{"text": "`eta/BW` := eval(`eta/prime_simplex`);\n`gamma/BW` := eval(`gamma/prime_simplex`);\n`gamma_min/BW` := eval(`gamma_min/prime_simplex`);\n", "meta": {"hexsha": "28b7223dbb4428d8f28c1f45570dd8ef0cab2db9", "size": 133, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/BW.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/BW.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/BW.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": 33.25, "max_line_length": 50, "alphanum_fraction": 0.6842105263, "num_tokens": 44, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6825737344123242, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.39937467983346064}} {"text": "# The block below either calculates or reads from file the alternative\n# Boys immersion, calibrated to have special behaviour at the points\n# [+/- 1, +/- 1, +/- 1]/sqrt(3).\n\nif false then \n make_boys_embedding_alt():\n save(boys_M0,boys_M1,boys_a1,boys_embedding_alt,cat(data_dir,\"/boys_embedding_alt.m\")):\nelse \n read(cat(data_dir,\"/boys_embedding_alt.m\")):\nfi:\n\nbef := (x) -> evalf(boys_embedding_alt(x)):\n\ncheck_bef := proc()\n _ASSERT(\n max(evalf([\n dd(bef(u[0]),u[0]),\n dd(bef(u[1]),u[6]),\n dd(bef(u[2]),u[5]),\n dd(bef(u[3]),u[4]),\n dd(bef(u[4]),u[4]),\n dd(bef(u[5]),u[5]),\n dd(bef(u[6]),u[6]),\n dd(bef(u[7]),u[0])\n ])) < 10^(-6),\n \"bef(u[i])=u[j] for expected pairs (i,j)\"\n );\nend:\n\n# Miscellaneous functions\ndp := `dot/R`(3):\ndd := `d_2/R`(3):\n`mmu/H` := apply_assoc(`mu/H`,[0,0,0,1]):\nrot := (x) -> [x[2],x[3],x[1]]:\n\n# Unit quaternions.\nii[1] := [1,0,0,0]: \nii[2] := [0,1,0,0]: \nii[3] := [0,0,1,0]: \nii[4] := [0,0,0,1]:\n\n# Misccellaneous quaternions\nzt[1] := [1,1+sqrt(3),1-sqrt(3),0] /~ 3:\nzt[2] := [1-sqrt(3),1,1+sqrt(3),0] /~ 3:\nzt[3] := [1+sqrt(3),1-sqrt(3),1,0] /~ 3:\nal := [ 1, 1, 1, 0] /~ sqrt(3):\nom := [ 1, 1, 1, 1] /~ 2:\nob := [-1,-1,-1, 1] /~ 2:\n\n# Various unit vectors in R3. For each i, the vectors u[i], v[i] and w[i]\n# form an orthonormal frame. z[i] is in the plane spanned by u[0] and u[i]\n# and is orthogonal to u[0].\n\nu := table(): v := table(): w := table(): z := table():\nu[ 0] := [ 1, 1, 1] /~ sqrt(3): v[ 0] := [ 2,-1,-1] /~ sqrt(6): w[ 0] := [ 0, 1,-1] /~ sqrt(2): \nu[ 1] := [ 1, 1,-1] /~ sqrt(3): v[ 1] := [ 2,-1, 1] /~ sqrt(6): w[ 1] := [ 0,-1,-1] /~ sqrt(2): z[ 1] := [ 1, 1,-2] /~ sqrt(6):\nu[ 2] := [ 1,-1, 1] /~ sqrt(3): v[ 2] := [-1, 1, 2] /~ sqrt(6): w[ 2] := [-1,-1, 0] /~ sqrt(2): z[ 2] := [ 1,-2, 1] /~ sqrt(6): \nu[ 3] := [-1, 1, 1] /~ sqrt(3): v[ 3] := [ 1, 2,-1] /~ sqrt(6): w[ 3] := [-1, 0,-1] /~ sqrt(2): z[ 3] := [-2, 1, 1] /~ sqrt(6): \nu[ 4] := [ 1,-1,-1] /~ sqrt(3): v[ 4] := [-1,-2, 1] /~ sqrt(6): w[ 4] := [-1, 0,-1] /~ sqrt(2): z[ 4] := [ 2,-1,-1] /~ sqrt(6): \nu[ 5] := [-1, 1,-1] /~ sqrt(3): v[ 5] := [ 1,-1,-2] /~ sqrt(6): w[ 5] := [-1,-1, 0] /~ sqrt(2): z[ 5] := [-1, 2,-1] /~ sqrt(6): \nu[ 6] := [-1,-1, 1] /~ sqrt(3): v[ 6] := [-2, 1,-1] /~ sqrt(6): w[ 6] := [ 0,-1,-1] /~ sqrt(2): z[ 6] := [-1,-1, 2] /~ sqrt(6): \nu[ 7] := [-1,-1,-1] /~ sqrt(3): v[ 7] := [-2, 1, 1] /~ sqrt(6): w[ 7] := [ 0, 1,-1] /~ sqrt(2):\n\npol := unapply(expand(cos(s) *~ u[0] +~ sin(s) *~ (cos(t) *~ v[0] +~ sin(t) *~ w[0])),s,t):\npol0 := (s,t) -> [cos(s),sin(s)*cos(t),sin(s)*sin(t)]:\n\n# The function wave(t) has trigonometric polynomial entries and lies on\n# the unit sphere, passing through all the points u[1],...,u[6].