# lagrange -> Berechnung des Lagrange-Formalismus\n# worldframe -> Berechnung basierend auf Energien aus Welt-KS (KS W)\n# par12 -> Parametersatz 1 (Schwerpunkt als Parameter: SX,SY,SZ) oder Parametersatz 2 (1. und 2. Moment MX,MY,MZ,...)\n# Autor\n# Moritz Schappler, schappler@irt.uni-hannover.de, 2016-03\n# (C) Institut fuer Regelungstechnik, Leibniz Universitaet Hannover\n# Sources\n# [GautierKhalil1990] Direct Calculation of Minimum Set of Inertial Parameters of Serial Robots\n# [KhalilDombre2002] Modeling, Identification and Control of Robots\n# [Ortmaier2014] Vorlesungsskript Robotik I\n# Initialization\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\n# Einstellungen f\u00fcr Code-Export: Optimierungsgrad (2=h\u00f6chster) und Aktivierung jedes Terms.\ncodegen_opt := 2:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../helper/proc_Lagrange1\":\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../transformation/proc_trotx\": \nread \"../transformation/proc_troty\": \nread \"../transformation/proc_trotz\": \nread \"../transformation/proc_transl\": \nread \"../transformation/proc_trafo_mdh\": \nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", robot_name):\nread sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name): \nkin_constraints_exist := kin_constraints_exist: # nur zum Absch\u00e4tzen der Komplexit\u00e4t\n;\n# Einstellungen f\u00fcr Term-Vereinfachungen: 0=keine, 1=dTdq_s, 2=auch dTdq_s, 3=auch dTdqDdt_s\nif not assigned(simplify_options) or simplify_options(8)=-1 then # Standard-Einstellungen:\n # Die Vereinfachung ist ein Kompromiss aus Laufzeit des Programms und G\u00fcte der Ergebnisse\n # Bei zu komplizierten Termen st\u00fcrzt Maple bei der Vereinfachung unvorhersehbar ab.\n # Annahme: Bei kinematischen Zwangsbedingungen werden die Terme zu kompliziert.\n if not kin_constraints_exist then # normale serielle Ketten und Baumstrukturen\n use_simplify := 0: # Standardm\u00e4\u00dfig aus\n else # mit kinematischen Zwangsbedingungen\n use_simplify := 1: # Annahme, dass Optimierung der Gravitations-Terme noch m\u00f6glich ist\n end if:\nelse # Benutzer-Einstellungen:\n use_simplify := simplify_options(8): # achter Eintrag ist f\u00fcr Lagrange\nend if:\n\n# Kennung des Parametersatzes, f\u00fcr den die Dynamikfunktionen erstellt werden sollen. Muss im Repo und in der mpl-Datei auf 1 gelassen werden, da die folgende Zeile mit einem Skript verarbeitet wird.\ncodegen_dynpar := 1:\n# Ergebnisse der Energie laden\nif codegen_dynpar = 1 then\n read sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par1_maple.m\", robot_name, base_method_name):\n read sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_worldframe_par1_maple.m\", robot_name, base_method_name):\nelif codegen_dynpar = 2 then\n read sprintf(\"../codeexport/%s/tmp/energy_potential_floatb_%s_worldframe_par2_maple.m\", robot_name, base_method_name):\n read sprintf(\"../codeexport/%s/tmp/energy_kinetic_floatb_%s_linkframe_par2_maple.m\", robot_name, base_method_name):\nelse\n printf(\"Energiefunktionen nur f\u00fcr Parametersatz 1 oder 2 definiert\\n\"):\nend:\nT := T:\nU_grav := U_grav:\nprintf(\"%s. Generiere Terme des Lagrange-Formalismus f\u00fcr %s mit Parametersatz %d und %s\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name, codegen_dynpar, base_method_name):\n\n# Lagrange Formalismus (mit Funktion)\ntmp_t1:=time():\nOutputLagrange := Lagrange1(T, U_grav, NQ):\ndTdqDdt_s := OutputLagrange[1]:\ndTdq_s := OutputLagrange[2]:\ndUdq_s := OutputLagrange[3]:\nprintf(\"%s. Lagrange-Formalismus f\u00fcr %s mit Parametersatz %d und %s berechnet. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name, codegen_dynpar, base_method_name, time()-tmp_t1):\n# Terme vereinfachen: Einzeln und komponentenweise\nif use_simplify>=1 then\n # Term dUdq_s\n tmp_t1:=time(): tmp_l1 := length(dUdq_s):\n printf(\"%s. Beginne Vereinfachung: Lagrange-Term dU/dq (Param. %d). L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, tmp_l1):\n for i from 1 to NQ do\n dUdq_s[i,1] := simplify2(dUdq_s[i,1]):\n end do:\n tmp_t2:=time(): tmp_l2 := length(dUdq_s):\n printf(\"%s. Lagrange-Term dU/dq (Param. %d) vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\nif use_simplify>=2 then # Die Terme k\u00f6nnen sehr kompliziert sein. Daher nicht immer vereinfachen.\n # Term dTdq_s\n for i from 1 to NQ do\n tmp_t1:=time(): tmp_l1 := length(dTdq_s[i,1]):\n printf(\"%s. Beginne mit Vereinfachung von Lagrange-Term dT/dq (Param. %d; Komponente %d/%d). L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, i, NQ, tmp_l1):\n dTdq_s[i,1] := simplify2(dTdq_s[i,1]):\n tmp_t2:=time(): tmp_l2 := length(dTdq_s[i,1]):\n printf(\"%s. Lagrange-Term dT/dq (Param. %d; Komponente %d/%d) vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, i, NQ, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end do:\nend if:\nif use_simplify>=3 then\n # Term dTdqDdt_s\n for i from 1 to NQ do\n tmp_t1:=time(): tmp_l1 := length(dTdqDdt_s[i,1]):\n printf(\"%s. Beginne mit Vereinfachung von Lagrange-Term d(dT/dqD)/dt (Param. %d; Komponente %d/%d). L\u00e4nge: %d.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, i, NQ, tmp_l1):\n dTdqDdt_s[i,1] := simplify2(dTdqDdt_s[i,1]):\n tmp_t2:=time(): tmp_l2 := length(dTdqDdt_s[i,1]):\n printf(\"%s. Lagrange-Term d(dT/dqD)/dt (Param. %d; Komponente %d/%d) vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar, i, NQ, tmp_l1, tmp_l2, tmp_t2-tmp_t1):\n end do:\nend if:\nsave dUdq_s, sprintf(\"../codeexport/%s/tmp/floatb_%s_lagrange_dUdq_s_par%d_maple.m\", robot_name, base_method_name, codegen_dynpar):\nsave dTdq_s, sprintf(\"../codeexport/%s/tmp/floatb_%s_lagrange_dTdq_s_par%d_maple.m\", robot_name, base_method_name, codegen_dynpar):\nsave dTdqDdt_s, sprintf(\"../codeexport/%s/tmp/floatb_%s_lagrange_dTdqDdt_s_par%d_maple.m\", robot_name, base_method_name, codegen_dynpar):\nprintf(\"%s. Lagrange-Formalismus durchgef\u00fchrt und Ergebnisse gespeichert (Dynamik-Parametersatz %d)\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), codegen_dynpar):\n\n\n", "meta": {"hexsha": "36253459f5d181b80a405ffc08b4e8be394c6efa", "size": 6982, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_dynamics/robot_tree_floatb_rotmat_lagrange_worldframe_par12.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_dynamics/robot_tree_floatb_rotmat_lagrange_worldframe_par12.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_dynamics/robot_tree_floatb_rotmat_lagrange_worldframe_par12.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 52.4962406015, "max_line_length": 198, "alphanum_fraction": 0.7373245488, "num_tokens": 2335, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8539127678225575, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.5125085030707611}} {"text": "`phi/F1bar/ord` := (A::set) -> proc(x)\n return sort([op(A)],(a,b) -> ((a=b) or (op(x[{a,b}][a]) < op(x[{a,b}][b]))));\nend:\n\n######################################################################\n# Apply the isomorphism R^1 = R\n\n`trim/F1bar` := (A::set) -> proc(x)\n local u,x0,P,T,a;\n\n x0 := table();\n P := `list_elements/big_subsets`(A);\n for T in P do\n u := `bottom_normalise/SW`(1)(T)(x[T]); \n x0[T] := table();\n for a in T do \n x0[T][a] := op(u[a]);\n od;\n od;\n\n return eval(x0):\nend:\n\n######################################################################\n\n`subcritical_tree/F1bar` := (A::set) -> proc(x)\n local x0,R,n,SS,i,j,J,J1,g1,g2,is_subcritical,a,k;\n\n x0 := `trim/F1bar`(A)(x);\n\n R := `phi/F1bar/ord`(A)(x);\n n := nops(A);\n SS := seq({a},a in A);\n\n for i from 1 to n-1 do \n for j from i+1 to n do\n J := {seq(R[k],k=i..j)};\n is_subcritical := true;\n if i > 1 then\n J1 := {R[i-1],op(J)};\n g1 := `gap/real_functions`(J )(x0[J1]);\n g2 := `gap/real_functions`(J1)(x0[J1]);\n if g2 = g1 then\n is_subcritical := false;\n fi;\n fi;\n if j < n then\n J1 := {op(J),R[j+1]};\n g1 := `gap/real_functions`(J )(x0[J1]);\n g2 := `gap/real_functions`(J1)(x0[J1]);\n if g2 = g1 then\n is_subcritical := false;\n fi;\n fi;\n\n if is_subcritical then\n SS := SS,J;\n fi;\n od;\n od;\n SS := {SS};\n return SS;\nend:\n\n######################################################################\n\n`theta/F1bar/K` := (A::set) -> proc(x)\n local x0,R,n,SS,i,j,k,J,J1,t,parent;\n\n x0 := `trim/F1bar`(A)(x);\n R := `phi/F1bar/ord`(A)(x);\n SS := `subcritical_tree/F1bar`(A)(x);\n parent := parent_map(A)(SS);\n n := nops(A);\n t := table();\n\n for i from 1 to n do \n for j from i to n do \n J := {seq(R[k],k=i..j)};\n if nops(J) = 1 or nops(J) = n then\n t[J] := 1; \n elif not(member(J,SS)) then\n t[J] := 0;\n else\n J1 := parent[J];\n t[J] := 1 - `gap/real_functions`(J)(x0[J1])/\n `gap/real_functions`(J1)(x0[J1]);\n fi;\n od;\n od;\n\n return [R,eval(t)];\nend:\n\n######################################################################\n\n`phi/K/F1bar` := (A::set) -> proc(Rt)\n local R,t,n,r,i,j,k,l,x,P,Q,Q1,J,M,M1,m,T,U;\n\n R,t := op(Rt);\n \n n := nops(A);\n r := table();\n for i from 1 to n do r[R[i]] := i; od;\n\n x := table();\n m := table();\n\n P := `list_elements/big_subsets`(A);\n Q := {seq(seq([seq(R[k],k=i..j)],j=i..n),i=1..n)};\n Q1 := select(J -> nops(J)>1,Q);\n\n for J in Q do\n m[J] := table();\n M := select(U -> ({op(J)} minus {op(U)} <> {}),Q);\n for i from 1 to nops(J) - 1 do\n M1 := select(U -> member(J[i],U) and member(J[i+1],U),M);\n m[J][J[i]] := mul(1-t[{op(U)}],U in M1);\n od;\n od;\n\n for T in P do \n x[T] := table();\n i := min(op(map(a -> r[a],T)));\n j := max(op(map(a -> r[a],T)));\n J := [seq(R[k],k=i..j)];\n for k from i to j do\n if member(R[k],T) then\n x[T][R[k]] := [add(m[J][R[l]],l=i..k-1)];\n fi\n od;\n od;\n\n return eval(x);\nend:\n", "meta": {"hexsha": "1a89d51cc107b1be3037b2443027396f621a183b", "size": 2914, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/fulton/F1bar.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/fulton/F1bar.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/fulton/F1bar.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 21.4264705882, "max_line_length": 78, "alphanum_fraction": 0.4440631434, "num_tokens": 1067, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8128673269042768, "lm_q2_score": 0.6297746004557471, "lm_q1q2_score": 0.5119231960246721}} {"text": "######################################################################\n\n`eta/height_functions`:= (A::set) -> `if`(nops(A)=1,table(A=0),FAIL);\n\n######################################################################\n\n`gamma/height_functions`:= (A::set,B::set) -> (p) -> proc(j,h)\n local k,P,phi,b0,b1,m,U,pU,b;\n\n k := table();\n P := `list_elements/nonempty_subsets`(A);\n\n phi := table();\n for b0 in B do\n m := 1;\n for b1 in B do\n if b1 <> b0 then m := min(m,j[{b0,b1}]); fi;\n od;\n phi[b0] := m;\n od;\n\n for U in P do\n pU := map(u -> p[u],U);\n if nops(pU) > 1 then \n k[U] := j[pU];\n else \n b := op(pU);\n k[U] := phi[b] * h[b][U];\n fi;\n od;\n\n return eval(k);\nend;\n\n######################################################################\n\n`gamma_min/height_functions`:= (A::set,B::set) -> (p) -> proc(j,h)\n local k,P,phi,b0,b1,m,U,pU,b;\n\n k := table();\n P := `list_elements/nonempty_subsets`(A);\n\n phi := table();\n for b0 in B do\n m := 1;\n for b1 in B do\n if b1 <> b0 then m := min(m,j[{b0,b1}]); fi;\n od;\n phi[b0] := m;\n od;\n\n for U in P do\n pU := map(u -> p[u],U);\n if nops(pU) > 1 then \n k[U] := j[pU];\n else \n b := op(pU);\n k[U] := min(phi[b] , h[b][U]);\n fi;\n od;\n\n return eval(k);\nend;\n", "meta": {"hexsha": "7aa7508cd3bf94673d6d8395cf3c5aa54f20cd3e", "size": 1217, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/height_functions.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/height_functions.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/height_functions.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 19.015625, "max_line_length": 70, "alphanum_fraction": 0.4116680362, "num_tokens": 418, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7690802264851919, "lm_q2_score": 0.665410558746814, "lm_q1q2_score": 0.5117541032266378}} {"text": "read \"../IdentifiabilityODE.mpl\";\n\nsys := [\ndiff(EGF_EGFR(t), t) = reaction_1_k1*EGF_EGFR(t) - reaction_9_k1*EGF_EGFR(t) - reaction_1_k2*EGF_EGFR(t),\ndiff(EGFR(t), t) = -reaction_1_k1*EGF_EGFR(t) + reaction_1_k2*EGF_EGFR(t) - EGFR(t)*EGFR_turnover + EGFR_turnover*pro_EGFR(t),\ndiff(pEGFR(t), t) = -reaction_4_k1*pEGFR(t) + reaction_9_k1*EGF_EGFR(t) - pEGFR(t)*Akt(t)*reaction_2_k1 + reaction_3_k1*pEGFR_Akt(t) + pEGFR_Akt(t)*reaction_2_k2,\ndiff(pAkt_S6(t), t) = pAkt(t)*reaction_5_k1*S6(t) - reaction_6_k1*pAkt_S6(t) - pAkt_S6(t)*reaction_5_k2,\ndiff(pEGFR_Akt(t), t) = pEGFR(t)*Akt(t)*reaction_2_k1 - reaction_3_k1*pEGFR_Akt(t) - pEGFR_Akt(t)*reaction_2_k2,\ndiff(pAkt(t), t) = -pAkt(t)*reaction_7_k1 - pAkt(t)*reaction_5_k1*S6(t) + reaction_6_k1*pAkt_S6(t) + reaction_3_k1*pEGFR_Akt(t) + pAkt_S6(t)*reaction_5_k2,\ndiff(S6(t), t) = pS6(t)*reaction_8_k1 - pAkt(t)*reaction_5_k1*S6(t) + pAkt_S6(t)*reaction_5_k2,\ndiff(pS6(t), t) = -pS6(t)*reaction_8_k1 + reaction_6_k1*pAkt_S6(t),\ndiff(Akt(t), t) = pAkt(t)*reaction_7_k1 - pEGFR(t)*Akt(t)*reaction_2_k1 + pEGFR_Akt(t)*reaction_2_k2,\ny1(t) = pEGFR(t)*a1 + a1*pEGFR_Akt(t),\ny2(t) = a2*pAkt(t) + a2*pAkt_S6(t),\ny3(t) = pS6(t)*a3\n];\nCodeTools[CPUTime](IdentifiabilityODE(sys, GetParameters(sys)));", "meta": {"hexsha": "eacc745397f7208a5a13f7d54e4211dc6e2d25db", "size": 1240, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarking/SIAN/Akt-pathway.mpl", "max_stars_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_stars_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 42, "max_stars_repo_stars_event_min_datetime": "2021-07-14T14:30:56.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-23T16:49:40.000Z", "max_issues_repo_path": "benchmarking/SIAN/Akt-pathway.mpl", "max_issues_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_issues_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 25, "max_issues_repo_issues_event_min_datetime": "2021-07-15T21:15:31.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T19:50:55.000Z", "max_forks_repo_path": "benchmarking/SIAN/Akt-pathway.mpl", "max_forks_repo_name": "iliailmer/StructuralIdentifiability.jl", "max_forks_repo_head_hexsha": "29f1104e357f2f2942ff5477871856d80518a6ed", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2021-08-28T14:40:36.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-02T19:21:47.000Z", "avg_line_length": 72.9411764706, "max_line_length": 162, "alphanum_fraction": 0.7169354839, "num_tokens": 561, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.857768108626046, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.5116013317932897}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n(* prefix:\n gga_k_lgap_params *params;\n\n assert(p->params != NULL);\n params = (gga_k_lgap_params * ) (p->params);\n*)\n\n(* Equation (20) *)\nlgap_f0 := s -> 1 + params_a_kappa*(1-exp(-add(params_a_mu[i]*s^(i), i=1..3))):\nlgap_f := x -> lgap_f0(X2S*x):\n\nf := (rs, z, xt, xs0, xs1) ->\n gga_kinetic(lgap_f, rs, z, xs0, xs1):\n", "meta": {"hexsha": "e02083352df28994b70bf225265e229cd64785ef", "size": 580, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_lgap.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_lgap.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_k_lgap.