\nwave := unapply(\n(sin(3*t)/3) *~ u[0] +~ \n((sqrt(2)/3-1/2) * sin(5*t)) *~ v[0] +~\n((sqrt(2)/3-1/2) * cos(5*t) * (-1)) *~ w[0] +~\n((sqrt(2)/3+1/2) * sin(t)) *~ v[0] +~\n((sqrt(2)/3+1/2) * cos(t)) *~ w[0],\nt):\n\n# wband(t,s) parametrises a band with wave(t) = wband(t,0) at the centre\nwave_normal := unapply(combine(expand(simplify(expand(cross_product(wave(t),map(diff,wave(t),t)))))),t):\nwband := unapply(sin(s) *~ wave_normal(t) +~ cos(s) *~ wave(t),t,s):\n\ncheck_wband := proc()\n _ASSERT(\n simplify(expand(dp(wave(t),wave(t)) - 1)) = 0,\n \"wave(t) is a unit vector\"\n );\n\n _ASSERT(\n simplify(expand(wave(t - Pi/3) +~ rot(wave(t)))) = [0$3],\n \"wave(t) is Z/3-equivariant\"\n );\n\n _ASSERT(\n {seq(simplify(wave((2 * i - 1) * Pi/6) -~ u[[1,4,2,6,3,5][i]]),i=1..6)} = {[0$3]},\n \"wave(t) passes through u[1],...,u[6]\"\n );\nend:\n\n# A band in S2 with central circle perpendicular to u[0]\nhband := (t,s) ->\n sin(s) *~ u[0] +~ cos(s) *~ (cos(t) *~ v[0] +~ sin(t) *~ w[0]):\n\n# A family of bands in S2 whose central circles are lines of longitude\n# (with u[0] as the North pole).\n\nvband := (p) -> unapply(combine(\n cos(s) *~ ( cos(t) *~ (cos(p) *~ v[0] +~ sin(p) *~ w[0]) +~ sin(t) *~ u[0]) +~ \n sin(s) *~ ( -sin(p) *~ v[0] +~ cos(p) *~ w[0] )),\n t,s):\n\ncheck_bands := proc()\n _ASSERT(simplify(hband(0,0) -~ vband(0)(0,0)) = [0$3],\n \"Intersection of hband and vband(0)\");\n \n _ASSERT(simplify(hband(Pi/6,0) -~ vband(Pi/6)(0,0)) = [0$3],\n \"Intersection of hband and vband(Pi/6)\");\n \n _ASSERT(vband(0)(Pi/2,0) -~ u[0] = [0$3],\"u[0] on vband(0)\");\n\n _ASSERT(simplify(vband(0)(Pi-arctan(sqrt(2)/4),0) -~ u[3]) = [0$3],\"u[3] on vband(0)\");\n\n _ASSERT(simplify(vband(0)(-arctan(sqrt(2)/4),0) -~ u[4]) = [0$3],\"u[4] on vband(0)\");\n\n _ASSERT(vband(Pi/6)(Pi/2,0) -~ u[0] = [0$3],\"u[0] on vband(Pi/6)\");\n \n _ASSERT({\n simplify(wband( Pi/6,0) -~ u[1]),\n simplify(wband(3 * Pi/6,0) -~ u[4]),\n simplify(wband(5 * Pi/6,0) -~ u[2]),\n simplify(wband(7 * Pi/6,0) -~ u[6]),\n simplify(wband(9 * Pi/6,0) -~ u[3]),\n simplify(wband(11* Pi/6,0) -~ u[5])} = {[0$3]},\n \"u[1],...,u[6] on wband\");\n \n _ASSERT({\n simplify(wband( 0,0) -~ hband(15*Pi/6,0)),\n simplify(wband( Pi/3,0) -~ hband(13*Pi/6,0)),\n simplify(wband( 2 * Pi/3,0) -~ hband(11*Pi/6,0)),\n simplify(wband( 3 * Pi/3,0) -~ hband( 9*Pi/6,0)),\n simplify(wband( 4 * Pi/3,0) -~ hband( 7*Pi/6,0)),\n simplify(wband( 5 * Pi/3,0) -~ hband( 5*Pi/6,0))} = {[0$3]},\n \"Intersections of wband with hband\");\n \n _ASSERT(\n simplify(expand(hband(t-2*Pi/3,s) -~ rot(hband(t,s)))) = [0$3],\n \"hband is Z/3-equivariant\");\n \n _ASSERT(\n simplify(expand(hband(t+Pi/3,-s) +~ rot(hband(t,s)))) = [0$3],\n \"hband is Z/6-equivariant\");\n \n _ASSERT(vband(0)(t+Pi,-s) +~ vband(0)(t,s) = [0$3],\n \"vband(0) is Z/2-equivariant\");\n \n _ASSERT(vband(Pi/6)(t+Pi,-s) +~ vband(Pi/6)(t,s) = [0$3],\n \"vband(Pi/6) is Z/2-equivariant\");\n \n _ASSERT(simplify(expand(wband(t-Pi/3,0) +~ rot(wband(t,0)))) = [0$3],\n \"wband is Z/6-equivariant\");\n\n _ASSERT(wband(t+Pi,0) +~ wband(t,0) = [0$3],\n \"wband is Z/2-equivariant\");\n\nend:\n\n# An embedding of the Mobius band in R^3 whose centra curve is\n# a circle of radius sqrt(8/9) on S2 passing through u[1],u[2] and u[3],\n# and perpendicular to u[0].\n\ntriple_mobius := unapply(\n(1 + s * cos(3*t)) *~ ((1/3) *~ u[0] +~ sqrt(8/9) *~ (cos(2*t) *~ v[0] +~ sin(2*t) *~ w[0])) +~ \n (s * sin(3*t) * sqrt(2/27)) *~ [cos(2*t)-2,cos(2*t-2*Pi/3)-2,cos(2*t+2*Pi/3)-2],\nt,s):\n\n\ncheck_triple_mobius := proc()\n _ASSERT(\n simplify(expand(dp(triple_mobius(t,0),triple_mobius(t,0)) - 1)) = 0,\n \"triple_mobius(t,0) is a unit vector\");\n\n _ASSERT(\n expand(dp(triple_mobius(t,0),u[0]) - 1/3) = 0,\n \"triple_mobius(t,0) lies in a plane perpendicular to u[0]\");\n\n _ASSERT(\n simplify(expand(dp(map(coeff,expand(triple_mobius(t,s)),s),map(diff,triple_mobius(t,0),t)))) = 0,\n \"The triple_mobius() offset vector is perpendicular to the line of the central circle\" \n );\n\n _ASSERT({\n simplify(triple_mobius( Pi/6,0) -~ u[1]),\n simplify(triple_mobius(5*Pi/6,0) -~ u[2]),\n simplify(triple_mobius(3*Pi/6,0) -~ u[3])} = {[0$3]},\n \"u[1],u[2],u[3] on triple_mobius()\");\n\n _ASSERT(\n abs(twist_number(triple_mobius) - 3) < 10^(-6),\n \"triple_mobius() twist number is 3\"\n );\nend:\n\n# This is a smooth map R -> R^3 whose image is close to an equilateral\n# triangle \nsmooth_triangle := unapply([\n 3 * cos(2*t- Pi/3) + cos(4*t-5*Pi/3),\n 3 * cos(2*t-5*Pi/3) + cos(4*t- Pi/3),\n 3 * cos(2*t-3*Pi/3) + cos(4*t-3*Pi/3)\n] /~ (sqrt(27)) +~ u[0]/~3,t):\n\nsmooth_triangle_p := Pi/4:\n\nsmooth_triangle_offset := \n unapply(( sin(3*(t-Pi/4))*sqrt(2/3)) *~ [cos(2*t- Pi/3),cos(2*t-5*Pi/3),cos(2*t-3*Pi/3)] +~\n (-cos(3*(t-Pi/4))) *~ u[0],t):\n\ntriangle_mobius := unapply(\n smooth_triangle(t) +~ s *~ smooth_triangle_offset(t),\n t,s\n):\n\ncheck_smooth_triangle := proc()\n local t;\n\n _ASSERT(\n simplify(expand(smooth_triangle(t-2*Pi/3) -~ rot(smooth_triangle(t)))) = [0$3],\n \"smooth_triangle is Z/3-equivariant\"\n );\n \n _ASSERT({\n simplify(expand(smooth_triangle( 0) -~ u[1])),\n simplify(expand(smooth_triangle( Pi/3) -~ u[2])),\n simplify(expand(smooth_triangle(2*Pi/3) -~ u[3]))} = {[0$3]},\n \"u[1],u[2],u[3] on smooth_triangle\"\n );\n\n _ASSERT(\n abs(twist_number(triangle_mobius) - 3) < 10^(-6),\n \"triangle_mobius() twist number is 3\"\n );\nend:\n\nmake_band_plots := proc()\n global hband_plot,vband_plot,wband_plot,triangle_mobius_plot,usphere_plot,frame_plot;\n local s,t,opts;\n\n opts := t=0..2*Pi,s=-0.2..0.2,style=patchnogrid,scaling=constrained,axes=none;\n\n vband_plot := table():\n \n hband_plot := plot3d(hband(t,s),opts);\n vband_plot[0] := plot3d(vband(0)(t,s),opts);\n vband_plot[Pi/6] := plot3d(vband(Pi/6)(t,s),opts);\n wband_plot := plot3d(wband(t,s),opts);\n\n triangle_mobius_plot := plot3d(triangle_mobius(t,s),opts);\n\n usphere_plot := plot3d(\n cos(s) *~ u[0] +~ sin(s) *~ (cos(t) *~ v[0] +~ sin(t) *~ w[0]),\n s=0..Pi,t=0..2*Pi,colour=grey,style=wireframe,\n scaling=constrained,axes=none\n ):\n\n frame_plot := display(\n usphere_plot,\n point(u[0],colour=red,symbolsize=20),\n seq(point(u[i],colour=blue,symbolsize=20),i=1..3),\n seq(point(u[i],colour=cyan,symbolsize=20),i=4..6),\n point(u[7],colour=magenta,symbolsize=20),\n seq(spacecurve(cos(t) *~ u[0] +~ sin(t) *~ z[i],t=0..arccos(1/3),colour=orange),i=1..3),\n seq(spacecurve(cos(t) *~ u[0] +~ sin(t) *~ z[i],t=arccos(1/3)..Pi,colour=green),i=1..3),\n seq(spacecurve(cos(t) *~ u[7] +~ sin(t) *~ z[i],t=0..arccos(1/3),colour=orange),i=4..6),\n seq(spacecurve(cos(t) *~ u[7] +~ sin(t) *~ z[i],t=arccos(1/3)..Pi,colour=green),i=4..6),\n spacecurve(cos(t) *~ v[0] +~ sin(t) *~ w[0],t=0..2*Pi,colour=cyan),\n seq(point(cos(k*Pi/6) *~ v[0] +~ sin(k*Pi/6) *~ w[0],colour=black,symbolsize=20),k=0..11),\n spacecurve(wave(t),t=0..2*Pi,colour=black),\n scaling=constrained,axes=none\n ):\n\n save(hband_plot,vband_plot,wband_plot,triangle_mobius_plot,frame_plot,usphere_plot,\n cat(data_dir,\"/boys_band_plots.m\"));\nend:\n\nload_band_plots := proc()\n read(cat(data_dir,\"/boys_band_plots.m\"));\nend:\n\nmake_band_be_plots := proc()\n global hband_be_plot,vband_be_plot,wband_be_plot;\n local s,t,opts;\n\n opts := t=0..Pi,s=-0.2..0.2,numpoints=10000,style=patchnogrid,scaling=constrained,axes=none;\n\n vband_be_plot := table():\n \n hband_be_plot := plot3d(bef(hband(t,s)),opts);\n vband_be_plot[0] := plot3d(bef(vband(0)(t,s)),opts);\n vband_be_plot[Pi/6] := plot3d(bef(vband(Pi/6)(t,s)),opts);\n wband_be_plot := plot3d(bef(wband(t,s)),opts);\n\n save(hband_be_plot,vband_be_plot,wband_be_plot,\n cat(data_dir,\"/boys_band_be_plots.m\"));\nend:\n\nload_band_be_plots := proc()\n read(cat(data_dir,\"/boys_band_be_plots.m\"));\nend:\n\n\n# If f : R2 -> R3 with f(t+2*Pi=f(t) this measures the amount of twisting,\n# so a standard Mobius band gives 1 and the maps triple_mobius and\n# triangle_mobius give 3.\n\ntwist_number := proc(f)\n local N,e,a,b,c,z,i;\n N := 24;\n e := 0.001;\n a := table():\n b := table():\n c := table():\n z := table():\n for i from 0 to 2*N-1 do \n a[i] := evalf(f(i*Pi/N,0));\n b[i] := evalf((f(i*Pi/N,e) -~ f(i*Pi/N,-e))/~e);\n b[i] := b[i] /~ sqrt(dp(b[i],b[i]));\n od:\n a[2*N] := a[0]; a[2*N+1] := a[1]; \n b[2*N] := b[0]; b[2*N+1] := b[1];\n\n for i from 0 to 2*N do \n c[i] := cross_product(u[0],a[i+1] -~ a[i]);\n c[i] := c[i] /~ sqrt(dp(c[i],c[i]));\n z[i] := dp(b[i],c[i]) + I * dp(b[i],u[0]);\n od:\n\n return evalf(add(argument(z[i+1]/z[i]),i=0..2*N-1) / (2*Pi));\nend:\n\n# For a homogeneous quadratic map q : R4 -> R, return the matrix M\n# such that q(x) = x^T M x.\n\nquadratic_coeffs := proc(u)\n local M,i,j,c;\n\n M := Matrix(4,4,shape=symmetric):\n for i from 1 to 4 do M[i,i] := coeff(u,x[i],2); od:\n \n for i from 1 to 3 do \n for j from i+1 to 4 do \n c := coeff(coeff(u,x[i],1),x[j],1)/2;\n M[i,j] := c;\n M[j,i] := c;\n od:\n od:\n\n return M;\nend:\n\n# Construct a matrix of coefficients for a discrete Fourier transform.\n# This will use 2*N sample points and return a trigonometric polynomial\n# of degree d.\n\nset_fourier_matrix := proc(N,d)\n global fourier_N,fourier_d,fourier_matrix;\n local Pi0,T,i,j,k;\n\n Pi0 := evalf(Pi);\n T := Matrix(2*d+1,2*N):\n for i from 1 to 2*N do \n T[1,i] := 1/(2*N);\n for k from 1 to d do \n T[2*k ,i] := sin(i*k*Pi0/N)/N;\n T[2*k+1,i] := cos(i*k*Pi0/N)/N;\n od:\n od:\n\n fourier_N := N;\n fourier_d := d;\n fourier_matrix := T;\n return T;\nend:\n\nset_fourier_matrix(480,12):\n\n# Calculate an approximate Fourier series for bef o b, for a function\n# b : R2 -> S2 with b(t + 2*Pi,s) = b(t,s). The result is returned as\n# a table with many different entries.\n\nfourier_approx := proc(b)\n local t,c,Pi0,d,N,U,F,m,k,e,cxyz,cuvw;\n\n c := table():\n Pi0 := evalf(Pi);\n d := fourier_d;\n N := fourier_N;\n U := map(evalf,Transpose(Matrix([u[0],v[0],w[0]])));\n e := 10.^(-3);\n\n c[\"vals\"] := [seq(evalf(b(i*Pi0/N, 0)),i=1..2*N)];\n c[\"offset0\"] := [seq(evalf(b(i*Pi0/N, e)),i=1..2*N)];\n c[\"offset1\"] := [seq(evalf(b(i*Pi0/N,-e)),i=1..2*N)];\n\n c[\"vals_be\"] := map(bef,c[\"vals\"]);\n c[\"offset0_be\"] := map(bef,c[\"offset0\"]);\n c[\"offset1_be\"] := map(bef,c[\"offset1\"]);\n c[\"vals_dbe\"] :=\n [seq((c[\"offset0_be\"][i] -~ c[\"offset1_be\"][i]) /~ (2*e),i=1..2*N)];\n \n c[\"coeffs_be\"] := fourier_matrix . Matrix(c[\"vals_be\"]);\n c[\"uvw_coeffs_be\"] := c[\"coeffs_be\"] . U;\n c[\"coeffs_dbe\"] := fourier_matrix . Matrix(c[\"vals_dbe\"]);\n c[\"uvw_coeffs_dbe\"] := c[\"coeffs_dbe\"] . U;\n\n for k in [\"coeffs_be\",\"uvw_coeffs_be\",\"coeffs_dbe\",\"uvw_coeffs_dbe\"] do\n c[k] := trim(c[k],10.