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 25.2173913043, "max_line_length": 79, "alphanum_fraction": 0.6379310345, "num_tokens": 205, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8740772253241803, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.5114235933999357}} {"text": "(*\n Copyright (C) 2020 Susi Lehtola\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: mgga_exc *)\n(* prefix:\n mgga_c_r2scan_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_r2scan_params * )(p->params);\n*)\n\n$include \"mgga_c_rscan.mpl\"\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\n(* These come from pbe correlation *)\nparams_a_gamma := (1 - log(2))/Pi^2:\nmgamma := params_a_gamma:\n\n(* r2scan values *)\nparams_a_dp2 := 0.361:\n\n(* Equation (S6) *)\nr2scan_alpha := (z, xt, ts0, ts1) -> (t_total(z, ts0, ts1) - xt^2/8) / (K_FACTOR_C*t_total(z, 1, 1) + params_a_eta*xt^2/8):\n\n(* Equation (S26) *)\nr2scan_f_alpha_neg := a -> exp(-params_a_c1*a/(1 - a)):\nr2scan_f_alpha := (a, ff) -> my_piecewise5(\n a <= 0, r2scan_f_alpha_neg(m_min(a, 0)),\n a <= 2.5, rscan_f_alpha_small(m_min(a, 2.5), ff),\n rscan_f_alpha_large(m_max(a, 2.5))):\n\n(* Equation (S28) *)\nr2scan_d := z -> (opz_pow_n(z,5/3) + opz_pow_n(-z,5/3))/2:\n\n(* Equation (S33): beta(rs), this is the same as in gga_c_regtpss *)\nbeta_a := 0.066724550603149220:\nbeta_b := 0.1:\nbeta_c := 0.1778:\nmbeta := (rs) -> beta_a*(1 + beta_b*rs)/(1 + beta_c*rs):\n\n(* Equation (S30) *)\nw1 := (rs, z) -> exp(-f_pw(rs, z)/(mgamma*mphi(z)^3)) - 1:\n\n(* Equation (S27); note that the paper indexes starting from zero *)\nr2scan_dfc2 := ff -> add(i*ff[8-i], i=1..7):\n\n(* According to James Furness, this is LSDA0 - see also Equation (S25) *)\nr2scan_elsda0 := (rs, z) -> scan_eclda0(rs)*scan_Gc(z):\n(* while LSDA1 is just Perdew-Wang *)\nr2scan_elsda1 := (rs, z) -> f_pw(rs, z):\n\n(* Derivatives wrt rs *)\nr2scan_delsda0 := (rs, z) -> eval(diff(r2scan_elsda0(x1, x2), x1), [x1=rs, x2=z]):\nr2scan_delsda1 := (rs, z) -> eval(diff(r2scan_elsda1(x1, x2), x1), [x1=rs, x2=z]):\n\n(* Equation (S34) *)\nr2scan_dy := (rs, z, s) -> r2scan_dfc2(rscan_fc)/(27 * mgamma * r2scan_d(z) * mphi(z)^3 * w1(rs, z)) * (\n + 20*rs*(r2scan_delsda0(rs, z) - r2scan_delsda1(rs, z))\n - 45*params_a_eta*(r2scan_elsda0(rs, z) - r2scan_elsda1(rs, z))\n ) * s^2*exp(-s^4/params_a_dp2^4):\n\n(* Equation (S32) *)\nr2scan_y := (rs, z, t) -> mbeta(rs)*t^2/(mgamma*w1(rs, z)):\n\n(* Equation (S31) *)\nr2scan_g := (rs, z, s, t) -> 1/(1 + 4*(r2scan_y(rs, z, t) - r2scan_dy(rs, z, s)))^(1/4):\n\n(* Equation (S29) *)\nfH := (rs, z, s, t) -> mgamma*mphi(z)^3*log(1 + w1(rs, z)*(1 - r2scan_g(rs, z, s, t))):\n\n(* Now we can build ec1 from (S24) *)\nr2scan_ec1 := (rs, z, s, t) -> f_pw(rs, z) + fH(rs, z, s, t):\n\n(* Equation (S35)-(S41) are same as SCAN *)\nr2scan_ec0 := (rs, z, s) -> scan_e0(rs, z, s):\n\n(* and the functional itself *)\nr2scan_f := (rs, z, xt, xs0, xs1, ts0, ts1) ->\n r2scan_ec1(rs, z, X2S*2^(1/3)*xt, tt(rs, z, xt)) + r2scan_f_alpha(r2scan_alpha(z, xt, ts0, ts1), rscan_fc)*(\n + r2scan_ec0(rs, z, X2S*2^(1/3)*xt) - r2scan_ec1(rs, z, X2S*2^(1/3)*xt, tt(rs, z, xt))):\n\nf := (rs, z, xt, xs0, xs1, us0, us1, ts0, ts1) ->\n r2scan_f(rs, z, xt, xs0, xs1, ts0, ts1):\n", "meta": {"hexsha": "99c572e89c3ae5ae29075f19e4bf15b89f3c094d", "size": 3076, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_r2scan.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_r2scan.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/mgga_exc/mgga_c_r2scan.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 33.8021978022, "max_line_length": 123, "alphanum_fraction": 0.6115084525, "num_tokens": 1284, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8354835289107307, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5107995685602035}} {"text": "######################################################################\n# trees(A) is the set of trees on A\n# (Section sec-trees)\n\n`is_element/trees` := (A::set) -> proc(TT)\n local n,i,j,T,U,is_min,M;\n global reason;\n\n if not type(TT,set) then\n reason := [convert(procname,string),\"TT is not a set\",TT];\n return false;\n fi;\n\n n := nops(TT);\n is_min := table;\n for i from 1 to n do\n is_min[i] := true;\n T := TT[i];\n if not type(T,set) and T <> {} and T minus A = {} then\n reason := [convert(procname,string),\"T is not a nonempty subset of A\",T,A];\n return false;\n fi;\n od;\n\n # Now check nesting, and along the way, check which sets are minimal.\n for i from 1 to n do\n T := TT[i];\n for j from 1 to i-1 do\n U := TT[j];\n if T intersect U <> {} then\n if T minus U = {} then \n is_min[j] := false;\n else\n if U minus T = {} then\n is_min[i] := false;\n else\n reason := [convert(procname,string),\"T and U are neither disjoint nor nested\",T,U];\n return false;\n fi;\n fi;\n fi;\n od;\n od;\n\n # Check that the union of the minimal sets is A.\n M := NULL;\n for i from 1 to n do\n if is_min[i] then M := M,op(TT[i]); fi;\n od;\n if A minus {M} <> {} then\n reason := [convert(procname,string),\"The minimal sets do not cover A\",M,A];\n return false;\n fi;\n\n return true;\nend;\n\n######################################################################\n\n`is_equal/trees` := (A::set) -> (TT,UU) -> evalb(TT = UU);\n\n######################################################################\n\n`is_leq/trees` := (A::set) -> (TT,UU) -> evalb(TT minus UU = {});\n\n######################################################################\n\n`is_separated/trees` := (A::set) -> proc(TT)\n local a;\n return evalb({seq({a},a in A)} minus TT = {});\nend:\n\n######################################################################\n# Suppose we have a set A, a tree TT on A, a set T in TT, and a point a that\n# does not lie in A. We can then construct a new tree on A u {a} by attaching\n# a to the node T. There are two slightly different ways to do this. \n# We can either attach a to a new node just above T, or we can attach a to \n# the node T itself. (However, the second version is invalid if |T|=1).\n\n`attach_to_tree` := (A::set) -> proc(TT,T,a,above_) \n local above,CT,SCT,NCT;\n\n above := `if`(nargs > 3, above_, false);\n\n if not(`is_element/trees`(A)(TT) and\n member(T,TT) and\n not(member(a,A))) then\n return FAIL;\n fi;\n\n if nops(T)=1 and not(above) then \n return FAIL;\n fi;\n\n # Sets that contain (or are equal to) T\n CT := select(U -> (T minus U = {}),TT);\n\n SCT := CT minus {T};\n\n # Sets that do not contain T\n NCT := TT minus CT;\n\n if above then\n return {{a},op(NCT),T,op(map(U -> U union {a},CT))};\n else\n return {{a},op(NCT),op(map(U -> U union {a},CT))};\n fi;\nend;\n\n######################################################################\n\n`random_element/trees`:= (A::set) -> proc()\n local n,a,A1,T0,T1,T,above;\n\n # Degenerate cases for small A \n if A={} then return {}; fi;\n if nops(A)=1 then return {A}; fi;\n\n # If A is not too small, we write it as {a} union A1. Then we recursively\n # choose a random tree on A1, and attach a to it.\n\n n := nops(A);\n a := A[rand(1..n)()];\n A1 := A minus {a};\n if n = 2 then\n above := true;\n else\n above := evalb(rand(0..1)() = 1);\n fi;\n\n T0 := `random_element/trees`(A1)();\n T1 := select(U -> nops(U) > 1,T0);\n\n if above then\n T := T0[rand(1..nops(T0))()];\n else\n T := T1[rand(1..nops(T1))()];\n fi;\n\n T := `attach_to_tree`(A1)(T0,T,a,above);\n \n return T;\nend;\n\n######################################################################\n\n`big_sets/trees` := (TT) -> select(T -> nops(T) > 1,TT);\n\n######################################################################\n# Given a tree TT, this returns a table P indexed by the non-maximal\n# elements of TT, such that P[T] is the parent of T in TT.\n\n`parent_map` := (A::set) -> proc(TT) \n local TS,n,i,j,T,U,parent;\n\n # if not(`is_element/trees`(A)(TT)) then return FAIL; fi;\n\n TS := sort([op(TT)],(a,b) -> (nops(a) < nops(b)));\n n := nops(TS);\n parent := table();\n\n for i from 1 to n do\n T := TS[i];\n parent[T] := FAIL;\n for j from i+1 to n do\n U := TS[j];\n if T minus U = {} then\n parent[T] := U;\n break;\n fi;\n od;\n od;\n \n return eval(parent);\nend;\n\n######################################################################\n# Given a tree TT, this returns a table C indexed by the \n# elements of TT, such that C[T] is the set of children of T in\n# TT. In particular, C[T] = {} if T is minimal.\n\n`children_map` := (A::set) -> proc(TT)\n local parent,children,TT0,T,U;\n\n parent := eval(`parent_map`(A)(TT));\n\n children := table();\n for T in TT do \n children[T] := {};\n od:\n\n TT0 := TT minus {A};\n\n for T in TT0 do \n U := parent[T];\n if U <> FAIL then \n children[U] := {op(children[U]),T};\n fi;\n od; \n\n return eval(children);\nend;\n\n######################################################################\n\ncorolla := proc(A::set)\n local a;\n return {A,seq({a},a in A)};\nend:\n\n", "meta": {"hexsha": "e77070aeef9859a21fca0ccfb8ec5904931841e2", "size": 5009, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/trees.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/trees.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/trees.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 23.7393364929, "max_line_length": 89, "alphanum_fraction": 0.5016969455, "num_tokens": 1457, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7371581626286833, "lm_q2_score": 0.6926419767901475, "lm_q1q2_score": 0.5105866869701242}} {"text": "\n# Kinematik f\u00fcr parallelen Roboter\n# Einleitung\n# Berechnung der Jacobi-Matrix des parallelen Roboters\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# para -> Berechnung f\u00fcr eine parallelen Roboter\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# kinematics -> Berechnung der Kinematik\n# Autor\n# Tim Job (Studienarbeit bei Moritz Schappler), 2018-12\n# Moritz Schappler, moritz.schappler@imes.uni-hannover.de\n# (C) Institut f\u00fcr Mechatronische Systeme, Universit\u00e4t Hannover\n# Sources\n# [Abdellatif2007] Modellierung, Identifikation und robuste Regelung von Robotern mit parallelkinematischen Strukturen\n# [Job2018_S759] Job, T. (Studienarbeit; Betreuer Moritz Schappler): Implementierung einer strukturunabh\u00e4ngigen Dynamikmodellierung f\u00fcr parallelkinematische Maschinen (2018)\n# Initialization\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn \u00fcber Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\n#with(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools): # F\u00fcr Zeitausgabe\n;\n# Einstellungen f\u00fcr Code-Export: Optimierungsgrad (2=h\u00f6chster) und Aktivierung jedes Terms.\n#codegen_act := true: # noch nicht implementiert\ncodegen_debug := false:\ncodegen_opt := 2:\ncodeexport_invdyn := true:\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\": \nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../helper/proc_vec2skew\":\nread \"../transformation/proc_rotx\": \nread \"../transformation/proc_roty\": \nread \"../transformation/proc_rotz\": \nread \"../robot_codegen_definitions/robot_env_par\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", leg_name):\n# Definitionen f\u00fcr parallel Roboter laden\nread \"../robot_codegen_definitions/robot_env_par\":\nread sprintf(\"../codeexport/%s/tmp/para_definitions\", robot_name):\n# Lade \"robotics_repo_path\"-File mit Link zum \"imes-robotics-matlab\"-Repo\nread(\"../robotics_repo_path\"):\n# Lade die Funktionen aus dem \"imes-robotics-matlab\"-Repo\nread(sprintf(\"%s/transformation/maple/proc_eul%s2r\", robotics_repo_path, angleConvLeg)):\n# Kennung des Parametersatzes, f\u00fcr den die Dynamikfunktionen erstellt werden sollen. Muss im Repo und in der mpl-Datei auf 1 gelassen werden, da die folgende Zeile mit einem Skript verarbeitet wird.\ncodegen_dynpar := 2:\n# Link-Index, f\u00fcr den die Jacobi-Matrix aufgestellt wird. Hier wird angenommen, dass der Endeffektor das letzte Segment (=Link) ist. Die Jacobi-Matrix kann hier aber f\u00fcr beliebige Segmente aufgestellt werden. (0=Basis)\nLIJAC:=NL-1:\n# Ergebnisse der analytischen Jacobi-Matrix (Translatorisch)\nread sprintf(\"../codeexport/%s/tmp/jacobia_transl_%d_maple.m\", leg_name, LIJAC):\nread \"../robot_codegen_definitions/robot_env_par\":\nb_transl := b_transl:\n# Setze Parameter aus serieller Berechnung zu null.\npx, py, pz := 0, 0, 0:\nalphaxs_base, betays_base, gammazs_base := 0, 0, 0: \nrxs_base, rys_base, rzs_base := 0, 0, 0:\n# Merke Startzeit f\u00fcr Debug-Ausgabe\nst := time():\n# Additional Kinematics\n# Definition der Koppelpunkte f\u00fcr jedes Bein und der EE-Koordinaten/-Geschwindigkeiten/-Beschleunigungen\ntmp := Matrix(3,1,[xP[1],yP[1],zP[1]]):\nfor j to 3 do:\n if (xE_s(j) = 0) then\n tmp(j,1) := 0:\n end if:\n end do:\nfor i to N_LEGS do\n P||i := ;\n for j to 3 do:\n if (xE_s(j) = 0) then\n P||i(j,1) := 0:\n end if:\n end do:\n j := i+1:\n if i <> 1 then\n tmp := :\n end:\nend do:\nP_i := tmp:\n#rhs||i := parse(sprintf(\"eul%s2r\",angleConvLeg))(xE_s(4..6)).P||i+Matrix(xE_s(1..3,1)):\n# Jacobi Matrices (JB1/U1) + Derivates\n# Berechnung der Jacobi-Matrix der inversen Kinematik: Koppelpunktgeschwindigkeiten P -> Gelenkgeschwindigkeiten\n# Abdellatif2007 S.37 unten\n\ntransDOF := nops(indets(xE_s(1..3,1))):\nJB1 := (parse(sprintf(\"eul%s2r\",angleConvLeg))(frame_A_i(1..3,1)).b_transl)(1..transDOF,1..NQJ_parallel):\ntry:\n JB1inv := MatrixInverse(JB1):\ncatch:\n printf(\"%s. Jacobi-Matrix JB1 ist singul\u00e4r. Rang ist %d/%d. Abbruch der Berechnungen. Keine Berechnung der PKM-Dynamik m\u00f6glich.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), Rank(JB1), RowDimension(JB1)):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend try:\nfor i from 1 to 3-transDOF do\n JB1inv := ;\nend do:\nfor i from 1 to 3-transDOF do\n JB1 := ;\nend do:\nJB1inv := simplify2(JB1inv):\nJB1 := simplify2(JB1):\n\n# Berechnung der Matrix Ui: EE-Geschwindigkeiten -> Koppelpunktgeschwindigkeiten P. i steht f\u00fcr den Index des jeweiligen Beines\n# Abdellatif2007 S.21 (2.21)\nfor i to N_LEGS do\n r||i := P||i:\n if angleConv = X_Y_Z then\n r||i := vec2skew(rotx(xE_t(4)).roty(xE_t(5)).rotz(xE_t(6)).r||i):\n elif angleConv = Z_Y_X then\n r||i := vec2skew(rotz(xE_t(4)).roty(xE_t(5)).rotx(xE_t(6)).r||i):\n end:\n \n r||i := vec2skew(parse(sprintf(\"eul%s2r\",angleConvLeg))(xE_t(4..6)).P||i);\n ones := Matrix(3,3,shape=identity):\n U||i := simplify():\n U||i||D := simplify(diff~(U||i,t)): #dU berechnen\n #U||i||D := convert_t_s(U||i||D): #dU berechnen\n #U||i := convert_t_s(U||i):\nend do:\n\n# Ermittlung des Robotertyps, um sp\u00e4ter die Gesamt-Jacobi-Matrix reduzieren zu k\u00f6nnen\nrobotType := 1:\ncounter := 0:\nfor i from 4 to 6 do\n if xE_t(i) = 0 then\n counter := counter + 1:\n end if:\nend do:\nif counter = 2 then\n robotType := 2:\n for i from 1 to 3 do\n if not(xE_t(i+3) = 0) then\n rotPlanar := substring(angleConvLeg,i);\n end if:\n end do:\nelif counter = 3 then\n robotType := 3:\nend if:\nrotPlanar:\n\n# Erstelle die Matrizen f\u00fcr jedes Bein.\nU_i := Copy(U1):\nUD_i := Copy(U1D):\nROW := RowDimension(U1):\nCOLUMN := ColumnDimension(U1):\n# Substituiere die zeitabh\u00e4ngigen EE-Koordinaten mit den oben definierten zeitunabh\u00e4ngigen Koordinaten\nfor i to N_LEGS do\n for j to 3 do\n for k to 6 do\n for l from 4 to 6 do\n U||i(j,k) := subs(xE_t(l)=xE_s(l),U||i(j,k)):\n U||i||D(j,k) := subs({xED_t(l)=xED_s(l),xE_t(l)=xE_s(l)},U||i||D(j,k)):\n end do:\n end do:\n end do:\n U_i(1..ROW,1..COLUMN,i) := U||i:\n UD_i(1..ROW,1..COLUMN,i) := U||i||D:\nend do:\nprintf(\"[%s] Koppelpunkt-Jacobi-Matrizen (bezogen auf B) der Beinketten berechnet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Berechnung von JB1D\nJB1 := convert_s_t(JB1):\nJB1D := diff~(JB1,t):\nJB1D := simplify(JB1D):\nJB1D := simplify(convert_t_s(JB1D)):\nJB1 := simplify(convert_t_s(JB1)):\nprintf(\"[%s] Zeitableitung der Koppelpunkt-Jacobi-Matrizen (bezogen auf B) der Beinketten berechnet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nJB1inv := convert_s_t(JB1inv):\nJB1Dinv := diff~(JB1inv,t):\nJB1Dinv := convert_t_s(JB1Dinv):\nJB1inv := convert_t_s(JB1inv):\nprintf(\"[%s] Zeitableitung der inversen Koppelpunkt-Jacobi-Matrizen (bezogen auf B) der Beinketten berechnet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n\n\n# Berechne Jacobi-Matrizen f\u00fcr jedes Bein\n# Dupliziere alle berechneten Matrizen. i steht f\u00fcr den Index des jeweiligen Beines\n\nJBinv_i := Copy(JB1inv):\nJBD_i := Copy(JB1D):\nJBDinv_i := Copy(JB1Dinv):\nJB_i := Copy(JB1):\n#Jinv_DoThanh_i := Copy(Jinv_DoThanh||1):\nROW := RowDimension(JB1):\nCOLUMN := ColumnDimension(JB1):\nfor i to N_LEGS do\n JB||i||D := Copy(JB1D):\n JB||i||Dinv := Copy(JB1Dinv):\n JB||i||inv := Copy(JB1inv):\n JB||i := Copy(JB1):\nend do:\n\n# Substituiere in jeder Matrix den Winkel Alpha (Verdrehung in der Basis) und die Gelenkkoordinaten und -geschwindigkeiten\nfor k from 1 by 1 to N_LEGS do \n\tfor i to ROW do\n\t\tfor j to COLUMN do\n\t\t\tfor l to 3 do\n\t\t\t\tJB||k||D(i,j):=subs({frame_A_i(l,1)=frame_A_i(l,k)},JB||k||D(i,j)):\n\t\t\t\tJB||k||inv(j,i):=subs({frame_A_i(l,1)=frame_A_i(l,k)},JB||k||inv(j,i)):\n\t\t\t\tJB||k||Dinv(j,i):=subs({frame_A_i(l,1)=frame_A_i(l,k)},JB||k||Dinv(j,i)):\n\t\t\t\tJB||k(i,j):=subs({frame_A_i(l,1)=frame_A_i(l,k)},JB||k(i,j)):\n\t\t\tend do:\n \t\tfor m to NQJ_parallel do #alpha\n\t\t\t\t#tmp := VARS(m):\n \t\t\tn := m + (k-1)*NQJ_parallel:\n \t\t\tJB||k||D(i,j):=subs({qJD_i_s(m,1)=qJD_i_s(m,k),qJ_i_s(m,1)=qJ_i_s(m,k)},JB||k||D(i,j)):\n \t\t\tJB||k||inv(j,i):=subs({qJ_i_s(m,1)=qJ_i_s(m,k)},JB||k||inv(j,i)):\n \t\t\tJB||k||Dinv(j,i):=subs({qJD_i_s(m,1)=qJD_i_s(m,k),qJ_i_s(m,1)=qJ_i_s(m,k)},JB||k||Dinv(j,i)):\n \t\t\tJB||k(i,j):=subs({qJ_i_s(m,1)=qJ_i_s(m,k)},JB||k(i,j)):\n \t\tend do:\n \t\tend do:\n \tend do:\n \tJB_i(1..ROW,1..COLUMN,k) := JB||k:\n \tJBD_i(1..ROW,1..COLUMN,k) := JB||k||D:\n \tJBinv_i(1..COLUMN,1..ROW,k) := JB||k||inv:\n \tJBDinv_i(1..COLUMN,1..ROW,k) := JB||k||Dinv:\n \tfor i to N_LEGS do\n\t\tfor j to 6 do\n\t\t\t#Jinv_DoThanh||k(i,j):=subs({frame_A_i(l,1)=frame_A_i(l,k)},Jinv_DoThanh||k(i,j)):\n\t\tend do:\n\t\tfor m to NQJ_parallel do\n\t\t\tn := m + (k-1)*NQJ_parallel:\n\t\t\t#Jinv_DoThanh||k(i,j):=subs({qJ_i_s(m,1)=qJ_i_s(m,k)},Jinv_DoThanh||k(i,j)):\n\t\tend do:\n\tend do:\n\t#Jinv_DoThanh_i(1..COLUMN,1..ROW,k) := Jinv_DoThanh||k:\nend do:\nprintf(\"[%s] Jacobi-Matrizen der Beinketten berechnet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Gesamt Jacobi-Matrix\n# Berechnung der inv. Jacobi-Matrix: EE-Geschwindigkeiten -> aktive Gelenkgeschwindigkeiten\n# Abdellatif2007 S.21 (2.22)\nif type(AKTIV,scalar) then\n AKTIV := Matrix(N_LEGS,1,AKTIV);\nend if:\nTmp := simplify(JB1inv[AKTIV(1,1),1..3].U1):\nfor i from 2 to N_LEGS do\n Tmp := :\nend do:\nJinv := Tmp:\n\n# Reduziere die Gesamt-Jacobi-Matrix auf Freiheitsgrade des Roboters\nprintf(\"[%s] Starte Reduzierung der Gesamt-Jacobi-Matrix. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nIdentMat := IdentityMatrix(6,6):\nIdentMatMas := IdentityMatrix(6,6):\ncounter := 0:\nfor i to 3 do\n if not(xE_t(i) = 0) then\n if counter = 0 then\n counter := 1;\n JinvRed := Column(Jinv, i);\n pivotMat := IdentMat(i,..);\n else \n JinvRed := ;\n pivotMat := ;\n end if;\n end if:\nend do:\nif robotType = 2 then\n if rotPlanar = z then\n JinvRed := ;\n pivotMat := ;\n elif rotPlanar = y then\n JinvRed := ;\n pivotMat := ;\n elif rotPlanar = x then\n JinvRed := ;\n pivotMat := ;\n end if;\nelif robotType = 1 then\n if counter = 0 then\n JinvRed := Jinv(..,1..3);\n pivotMat := IdentMat(4..6,..);\n else\n JinvRed := ;\n pivotMat := ;\n end if;\nend if;\ncounter := 0:\nfor i from 1 to 6 do\n if not(xE_t(i) = 0) then\n if counter = 0 then\n counter := 1;\n pivotMatMas := IdentMat(i,..);\n else \n pivotMatMas := ;\n end if;\n end if:\nend do:\nJinv := JinvRed:\nJinv := simplify(Jinv):\n# Export\nprintf(\"[%s] Beginne mit Code-Export. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Maple-Export\nsave pivotMat, pivotMatMas, P_i, Jinv, JB_i, JBD_i, JBinv_i, JBDinv_i, U_i, UD_i, sprintf(\"../codeexport/%s/tmp/kinematics_%s_platform_maple.m\", robot_name, base_method_name):\nMatlabExport(Jinv, sprintf(\"../codeexport/%s/tmp/Jinv_para_matlab.m\", robot_name), codegen_opt):\n\n", "meta": {"hexsha": "33bc32da401ebaa70c3cb27fd41d4fe9e76aa693", "size": 11309, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_parallel/robot_para_rotmat_kinematics.mpl", "max_stars_repo_name": "SchapplM/robsynth-modelgen", "max_stars_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 2, "max_stars_repo_stars_event_min_datetime": "2020-05-25T07:31:46.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-15T09:54:50.000Z", "max_issues_repo_path": "robot_codegen_parallel/robot_para_rotmat_kinematics.mpl", "max_issues_repo_name": "SchapplM/robsynth-modelgen", "max_issues_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": "robot_codegen_parallel/robot_para_rotmat_kinematics.mpl", "max_forks_repo_name": "SchapplM/robsynth-modelgen", "max_forks_repo_head_hexsha": "33b345ae0dd6ec4aa15499ab3d43edbbded0bea5", "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": 37.5714285714, "max_line_length": 218, "alphanum_fraction": 0.6719427005, "num_tokens": 4169, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8397339676722393, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5102754046120639}} {"text": "`is_element/tree_Fbar_alt` := (N::posint) -> (A::set) -> (TT) -> proc(x)\n local TT1,P,children,T,UU,UU1;\n global reason;\n\n TT1 := select(T -> nops(T) > 1,TT);\n\n if not(type(x,table)) then\n reason := [convert(procname,string),\"x is not a table\",x]; \n return false;\n fi;\n\n P := sort(map(sort,map(op,{indices(x)})));\n\n if P <> TT1 then\n reason := [convert(procname,string),\"x is not indexed by the big sets in TT\",P,TT1]; \n return false;\n fi;\n\n children := children_map(A)(TT);\n \n for T in TT1 do\n UU := children[T];\n UU1 := select(U -> (nops(U) > 1),UU);\n \n if not(`is_element/D/Fbar`(N)(UU1,UU)(x[T])) then\n reason := [convert(procname,string),\"x[T] is not in D(C1,C)\",x[T],N,T,reason]; \n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_equal/tree_Fbar_alt` := (N::posint) -> (A::set) -> (TT) -> proc(x,y)\n local TT1,P,children,T,UU,UU1;\n\n TT1 := select(T -> nops(T) > 1,TT);\n\n children := children_map(A)(TT);\n \n for T in TT1 do\n UU := children[T];\n UU1 := select(U -> (nops(U) > 1),UU);\n \n if not(`is_equal/D/Fbar`(N)(UU1,UU)(x[T],y[T])) then\n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`random_element/tree_Fbar_alt` := (N::posint) -> (A::set) -> (TT) -> proc()\n local x,TT1,children,T,UU,UU1;\n\n x := table();\n\n TT1 := select(T -> nops(T) > 1,TT);\n children := children_map(A)(TT);\n\n for T in TT1 do\n UU := children[T];\n UU1 := select(U -> (nops(U) > 1),UU);\n x[T] := `random_element/D/Fbar`(N)(UU1,UU)();\n od;\n\n return eval(x);\nend;\n\n######################################################################\n# From tree_Fbar_alt to tree_Fbar\n\n`theta/tree_Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(ty)\n local TT1,children,z,t,y,C,n,pi,w,w0,a,m,T,U;\n\n TT1 := select(T -> nops(T) > 1,TT);\n TT1 := sort([op(TT1)],(U1,U2) -> (nops(U1) < nops(U2)));\n children := children_map(A)(TT);\n z := table();\n t := table();\n y := table();\n\n for T in TT1 do \n z[T] := table();\n t[T],y[T] := op(ty[T]);\n C := children[T];\n n := combine(simplify(sqrt(add(`norm_2/R`(N)(y[T][a])^2,a in C))));\n pi := table();\n for U in C do \n for a in U do \n pi[a] := U;\n od;\n od;\n w := table();\n w0 := [0$N];\n for a in T do \n w[a] := y[T][pi[a]];\n w0 := combine(simplify(w0 +~ w[a]));\n od;\n w0 := combine(simplify(w0 /~ nops(T)));\n for a in T do \n w[a] := combine(simplify(w[a] -~ w0));\n od;\n m := combine(simplify(sqrt(add(`norm_2/R`(N)(w[a])^2,a in T))));\n if is(m > 0) then\n for a in T do \n w[a] := combine(simplify((n/m) *~ w[a]));\n od;\n fi;\n for U in C do \n if nops(U) > 1 then\n for a in U do\n w[a] := combine(simplify(w[a] +~ t[T][U] *~ z[U][a]));\n od;\n fi;\n od;\n z[T] := eval(w);\n od:\n\n return eval(z);\nend;\n\n######################################################################\n# From tree_Fbar to tree_Fbar_alt\n\n`phi/tree_Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(x)\n local TT1,children,x1,t,y0,y,ty,C,C1,n,m,T,U,a;\n\n TT1 := select(T -> nops(T) > 1,TT);\n children := children_map(A)(TT);\n x1 := table();\n t := table();\n y0 := table();\n y := table();\n ty := table();\n\n for T in TT1 do \n x1[T] := `normalise_2/SW`(N)(T)(x[T]);\n t[T] := table();\n y0[T] := table();\n y[T] := table();\n C := children[T];\n C1 := select(U -> nops(U) > 1,C);\n n := 0;\n for U in C do \n y0[T][U] := simplify(expand(`sum/vector_functions`(N)(U)(x1[T]) /~ nops(U)));\n n := simplify(expand(n + `norm_2/R`(N)(y0[T][U])^2));\n if nops(U) > 1 then \n t[T][U] := simplify(expand(sqrt(add(`norm_2/R`(N)(x1[T][a] -~ y0[T][U])^2,a in U))));\n fi;\n od;\n if is(n > 0) then\n y[T] := `normalise_2/SW`(N)(C)(y0[T]);\n m := combine(simplify(expand(rationalize(sqrt(1 - add(t[T][U]^2,U in C1))))));\n for U in C do \n y[T][U] := combine(simplify(expand(m *~ y[T][U])));\n od;\n else\n for U in C do \n y[T][U] := [0$N];\n od;\n fi;\n ty[T] := [eval(t[T]),eval(y[T])];\n od:\n\n return eval(ty);\nend:\n", "meta": {"hexsha": "90f6d0e1441869cb103e3c9b4d714fef85b7657c", "size": 4000, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/fulton/tree_Fbar_alt.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/fulton/tree_Fbar_alt.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/fulton/tree_Fbar_alt.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 23.2558139535, "max_line_length": 90, "alphanum_fraction": 0.4925, "num_tokens": 1429, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581097540519, "lm_q2_score": 0.6406358411176238, "lm_q1q2_score": 0.5097271023843457}} {"text": "# gpgcd-bezout-test 2nd variation\n# GPGCD test routines for Bezout resultant\n# Akira Terui, Boming Chi, October 2018\n\nwith (LinearAlgebra);\nwith (PolynomialTools);\nwith (ArrayTools);\nwith (VectorCalculus);\n\n# The update function\nbezout_update := proc (Btemplate, J, degH, F0, G0, V0, F1, G1, V1, alpha)\nlocal i, j, dimF, dimG, dimV, dimVV1, F1poly, G1poly, B1, VV1, Q1, P1, R1, dim, BB, vlist, varlist, F0grad, F1grad, subslistB, subslistV, sublist, J1, Jrow, Jcol, A1, D1, DD1, DD2, VV2, F2, G2, V2, Normfg, st;\n # Jrow, Jcol, A1, R1, D1, f, k, B2, V2;\n\n # inputs:\n\n # B: Bezout matrix (template)\n # J: Jacobi matrix (template)\n # degH: degree of the approximate GCD\n # F0, G0: initial coefficient vector of F and G\n # F1, G1: current coefficient vector of F and G\n # V0: initial singular vector of the Bezout matrix\n # V1: current singular vector of the Bezout matrix\n # alpha: step width for an iteration\n\n # outputs:\n \n # F2, G2: new (updated) coefficient vector of F and G\n # V2: new (updated) singular vector of the Bezout matrix\n # Normfg: the distance between F1, G1 and F2, G2\n\n # find dimension of initial coefficient vector( F0, G0 and V0)\n\n dimF := Dimension(F0);\n dimG := Dimension(G0);\n dimV := Dimension(V0);\n userinfo(2, bezout_update, `[dimF, dimG, dimV] =`,\n print([dimF, dimG, dimV]));\n\n # construct polynomials from coefficient vector( F1 and G1)\n\n st := time();\n F1poly := FromCoefficientVector(F1, x);\n G1poly := FromCoefficientVector(G1, x);\n st := time() - st;\n userinfo(1, bezout_update, `stpoly=`, print(st));\n userinfo(2, bezout_update, `F1poly=`, print(F1poly));\n userinfo(2, bezout_update, `G1poly=`, print(G1poly));\n\n # construct substitution table for B1 & J1\n\n st := time();\n sublist := [seq(f[j] = F1[j+1], j=0..(dimF-1)), seq(g[j] = G1[j+1], j=0..(dimG-1)), seq(v[j] = V1[j], j=1..dimV)];\n st := time() - st;\n userinfo(1, bezout_update, `stsublist=`, print(st));\n userinfo(2, bezout_update, `sublist = `, print(sublist, whattype(sublist)));\n\n # construct Bezout Matrix of F1 and G1 -> B1\n\n st := time();\n B1 := BezMatrix(F1poly, G1poly, x);\n userinfo(2, bezout_update, `B1 =`, print(B1));\n st := time() - st;\n userinfo(1, bezout_update, `stB1=`, print(st));\n\n # construct vector of objective function\n\n st := time();\n VV1 := ;\n userinfo(2, bezout_update, `VV1 =`, print(VV1, whattype(VV1)));\n dimVV1 := dimF + dimG + dimV;\n st := time() - st;\n userinfo(1, bezout_update, `stVV1=`, print(st));\n\n # evaluate the constraint value -> Q1\n \n st := time();\n Q1 := B1 . V1[ 1 .. dimF-1 ];\n st := time() - st;\n userinfo(1, bezout_update, `stQ1=`, print(st));\n userinfo(2, bezout_update, `Q1 =`, print(Q1, whattype(Q1)));\n\n st := time();\n P1 := < (F1 - F0), (G1 - G0), Vector(dimV, datatype=double) >;\n st := time() - st;\n userinfo(1, bezout_update, `stP1=`, print(st));\n userinfo(2, bezout_update, `P1 =`, print(P1, whattype(P1)));\n\n # construct right-hand-side vector -> R1\n\n st := time();\n R1 := - ;\n st := time() - st;\n userinfo(1, bezout_update, `stR1=`, print(st));\n userinfo(2, bezout_update, `R1 =`, print(R1, whattype(R1)));\n\n\n\n # construct Jacobian matrix -> J1\n\n st := time();\n J1 := subs(sublist, J);\n st := time() - st;\n userinfo(1, bezout_update, `stJ1=`, print(st));\n userinfo(2, bezout_update, `J1 = `, print(J1, whattype(J1)));\n\n # construct coefficient matrix for the linear system -> A1\n\n st := time();\n Jrow, Jcol := Dimension(J);\n A1 := Matrix(Jrow+Jcol);\n for i from 1 to Jcol do A1(i,i):=1 end do:\n for i from 1 to Jrow do for j from 1 to Jcol do A1(i+Jcol,j):=J1(i,j) end do end do:\n for i from 1 to Jcol do for j from 1 to Jrow do A1(i,j+Jcol):=-J1(j,i) end do end do:\n st := time() - st;\n userinfo(1, bezout_update, `stA1=`, print(st));\n userinfo(2, bezout_update, `A1 =`, print(A1));\n\n # solve the linear system: A1 . D1 == R1\n\n st := time();\n D1 := LinearSolve(A1, R1);\n st := time() - st;\n userinfo(1, bezout_update, `stD1=`, print(st));\n userinfo(2, bezout_update, `D1 =`, print(D1));\n\n DD1 := D1[1..dimVV1];\n userinfo(2, bezout_update, `DD1 =`, print(DD1));\n\n DD2 := D1[1..(dimF+dimG)];\n userinfo(2, bezout_update, `DD2 =`, print(DD2));\n \n st := time();\n VV2 := (VV1 + alpha * DD1)[..,1];\n st := time() - st;\n userinfo(1, bezout_update, `stVV2=`, print(st));\n userinfo(2, bezout_update, `VV2 =`, print(VV2, whattype(VV2)));\n\n F2 := VV2[1..dimF];\n G2 := VV2[(dimF + 1)..(dimF + dimG)];\n V2 := VV2[(dimF + dimG + 1)..(dimVV1)]; \n Normfg := LinearAlgebra:-Norm(DD2,2);\n userinfo(2, bezout_update, `Normfg =`, print(Normfg));\n \n return F2, G2, V2, Normfg;\n \nend proc:\n\n# The initial function\nbezout_gpgcd := proc(F, G, x, degH, stopcriterion, alpha)\nlocal degF, degG, hh, Ftemplate, Gtemplate, Btemplate, V, BV, i, j, m, n, J, Fcoef, Gcoef, B, V0, VV0, v0, st, st0, st1, st2, ff, gg, DF, DG, DD, numofiteration, sublist, B0;\n\n # inputs: \n\n # F: the initial polynomial F\n # G: the initial polynomial G\n # degH: the degree of the approximate GCD\n # alpha: step width for an iteration\n\n # outputs:\n\n # ff, gg: the polynomials finally we get\n # hh: the approximate GCD finally we get\n # DF, DG: the perturbation of ff and gg\n # DD: the whole perturbation\n # numofiteration: number of iterations\n # B0: the Bezout Matrix of ff and gg\n\n # Construct the Bezout matrix of the initial polynomials\n\n st0 := time();\n degF := degree(F,x);\n degG := degree(G,x);\n # if degF < degG then degF, degG := degG, degF; F, G := G, F end if;\n userinfo(2, bezout_update, `degG =`, print(degG));\n Ftemplate := add(f[i]*x^i, i=0..degF);\n Gtemplate := add(g[i]*x^i, i=0..degG);\n userinfo(2, bezout_update, `Gtemplate =`, print(Gtemplate)); st := time();\n Btemplate := BezMatrix(Ftemplate, Gtemplate, x);\n\n # Construct the Jacobian matrix\n\n st := time() - st;\n userinfo(1, bezout_update, `stBtemplate=`, print(st));\n V := Vector(degF,symbol=v);\n BV := Vector(degF);\n for i from 1 to degF do BV[i] := add(Btemplate[i,j]*V[j], j=1..degF) end do;\n userinfo(2, bezout_update, `BV =`, print(BV));\n st := time();\n J := bezout_jacobian(degF, degG, Btemplate);\n st := time() - st;\n userinfo(1, bezout_update, `stJtemplate=`, print(st));\n userinfo(1, bezout_update, `J =`, print(J));\n \n # Construct coefficient vectors\n\n Fcoef := PolynomialTools:-CoefficientVector(F, x);\n Gcoef := PolynomialTools:-CoefficientVector(G, x);\n \n # Construct singular vector of the d-th from the right side\n\n B := BezMatrix(F, G, x);\n V0 := LinearAlgebra:-Transpose(LinearAlgebra:-SingularValues(B, output='Vt'));\n v0 := V0[..,-degH];\n userinfo(2, bezout_update, `v0 =`, print(v0));\n st1 := time() - st0;\n userinfo(1, bezout_update, `stbeforeiteration=`, print(st1));\n ff, gg, hh, DF, DG, DD, numofiteration, B0 := bezout_iteration(Btemplate, J, degF, degG, degH, Fcoef, Gcoef, v0, Fcoef, Gcoef, v0, stopcriterion, 1.0, 0);\n st2 := time() - st0;\n userinfo(1, bezout_update, `stwholeiteration=`, print(st2));\n\n return ff, gg, hh, DF, DG, DD, numofiteration, B0;\n # return B, J, V0, v0\nend proc:\n\n# The Jacobian Matrix\nbezout_jacobian := proc (m, n, Btemplate)\nlocal J, i, j;\n\n # inputs: \n # degF, degG\uff1a the degree of polynomials F and G\n\n J := Matrix(m, 2*m + n + 2);\n\n for i from 1 to m do for j from i+1 to m+1 do J(i,j):= -g[i-1]*v[j-1] end do end do;\n for i from 2 to m do for j from i+1 to m+1 do J(i,j):= J(i,j)+J(i-1,j-1) end do end do;\n\n for j from 1 to n do for i from j to n do J(i,j):= g[i]*v[j] end do end do;\n for j from n-1 by -1 to 1 do for i from n-1 by -1 to j do J(i,j):= J(i,j)+J(i+1,j+1) end do end do;\n \n for i from 1 to n+1 do for j from i+m+2 to m+n+2 do J(i,j):= f[i-1]*v[j-m-2] end do end do;\n for i from 2 to n+1 do for j from i+m+2 to m+n+2 do J(i,j):= J(i,j)+J(i-1,j-1) end do end do;\n\n for j from m+2 to 2*m+1 do for i from j-m-1 to m do J(i,j):= -f[i]*v[j-m-1] end do end do;\n for j from 2*m by -1 to m+2 do for i from m-1 by -1 to j-m-1 do J(i,j):= J(i,j)+J(i+1,j+1) end do end do;\n\n for j from m+n+3 to 2*m+n+2 do for i from 1 to m do J(i,j):= Btemplate(i,j-m-n-2) end do end do;\n return J\nend proc:\n\n# The iteration function\nbezout_iteration := proc (Btemplate, J, degF, degG, degH, F0, G0, V0, F1, G1, V1, stopcriterion, alpha, numofiteration)\nlocal FF, GG, VV, Normfg, B, ff, gg, f0, g0, DF, DG, DD, hh, st, numofiteration0, sublist;\n\n # inputs: \n\n # Btemplate: the template of the Bezout Matrix\n # J: the template of the Jacobian Matrix\n # degF, degG: the degree of the initial polynomials\n # degH: the degree of the approximate GCD\n # F0, G0: initial coefficient vector of F and G\n # F1, G1: current coefficient vector of F and G\n # V0: initial singular vector of the Bezout matrix\n # V1: current singular vector of the Bezout matrix\n # alpha: step width for an iteration\n # stopcriterion: the stop criterion\n # numofiteration: number of current iteration( initial number of iteration: 0)\n\n # outputs:\n\n # ff, gg: the polynomials