^(-6));\n od:\n\n F := [1,seq(op([sin(k*t),cos(k*t)]),k=1..d)];\n c[\"approx_be\"] := unapply(convert(Transpose(Vector(F)) . c[\"coeffs_be\" ],list),t);\n c[\"approx_dbe\"] := unapply(convert(Transpose(Vector(F)) . c[\"coeffs_dbe\"],list),t);\n c[\"approx\"] := unapply(c[\"approx_be\"](t) +~ c[\"approx_dbe\"](t) *~ s,t,s);\n\n for k in [\"coeffs_be\",\"uvw_coeffs_be\",\"coeffs_dbe\",\"uvw_coeffs_dbe\"] do\n c[k] := convert(c[k],listlist);\n od:\n\n return eval(c):\nend:\n\nif false then\n vband_approx := table():\n printf(\"hband\\n\");\n hband_approx := fourier_approx(hband):\n printf(\"vband 0\\n\");\n vband_approx[0] := fourier_approx(vband(0)):\n printf(\"vband 1\\n\");\n vband_approx[Pi/6] := fourier_approx(vband(Pi/6)):\n printf(\"wband\\n\");\n wband_approx := fourier_approx(wband):\n save(hband_approx,vband_approx,wband_approx,\n cat(data_dir,\"/boys_approx.m\")):\nelse\n read(cat(data_dir,\"/boys_approx.m\")):\nfi:\n\nmake_approx_plot := proc(a)\n a[\"plot\"] := \n plot3d(a[\"approx\"](t,s),t=0..2*Pi,s=-0.1..0.1,\n style=patchnogrid,scaling=constrained,axes=none,args[2..-1]):\n return a[\"plot\"];\nend:\n\nmake_approx_plots := proc()\n global ribbon_plot;\n local opts;\n \n make_approx_plot(hband_approx,numpoints=5000):\n make_approx_plot(vband_approx[0],numpoints=8000):\n make_approx_plot(vband_approx[Pi/6],numpoints=5000):\n make_approx_plot(wband_approx,numpoints=5000):\n\n opts := t=0..2*Pi,s=-0.02..0.02,numpoints=6000,style=patchnogrid:\n\n ribbon_plot := \n display(\n plot3d(vband_approx[0][\"approx\"](t,s), opts,colour=red),\n plot3d(rot(vband_approx[0][\"approx\"](t,s)), opts,colour=red),\n plot3d(rot(rot(vband_approx[0][\"approx\"](t,s))), opts,colour=red),\n plot3d(vband_approx[Pi/6][\"approx\"](t,s), opts,colour=blue),\n plot3d(rot(vband_approx[Pi/6][\"approx\"](t,s)), opts,colour=blue),\n plot3d(rot(rot(vband_approx[Pi/6][\"approx\"](t,s))),opts,colour=blue),\n plot3d(hband_approx[\"approx\"](t,s), opts,colour=green),\n plot3d(wband_approx[\"approx\"](t,s), opts,colour=magenta),\n scaling=constrained,axes=none\n );\n\nend:\n\n# Given asome approximate Fourier transforms, try to work out the general\n# form. For coefficients of small absolute value, we assume that they\n# are really supposed to be zero. For coefficients that are sufficiently\n# cloe, we assume that they should actually be the same. Signs are\n# inserted to ensure that the values of all parameters should be positive.\n\nreset_outline := proc()\n global outline_k,outline_a;\n outline_k := 0;\n outline_a := table():\nend:\n\nreset_outline():\n\nmake_outline := proc(b)\n global outline_k,outline_a;\n local p,q,i,j,k,m,vp,d,x,F,found;\n\n p := [op(map(op,b[\"uvw_coeffs_be\"])),\n op(map(op,b[\"uvw_coeffs_dbe\"]))];\n\n q := NULL:\n\n for i from 1 to nops(p) do\n vp := p[i];\n if abs(vp) < 0.05 then\n q := q,0;\n else\n found := false;\n for j from 1 to outline_k do \n if abs(vp - outline_a[j]) < 0.001 then\n q := q,a[j];\n found := true;\n break;\n fi;\n if abs(vp + outline_a[j]) < 0.001 then\n q := q,-a[j];\n found := true;\n break;\n fi;\n od:\n if not(found) then\n outline_k := outline_k + 1;\n outline_a[outline_k] := abs(vp);\n q := q,signum(vp) * a[outline_k];\n fi;\n fi;\n od:\n \n q := [q];\n \n m := nops(q)/6;\n d := (m-1)/2;\n q := [[seq([q[3*i-2],q[3*i-1],q[3*i]],i=1..m)],\n [seq([q[3*i-2],q[3*i-1],q[3*i]],i=m+1..2*m)]];\n\n b[\"uvw_coeffs_be_outline\"] := q[1];\n