finally we get\n # hh: the approximate GCD finally we get\n # DF, DG: the perturbation of ff and gg\n # DD: the whole perturbation\n # numofiteration: number of current iteration\n # B0: the Bezout Matrix of ff and gg\n\n FF, GG, VV, Normfg := bezout_update(Btemplate, J, degH, F0, G0, V0, F1, G1, V1, alpha);\n if Normfg < stopcriterion then\n userinfo(2, bezout_update, `FF=`, print(FF)); \n st := time();\n f0 := FromCoefficientVector(F0,x);\n g0 := FromCoefficientVector(G0,x);\n ff := FromCoefficientVector(FF,x);\n gg := FromCoefficientVector(GG,x);\n DF := Norm(PolynomialTools:-CoefficientVector(ff-f0,x),2);\n DG := Norm(PolynomialTools:-CoefficientVector(gg-g0,x),2);\n DD := sqrt(DF^2+DG^2);\n sublist := [seq(f[j] = FF[j+1], j=0..degF), seq(g[j] = GG[j+1], j=0..degG)];\n B := BezMatrix(ff, gg, x);\n userinfo(2, bezout_update, `B=`, print(B)); \n hh := bezout_gcd(B, max(degF, degG), degH);\n st := time() - st;\n userinfo(1, bezout_update, `stafteriteration=`, print(st)); \n return ff, gg, hh, DF, DG, DD, numofiteration, B; \n else\n numofiteration0 := numofiteration + 1;\n userinfo(2, bezout_update, `numofiteration0 =`, print(numofiteration0));\n return bezout_iteration(Btemplate, J, degF, degG, degH, F0, G0, V0, FF, GG, VV, stopcriterion, alpha, numofiteration0); end if\nend proc:\n\n # Find Bezout Matrix from coefficient vector\n\nBezMatrix := proc(F, G, x)\nlocal degF, degG, Bez, Bez1, i, j, fv, gv, gv0;\n\n # inputs: \n # F: the polynomial F\n # G: the polynomial G\n\n # outputs:\n\n # Bez: the Bezout Matrix of F and G\n\n degF := degree(F, x);\n degG := degree(G, x); \n fv := CoefficientVector(F, x);\n gv0 := CoefficientVector(G, x);\n gv := Vector(degF+1);\n for i from 1 to degG+1 do gv(i):=gv0(i) end do;\n\n # let the degree of F be the larger one\n\n #if degF < degG then F, G := G, F ; degF, degG := degG, degF end if;\n\n # construct the Bezout Matrix\n\n Bez := Matrix(degF);\n\n for j from 1 to degF do \n for i from 1 to j do\n Bez(i,j) := fv[i]*gv[j+1]-gv[i]*fv[j+1]\n end do\n end do;\n\n for i from 2 to degF-1 do\n for j from i to degF-1 do\n Bez(i,j) := Bez(i,j)+Bez(i-1,j+1)\n end do\n end do;\n\n for j from 1 to degF-1 do \n for i from j+1 to degF do\n Bez(i,j) := Bez(j,i)\n end do\n end do;\n\n return Bez\nend proc:\n\n# Find norm between two polynomials\n\nnormpoly := proc(f, g, x)\nlocal n;\n\n n := Norm(CoefficientVector(f-g, x),2);\n return n\nend proc:\n\n# Find GCD of polynomials from their Bezout Matrix\n\nbezout_gcd := proc (B, n, h)\nlocal p, l, u, b, i, j, X, k, y, CoeffVector, gcdB;\n\n # inputs: \n # B: the Bezout Matrix\n # n: the degree of the Bezout Matrix\n # k: the degree of GCD\n\n # outputs:\n\n # gcdB: the GCD calculated by the Bezout Matrix\n\n p,l,u:=LUDecomposition(B[..,h+1..n]);\n CoeffVector := Vector(h+1);\n CoeffVector(h+1) := 1;\n for k from 1 to h do\n b:=Transpose(p).B[..,k];\n y:=Vector(1..n);\n for i from 1 to n do y(i):=b(i)-add(l[i,j]*y[j],j=1..i-1) end do:\n X:=Vector(1..n-h);\n for i from 1 to n-h do X(n-h+1-i):=(y(n-h+1-i)-add(u[n-h+1-i,j]*X[j],j=n-h+2-i..n-h))/u(n-h+1-i,n-h+1-i) end do:\n CoeffVector(k) := X(1);\n end do:\n #p,l,u:=LUDecomposition(B[1..n-h,h+1..n]);\n #CoeffVector := Vector(h+1);\n #CoeffVector(h+1) := 1;\n #for k from 1 to h do\n # LinearSolve([p,l,u],B[..,k],method=LU);\n #end do:\n gcdB := FromCoefficientVector(CoeffVector,x);\n return gcdB\nend proc:\n\n", "meta": {"hexsha": "78ec49a47a6e2d0d0104fb49930721fa2b0b88c9", "size": 13148, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Maple/gpgcd-bezout.mpl", "max_stars_repo_name": "ct1counter/bezout-gpgcd", "max_stars_repo_head_hexsha": "e04acea5ae103ecef13b90ac4f6853003b011ef1", "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": "Maple/gpgcd-bezout.mpl", "max_issues_repo_name": "ct1counter/bezout-gpgcd", "max_issues_repo_head_hexsha": "e04acea5ae103ecef13b90ac4f6853003b011ef1", "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": "Maple/gpgcd-bezout.mpl", "max_forks_repo_name": "ct1counter/bezout-gpgcd", "max_forks_repo_head_hexsha": "e04acea5ae103ecef13b90ac4f6853003b011ef1", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2020-07-29T07:06:07.000Z", "max_forks_repo_forks_event_max_datetime": "2020-07-29T07:06:07.000Z", "avg_line_length": 34.1506493506, "max_line_length": 209, "alphanum_fraction": 0.5886826894, "num_tokens": 4561, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8031737963569014, "lm_q2_score": 0.6334102705979902, "lm_q1q2_score": 0.5087385316876399}} {"text": "with(RegularChains):\nwith(SemiAlgebraicSetTools):\nwith(ListTools):\n\nEvalCertification := module()\noption package;\n\nexport HolderInformationForPolynomial, \n\t HolderInformationForExponential, \n\t HolderInformationForRationalPolynomial, \n\t EstimateRootsAndCertifyEvaluations,\n\t ExpandToImaginaryAndReal;\n\n#ExpandToImaginaryAndReal,\nlocal SqrFreeFactorization,\n\t SingleEqualityToEstimate,\n\t BoxEqualitiesToEstimate,\n\t EstimateAndClassifySolutions,\n\t HolderDataToCertificationTolerance,\n\t EvaluateFunctionAtRoot;\n\n# Compute a square free factorization of a polynomial \n# along with multiplicities\nSqrFreeFactorization := proc(F) \n\tlocal FsqrFree, fa, CurrOutput, j, k; FsqrFree := sqrfree(F); \n\tFsqrFree := FsqrFree[2]; CurrOutput := []; \n\tfor j to nops(FsqrFree) do \n\t\tfa := ifelse(type(factor(FsqrFree[j][1]), `+`), [FsqrFree[j][1]], convert(factor(FsqrFree[j][1]), list)); \n\t\tfor k to nops(fa) do \n\t\t\tCurrOutput := [op(CurrOutput), [fa[k], FsqrFree[j][2]]]; \n\t\tend do; \n\tend do; \n\treturn CurrOutput; \nend proc;\n\n# Expand a list of polynomials to list with real and \n# imaginary parts separated\nExpandToImaginaryAndReal := proc(F) \n\tlocal vars, imaginary_variables, expanded_equations, i; \n\tvars := indets(F); \n\timaginary_variables := [seq(b[i], i = 1 .. nops(vars))]; \n\texpanded_equations := expand(subs([seq(vars[i] = Complex(vars[i], imaginary_variables[i]), i = 1 .. nops(vars))], F)); \n\treturn [[op(subs(I = 0, expanded_equations)), op([seq(coeff(expanded_equations[i], I), i = 1 .. nops(expanded_equations))])], [seq(vars[i]^2 + imaginary_variables[i]^2 - 1, i = 1 .. nops(vars))]]; \nend proc;\n\nSingleEqualityToEstimate := proc(equality) \n\treturn ifelse(type(rhs(equality), 'list'), 1/2*rhs(equality)[2] + 1/2*rhs(equality)[1], rhs(equality)); \nend proc;\n\nBoxEqualitiesToEstimate := proc(equalities) \n\tlocal reduced_equalities; \n\treduced_equalities := map(SingleEqualityToEstimate, equalities); \n\treturn Complex(reduced_equalities[1], reduced_equalities[2]); \nend proc;\n\n\n# Estimate the solution of univarite polynomial F and classify \n# by whether the imaginary norm is > 1, < 1, or = 1\nEstimateAndClassifySolutions := proc(F, epsilon) \n\t# INPUT: Squarefree polynomial F in format [polynomial,power], \n\t# estimation error epsilon\n\n\t# OUTPUT: [list_of_estimates_for_norm_1_solutions,list_of_estimates_for_norm_<_1_solutions,\n\t# \t\t list_of_estimates_for_norm_>_1_solutions]\n\tlocal actual_polynomial, system_with_imaginary_parts, equations, \n\t\t norms, R, norm_1_boxes, norm_1_values, norm_greater_boxes, \n\t\t norm_greater_values, norm_less_boxes, norm_less_values, i, \n\t\t norm_1_values_refined, norm_greater_values_refined, norm_less_values_refined; \n\tactual_polynomial := [F[1]]; \n\tsystem_with_imaginary_parts := ExpandToImaginaryAndReal(actual_polynomial); \n\tequations := system_with_imaginary_parts[1]; \n\tnorms := system_with_imaginary_parts[2]; \n\tR := PolynomialRing([seq(indets(norms)[i], i = 1 .. nops(indets(norms)))]); \n\tnorm_1_boxes := RealRootIsolate([op(equations)], [], [], [], R, 'abserr' = epsilon); \n\tnorm_1_values := map(BoxValues, norm_1_boxes, R); \n\tnorm_1_values_refined := map(BoxEqualitiesToEstimate, norm_1_values); \n\tnorm_1_values_refined := [seq(Record(\"value\"=norm_1_values_refined[i]), i = 1 .. nops(norm_1_values_refined))]; \n\treturn [op(norm_1_values_refined)]; \nend proc;\n\n# Compute local Lipschitz constant for univarite polynomial F at a point\n# given an estimate for that point and a bound on that estimate's accuracy\nHolderInformationForPolynomial := proc(F, PointEstimate, EstimateAccuracy)\n\t# INPUT: Univariate polynomial F, \n\t# an estimate PointEstimate of a point in F's domain (could be real or complex),\n\t# an upper bound EstimateAccuracy on the distance from PointEstimate to the\n\t# actual root\n\n\t# OUTPUT: A Record of the form [exponent,constant] such that\n\t# F is certifiably Holder with those values\n\tlocal deg, Derivatives, HolderConstant, HolderExponent, i; \n\tdeg := degree(F); \n\tif deg > 0 then\t\t\n\t\tDerivatives := Vector();\n\t\tDerivatives(1) := diff(F, indets(F)[1] $ 1);\n\t\tfor i from 2 to deg do\n\t \tDerivatives(i) := diff(Derivatives(i - 1), indets(F)[1] $ 1);\n\t\tend do;\n\t\tDerivatives := convert(Derivatives, list); \n\t\tHolderConstant := add((EstimateAccuracy)^(i - 1)*abs(subs(indets(F)[1] = PointEstimate, Derivatives[i]))/(i - 1)!, i = 1 .. deg);\n\telse HolderConstant := 0;\n\tend if;\n\tHolderExponent := 1; \n\treturn Record('exponent'=HolderExponent,'constant'=HolderConstant,'avoid_roots'=false,'max_degree'=deg-1);\nend proc;\n\n# Holder information for exponentials of the form x^alpha\nHolderInformationForExponential := proc(function_exponent) \n\tlocal output_function; \n\toutput_function := proc(F, PointEstimate, EstimateAccuracy)\n\t\treturn Record('exponent'=function_exponent,'constant'=1,'avoid_roots'=false,'max_degree'=1);\n\tend proc; \n\treturn output_function; \nend proc;\n\nHolderInformationForRationalPolynomial := proc(P, PointEstimate, EstimateAccuracy,domain_estimate:=false) \n # INPUT: Univariate rational polynomial of the form F/G\n\n # OUTPUT: A record of the form [exponent, constant] such that \n # F/G is certifiably Holder with those values\n\tlocal F, G, differential_numerator, numerator_constant, max_value, \n\t\t denominator_constant, min_value,FactorsAndMultiplicities,ClassifiedRoots,MINIMUM_NONZERO; \n\tif domain_estimate then\t\t\n\t\tFactorsAndMultiplicities := SqrFreeFactorization(denom(simplify(P)));\n\t\tClassifiedRoots := map(EstimateAndClassifySolutions, FactorsAndMultiplicities, EstimateAccuracy);\n\t\tClassifiedRoots := FlattenOnce(ClassifiedRoots);\n\t\treturn Record('avoid_roots'=[seq(ClassifiedRoots[i]:-value,i=1..nops(ClassifiedRoots))]);\n\tend if;\n\n\tMINIMUM_NONZERO := 3*10^(-10);\n\tF := numer(simplify(P)); \n\tG := denom(simplify(P)); \n\t\n\tif type(F, integer) then \n\t\tdifferential_numerator := -diff(G, indets(G)[1] $ 1)*F; \n\telif type(G, integer) then \n\t\tdifferential_numerator := G*diff(F, indets(F)[1] $ 1); \n\telse differential_numerator := -diff(G, indets(G)[1] $ 1)*F + G*diff(F, indets(F)[1] $ 1); \n\tend if; \t\n\tnumerator_constant := HolderInformationForPolynomial(differential_numerator, PointEstimate, EstimateAccuracy):-constant; \n\n\tif type(differential_numerator, integer) then \n\t\tmax_value := abs(differential_numerator) + numerator_constant*EstimateAccuracy; \n\telse max_value := abs(subs(indets(differential_numerator)[1] = PointEstimate, differential_numerator)) + numerator_constant*EstimateAccuracy; \n\tend if; \n\tif type(G, integer) then \n\t\tdenominator_constant := 1; \n\telse denominator_constant := HolderInformationForPolynomial(G^2, PointEstimate, EstimateAccuracy):-constant; \n\tend if; \n\tif evalb(numerator_constant = denominator_constant) then\n\t\treturn MINIMUM_NONZERO;\n\tend if;\n\tif type(G, integer) then\n\t\tmin_value := G^2 - denominator_constant*EstimateAccuracy; \n\telse min_value := abs(subs(indets(G)[1] = PointEstimate, G))^2 - denominator_constant*EstimateAccuracy; \n\tend if; \n\n\treturn Record('exponent'=1,'constant'=max_value/min_value,'max_degree'=1);\nend proc;\n\nHolderDataToCertificationTolerance := proc(HolderData, ErrorTolerance) \n\tlocal HolderConstant, HolderExponent,RoundedDigitsTolerance,RoundedCertNegativeExponent;\n\tHolderExponent := HolderData:-exponent;\n\tHolderConstant := HolderData:-constant;\n\tRoundedDigitsTolerance := max(-floor(log[10](ErrorTolerance^HolderData:-max_degree)),1) + 1;\n\tif evalf[RoundedDigitsTolerance](HolderConstant) <= 2*10^(-RoundedDigitsTolerance) then\n\t\treturn 0;\n\tend if;\n\tRoundedCertNegativeExponent := floor(-log[10](ErrorTolerance/HolderConstant)/HolderExponent);\n\treturn min(1/10^RoundedCertNegativeExponent, ErrorTolerance, 1);\nend proc;\n\nEvaluateFunctionAtRoot := proc(Function, Root, Precision)\n\tlocal SymbolicEval,DigitsBeforeDecimalPoint,DigitsAfterDecimalPoint;\n\tif type(Function,procedure) then\n\t\tSymbolicEval := Function(Root);\n\telse\n\t\tSymbolicEval := subs(indets(Function)[1]=Root,Function);\n\tend if;\n\tif evalb(SymbolicEval=0) then\n\t\treturn 0;\n\tend if;\n\t# Precision calculation: Figure out necessary number of digits\n\t# in front of the decimal point, figure out the same for after\n\t# the decimal point, then add them together.\n\tDigitsBeforeDecimalPoint := max(ceil(evalf[1](log[10](abs(SymbolicEval)))),1); \n\tDigitsAfterDecimalPoint := max(-floor(log[10](Precision)),0);\n\treturn evalf[max(1,DigitsBeforeDecimalPoint+DigitsAfterDecimalPoint+1)](SymbolicEval);\nend proc;\n\nEstimateRootsAndCertifyEvaluations := proc(PolynomialToSolve, FunctionsToEvaluate, HolderEstimationProcedure, ErrorTolerance, AbandonThreshold := 10^(-100)) \n\tlocal FactorsAndMultiplicities, Multiplicities, ClassifiedRoots, \n\t RootsWithoutAdditionalInformation, HolderBounds, HolderCertificationBounds, \n\t SharpenedRootTolerance, ClassifiedRootsWithMultiplicities, WorkingTolerance, ActualTolerance, \n\t i, j,arguments_for_output,root_information_for_output,evaluation_information_for_output,current_evals,\n\t minimum_gap,current_roots,holder_function,function_roots,estimated_gap_values;\n\tFactorsAndMultiplicities := SqrFreeFactorization(expand(PolynomialToSolve));\n\tMultiplicities := [seq(FactorsAndMultiplicities[i][2], i = 1 .. nops(FactorsAndMultiplicities))];\n\tSharpenedRootTolerance := 0;\n\t# We need to make sure all estimates are at least 1/10th sharper \n\t# than the desired number because rounding error in the last reported digit\n\t# could result in that amount of error\n\tActualTolerance := ErrorTolerance - (1/10)*ErrorTolerance;\n\tWorkingTolerance := max(1/10,ActualTolerance);\n\n\t# First Holder information step: Tightening the precision\n\t# to avoid places where the evaluation functions aren't \n\t# defined. We need that there are no undefined points\n\t# with 2*WorkingTolerance of the function to solve's\n\t# estimated roots \n\tfor i to nops(FunctionsToEvaluate) do\n\t\tminimum_gap := 0;\n\t\tif type(HolderEstimationProcedure,list) then \n\t\t\tholder_function := HolderEstimationProcedure[i];\n\t\telse\n\t\t\tholder_function := HolderEstimationProcedure;\n\t\tend if;\n\t\t# Note: Minimum gap often contains square roots and Maple doesn't \n\t\t# automatically compare expressions with abs in them symbolically.\n\t\t# For minimum_gap we can just square, for others we need to evaluate \n\t\t# and be careful with precision\n\t\twhile minimum_gap^2 <= (6*WorkingTolerance)^2 and WorkingTolerance > AbandonThreshold do\n\t\t\tif minimum_gap^2 > 0 then\n\t\t\t\tWorkingTolerance := min(WorkingTolerance/2,minimum_gap/(6*WorkingTolerance));\n\t\t\tend if;\n\t\t\tfunction_roots := holder_function(FunctionsToEvaluate[i],1.1,WorkingTolerance,true):-avoid_roots;\t\n\t\t\tif evalb(function_roots=false) then \n\t\t\t\tbreak;\n\t\t\tend if;\t\n\t\t\tClassifiedRoots := map(EstimateAndClassifySolutions, FactorsAndMultiplicities, WorkingTolerance);\n\t\t\tClassifiedRoots := FlattenOnce(ClassifiedRoots);\n\t\t\tcurrent_roots := [seq(ClassifiedRoots[j]:-value, j = 1 .. nops(ClassifiedRoots))];\n\t\t\testimated_gap_values := FlattenOnce([ seq([seq(abs(function_roots[j] - current_roots[k]),k=1..nops(current_roots))],j=1..nops(function_roots)) ]);\n\t\t\tminimum_gap := min(estimated_gap_values);\n\t\t\t# Need to round down to some rational representation \n\t\t\t# to keep things rational\n\t\t\tminimum_gap := convert(evalf[10](minimum_gap)-2*10^(-10),rational);\t\t\t\n\t\tend do \n\tend do;\n\n\t# At this point we've reduced to a good enough tolerance to \n\t# find local Holder information while dodging points not in the domains \n\t# of the functions to evaluate. Proceed to find that information, sharpen tolerance, \n\t# and give final results.\n\twhile SharpenedRootTolerance = 0 and AbandonThreshold < WorkingTolerance do \n\t\tClassifiedRoots := map(EstimateAndClassifySolutions, FactorsAndMultiplicities, WorkingTolerance);\n\t\tClassifiedRoots := FlattenOnce(ClassifiedRoots);\n\t\tRootsWithoutAdditionalInformation := [seq(ClassifiedRoots[i]:-value, i = 1 .. nops(ClassifiedRoots))];\n\t\tif type(HolderEstimationProcedure, list) then\n\t\t\tif nops(HolderEstimationProcedure) <> nops(FunctionsToEvaluate) then \n\t\t\t\terror \"Number of Holder estimation procedures is different than the number of functions to evaluate.