b[\"uvw_coeffs_dbe_outline\"] := q[2];\n\n x := [0,0,0];\n F := [1,seq(op([sin(k*t),cos(k*t)]),k=1..d)];\n\n b[\"outline_be\"] := unapply(\n add(F[i] * q[1][i][1],i=1..m) *~ u[0] +~ \n add(F[i] * q[1][i][2],i=1..m) *~ v[0] +~ \n add(F[i] * q[1][i][3],i=1..m) *~ w[0],t);\n\n b[\"outline_dbe\"] := unapply(\n add(F[i] * q[2][i][1],i=1..m) *~ u[0] +~ \n add(F[i] * q[2][i][2],i=1..m) *~ v[0] +~ \n add(F[i] * q[2][i][3],i=1..m) *~ w[0],t);\nend:\n\n# Here we find the general form of the Fourier coefficients for bef o f\n# with f in {hband, vband(0), vband(Pi/6), wband}. Then we construct a list\n# of relations that must be imposed to ensure that the approximations fit\n# together correctly and have the expected behaviour at the points u[i].\n\nfind_approx_form := proc()\n global approx_form_rels,approx_form_sols;\n local t;\n \n reset_outline():\n make_outline(hband_approx):\n make_outline(vband_approx[0]):\n make_outline(vband_approx[Pi/6]):\n make_outline(wband_approx):\n\n approx_form_rels := expand(simplify(map(op,expand([\n hband_approx[\"outline_be\"](0) -~ vband_approx[0][\"outline_be\"](0),\n hband_approx[\"outline_be\"](Pi/6) -~ vband_approx[Pi/6][\"outline_be\"](0),\n vband_approx[0][\"outline_be\"](Pi/2) -~ u[0],\n vband_approx[Pi/6][\"outline_be\"](Pi/2) -~ u[0],\n vband_approx[0][\"outline_be\"](Pi - arctan(sqrt(2)/4)) -~ u[4],\n vband_approx[0][\"outline_be\"]( - arctan(sqrt(2)/4)) -~ u[4],\n wband_approx[\"outline_be\"]( Pi/6,0) -~ u[6],\n wband_approx[\"outline_be\"]( 3 * Pi/6,0) -~ u[4],\n wband_approx[\"outline_be\"]( 5 * Pi/6,0) -~ u[5],\n wband_approx[\"outline_be\"]( 7 * Pi/6,0) -~ u[6],\n wband_approx[\"outline_be\"]( 9 * Pi/6,0) -~ u[4],\n wband_approx[\"outline_be\"](11 * Pi/6,0) -~ u[5],\n wband_approx[\"outline_be\"]( 0,0) -~ hband_approx[\"outline_be\"](15*Pi/6,0),\n wband_approx[\"outline_be\"]( Pi/3,0) -~ hband_approx[\"outline_be\"](13*Pi/6,0),\n wband_approx[\"outline_be\"]( 2 * Pi/3,0) -~ hband_approx[\"outline_be\"](11*Pi/6,0),\n wband_approx[\"outline_be\"]( 3 * Pi/3,0) -~ hband_approx[\"outline_be\"]( 9*Pi/6,0),\n wband_approx[\"outline_be\"]( 4 * Pi/3,0) -~ hband_approx[\"outline_be\"]( 7*Pi/6,0),\n wband_approx[\"outline_be\"]( 5 * Pi/3,0) -~ hband_approx[\"outline_be\"]( 5*Pi/6,0),\n map(coeffs,expand(hband_approx[\"outline_be\"](t-2/3*Pi) -~ rot(hband_approx[\"outline_be\" ](t))),{sin(t),cos(t)}),\n map(coeffs,expand(hband_approx[\"outline_dbe\"](t-2/3*Pi) -~ rot(hband_approx[\"outline_dbe\"](t))),{sin(t),cos(t)}),\n map(coeffs,expand(hband_approx[\"outline_be\"](t+Pi/3) -~ rot(hband_approx[\"outline_be\" ](t))),{sin(t),cos(t)}),\n map(coeffs,expand(hband_approx[\"outline_dbe\"](t+Pi/3) +~ rot(hband_approx[\"outline_dbe\"](t))),{sin(t),cos(t)}),\n map(coeffs,expand(vband_approx[0][\"outline_be\"](t+Pi) -~ vband_approx[ 0][\"outline_be\" ](t)) ,{sin(t),cos(t)}),\n map(coeffs,expand(vband_approx[0][\"outline_dbe\"](t+Pi) +~ vband_approx[ 0][\"outline_dbe\"](t)) ,{sin(t),cos(t)}),\n map(coeffs,expand(vband_approx[Pi/6][\"outline_be\"](t+Pi) -~ vband_approx[Pi/6][\"outline_be\" ](t)) ,{sin(t),cos(t)}),\n map(coeffs,expand(vband_approx[Pi/6][\"outline_dbe\"](t+Pi)-~ vband_approx[Pi/6][\"outline_dbe\"](t)) ,{sin(t),cos(t)}),\n map(coeffs,expand(wband_approx[\"outline_be\"](t-Pi/3) -~ rot(wband_approx[\"outline_be\" ](t))),{sin(t),cos(t)}),\n simplify(expand(dp(hband_approx[\"outline_dbe\"](Pi/12),u[0]))),\n #simplify(expand(dp(wband_approx[\"outline_dbe\"](Pi/12),u[0]))),\n