\";\n\t\t\tend if;\n\t\t\tHolderBounds := [seq(map[2](HolderEstimationProcedure[i], FunctionsToEvaluate[i], RootsWithoutAdditionalInformation, 2*WorkingTolerance), i = 1 .. nops(FunctionsToEvaluate))];\n\t\telse\n\t\t\tHolderBounds := [seq(map[2](HolderEstimationProcedure, FunctionsToEvaluate[i], RootsWithoutAdditionalInformation, 2*WorkingTolerance), i = 1 .. nops(FunctionsToEvaluate))];\n\t\tend if;\n\t\tHolderBounds := FlattenOnce(HolderBounds);\n\t\tHolderCertificationBounds := map(HolderDataToCertificationTolerance, HolderBounds, min(ActualTolerance,WorkingTolerance/2));\n\t\tSharpenedRootTolerance := min(HolderCertificationBounds);\n\t\tWorkingTolerance := 1/10*WorkingTolerance;\n\tend do;\n\tif SharpenedRootTolerance = 0 then \n\t\terror \"Insufficient precision available to certify evaluations.\";\n\tend if;\n\tClassifiedRoots := map(EstimateAndClassifySolutions, FactorsAndMultiplicities, SharpenedRootTolerance);\n\tClassifiedRoots := FlattenOnce(ClassifiedRoots);\n\targuments_for_output := Record(\"polynomial\"=PolynomialToSolve,\"evaluated_functions\"=FunctionsToEvaluate,\"error_tolerance\"=ActualTolerance);\n\troot_information_for_output := Record(\"root_values\"=[seq(ClassifiedRoots[i]:-value, i=1..nops(ClassifiedRoots))], \"root_multiplicities\"=Multiplicities);\n\tevaluation_information_for_output := Record();\n\tfor i to nops(FunctionsToEvaluate) do\n\t\tcurrent_evals := Record(\"evaluations_functions_\"||i=map[2](EvaluateFunctionAtRoot,FunctionsToEvaluate[i],root_information_for_output:-root_values,ActualTolerance));\n\t\tevaluation_information_for_output := Record[evaluation_information_for_output,current_evals]();\n\tend do;\n\treturn Record[arguments_for_output,root_information_for_output,evaluation_information_for_output]();\nend proc;\n\nend module:", "meta": {"hexsha": "ff917ac0ef743898cae9167af4d730a2337c6523", "size": 13682, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "EvalCertification.mpl", "max_stars_repo_name": "P-Edwards/EvalCertification", "max_stars_repo_head_hexsha": "fd4dc2e1f4cedb64e24bf0a4477128fbe4143d6b", "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": "EvalCertification.mpl", "max_issues_repo_name": "P-Edwards/EvalCertification", "max_issues_repo_head_hexsha": "fd4dc2e1f4cedb64e24bf0a4477128fbe4143d6b", "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": "EvalCertification.mpl", "max_forks_repo_name": "P-Edwards/EvalCertification", "max_forks_repo_head_hexsha": "fd4dc2e1f4cedb64e24bf0a4477128fbe4143d6b", "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": 49.3935018051, "max_line_length": 198, "alphanum_fraction": 0.7680894606, "num_tokens": 3708, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8031737869342623, "lm_q2_score": 0.6334102567576901, "lm_q1q2_score": 0.5087385146030774}} {"text": "read(\"est_pi.mpl\"):\nprintf(\"\\nDoing calculation using loop:\\n\\n\"):\nest_pi(n):\nprintf(\"\\nDoing calculation using sum:\\n\\n\"):\nnative_est_pi(n):", "meta": {"hexsha": "26f4f9feb0194c30944dd61441a94ca6eda22dbb", "size": 141, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple_pi_dir/run.mpl", "max_stars_repo_name": "adrianjhpc/pi_examples", "max_stars_repo_head_hexsha": "ba624038a865e194b361d783a0e8647f2a9bb376", "max_stars_repo_licenses": ["CC0-1.0"], "max_stars_count": 19, "max_stars_repo_stars_event_min_datetime": "2016-04-13T11:39:40.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-29T19:22:06.000Z", "max_issues_repo_path": "maple_pi_dir/run.mpl", "max_issues_repo_name": "adrianjhpc/pi_examples", "max_issues_repo_head_hexsha": "ba624038a865e194b361d783a0e8647f2a9bb376", "max_issues_repo_licenses": ["CC0-1.0"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2016-05-24T11:28:57.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-14T16:22:17.000Z", "max_forks_repo_path": "maple_pi_dir/run.mpl", "max_forks_repo_name": "adrianjhpc/pi_examples", "max_forks_repo_head_hexsha": "ba624038a865e194b361d783a0e8647f2a9bb376", "max_forks_repo_licenses": ["CC0-1.0"], "max_forks_count": 7, "max_forks_repo_forks_event_min_datetime": "2017-10-12T15:08:45.000Z", "max_forks_repo_forks_event_max_datetime": "2022-02-25T09:35:21.000Z", "avg_line_length": 28.2, "max_line_length": 46, "alphanum_fraction": 0.7163120567, "num_tokens": 38, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7520125737597972, "lm_q2_score": 0.6757646075489391, "lm_q1q2_score": 0.508183481778657}} {"text": "`delta/F3` := (N::posint) -> (x) -> [\n `delta/F`(N)({1,2,3})(1,2)(x),\n `delta/F`(N)({1,2,3})(2,3)(x),\n `delta/F`(N)({1,2,3})(3,1)(x)\n];\n\n`Delta/F3` := (N::posint) -> (u) -> [u,u];\n\n`f_plus/F3` := (N::posint) -> proc(vw)\n local v,w;\n v,w := op(vw);\n return [-~ v,v,v -~ w];\nend:\n\n`f_minus/F3` := (N::posint) -> proc(vw)\n local v,w;\n v,w := op(vw);\n return [-~ v,v,w -~ v];\nend:\n\n`g_plus/F3` := (N::posint) -> proc(vw)\n local v,w;\n v,w := op(vw);\n return [v,-~ w, -~ v];\nend:\n\n`g_minus/F3` := (N::posint) -> proc(vw)\n local v,w;\n v,w := op(vw);\n return [v,-~ v, -~ w];\nend:\n\n######################################################################\n\n`is_element/X/F3` := (N::posint) -> proc(xyz)\n global reason;\n local tag,x,y,z;\n\n tag := \"is_element/X/F3\";\n\n if not(type(xyz,list) and nops(xyz) = 3) then\n reason := [tag,\"xyz is not a list of length 3\",xyz];\n return false;\n fi;\n\n x,y,z := op(xyz);\n if not(`is_element/R`(N)(x) and \n `is_element/R`(N)(y) and \n `is_element/R`(N)(z)) then\n reason := [tag,\"x, y and z are not vectors in R^N\",x,y,z];\n return false;\n fi;\n\n if (x -~ y = [0$N] or y -~ z = [0$N] or z -~ x = [0$N]) then\n reason := [tag,\"x, y and z are not distinct\",x,y,z];\n return false;\n fi;\n\n if x +~ y <> [0$N] then\n reason := [tag,\"x+y <> 0\",x,y];\n return false;\n fi;\n\n if `norm_2/R`(N)(x) <> 1 or `norm_2/R`(N)(y) <> 1 then\n reason := [tag,\"x and y are not normalised\",x,y];\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/X/F3` := (N::posint) -> (xyz0,xyz1) ->\n evalb(simplify(xyz0 -~ xyz1) = [[0$N]$3]);\n\n`is_leq/X/F3` := NULL;\n`list_elements/X/F3` := NULL;\n`count_elements/X/F3` := NULL;\n\n`random_element/X/F3` := (N::posint) -> proc()\n local x,y,z;\n x := `random_element/sphere`(N-1)();\n y := -~ x;\n z := `random_element/R`(N)();\n while z = x or z = y do \n z := `random_element/R`(N)();\n od;\n return [x,y,z];\nend:\n\n######################################################################\n\n`is_element/Y/F3` := (N::posint) -> proc(xyz)\n local tag,x,y,z;\n global reason;\n \n tag := \"is_element/Y/F3\";\n\n if not(`is_element/X/F3`(N)(xyz)) then\n reason := [tag,\"xyz in not in X\",xyz,reason];\n return false; \n fi;\n\n x,y,z := op(xyz);\n if `d_2/R`(N)(z,x) <> 1 and `d_2/R`(N)(z,y) <> 1 then\n reason := [tag,\"z is not at distance 1 from x or y\",x,y,z];\n return false; \n fi; \n\n return true;\nend:\n\n`is_equal/Y/F3` := (N::posint) -> (xyz0,xyz1) ->\n evalb(simplify(xyz0 -~ xyz1) = [[0$N]$3]);\n\n`is_leq/Y/F3` := NULL;\n`list_elements/Y/F3` := NULL;\n`count_elements/Y/F3` := NULL;\n\n`random_element/Y/F3` := (N::posint) -> proc()\n local x,y,w,z;\n x := `random_element/sphere`(N-1)();\n y := -~ x;\n w := `random_element/sphere`(N-1)();\n if rand(0..1)() = 0 then\n z := x +~ w;\n else \n z := y +~ w;\n fi;\n return [x,y,z];\nend:\n\n######################################################################\n\n`is_element/D_plus/F3` := (N::posint) -> proc(xyz)\n local tag,x,y,z;\n global reason;\n tag := \"is_element/D_plus/F3\";\n\n if not(`is_element/X/F3`(N)(xyz)) then\n reason := [tag,\"xyz in not in X\",xyz,reason];\n return false; \n fi;\n\n x,y,z := op(xyz);\n if `d_2/R`(N)(z,y) > 1 then\n reason := [tag,\"z is not at distance <= 1 from y\",x,y,z];\n return false; \n fi; \n\n return true;\nend:\n\n`is_equal/D_plus/F3` := (N::posint) -> (xyz0,xyz1) ->\n evalb(simplify(xyz0 -~ xyz1) = [[0$N]$3]);\n\n`is_leq/D_plus/F3` := NULL;\n`list_elements/D_plus/F3` := NULL;\n`count_elements/D_plus/F3` := NULL;\n\n`random_element/D_plus/F3` := (N::posint) -> proc()\n local x,y,w,z;\n x := `random_element/sphere`(N-1)();\n y := -~ x;\n\n if rand(0..5)() = 0 then\n z := [0$N];\n else \n w := `random_element/sphere`(N-1)() *~ rand(1..5)()/5;\n z := y +~ w;\n fi;\n return [x,y,z];\nend:\n\n######################################################################\n\n`is_element/D_minus/F3` := (N::posint) -> proc(xyz)\n local tag,x,y,z;\n global reason;\n\n tag := \"is_element/D_minus/F3\";\n\n if not(`is_element/X/F3`(N)(xyz)) then\n reason := [tag,\"xyz in not in X\",xyz,reason];\n return false; \n fi;\n\n x,y,z := op(xyz);\n if `d_2/R`(N)(z,x) > 1 then\n reason := [tag,\"z is not at distance <= 1 from x\",x,y,z];\n return false; \n fi; \n\n return true;\nend:\n\n`is_equal/D_minus/F3` := (N::posint) -> (xyz0,xyz1) ->\n evalb(simplify(xyz0 -~ xyz1) = [[0$N]$3]);\n\n`is_leq/D_minus/F3` := NULL;\n`list_elements/D_minus/F3` := NULL;\n`count_elements/D_minus/F3` := NULL;\n\n`random_element/D_minus/F3` := (N::posint) -> proc()\n local x,y,w,z;\n x := `random_element/sphere`(N-1)();\n y := -~ x;\n\n if rand(0..5)() = 0 then\n z := [0$N];\n else \n w := `random_element/sphere`(N-1)() *~ rand(1..5)()/5;\n z := x +~ w;\n fi;\n return [x,y,z];\nend:\n\n######################################################################\n\n`is_element/D_zero/F3` := (N::posint) -> proc(xyz)\n local tag,x,y,z;\n global reason;\n \n tag := \"is_element/D_zero/F3\";\n\n if not(`is_element/X/F3`(N)(xyz)) then\n reason := [tag,\"xyz in not in X\",xyz,reason];\n return false; \n fi;\n\n x,y,z := op(xyz);\n if `d_2/R`(N)(z,x)^2 < 1 or `d_2/R`(N)(z,y)^2 < 1 then\n reason := [tag,\"z is not at distance >= 1 from x and y\",x,y,z];\n return false; \n fi; \n\n return true;\nend:\n\n`is_equal/D_zero/F3` := (N::posint) -> (xyz0,xyz1) ->\n evalb(simplify(xyz0 -~ xyz1) = [[0$N]$3]);\n\n`is_leq/D_zero/F3` := NULL;\n`list_elements/D_zero/F3` := NULL;\n`count_elements/D_zero/F3` := NULL;\n\n`random_element/D_zero/F3` := (N::posint) -> proc()\n local x,y,w,z,r,i;\n x := `random_element/sphere`(N-1)();\n y := -~ x;\n\n z := x;\n r := 0;\n while r < 1 do\n if rand(0..5)() = 0 then\n w := `random_element/sphere`(N-1)();\n if rand(0..1)() = 0 then\n z := x +~ w;\n else\n z := y +~ w;\n fi;\n else\n z := `random_element/sphere`(N-1)(100) *~ (rand(1..300)()/100);\n fi;\n r := min(add((x[i]-z[i])^2,i=1..N),add((y[i]-z[i])^2,i=1..N));\n od:\n\n return [x,y,z];\nend:\n\n######################################################################\n\n`q_plus/F3` := (N::posint) -> proc(xyz)\n local x,y,z;\n x,y,z := op(xyz);\n return y +~ (z -~ y) /~ `norm_2/R`(N)(z -~ y); \nend:\n\n######################################################################\n\n`q_minus/F3` := (N::posint) -> proc(xyz)\n local x,y,z;\n x,y,z := op(xyz);\n return y +~ (z -~ x) /~ `norm_2/R`(N)(z -~ x); \nend:\n\n######################################################################\n\n`q_zero/F3` := (N::posint) -> proc(xyz)\n local x,y,z;\n x,y,z := op(xyz);\n if z = [0$N] then\n return [0$N];\n else\n return (2*`dot/R`(N)(y,z)/`norm_2/R`(N)(z)^2) *~ z;\n fi;\nend:\n\n######################################################################\n\n`q/F3` := (N::posint) -> proc(xyz)\n local x,y,z;\n x,y,z := op(xyz);\n if `is_element/D_plus/F3`(N)(xyz) then\n return `q_plus/F3`(N)(xyz);\n elif `is_element/D_minus/F3`(N)(xyz) then\n return `q_minus/F3`(N)(xyz);\n else\n return `q_zero/F3`(N)(xyz);\n fi;\nend:\n\n`r/F3` := (N::posint) -> proc(xyz)\n local x,y,z,x0,y0,z0,n0;\n x,y,z := op(xyz);\n\n x0 := (x -~ y)/~2;\n n0 := `norm_2/R`(N)(x0);\n x0 := x0 /~ n0;\n y0 := -~ x0;\n z0 := (z -~ ((x +~ y)/~2))/~ n0;\n return [x0,y0,`q/F3`(N)([x0,y0,z0])];\nend:\n\n", "meta": {"hexsha": "79287209fb23a7157f1d8c8ed8197c37cbc5007c", "size": 6997, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/F3.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/F3.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/F3.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 21.5956790123, "max_line_length": 70, "alphanum_fraction": 0.4883521509, "num_tokens": 2588, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7931059511841119, "lm_q2_score": 0.640635854839898, "lm_q1q2_score": 0.508092109015444}} {"text": "######################################################################\n\n`eta/stasheff_star` := proc(A::set)\n if nops(A) <> 1 then return FAIL; fi;\n return [[op(A)],table([A = 1])];\nend;\n\n`gamma/stasheff_star` := (A::set,B::set) -> (p) -> proc(U,V)\n local R,S,T,r,s,t,b,n,JJ,J,pJ,J1,i,j,k;\n\n S,s := op(U);\n R := table();\n r := table();\n for b in B do \n R[b],r[b] := op(V[b]);\n od;\n\n T := [seq(op(R[b]),b in S)];\n\n t := table();\n\n n := nops(T);\n JJ := {seq(seq({seq(T[k],k=i..j)},j=i..n),i=1..n)};\n for J in JJ do\n pJ := map(j -> p[j],J);\n J1 := select(j -> member(p[j],pJ),A);\n if J = J1 then\n t[J] := s[pJ];\n elif nops(pJ) = 1 then\n t[J] := r[op(pJ)][J];\n else\n t[J] := 0;\n fi;\n od:\n\n return [T,eval(t)];\nend;\n\n", "meta": {"hexsha": "3014544eb9976aaa2fa1650c0aff4915a7d0731b", "size": 724, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/stasheff_star.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/stasheff_star.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/stasheff_star.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 18.5641025641, "max_line_length": 70, "alphanum_fraction": 0.4240331492, "num_tokens": 274, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8006920020959544, "lm_q2_score": 0.6334102636778401, "lm_q1q2_score": 0.5071665321723362}} {"text": " # a function returning (i + j) * -998\n func $foo (\n# var %i xxx,\n var %i i32,\n var %j i32,\n var %k i32) i32 { \n return (\n select i32 (\n dread i32 %i, \n dread i32 %j, \n dread i32 %k))}\n\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "12acd02e4a9d9cc1617d25cfab42c5ff660b8eb0", "size": 314, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0078-mapleall-irbuild-edge-ternary/Main.mpl", "max_stars_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_stars_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 796, "max_stars_repo_stars_event_min_datetime": "2019-08-30T16:20:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-25T14:45:06.000Z", "max_issues_repo_path": "test/testsuite/irbuild_test/I0078-mapleall-irbuild-edge-ternary/Main.mpl", "max_issues_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_issues_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 16, "max_issues_repo_issues_event_min_datetime": "2019-08-30T18:04:08.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-19T05:02:58.000Z", "max_forks_repo_path": "test/testsuite/irbuild_test/I0078-mapleall-irbuild-edge-ternary/Main.mpl", "max_forks_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_forks_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 326, "max_forks_repo_forks_event_min_datetime": "2019-08-30T16:11:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-26T12:31:17.000Z", "avg_line_length": 19.625, "max_line_length": 43, "alphanum_fraction": 0.5477707006, "num_tokens": 120, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6992544335934766, "lm_q2_score": 0.7248702821204019, "lm_q1q2_score": 0.5068687585528453}} {"text": " ReparamDetermined := proc(lo :: LO(name, anything), kb::t_kb)\n local h;\n h := op(1,lo);\n LO(h,\n evalindets(op(2,lo),\n 'And'('specfunc({Int,int})',\n 'anyfunc'(anything, 'name=anything')),\n g -> `if`(determined(op(1,g),h), reparam(g,h,kb), g)))\n end proc;\n\n determined := proc(e, h :: name)\n local i;\n for i in indets(e, 'specfunc({Int,int})') do\n if hastype(IntegrationTools:-GetIntegrand(i),\n 'applyintegrand'('identical'(h),\n 'dependent'(IntegrationTools:-GetVariable(i)))) then\n return false\n end if\n end do;\n return true\n end proc;\n\n #Beginning of Carl's code devoted to disintegration and the reparametrization (aka change\n #of variables) of integrals and sums.\n\n #Finds the innermost Ints or Sums in an expression, that is, those which\n #don't contain further Ints or Sums\n innermostIntSum:= proc(e::anything, $)::set(specfunc({Int,Sum}));\n select(IS-> nops(indets(IS, specfunc({Int,Sum}))) = 1, indets(e, specfunc({Int,Sum})))\n end proc;\n\n #my substitute for IntegrationTools:-Change\n ChangeVarInt:= proc(J::specfunc(Int), target::algebraic, $)\n local\n newJ, #What J will become.\n x::name:= op([2,1], J),\n u::name:= gensym(x), #new variable of integration\n s, #What x will become\n F #Boolean: flip integral?\n ;\n s:= {solve({u = target}, {x})};\n if nops(s) = 0 then\n userinfo(1, 'reparam', \"Can't solve substitution target.\");\n return J\n end if;\n if nops(s) > 1 then\n userinfo(1, 'reparam', \"Case of multi-branched substitution not handled.\");\n return J\n end if;\n s:= s[];\n\n newJ:= Int(\n eval(implicitdiff(u = target, x, u)*op(1,J), s),\n u=\n limit(target, x= op([2,2,1], J), right).. #lower limit\n limit(target, x= op([2,2,2], J), left), #upper limit\n op(3.., J) #optional Int args (unlikely to be used)\n );\n\n #If lower limit > upper limit, then flip limits of integration.\n F:= is(op([2,2,1], newJ) > op([2,2,2], newJ));\n if F::truefalse then\n if F then\n userinfo(2, reparam, \"Switching limits:\", op([2,2], newJ));\n newJ:= IntegrationTools:-Flip(newJ)\n end if\n else #If inequality can't be decided, then don't reverse.\n userinfo(1, reparam, \"Can't order new limits:\", op([2,2], newJ))\n end if;\n newJ\n end proc;\n\n #main procedure for int/sum reparamterizations\n reparam:= proc(e::algebraic, h::symbol, ctx::{list,t_kb}:= [], $)\n local\n J:= innermostIntSum(e), #the integral or sum\n newJ, #What J will become possible subs target(s)\n oldarg:=\n map2(op, 2, indets(e, specfunc(applyintegrand))),\n kb := build_kb(ctx,\"reparam\"),\n newarg, Jbnds, del\n ;\n if not(oldargs::{algebraic, set(algebraic), list(algebraic)}) then\n userinfo(2, 'procname', \"Unexpected arguements to applyintegrand\");\n return e;\n end if;\n if nops(J) = 0 then\n userinfo(2, 'procname', \"No sum or integral found.\");\n return e\n end if;\n if nops(J) > 1 then\n userinfo(1, 'procname', \"Case of multiple innermost Int or Sums not yet handled.\");\n return e\n end if;\n J:= J[];\n if J::specfunc(Sum) then\n userinfo(1, 'procname', \"Sums not yet handled.\");\n return e\n end if;\n if hastype(op(1,J), t_pw_or_part) then\n userinfo(1, 'procname', \"Reparam of piecewise body not yet handled.\");\n return e;\n end if;\n if nops(oldarg) <> 1 then\n userinfo(1, 'procname', \"More than 1 reparam possible:\", oldarg);\n return e\n end if;\n oldarg:= oldarg[]; #Extract the reparam target.\n\n Jbnds := op([2,2], J);\n del := simplify_assuming(op(2,Jbnds)-op(1,Jbnds), kb);\n if del in {-1,1} then\n userinfo(2, 'procname', \"No need for a reparameterization (bound diff is 1).\");\n return e;\n end if;\n if has(Jbnds, infinity) then\n userinfo(2, 'procname', \"Reparam of infinity bounds probably won't work.\");\n return e;\n end if;\n\n # if the arg to applyintegrand is not a variable or a datum or an index\n # into an array\n if oldarg::And(Not({symbol, function, indexed, list})) then\n newarg := oldarg;\n # if the bounds don't contain infinity, do not have a difference of 1\n # and contain a product of that variable\n elif oldarg::symbol and\n op(1,J)::`*` and\n select(type, [op(op(1,J))], identical(oldarg))<>[]\n then\n newarg := oldarg/del;\n else\n userinfo(2, 'procname', \"No need for a reparameterization.\");\n return e\n end if;\n\n #Make the change of vars.\n newJ:= kb_assuming_mb(ChangeVarInt@op, [J, newarg], kb, _->FAIL);\n\n if newJ = 0 or not(newJ::specfunc(Int)) or newJ=FAIL then\n userinfo(\n 1, 'procname',\n printf(\n \"Invalid reparam, likely due to improper handling of an infinity issue.\\n\"\n \"u subs:%a\",\n #Reformat the ChangeVarInt command for readability.\n subs(\n x= ':-x',\n 'ChangeVarInt'(\n subsindets(\n J,\n specfunc(applyintegrand),\n f-> ':-h'(op(2,f)))),\n newarg)));\n return e;\n end if;\n subs(J= newJ, e)\n end proc;\n", "meta": {"hexsha": "75a322c09a8819930698e6f3426210416e7feeac", "size": 5287, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Reparam.mpl", "max_stars_repo_name": "vmchale/hakaru", "max_stars_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 327, "max_stars_repo_stars_event_min_datetime": "2015-01-03T08:56:51.000Z", "max_stars_repo_stars_event_max_datetime": "2022-01-24T12:12:06.000Z", "max_issues_repo_path": "maple/NewSLO/Reparam.mpl", "max_issues_repo_name": "vmchale/hakaru", "max_issues_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 155, "max_issues_repo_issues_event_min_datetime": "2015-05-05T17:57:22.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T15:43:39.000Z", "max_forks_repo_path": "maple/NewSLO/Reparam.mpl", "max_forks_repo_name": "vmchale/hakaru", "max_forks_repo_head_hexsha": "78922e13876e449d6812a55a11bf84c8eb0af4d6", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 38, "max_forks_repo_forks_event_min_datetime": "2015-01-23T16:25:37.000Z", "max_forks_repo_forks_event_max_datetime": "2021-03-14T15:09:12.000Z", "avg_line_length": 33.251572327, "max_line_length": 91, "alphanum_fraction": 0.5783998487, "num_tokens": 1583, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8289387914176258, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.5067982340369768}} {"text": "InvClassify:=module()\n option package;\n export doClassify, # \u8fdb\u884c\u5206\u7c7b\n InvSol, # \u89e3\u5bf9\u8c61\n RepSol; # \u4ee3\u8868\u5143\u5bf9\u8c61\n local ModuleLoad;\n\n$include \"headers.mpl\"\n\n$include \"InvSol.mpl\"\n$include \"RepSol.mpl\"\n\n$include \"Basic.mpl\"\n$include \"Classifyer.mpl\"\n$include \"Combine.mpl\"\n$include \"Condition.mpl\"\n$include \"Fetch.mpl\"\n$include \"InvOrder.mpl\"\n$include \"Interaction.mpl\"\n$include \"InvSimplify.mpl\"\n$include \"Logout.mpl\"\n$include \"Utils.mpl\"\n\n ModuleLoad:=proc()\n PDETools:-declare(quiet):\n end proc:\n ModuleLoad();\n\n # \u8fdb\u884c\u5206\u7c7b\n doClassify:=proc(vv::list)\n local As,A,eqs,sols,reps;\n As,A,eqs:=getTransMatAndPDE(vv);\n classify(A,As,eqs);\n sols:=getSols();\n reps:=buildReps(sols);\n return reps;\n end proc:\n\nend module:", "meta": {"hexsha": "fa4c96fe8f32f3377c8b58f9849fc63208e8f18b", "size": 866, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "old/InvClassify.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-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": "old/InvClassify.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "old/InvClassify.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.2051282051, "max_line_length": 51, "alphanum_fraction": 0.5750577367, "num_tokens": 256, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8031737963569016, "lm_q2_score": 0.6297745935070806, "lm_q1q2_score": 0.5058184511162065}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: work_mgga_c *)\n(* prefix:\n mgga_c_m05_params *params;\n\n assert(p->params != NULL);\n params = (mgga_c_m05_params * )(p->params);\n*)\n\n$define lda_c_pw_params\n$define lda_c_pw_modified_params\n$include \"lda_c_pw.mpl\"\n\n$include \"b97.mpl\"\n\nm05_comp := (rs, z, spin, xs, ts) ->\n + lda_stoll_par(f_pw, rs, z, 1)\n * b97_g(params_a_gamma_ss, params_a_css, xs)\n * Fermi_D(xs, ts):\n\n(* The parallel and perpendicular components of the energy *)\nm05_fpar := (rs, z, xs0, xs1, ts0, ts1) ->\n + m05_comp(rs, z, 1, xs0, ts0)\n + m05_comp(rs, -z, -1, xs1, ts1):\n\nm05_fperp := (rs, z, xs0, xs1, ts0, ts1) ->\n + lda_stoll_perp(f_pw, rs, z)\n * b97_g(params_a_gamma_ab, params_a_cab, sqrt(xs0^2 + xs1^2)):\n\nf_m05 := (rs, z, xs0, xs1, ts0, ts1) ->\n + m05_fpar (rs, z, xs0, xs1, ts0, ts1)\n + m05_fperp(rs, z, xs0, xs1, ts0, ts1):\n\nf := (rs, z, xt, xs0, xs1, ts0, ts1, us0, us1) ->\n f_m05(rs, z, xs0, xs1, ts0, ts1):\n\n", "meta": {"hexsha": "c4e1de63b64c3a5771eba2b43340d963f29e29e6", "size": 1159, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-4.2.3/maple/mgga_c_m05.mpl", "max_stars_repo_name": "rdietric/lsms", "max_stars_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-4.2.3/maple/mgga_c_m05.mpl", "max_issues_repo_name": "rdietric/lsms", "max_issues_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-4.2.3/maple/mgga_c_m05.mpl", "max_forks_repo_name": "rdietric/lsms", "max_forks_repo_head_hexsha": "8d0d5f01186abf9a1cc54db3f97f9934b422cf92", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 26.3409090909, "max_line_length": 68, "alphanum_fraction": 0.636755824, "num_tokens": 462, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8479677737461008, "lm_q2_score": 0.5964331462646255, "lm_q1q2_score": 0.505756087226397}} {"text": "\n #Disintegration *\n #---------------*\n #Abbreviations:\n # wrt = \"with respect to\".\n # wrt var = \"a variable wrt which disintegration is performed\". There may be\n # more than one of these, in which case they are passed (in the 2nd arg)\n # as Pairs, possibly nested.\n # wrt-var type: Each wrt var may be continuous (Lebesgue), discrete (Counting),\n # point evaluation (Dirac), and there may be other types added later.\n disint:= module()\n export ModuleApply, `do`;\n local\n #Dispatch table for wrt-var types. For each, there is a \"cond constructor\",\n #a \"disintegrator\", and a \"disintegrator_arg_extractor\". The cond constructor\n #builds the associated relation in the master piecewise; the disintegrator\n #does the differentiation or whatever operator is analogous to differentiation\n #for that type after the measure has been `improve`d; and the\n #disintegrator_arg_extractor builds the 2nd arg to the disintegrator from\n #the t_disint_var passed in the 2nd arg of disint.\n #\n #APIs:\n # Indices:\n # Must be the op(0, ...) of the expression passed with the\n # wrt var.\n # cond_constructor: (algebraic,name)-> boolean (most likely, a relation)\n # disintegrator: (algebraic, {name, name=anything})-> algebraic\n # disintegrator_arg_extractor:\n # (`&M`(name, t_wrt_var_type))-> {name, name= anything}\n Wrt_var_types::static:= table([\n Lebesgue= Record(\n cond_constructor= `<=`,\n disintegrator= diff,\n disintegrator_arg_extractor= (A-> op(1,A)),\n disintegrator_type_extractor= [ (ll-> kb-> KB:-genLebesgue(op(1,ll), op(op(2,ll)), kb)), AlmostEveryReal ]\n ),\n Counting= Record(\n cond_constructor= `<=`,\n disintegrator= LREtools[delta],\n disintegrator_arg_extractor= (A-> op(1,A)),\n disintegrator_type_extractor= [ (ll-> kb-> KB:-genSummation(op(1,ll), op(op(2,ll)), kb)), HInt ]\n ),\n #Ret is aka Dirac.\n Ret= Record(\n cond_constructor= `=`,\n disintegrator='eval',\n disintegrator_arg_extractor= (A-> op(1,A)= op([2,1], A)),\n #E.g., (x &M Ret(3)) --> (x= 3).\n\n disintegrator_type_extractor= [ (ll -> kb -> (op(1,ll), kb)) ]\n # disintegrator_type_extractor= (ll-> kb-> KB:-genLet(op(1,ll), op([2,1],ll), kb))\n )\n ]),\n\n #types for disint wrt vars (2nd arg to disint)\n t_wrt_var_type,\n t_disint_var, #Curiosity: giving this a type `type` causes a kernel crash\n #during update-archive.\n t_disint_var_pair,\n ModuleLoad::static:= proc($) #Needed to declare types.\n TypeTools:-AddType(\n t_wrt_var_type,\n satisfies(t-> assigned(Wrt_var_types[op(0,t)]))\n );\n TypeTools:-AddType(t_disint_var, {name, name &M t_wrt_var_type});\n TypeTools:-AddType( #Caution: recursive type: Make sure base cases\n t_disint_var_pair, #are on left (a la McCarthy rule).\n 'Pair'(Or(t_disint_var, t_disint_var_pair) $ 2)\n )\n end proc,\n #end of types for disint\n\n DV::table, #wrt vars, with their types and conditions\n p::symbol, #\"pair\"--abstract representation\n #`path` is layers of fst(...) and snd(...) built by traversing tree\n #(Weird Maple syntax note: Module prefixes seem to be required for\n #assertion type checking. Failure to include them causes kernel crash\n #during execution.)\n path::{specfunc({Hakaru:-fst, Hakaru:-snd}), symbol},\n\n #Parses the 2nd arg---the wrt vars.\n # works by side-effect: accumulates \"paths\" to variables in T\n # via the module variable DV.\n traverse_var_tree::static:= proc(\n T::{t_disint_var, t_disint_var_pair}, $\n )::identical(NULL);\n local\n v::name, #the wrt var\n M::NewSLO:-disint:-t_wrt_var_type,\n pp, #iterator over [fst, snd]---the deconstructors of Pair\n vM, vK, mks, mk_ty, mk_ctx\n ;\n if T::t_disint_var then\n #Add a default wrt-var type if none appears.\n (v,M):= op(`if`(T::name, T &M 'Lebesgue'((-1,1)*~infinity), T));\n vK := op(0,M);\n vM := v &M M;\n mks := Wrt_var_types[vK]:-disintegrator_type_extractor;\n mk_ty := op(1,mks);\n if nops(mks)=2 then mk_ctx := ((e)->lam(v,op(2,mks)(),e));\n else mk_ctx := ((e)->e);\n end if;\n DV[v]:= Record(\n 'wrt_var_type'= M,\n 'path'= path,\n 'disintegrator_arg'=\n Wrt_var_types[vK]:-disintegrator_arg_extractor(vM),\n 'disintegrator_mktype'=mk_ty(vM),\n 'disintegrator_mkctx' =mk_ctx\n );\n path:= op(path) #Peel off outer layer: fst or snd.\n else #T::Pair(..., ...)---deconstruct recursively.\n for pp in [fst, snd] do path:= pp(path); thisproc(pp(T)) end do\n end if;\n NULL\n end proc, #disint:-traverse_var_tree\n\n subs_disint_data := proc(sub_vars, expr, $)\n local V:= [indices(DV, 'nolist')], v\n , vars := [indices(sub_vars, 'nolist')]\n , eqns := [seq(v=sub_vars[v], v=vars)]\n , sb := (x->subs(eqns,x));\n\n for v in V do\n DV[v]:-disintegrator_arg := sb(DV[v]:-disintegrator_arg);\n end do;\n\n sb(expr);\n end proc;\n\n ;\n ModuleApply := proc()::t_Hakaru;\n local todo,expr,t;\n expr, todo := disint:-`do`(args)[];\n for t in todo do expr := t(expr); end do; expr;\n end proc;\n\n `do` := proc(\n m::t_Hakaru,\n #var &M wrt-var type, or Pairs thereof\n A::{t_disint_var, t_disint_var_pair},\n ctx::t_kb_atoms:= [] #context: parameter assumptions, \"knowledge\"\n ):: [t_Hakaru, list(appliable)];\n local\n mc, #final integral to be passed to improve @ toLO; then result\n #of each disintegration step\n kb, var_rn := table(), mc_prts,\n V, #wrt vars\n v::name, #iterator over V\n improve_opts := [],\n todo := NULL,\n atodo := proc(z) todo := eval(todo), z; end proc,\n di, da\n ;\n if not {_rest} in {{'do_lam'},{}} then\n error \"bad extra args: %1\", {_rest};\n end if;\n\n #Init module variables.\n DV:= table();\n p:= gensym('p');\n path:= fst(p);\n\n traverse_var_tree(A); # collect information about A in DV\n V:= [indices(DV, 'nolist')];\n\n mc:= Bind(\n m, p,\n #The piecewise condition is a conjunction of conditions, each\n #condition formed from a (var,path) pair from DV.\n piecewise(\n And(seq(\n Wrt_var_types[op(0, DV[v]:-wrt_var_type)]:-\n cond_constructor(DV[v]:-path, v),\n v= V\n )),\n Ret(snd(p)),\n Msum()\n ));\n\n kb := empty;\n for v in ListTools[Reverse](V) do\n var_rn[v], kb := DV[v]:-disintegrator_mktype(kb);\n end do;\n kb := build_kb(ctx,\"disint\",kb);\n mc := subs_disint_data(var_rn, mc);\n\n atodo(x->toLO(x));\n atodo(x->improve(x, _ctx=kb,improve_opts));\n #Does the order of application of the disintegrators matter?\n #Theoretically, I think not, it's just like differentiation. As far\n #as Maple's ability to do the computation, maybe it matters.\n for v in V do\n di := Wrt_var_types[op(0, DV[v]:-wrt_var_type)]:-disintegrator;\n da := DV[v]:-disintegrator_arg;\n atodo(x->applyop(di, 2, x, da));\n atodo(x->improve(x, _ctx=kb,improve_opts));\n end do;\n\n atodo(x->fromLO(x, _ctx= kb));\n ## simplify integrals which do not mention the LO var (i.e. integrals in\n ## weights). this is a hack, we should do this inside of `improve'* in\n ## the correct place. It is required to see the correct output for\n ## d7_normalFB1.\n #\n ## * Or, some other simplifier, which does only specific things - note\n ## the simplification we hope to see here (in d7) can only be done after\n ## the application of the `diff'. So just chucking it into `improve'\n ## might not be the correct thing to do. Calling `improve' at all might\n ## be wrong since we roundtrip through pulling off domains and replacing\n ## them (this is sort of expensive..), although we may also want such\n ## simplifications here - the application of the `diff' might give a new\n ## domain problem that can be improved significanly.\n # 'Simplify' partitions in weights by converting them to piecewise and\n # letting piecewise simplify do the work; and evaluate integrals in weights\n atodo(x->\n subsindets( x, 'Weight(anything, anything)'\n , mw -> applyop(x->simplify_assuming(\n subsindets( subsindets(x,Partition,PartitionToPW)\n , And(specfunc(`Int`)\n ,satisfies(e->indets(e,specfunc(`exp`))<>{})\n )\n , value\n )\n , kb ), 1, mw)));\n\n atodo(x->subs_disint_data( table([seq(var_rn[v]=v, v=V)]), x));\n\n if 'do_lam' in {_rest} then\n for v in ListTools[Reverse](V) do\n atodo(x->DV[v]:-disintegrator_mkctx(x));\n end do;\n end if;\n\n [mc, [todo]];\n end proc; #disint:-ModuleApply\n ModuleLoad();\n end module; #disint\n ###################### end of Carl's code ######################\n", "meta": {"hexsha": "bfc2e4f5c4722fa26687763312ca7669f4020383", "size": 9569, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Disint.mpl", "max_stars_repo_name": "zaxtax/hakaru", "max_stars_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2015-02-07T17:57:04.000Z", "max_stars_repo_stars_event_max_datetime": "2016-01-29T19:40:24.000Z", "max_issues_repo_path": "maple/NewSLO/Disint.mpl", "max_issues_repo_name": "zaxtax/hakaru", "max_issues_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/NewSLO/Disint.mpl", "max_forks_repo_name": "zaxtax/hakaru", "max_forks_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "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": 39.8708333333, "max_line_length": 120, "alphanum_fraction": 0.5656808444, "num_tokens": 2617, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8311430520409023, "lm_q2_score": 0.6076631698328916, "lm_q1q2_score": 0.5050550215877587}} {"text": "(*\n Copyright (C) 2017 M.A.L. Marques\n\n This Source Code Form is subject to the terms of the Mozilla Public\n License, v. 2.0. If a copy of the MPL was not distributed with this\n file, You can obtain one at http://mozilla.org/MPL/2.0/.\n*)\n\n(* type: gga_exc *)\n\n# Note that the files have to be included in this specific order\n$define gga_x_pbe_params\n$include \"gga_x_pbe.mpl\"\n\n$include \"op.mpl\"\n\nop_qab := 2.3789:\nop_enhancement := xs -> pbe_f(xs):\n", "meta": {"hexsha": "29602d92ee786e9ed506bb37c34c474b93aa68ed", "size": 456, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pbe.mpl", "max_stars_repo_name": "pwang234/lsms", "max_stars_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 16, "max_stars_repo_stars_event_min_datetime": "2018-04-03T15:35:47.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-01T03:19:23.000Z", "max_issues_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pbe.mpl", "max_issues_repo_name": "pwang234/lsms", "max_issues_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": 8, "max_issues_repo_issues_event_min_datetime": "2019-07-30T13:59:18.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-31T17:43:35.000Z", "max_forks_repo_path": "libxc-5.1.6/maple/gga_exc/gga_c_op_pbe.mpl", "max_forks_repo_name": "pwang234/lsms", "max_forks_repo_head_hexsha": "6044153b6138512093e457bdc0c15c699c831778", "max_forks_repo_licenses": ["BSD-3-Clause"], "max_forks_count": 9, "max_forks_repo_forks_event_min_datetime": "2018-06-30T00:30:48.000Z", "max_forks_repo_forks_event_max_datetime": "2022-01-31T09:14:29.000Z", "avg_line_length": 24.0, "max_line_length": 68, "alphanum_fraction": 0.6973684211, "num_tokens": 140, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936430859597, "lm_q2_score": 0.658417500561683, "lm_q1q2_score": 0.504541145176964}} {"text": "# simplicial_interval(n) is just the set [n] = {0,1,...,n}\n\n`is_element/simplicial_interval` := (n::nonnegint) -> proc(k)\n type(k,nonnegint) and k <= n;\nend:\n\n`is_equal/simplicial_interval` := (n::nonnegint) -> (a,b) -> evalb(a = b);\n\n`is_leq/simplicial_interval` := (n::nonnegint) -> (a,b) -> evalb(a <= b);\n\n`list_elements/simplicial_interval` := proc(n::nonnegint)\n local i;\n [seq(i,i=0..n)];\nend:\n\n`count_elements/simplicial_interval` := (n::nonnegint) -> n+1;\n\n`random_element/simplicial_interval` := (n::nonnegint) -> proc()\n rand(0..n)();\nend:\n\n######################################################################\n\n`is_element/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n global reason;\n local N,M,i;\n \n N := {seq(i,i=0..n)};\n M := {seq(i,i=0..m)};\n \n if not(`is_element/maps`(N,M)(f)) then\n reason := [convert(procname,string),\"not a map from [n] to [m]\",reason];\n return false;\n fi;\n\n for i from 0 to n-1 do\n if not(f[i] <= f[i+1]) then\n reason := [convert(procname,string),\"f[i+1] > f[i]\",i,f[i+1],f[i]];\n return false;\n fi;\n od;\n\n return true;\nend:\n\n`to_list/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local i;\n return [seq(f[i],i=0..n)];\nend:\n\n`is_equal/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n evalb(`to_list/simplicial_maps`(n,m)(f) = `to_list/simplicial_maps`(n,m)(g));\nend:\n\n`is_leq/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n local u;\n u := `to_list/simplicial_maps`(n,m)(g) -~ `to_list/simplicial_maps`(n,m)(f);\n evalb( min(op(u)) >= 0 );\nend:\n\n# This assumes that \n# * p is a subset of {1,...,n} of size k\n# * q is a subset of {0,...,m} of size k+1\n# It returns the nondecreasing map f : {0,...,n} -> {0,...,m} such that\n# * The image of f is q\n# * { i > 0 : f(i) > f(i-1) } = p.\n \n`build/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(k,p,q)\n local pp,i,j,f;\n pp := [0,op(p),n+1];\n f := table();\n i := 0;\n for i from 0 to k do\n for j from pp[i+1] to pp[i+2]-1 do\n f[j] := q[i+1];\n od;\n od;\n\n return eval(f); \nend:\n\n`random_element/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc()\n local p,q,i,j,k,l,f;\n\n k := rand(0..min(n,m))();\n p := combinat[randcomb](n,k);\n q := combinat[randcomb](m+1,k+1) -~ 1;\n return `build/simplicial_maps`(n,m)(k,p,q);\nend:\n\n`list_elements/simplicial_maps` := proc(n::nonnegint,m::nonnegint)\n option remember;\n local i;\n \n if n = 0 then\n return [seq(`C/simplicial_maps`(0,i),i=0..m)];\n else\n if m = 0 then\n return [`C/simplicial_maps`(n,0)];\n else\n return [op(map(`I/simplicial_maps`(n,m-1),`list_elements/simplicial_maps`(n,m-1))),\n op(map(`T/simplicial_maps`(n-1,m),`list_elements/simplicial_maps`(n-1,m)))];\n fi;\n fi;\nend:\n\n`count_elements/simplicial_maps` := (n::nonnegint,m::nonnegint) -> binomial(n+m+1,m);\n\n# Constant maps\n`C/simplicial_maps` := proc(n::nonnegint,k::nonnegint)\n local i;\n table([seq(i=k,i=0..n)]);\nend:\n\n# Inclusion Delta(n,m) -> Delta(n,m+1)\n`I/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local i;\n table([seq(i=f[i],i=0..n)]);\nend:\n\n# Map Delta(n,m) -> Delta(n+1,m): extend by sending n+1 to m\n`T/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local i;\n table([seq(i=f[i],i=0..n),n+1=m]);\nend:\n\n# `delta/simplicial_maps`(n)(i) : [n] >-> [n+1]; image omits i \n`delta/simplicial_maps` := proc(n::nonnegint,i::nonnegint)\n local j;\n if i > n+1 then return FAIL; fi;\n return table([seq(j=j,j=0..i-1),seq(j=j+1,j=i..n)]);\nend:\n\n# `sigma/simplicial_maps`(n)(i) : [n] ->> [n-1]; takes the value i twice \n`sigma/simplicial_maps` := proc(n::nonnegint,i::nonnegint)\n local j;\n if i > n-1 then return FAIL; fi;\n return table([seq(j=j,j=0..i),seq(j=j-1,j=i+1..n)]);\nend:\n\n`id/simplicial_maps` := proc(n::nonnegint)\n local i;\n return table([seq(i=i,i=0..n)]);\nend:\n\n# `compose/simplicial_maps`(n,m,p)(f,g) assumes that f:[n] -> [m] and g:[m] -> [p],\n# and it returns the composite g o f : [n] -> [p].\n\n`compose/simplicial_maps` := (n::nonnegint,m::nonnegint,p::nonnegint) -> proc(f,g)\n local i;\n table([seq(i = g[f[i]],i=0..n)]);\nend:\n\n`is_wide/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n return evalb(f[0] = 0 and f[n] = m);\nend:\n\n`is_mono/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local i;\n\n if m < n then return false; fi;\n for i from 0 to n-1 do\n if f[i] = f[i+1] then return false; fi;\n od;\n return true;\nend:\n\n`is_epi/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local i,j;\n\n if n < m then return false; fi;\n if f[0] <> 0 then return false; fi;\n if f[n] <> m then return false; fi;\n\n j := 0;\n for i from 1 to n do\n if (f[i] <> j and f[i] <> j+1) then\n return false;\n fi;\n j := f[i];\n od;\n return true;\nend:\n\n# This assumes that f : [n] -> [m], and it returns [k,g,h] such that\n# g : [n] ->> [k] and h : [k] >-> [m] and f = h o g\n\n`factor/simplicial_maps` := (n::nonnegint,m::nonnegint) -> proc(f)\n local K,k,g,h,hi,i;\n \n K := sort([op({seq(f[i],i=0..n)})]);\n k := nops(K) - 1;\n h := table([seq(i=K[i+1],i=0..k)]);\n hi := table();\n for i from 0 to k do hi[h[i]] := i; od;\n g := table([seq(i = hi[f[i]],i=0..n)]);\n return [k,eval(g),eval(h)];\nend:\n\n`describe/simplicial_maps` := (n::nonnegint) -> proc(f)\n local i;\n cat(seq(nat_code[f[i]],i=0..n));\nend:\n\n######################################################################\n\n`is_element/simplicial_epi` := (n::nonnegint,m::nonnegint) -> proc(f)\n global reason;\n \n if not(`is_element/simplicial_maps`(n,m)(f)) then\n reason := [convert(procname,string),\"not a simplicial map from [n] to [m]\",reason];\n return false;\n fi;\n\n return `is_epi/simplicial_maps`(n,m)(f);\nend:\n\n`is_equal/simplicial_epi` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n `is_equal/simplicial_maps`(n,m)(f,g);\nend:\n\n`is_leq/simplicial_epi` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n `is_leq/simplicial_maps`(n,m)(f,g);\nend:\n\n`random_element/simplicial_epi` := (n::nonnegint,m::nonnegint) -> proc()\n local p,q,k,f,i;\n\n if n < m then return FAIL; fi;\n\n k := m;\n p := combinat[randcomb](n,k);\n q := [seq(i,i=0..m)];\n return `build/simplicial_maps`(n,m)(k,p,q);\nend:\n\n`list_elements/simplicial_epi` := proc(n::nonnegint,m::nonnegint) \n local P,L,S,f,i,j;\n\n P := combinat[choose]([seq(i,i=1..n)],m);\n L := [];\n for S in P do\n f := table();\n for i from 0 to S[1]-1 do f[i] := 0; od;\n for j from 1 to m-1 do \n for i from S[j] to S[j+1]-1 do f[i] := j; od;\n od;\n for i from S[m] to n do f[i] := m; od;\n L := [op(L),eval(f)]; \n od:\n\n return L;\nend:\n\n`count_elements/simplicial_epi` := (n::nonnegint,m::nonnegint) -> binomial(n,m);\n\n######################################################################\n\n`is_element/simplicial_mono` := (n::nonnegint,m::nonnegint) -> proc(f)\n global reason;\n \n if not(`is_element/simplicial_maps`(n,m)(f)) then\n reason := [convert(procname,string),\"not a simplicial map from [n] to [m]\",reason];\n return false;\n fi;\n\n return `is_mono/simplicial_maps`(n,m)(f);\nend:\n\n`is_equal/simplicial_mono` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n `is_equal/simplicial_maps`(n,m)(f,g);\nend:\n\n`is_leq/simplicial_mono` := (n::nonnegint,m::nonnegint) -> proc(f,g)\n `is_leq/simplicial_maps`(n,m)(f,g);\nend:\n\n`random_element/simplicial_mono` := (n::nonnegint,m::nonnegint) -> proc()\n local p,q,i,j,k,l,f;\n\n if n > m then return FAIL; fi;\n\n k := n;\n p := [seq(i,i=1..n)];\n q := combinat[randcomb](m+1,k+1) -~ 1;\n return `build/simplicial_maps`(n,m)(k,p,q);\nend:\n\n`list_elements/simplicial_mono` := proc(n::nonnegint,m::nonnegint) \n local P,L,S,f,i,j;\n\n P := combinat[choose]([seq(i,i=0..m)],n+1);\n L := [];\n for S in P do\n f := table();\n for i from 0 to n do f[i] := S[i+1]; od;\n L := [op(L),eval(f)]; \n od:\n\n return L;\nend:\n\n`count_elements/simplicial_mono` := (n::nonnegint,m::nonnegint) -> binomial(m+1,n+1);\n\n\n\n", "meta": {"hexsha": "a3ad713db967cfc43b4c7ae192bf8f4c136f9eb6", "size": 7735, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/simplicial.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/simplicial.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 25.1954397394, "max_line_length": 87, "alphanum_fraction": 0.5900452489, "num_tokens": 2861, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7662936324115011, "lm_q2_score": 0.6584174871563662, "lm_q1q2_score": 0.5045411278763047}} {"text": "(*\n \u4ea4\u6362\u5b50\u8868\u8ba1\u7b97\uff1a\n + \u8ba1\u7b97\u4ea4\u6362\u5b50\u7684\u8868\u8fbe\u5f0f\u5f62\u5f0f\u3002\n + \u5c06\u4ea4\u6362\u5b50\u7528\u751f\u6210\u5143\u8fdb\u884c\u7ebf\u6027\u8868\u51fa\u3002\n + \u8ba1\u7b97\u4f34\u968f\u53d8\u6362\u77e9\u9635\u3002\n + \u751f\u6210\u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\uff0c\u5e76\u6c42\u89e3\u4e0d\u53d8\u91cf\u3002\n*)\n$ifndef _BASIC_\n$define _BASIC_\n\n$include \"Logout.mpl\"\n$include \"InvSimplify.mpl\"\n\n$ifndef _HEADERS_\nPDETools:-declare(quiet):\nmacro(Pa=`\\x26\\x50\\x61\\x72\\x74\\x69\\x61\\x6C\\x44\\x3B`);# \u504f\u5bfc\u7b26\u53f7\u4f5c\u4e3a\u51fd\u6570\u540d\n$endif\n\nSymsHolder:=module()\n option object;\n export default_syms:={x,y,z,t,u,v,w}, # \u9ed8\u8ba4\u7b26\u53f7\u96c6\n syms:=default_syms, # \u5f53\u524d\u7b26\u53f7\u96c6\n pnames:={a,c,d,epsilon,Delta,phi}; # \u53d7\u4fdd\u62a4\u7684\u540d\u5b57\nend module:\n\n# \u4fee\u6539\u5fae\u5206\u7b97\u5b50\u7684\u7b26\u53f7\u96c6\u5408\nsetSymbols:=proc(s::set(name):=SymsHolder:-default_syms)\n description \"\u8bbe\u7f6e\u51fd\u6570\u7684\u53d8\u91cf\u540d\u96c6\u5408\";\n if ( s intersect SymsHolder:-pnames <> {}) then\n error \"\u53d8\u91cf\u4e0d\u80fd\u5305\u542b%1\",SymsHolder:-pnames;\n end if; \n SymsHolder:-syms:=s;\nend proc;\n\n# \u83b7\u53d6\u53d8\u91cf\u540d\u96c6\u5408\ngetSymbols:=proc()\n description \"\u83b7\u53d6\u53d8\u91cf\u540d\u96c6\u5408\";\n SymsHolder:-syms;\nend proc;\n\n# \u81ea\u5b9a\u4e49\u5fae\u5206\u7b97\u5b50\u64cd\u4f5c\uff0c\u4f5c\u7528\u5230\u51fd\u6570f\u4e0a\nd:=proc()\n description \"\u7528\u4e8e\u751f\u6210\u5fae\u5206\u7b97\u5b50\u8868\u8fbe\u5f0f\";\n if not {_passed} subset SymsHolder:-syms then\n error \"\u8868\u8fbe\u5f0f\u53ea\u80fd\u5305\u542b\u4ee5\u4e0b\u53d8\u91cf %1, \u53ef\u4ee5\u4f7f\u7528 setSymbols \u8bbe\u7f6e\u53d8\u91cf\u96c6\u5408\uff0c\u4f46\u662f\u4e0d\u80fd\u5305\u542b %2\",SymsHolder:-syms,SymsHolder:-pnames;\n end if;\n return diff(Pa(SymsHolder:-syms[]),_passed);\nend proc;\n\n# \u81ea\u5b9a\u4e49\u4ea4\u6362\u5b50\u8ba1\u7b97\u7b26\n`&c`:=proc(a,b)\n description \"\u8ba1\u7b97\u4e24\u4e2a\u751f\u6210\u5fae\u5206\u7b97\u5b50\u7684\u4ea4\u6362\u5b50\";\n expand(eval(subs(Pa(SymsHolder:-syms[])=b,a)-subs(Pa(SymsHolder:-syms[])=a,b)));\nend proc:\n\n(*\n* \u5c06\u8868\u8fbe\u5f0f\u5206\u89e3\u4e3a\u975e\u7ebf\u6027\u9879\u5e76\u63d0\u53d6\u7cfb\u6570\n* \u8f93\u5165\uff1a\n* f \u8868\u8fbe\u5f0f\n* \u8f93\u51fa\uff1a\n* T \u975e\u7ebf\u6027\u9879->\u7cfb\u6570 \u7684\u6620\u5c04\u8868\n*)\ngetKd:=proc(f)\n local T:=table(),kd;\n \n (* \n * \u5c06\u8868\u8fbe\u5f0f\u5206\u89e3\u4e3a\u975e\u7ebf\u6027\u57fa\u5e76\u63d0\u53d6\u7cfb\u6570\u7684\u9012\u5f52\u5b50\u51fd\u6570\n * \u8f93\u5165\uff1a\n * f \u8868\u8fbe\u5f0f\n * T \u4fdd\u5b58\u7ed3\u679c\u7684\u8868\n * \u8f93\u51fa\uff1a\n * T T\u4f1a\u88ab\u4fee\u6539\n *)\n kd:=proc(f,T)\n local i,p,v,x;\n if type(f,`+`) then\n for i from 1 to nops(f) do\n thisproc(op(i,f),T);\n end do;\n elif type(f,`*`) then\n p:=1;\n v:=1;\n for i from 1 to nops(f) do\n x:=op(i,f);\n if type(x,extended_numeric) then\n p:=p*x;\n else\n v:=v*x;\n end if;\n end do;\n T[v]:=p;\n else\n T[f]:=1;\n end if;\n return;\n end proc:\n \n kd(f,T);\n return eval(T);\nend proc:\n\n(*\n* \u83b7\u53d6\u8868\u8fbe\u5f0f\u5173\u4e8e\u7ed9\u5b9a\u975e\u7ebf\u6027\u9879\u96c6\u7684\u7cfb\u6570\u5411\u91cf\n* \u8f93\u5165\uff1a\n* f \u8868\u8fbe\u5f0f\n* s \u975e\u7ebf\u6027\u9879\u96c6\n* \u8f93\u51fa\uff1a\n* v \u7cfb\u6570\u5411\u91cf\n*)\ngetPmVec:=proc(f,s)\n local n,v,i,tb;\n tb:=getKd(f);\n n:=numelems(s);\n v:=Vector(n);\n for i from 1 to n do\n if assigned(tb[s[i]]) then\n v[i]:=tb[s[i]];\n end if;\n end do;\n return eval(v);\nend proc:\n\n(*\n* \u6c42\u89e3\u8868\u8fbe\u5f0f\u5173\u4e8e\u57fa\u7684\u7ebf\u6027\u8868\u51fa\n* \u8f93\u5165\uff1a\n* f \u8868\u8fbe\u5f0f\n* A \u57fa\u5173\u4e8e\u975e\u7ebf\u6027\u9879\u96c6\u7684\u7cfb\u6570\u77e9\u9635\n* stbs \u975e\u7ebf\u6027\u9879\u96c6\n* sbs \u57fa\u7684\u7b26\u53f7\u8868\u793a\n* \u8f93\u51fa\uff1a\n* r \u8868\u8fbe\u5f0f\u5173\u4e8e\u57fa\u7684\u7ebf\u6027\u8868\u51fa\uff0c\u6c42\u89e3\u5931\u8d25\u8fd4\u56de\u539f\u8868\u8fbe\u5f0f\n*)\nans2v:=proc(f,A,stbs)\n local r;\n try\n r:=LinearAlgebra[LinearSolve](A,getPmVec(f,stbs));\n catch:\n error \"\u6240\u7ed9\u751f\u6210\u5143\u4e0d\u80fd\u6784\u6210\u4e00\u7ec4\u57fa\";\n end try;\nend proc:\n\n\n(*\n* \u8ba1\u7b97\u6240\u6709\u7ed3\u679c\n* \u8f93\u5165\uff1a\u4e00\u7ec4\u751f\u6210\u5143\n* \u8f93\u51fa\uff1a\n* AD \u4f34\u968f\u53d8\u6362\u77e9\u9635\u7684\u6570\u7ec4\n* ADA A[1]*A[2]*...*A[n]\n* dts \u4e0d\u53d8\u91cf\u6570\u7ec4\n*)\ngetTransMatAndPDE:=proc(vv::list)\n local tbs,stbs,vvv,M,n,sbs,i,j,A,tmpv,MK,AD,ADA,ADT,BA,pPhi,eq,AList,dts,eqs;\n\n if not (indets(vv,name) subset SymsHolder:-syms) then\n error \"\u8868\u8fbe\u5f0f\u53ea\u80fd\u5305\u542b\u4ee5\u4e0b\u53d8\u91cf %1, \u53ef\u4ee5\u4f7f\u7528 setSymbols \u8bbe\u7f6e\u53d8\u91cf\u96c6\u5408\uff0c\u4f46\u662f\u4e0d\u80fd\u5305\u542b %2\",\n SymsHolder:-syms,SymsHolder:-pnames;\n end if; \n \n vvv:=expand(vv):\n n:=numelems(vvv):\n sbs:=Vector[row](1..n,i->v[i]):# \u751f\u6210\u5143\u7684\u8868\u793a\u7b26\u53f7\n flogf[2](\"Input:\");\n flog[2](seq(sbs[i]=vv[i],i=1..n));\n \n # \u8ba1\u7b97\u4ea4\u6362\u5b50\u77e9\u9635\uff0c\u8fd9\u91cc\u5f97\u5230\u7684\u662f\u5173\u4e8ef\u7684\u7ed3\u679c\uff0c\u9700\u8981\u8fdb\u4e00\u6b65\u7528\u57fa\u8868\u793a\n M:=Matrix(1..n, 1..n, (i, j)->vvv[i] &c vvv[j]):# \u4ea4\u6362\u5b50\u7684\u8868\u8fbe\u5f0f\u5f62\u5f0f\n MK:=Matrix(1..n,1..n);# \u4ea4\u6362\u5b50\u5173\u4e8e\u751f\u6210\u5143\u7684\u7cfb\u6570\u5411\u91cf\u77e9\u9635\n \n # \u5c06\u539f\u4ea4\u6362\u5b50\u8868\u7528\u57fa\u8868\u51fa\n tbs:=getKd~(vvv):# \u975e\u7ebf\u6027\u9879\u53ca\u5176\u7cfb\u6570\u6620\u5c04\u8868\n stbs:={map(indices,tbs,nolist)[]}:# \u975e\u7ebf\u6027\u9879\u96c6\n # \u751f\u6210\u5143\u5173\u4e8e\u975e\u7ebf\u6027\u9879\u96c6\u7684\u7cfb\u6570\u77e9\u9635\n A:=Matrix(1..numelems(stbs),1..numelems(tbs),\n (i,j)->`if`(assigned(tbs[j][stbs[i]]),tbs[j][stbs[i]],0)):\n # \u8ba1\u7b97\u6bcf\u4e2a\u4ea4\u6362\u5b50\u5173\u4e8e\u751f\u6210\u5143\u7684\u7cfb\u6570\n # \u8fd9\u91cc\u5c06\u4ea4\u6362\u5b50\u7684\u8868\u8fbe\u5f0f\u8f6c\u5316\u6210\u4e86\u751f\u6210\u5143\u7684\u7ebf\u6027\u8868\u51fa\n for i from 1 to n do\n for j from 1 to n do\n if (M(i,j)<>0) then\n if (i<=j) then\n tmpv:=ans2v(M(i,j),A,stbs);\n M(i,j):=sbs.tmpv;\n MK(i,j):=convert(tmpv,list);\n else\n M(i,j):=-M(j,i);\n MK(i,j):=-MK(j,i);\n end if;\n else\n MK(i,j):=convert(Vector[row](1..n),list);\n end if;\n end do;\n end do;\n flogf[2](\"Commutator table:\"); \n flog[2](M);\n\n \n # \u4f34\u968f\u77e9\u9635\n AD:=Array(1..n);\n ADA:=LinearAlgebra[IdentityMatrix](n);\n ADT:=Matrix(1..n,1..n);\n flogf[2](\"Adjoint transformation matrixes :\");\n for i from 1 to n do\n AD[i]:=LinearAlgebra[MatrixExponential](Matrix(convert(MK[i],list)),-epsilon[i]);\n ADA:=ADA.AD[i];\n ADT(i,1..n):=subs~(epsilon[i]=epsilon,(AD[i].sbs^%T)^%T);\n flogf[2](\"Adjoint transformation matrix of %a\",sbs[i]);\n flog[2](AD[i]);\n end do;\n flogf[2](\"General adjoint transformation matrix\");\n flog[2](ADA);\n\n flogf[2](\"Adjoint representation table:\");\n flog[2](ADT);\n\n # \u8ba1\u7b97\u4e0d\u53d8\u91cf\n BA:=Matrix(1..n,1..n,(i,j)->b[i]*a[j]);\n pPhi:=add(BA*~M);\n eqs:=getPDE(pPhi,sbs);\n return AD,ADA,eqs;\nend proc:\n\n# \u8ba1\u7b97\u4e0d\u53d8\u91cf\n# \u5df2\u5316\u7b80\u5e76\u6392\u5e8f\ngetInvariants:=proc(eqs)\n local res;\n res:=pdsolve(eqs);\n res:=res[];\n res:=[op(op(2,res))];\n res:=sortByComplexity(res);# \u6309\u7167\u590d\u6742\u5ea6\u5347\u5e8f\u8f93\u51fa\n flogf[0](\"\u89e3\u5f97\u7684\u4e0d\u53d8\u91cf\");\n map(x->flog[0]('Delta'[x]=res[x]),[seq(i,i=1..numelems(res))]);\n res:=simplifyInvariants(res);# \u4e0d\u53d8\u91cf\u5316\u7b80\n res:=sortByComplexity(res);# \u6309\u7167\u590d\u6742\u5ea6\u5347\u5e8f\u8f93\u51fa\n flogf[0](\"\u5316\u7b80\u540e\u7684\u4e0d\u53d8\u91cf\");\n map(x->flog[0]('Delta'[x]=res[x]),[seq(i,i=1..numelems(res))]);\n return res;\nend proc;\n\n(*\n* \u751f\u6210\u4e0d\u53d8\u91cf\u7684\u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\n* \u8f93\u5165\uff1a\n* p p=[w,v],w=sum(b[j]*v[j]),v=sum(a[i]*v[i])\n* sbs \u751f\u6210\u5143\u7b26\u53f7\u96c6 v[1],...,v[n]\n* \u8f93\u51fa\uff1a\n* \u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\n*)\ngetPDE:=proc(p,sbs)\n local n:=numelems(sbs),i,eq,eqs;\n uses phi=phi(seq(a[i],i=1..n));\n eq:=add(coeff(p,sbs[i])*diff(phi,a[i]),i=1..n);\n eqs:={seq(coeff(eq,b[i]),i=1..n)} minus {0};\nend proc:\n\n$endif", "meta": {"hexsha": "41e234a7379b00f33fb09a37e38a26ab00af1c95", "size": 5828, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/Basic.mpl", "max_stars_repo_name": "yu961549745/InvariantClassify", "max_stars_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_stars_repo_licenses": ["Apache-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": "InvClassify/Basic.mpl", "max_issues_repo_name": "yu961549745/InvariantClassify", "max_issues_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "InvClassify/Basic.mpl", "max_forks_repo_name": "yu961549745/InvariantClassify", "max_forks_repo_head_hexsha": "eeb14ca2b39679e5a2da0f23888681ec7e2edd84", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 22.9448818898, "max_line_length": 101, "alphanum_fraction": 0.5334591627, "num_tokens": 2531, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.8080672135527632, "lm_q2_score": 0.6224593312018546, "lm_q1q2_score": 0.5029889773141992}} {"text": "######################################################################\n\n`eta/ord_simplex_interior` := proc(A::set) \n if nops(A) <> 1 then return FAIL; fi;\n \n return [`eta/ord`(A),`eta/simplex_interior`(A)];\nend;\n\n`gamma/ord_simplex_interior` := (A::set,B::set) -> (p) -> proc(U,V)\n local RU,RV,xU,xV,b;\n\n RU := U[1];\n RV := table([seq(b = eval(V[b][1]),b in B)]);\n xU := U[2];\n xV := table([seq(b = eval(V[b][2]),b in B)]);\n return [`gamma/ord`(A,B)(p)(RU,RV),\n `gamma/simplex_interior`(A,B)(p)(xU,xV)];\nend;\n", "meta": {"hexsha": "60c10a208a11599635d572632cd46a948d9ce54e", "size": 517, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/ord_simplex_interior.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/ord_simplex_interior.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/ord_simplex_interior.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 27.2105263158, "max_line_length": 70, "alphanum_fraction": 0.4816247582, "num_tokens": 173, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7879311956428947, "lm_q2_score": 0.6370307806984444, "lm_q1q2_score": 0.501936424697052}} {"text": "######################################################################\n# Operad of orderings\n\n`eta/ord` := (A::set) -> `if`(nops(A)=1,[op(A)],FAIL);\n\n`gamma/ord` := (A::set,B::set) -> (p) -> proc(R,RR)\n local b;\n if not check_gamma_args(A,B,p,R,RR,`is_element/ord`) then\n return FAIL;\n fi;\n\n map(op,[seq(RR[b],b in R)]);\nend;\n\n", "meta": {"hexsha": "29fdd9752979500d749b7bc7afa0d79da68f82ad", "size": 328, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/ord.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/ord.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/operads/ord.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 21.8666666667, "max_line_length": 70, "alphanum_fraction": 0.4451219512, "num_tokens": 102, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7745833945721304, "lm_q2_score": 0.647798211152541, "lm_q1q2_score": 0.5017737373922889}} {"text": "`is_element/autorel` := (A::set) -> proc(R)\n `is_element/rel`(A,A)(R);\nend;\n\n`is_equal/autorel` := (A::set) -> (R,S) -> `is_equal/rel`(A,A)(R,S);\n`is_leq/autorel` := (A::set) -> (R,S) -> `is_leq/rel`(A,A)(R,S);\n`bot/autorel` := (A::set) -> `bot/rel`(A,A);\n`top/autorel` := (A::set) -> `top/rel`(A,A);\n\n`is_a_function/autorel` := (A::set) -> (R) -> `is_a_function/rel`(A,A)(R);\n`is_total/autorel` := (A::set) -> (R) -> `is_total/rel`(A,A)(R);\n\n`op/autorel` := (A::set) -> (R) -> `op/rel`(A,A)(R);\n\n`hash/autorel` := (A::set) -> (R) -> `hash/rel`(A,A)(R);\n`unhash/autorel` := (A::set) -> (r) -> `unhash/rel`(A,A)(r);\n\n`id/autorel` := (A::set) -> `id/rel`(A);\n\n`o/autorel` := (A::set) -> (S,R) -> `o/rel`(A,A,A)(S,R);\n\n`is_reflexive/autorel` := (A::set) -> proc(R)\n return evalb(`id/autorel`(A) minus R = {});\nend;\n\n`is_irreflexive/autorel` := (A::set) -> proc(R)\n return evalb(`id/autorel`(A) intersect R = {});\nend;\n\n`is_symmetric/autorel` := (A::set) -> proc(R)\n return evalb(R = `op/autorel`(A)(R));\nend;\n\n`is_antisymmetric/autorel` := (A::set) -> proc(R)\n return evalb(R intersect `op/autorel`(A)(R) = {});\nend;\n\n`is_transitive/autorel` := (A::set) -> proc(R)\n local RR;\n RR := `o/autorel`(A)(R,R);\n return evalb(`is_leq/autorel`(A)(RR,R));\nend;\n\n`is_separated/autorel` := (A::set) -> proc(R)\n return evalb((R intersect `op/autorel`(A)(R)) minus `id/autorel`(A) = {});\nend;\n\n`list_elements/autorel` := (A::set) -> `list_elements/rel`(A,A);\n`count_elements/autorel` := (A::set) -> 2^(nops(A)^2);\n\n`random_element/autorel` := (A::set) -> (p_) -> `random_element/rel`(A,A)(args);\n\n`transitive_closure/autorel` := (A::set) -> proc(R)\n local S,n0,n1;\n \n S := `id/autorel`(A) union R;\n n0 := 0;\n n1 := nops(S);\n while n1 > n0 do\n n0 := n1;\n S := `o/autorel`(A)(S,S);\n n1 := nops(S);\n od;\n\n return S;\nend;\n\n`cofunctor/autorel` := (A::set,B::set) -> (f) -> proc(R)\n local AA;\n \n AA := `top/autorel`(A);\n return select(aa -> member([f[aa[1]],f[aa[2]]],R),AA);\nend;\n\n`reindex_standard/autorel` := (A::set) -> proc(R)\n local n,i,f,N,R0;\n \n n := nops(A);\n f := table();\n for i from 1 to n do f[A[i]] := i; od;\n N := {seq(i,i=1..n)};\n R0 := map(aa -> [f[aa[1]],f[aa[2]]],R);\n return [N,R0];\nend;", "meta": {"hexsha": "b430d0400e17cc4ed0b8bd49f77c8dbfbcffdd23", "size": 2189, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/autorel.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/autorel.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/autorel.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 26.0595238095, "max_line_length": 80, "alphanum_fraction": 0.5445408862, "num_tokens": 940, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7956581000631542, "lm_q2_score": 0.6297746213017459, "lm_q1q2_score": 0.5010852786529396}} {"text": "single_case_Partition := module()\n uses Domain;\n\n export SimplName := \"Single case partition\";\n export SimplOrder := 11;\n\n export ModuleApply := proc(vs :: DomBound, sh :: DomShape, $)\n subsindets(sh, DomSplit, x->do_simp(op(x)));\n end proc;\n\n local do_simp := proc(p:: Partition,$)::DomShape;\n local r := Partition:-Simpl:-single_nonzero_piece_cps(\n proc(c,v) if v::DomConstrain then DConstrain(conv_bool(c),op(v)) else p end if\n end proc,p,_testzero=(x->x=DSum()));\n if r :: Partition then DSplit(r) else r end if;\n end proc;\n\n local conv_bool := proc(r, $)\n if r :: {specfunc(`And`), `and`} then\n op(map(conv_bool,r))\n else\n r\n end if;\n end proc;\nend module;\n\nredundant_Partition_Pieces := module()\n uses Domain;\n\n export SimplName := \"Redundant Partition pieces\";\n export SimplOrder := (10+1/2);\n\n export ModuleApply := proc(vs :: DomBound, sh :: DomShape, $)\n local as := Domain:-Bound:-toConstraints(vs, 'bound_types');\n subsindets(sh, DomSplit, proc(pr)\n local r; r := Partition:-Simpl(op(1,pr)) assuming op(as);\n if not r :: Partition then r else pr end if;\n end proc);\n end proc;\nend module;\n", "meta": {"hexsha": "a98f3b6d78c81dfc80a6c1205b234ee798b1ae99", "size": 1240, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_stars_repo_name": "zaxtax/hakaru", "max_stars_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_stars_repo_licenses": ["BSD-3-Clause"], "max_stars_count": 4, "max_stars_repo_stars_event_min_datetime": "2015-02-07T17:57:04.000Z", "max_stars_repo_stars_event_max_datetime": "2016-01-29T19:40:24.000Z", "max_issues_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_issues_repo_name": "zaxtax/hakaru", "max_issues_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "max_issues_repo_licenses": ["BSD-3-Clause"], "max_issues_count": null, "max_issues_repo_issues_event_min_datetime": null, "max_issues_repo_issues_event_max_datetime": null, "max_forks_repo_path": "maple/Domain/Improve/Partitions.mpl", "max_forks_repo_name": "zaxtax/hakaru", "max_forks_repo_head_hexsha": "03ac5b645815e99437e28d228e6c668753b2640e", "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": 30.243902439, "max_line_length": 90, "alphanum_fraction": 0.6064516129, "num_tokens": 341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7853085708384736, "lm_q2_score": 0.6370308082623217, "lm_q1q2_score": 0.5002657536165616}} {"text": "# An extended Stasheff tree is like a standard Stasheff tree, except that we\n# are allowed vertices with only one child, which we call nodes. By deleting\n# the nodes we obtain a standard Stasheff tree TT. For each T in TT we let\n# m[T] be the number of nodes lying just below T. The function m : TT -> N\n# is arbitrary and determines the original tree. We will write n for the\n# number of leaves (which are never nodes) and k for the number of vertices\n# that are neither leaves nor the root. Note that the root may or may not\n# be a node.\n#\n# We represent an extended Stasheff tree as the set of pairs [T,m[T]].\n\n`is_element/extended_stasheff_trees` := (n::posint,k::nonnegint) -> proc(UU)\n global reason;\n local TT,T,U,m,kk;\n\n if not (type(UU,set)) then\n reason := [\"is_element/extended_stasheff_trees\",\"UU is not a set\",UU];\n return false;\n fi;\n\n kk := 0;\n TT := NULL;\n \n for U in UU do\n if not(type(U,list) and nops(U) = 2) then\n reason := [\"is_element/extended_stasheff_trees\",\"U is not a list of length 2\",U,UU];\n return false;\n fi;\n T,m := op(U);\n if not(type(m,nonnegint)) then\n reason := [\"is_element/extended_stasheff_trees\",\"m is not a natural number\",m,U,UU];\n return false;\n fi;\n kk := kk + m + 1;\n TT := TT,T;\n od:\n\n TT := {TT};\n\n if not(`is_element/standard_stasheff_trees`(n)(TT)) then\n reason := [\"is_element/extended_stasheff_trees\",\"TT is not a standard Stasheff tree\",TT,reason]; \n return false;\n fi;\n\n kk := kk - n - 1;\n\n if kk <> k then\n reason := [\"is_element/extended_stasheff_trees\",\"wrong number of internal vertices\",kk,k,UU]; \n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/extended_stasheff_trees` := (n::posint,k::nonnegint) -> proc(UU0,UU1)\n return evalb(UU0 = UU1);\nend:\n\n`is_leq/extended_stasheff_trees` := NULL:\n\n`list_elements/extended_stasheff_trees` := proc(n::posint,k::nonnegint)\n local TTT,TT,T,P,p,i,j,UU,L,u;\n\n TTT := `list_elements/standard_stasheff_trees`(n);\n\n L := NULL;\n for TT in TTT do\n p := nops(TT);\n j := k - (p - n - 1);\n if j >= 0 then\n P := `list_elements/nat_partitions`(j,p);\n for u in P do\n UU := {seq([TT[i],u[i]],i=1..p)};\n L := L,UU;\n od:\n fi;\n od:\n return [L];\nend:\n\n`random_element/extended_stasheff_trees` := (n::posint,k::nonnegint) -> proc()\n local TT,m,P,UU,i;\n\n TT := `random_element/standard_stasheff_trees`(n)();\n while (nops(TT) > n + k + 1) do \n TT := `random_element/standard_stasheff_trees`(n)();\n od;\n m := nops(TT);\n \n P := `random_element/nat_partitions`(n+k+1-m,m)();\n UU := {seq([TT[i],P[i]],i=1..m)};\n return UU;\nend:\n\n`count_elements/extended_stasheff_trees` := (n::posint,k::nonnegint) ->\n binomial(n+k,n)*binomial(n+k,n-1)/(n+k);\n\n`node_count/extended_stasheff_trees` := proc(UU)\n local U;\n return add(U[2],U in UU);\nend:\n\n# This removes the nodes from an extended Stasheff tree to give an\n# ordinary Stasheff tree.\n\n`strip/extended_stasheff_tree` := proc(UU)\n map(U -> U[1],UU);\nend:\n\n`narayana_path/extended_stasheff_tree` := proc(UU)\n local TT,n,CC,C,m,u,l,UU0;\n\n TT := `strip/extended_stasheff_tree`(UU);\n n := max(op(map(op,TT)));\n CC := `root_children/standard_stasheff_tree`(n)(TT);\n\n # Number of nodes under the root\n m := select(U -> nops(U[1])=n,UU)[1][2];\n \n u := 1$m;\n\n for C in CC do\n l := min(op(C));\n UU0 := select(U -> U[1] minus C = {},UU);\n UU0 := map(U -> [U[1] -~ (l-1),U[2]],UU0);\n u := u,1,op(`narayana_path/extended_stasheff_tree`(UU0)),-1;\n od:\n \n u := u,(-1)$m;\n u := [u];\n return u;\nend:\n\n# This takes a pair of extended Stasheff trees and adds an edge\n# joining the roots, taking the root of the first one as the root\n# of the combined tree.\n`splice/extended_stasheff_tree` := (n0,k0) -> (n1,k1) -> proc(UU0,UU1)\n local UU2,R2,m,i;\n\n UU2 := map(U -> [U[1] +~ n0,U[2]],UU1);\n R2 := select(U -> nops(U[1]) = n1,UU2)[1];\n m := R2[2];\n if m > 0 then\n UU2 := UU2 minus {R2} union {[R2[1],m-1]};\n else\n UU2 := UU2 minus {R2};\n fi;\n return {op(UU0),op(UU2),[{seq(i,i=1..n0+n1)},0]};\nend:\n\n# This adds a new left-most leaf and connects it to the root.\n# This is essentially the same as splice(ZZ,UU), where ZZ is\n# the 0-corolla, which we have not allowed as an extended\n# Stasheff tree. However, it would be a bad idea to allow ZZ\n# here, because sprouting adds a leaf, which is inconsistent with\n# the usual effect of splicing on the leaf count.\n\n`sprout/extended_stasheff_tree` := (n,k) -> proc(UU)\n local UU2,R2,m,i;\n\n UU2 := map(U -> [U[1] +~ 1,U[2]],UU);\n R2 := select(U -> nops(U[1]) = n,UU2)[1];\n m := R2[2];\n if m > 0 then\n UU2 := UU2 minus {R2} union {[R2[1],m-1]};\n else\n UU2 := UU2 minus {R2};\n fi;\n return {[{1},0],op(UU2),[{seq(i,i=1..n+1)},0]};\nend:\n\n# This adds an extra node at the bottom\n# This is essentially the same as splice(UU,ZZ), where ZZ is\n# the 0-corolla, which we have not allowed as an extended\n# Stasheff tree.\n`grow/extended_stasheff_tree` := (n::posint,k::nonnegint) -> proc(UU)\n local R;\n R := select(U -> nops(U[1]) = n,UU)[1];\n return (UU minus {R}) union {[R[1],R[2]+1]};\nend:\n\n", "meta": {"hexsha": "a30b535f59707954b2affd26b35843ccc13fcb51", "size": 4975, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/extended_stasheff_trees.mpl", "max_stars_repo_name": "NeilStrickland/maple_lib", "max_stars_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/extended_stasheff_trees.mpl", "max_issues_repo_name": "NeilStrickland/maple_lib", "max_issues_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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/extended_stasheff_trees.mpl", "max_forks_repo_name": "NeilStrickland/maple_lib", "max_forks_repo_head_hexsha": "afdc262a183c56959a7c013e38a166824f7fc3d5", "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": 27.3351648352, "max_line_length": 100, "alphanum_fraction": 0.6430150754, "num_tokens": 1755, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7634837527911056, "lm_q2_score": 0.6548947290421275, "lm_q1q2_score": 0.5000014854121978}}