simplify(expand(dp(vband_approx[0][\"outline_dbe\"](Pi/6),u[0]))),\n simplify(expand(dp(vband_approx[Pi/6][\"outline_dbe\"](Pi/2),u[0]))),\n NULL])))):\n\n approx_form_sols := solve(approx_form_rels);\nend:\n\nmake_boys_cube_complex := proc()\n global boys_cube_complex;\n local N,T,V,P,E,F,C,i,j,k,e,a;\n \n T := table():\n N := 50;\n \n V := [seq(i,i=0..N-1)];\n T[\"vertices\"] := V;\n\n P := table():\n \n P[ 0] := [ 2, 2, 2]; P[ 1] := [ 2, 2,-2]; P[ 2] := [ 2,-2, 2]; P[ 3] := [-2, 2, 2];\n P[ 4] := [ 2,-2,-2]; P[ 5] := [-2, 2,-2]; P[ 6] := [-2,-2, 2]; P[ 7] := [-2,-2,-2];\n P[ 8] := [ 2, 2, 0]; P[ 9] := [ 2, 0, 2]; P[10] := [ 0, 2, 2]; P[11] := [ 0,-2,-2];\n P[12] := [-2, 0,-2]; P[13] := [-2,-2, 0]; P[14] := [ 2, 0,-2]; P[15] := [ 2,-2, 0];\n P[16] := [ 0,-2, 2]; P[17] := [-2, 0, 2]; P[18] := [-2, 2, 0]; P[19] := [ 0, 2,-2];\n P[20] := [ 2, 0, 0]; P[21] := [ 0, 0, 2]; P[22] := [ 0, 2, 0];\n P[23] := [-2, 0, 0]; P[24] := [ 0, 0,-2]; P[25] := [ 0,-2, 0];\n P[26] := [ 2, 1, 1]; P[27] := [ 2,-1, 1]; P[28] := [ 2,-1,-1]; P[29] := [ 2, 1,-1];\n P[30] := [ 1, 1, 2]; P[31] := [-1, 1, 2]; P[32] := [-1,-1, 2]; P[33] := [ 1,-1, 2];\n P[34] := [ 1, 2, 1]; P[35] := [ 1, 2,-1]; P[36] := [-1, 2,-1]; P[37] := [-1, 2, 1];\n P[38] := [-2,-1,-1]; P[39] := [-2, 1,-1]; P[40] := [-2, 1, 1]; P[41] := [-2,-1, 1];\n P[42] := [-1,-1,-2]; P[43] := [ 1,-1,-2]; P[44] := [ 1, 1,-2]; P[45] := [-1, 1,-2];\n P[46] := [-1,-2,-1]; P[47] := [-1,-2, 1]; P[48] := [ 1,-2, 1]; P[49] := [ 1,-2,-1];\n\n T[\"embedding_dim\"] := 3;\n T[\"embedding\"] := eval(P);\n T[\"cube_embedding\"] := eval(P);\n\n T[\"sphere_embedding\"] := table():\n for i in V do\n a := P[i];\n a := a /~ sqrt(add(a[i]^2,i=1..3));\n T[\"sphere_embedding\"][i] := a;\n od:\n \n E := NULL:\n for i from 0 to N-1 do\n for j from i + 1 to N-1 do\n a := sort(map(abs,P[j] -~ P[i]));\n if modp(P[i],2) *~ modp(P[j],2) = [0,0,0] and \n (a = [0,1,1] or a = [0,0,2]) then \n E := E,[i,j];\n fi;\n od:\n od:\n\n E := [E];\n T[\"edges\"] := E;\n\n F := NULL;\n for e in E do\n for k from e[2] + 1 to N-1 do\n if member([e[1],k],E) and member([e[2],k],E) then\n F := F,[op(e),k];\n fi;\n od:\n od:\n\n F := [F];\n T[\"faces\"] := F;\n T[\"max_simplices\"] := F;\n \n T[\"vertex_index\"] := table():\n\n for i in V do\n T[\"vertex_index\"][T[\"cube_embedding\"][i]] := i;\n T[\"vertex_index\"][T[\"sphere_embedding\"][i]] := i;\n od:\n\n T[\"hedges\"] := [14,28,15,48,16,32,17,40,18,36,19,44,14]:\n T[\"hedges\"] := map(sort,[seq([T[\"hedges\"][i],T[\"hedges\"][i+1]],i=1..nops(T[\"hedges\"])-1)]):\n\n T[\"wedges\"] := [1,14,4,15,2,16,6,17,3,18,5,19,1]:\n T[\"wedges\"] := map(sort,[seq([T[\"wedges\"][i],T[\"wedges\"][i+1]],i=1..nops(T[\"wedges\"])-1)]):\n\n C := table():\n\n for e in T[ \"edges\"] do C[e] := grey; od:\n for e in T[\"hedges\"] do C[e] := cyan; od:\n for e in T[\"wedges\"] do C[e] := black; od:\n\n C[[ 0, 8]] := orange: C[[ 0, 9]] := orange: C[[ 0,10]] := orange: C[[ 1, 8]] := orange:\n C[[ 2, 9]] := orange: C[[ 3,10]] := orange: C[[ 7,11]] := orange: C[[ 7,12]] := orange:\n C[[ 7,13]] := orange: C[[ 4,11]] := orange: C[[ 5,12]] := orange: C[[ 6,13]] := orange:\n C[[ 0,26]] := green: C[[ 0,34]] := green: C[[ 0,20]] := green: C[[20,26]] := green:\n C[[22,34]] := green: C[[21,30]] := green: C[[20,28]] := green: C[[22,36]] := green:\n C[[21,32]] := green: C[[ 4,28]] := green: C[[ 5,36]] := green: C[[ 6,32]] := green:\n C[[ 1,44]] := green: C[[ 2,48]] := green: C[[ 3,40]] := green: C[[24,44]] := green:\n C[[25,48]] := green: C[[23,40]] := green: C[[24,42]] := green: C[[25,46]] := green:\n C[[23,38]] := green: C[[ 7,42]] := green: C[[ 7,46]] := green: C[[ 7,38]] := green:\n\n T[\"edge_colour\"] := eval(C):\n\n T[\"cube_plot\"] := \n display(\n plot3d([ s, t,-1] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n plot3d([ s, t, 1] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n plot3d([ s,-1, t] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n plot3d([ s, 1, t] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n plot3d([-1, s, t] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n plot3d([ 1, s, t] *~ 1.99,s=-1..1,t=-1..1,style=patchnogrid,colour=grey),\n seq(line(P[e[1]],P[e[2]],colour=T[\"edge_colour\"][e]),e in T[\"edges\"]),\n axes=none\n );\n\n boys_cube_complex := eval(T):\n return eval(T);\nend:\n\nrefine_boys_cube_complex := proc()\n global refined_boys_cube_complex;\n local T0,TT,S,P,p;\n T0 := `condense/simplicial_complex`(make_boys_cube_complex()):\n `set_edges/simplicial_complex`(T0):\n `set_faces/simplicial_complex`(T0):\n `normalise_embedding/simplicial_complex`(T0):\n T0[\"boys_embedding\"] := map(bef,eval(T0[\"embedding\"])):\n TT := [eval(T0)]:\n\n# P := [0.8,0.6,0.4,0.3]:\n P := [0.8]:\n \n for p in P do \n S := select(e -> boys_edge_length(T0)(e) > p,T0[\"edges\"]):\n T0 := `partial_triangular_subdivision/simplicial_complex`(T0,S):\n `normalise_embedding/simplicial_complex`(T0):\n T0[\"sphere_embedding\"] := eval(T0[\"embedding\"]):\n T0[\"boys_embedding\"] := map(evalf,map(bef,T0[\"embedding\"])):\n TT := [op(TT),eval(T0)]:\n od:\n\n refined_boys_cube_complex := eval(T0):\n\n# save(refined_boys_cube_complex,cat(data_dir,\"/refined_boys_cube_complex.m\")):\n\n return eval(T0):\nend:\n\nedge_length := (T) -> e -> `d_2/R`(3)(T[\"embedding\"][e[1]],T[\"embedding\"][e[2]]):\nboys_edge_length := (T) -> e -> `d_2/R`(3)(T[\"boys_embedding\"][e[1]],T[\"boys_embedding\"][e[2]]):\n\nedge_length_plot := (T) ->\n listplot(sort(map(edge_length(T),[op(T[\"edges\"])]))):\nboys_edge_length_plot := (T) ->\n listplot(sort(map(boys_edge_length(T),[op(T[\"edges\"])]))):\n\nhomogeneous_basis := proc(d,x)\n return [seq(seq(x[1]^i*x[2]^j*x[3]^(d-i-j),j=0..d-i),i=0..d)];\nend:\n\nextend_cyclic := proc(p)\n local x;\n\n return unapply([p([x[1],x[2],x[3]]),\n p([x[2],x[3],x[1]]),\n p([x[3],x[1],x[2]])],x)\nend:\n\nmaybe_extend_cyclic := proc(p) \n if type(p(x),list) then\n return eval(p);\n else\n return extend_cyclic(p);\n fi;\nend:\n\nmake_quadric := proc()\n global general_quadric0,general_quadric,quadric_point_rels,quadric_point_sol,\n special_quadric0,special_quadric,hband_quadric,vband_quadric;\n local B,x,rels,sol;\n \n B := homogeneous_basis(4,x);\n general_quadric0 := unapply(add(a[i] * B[i],i=1..nops(B)),x):\n general_quadric := extend_cyclic(eval(general_quadric0));\n\n quadric_point_rels := [\n op(general_quadric(u[0]) -~ u[0]),\n op(general_quadric(u[1]) +~ u[1])\n ]:\n\n hband_quadric := \n map(collect,combine(simplify(expand(general_quadric(hband(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n vband_quadric[0] := \n map(collect,combine(simplify(expand(general_quadric(vband(0)(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n vband_quadric[Pi/6] := \n map(collect,combine(simplify(expand(general_quadric(vband(Pi/6)(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n quadric_point_sol := solve(quadric_point_rels);\n\n # We now construct a 6-parameter family of quadrics such that\n # - u[0] maps to u[0], with specified behaviour on the tangent space\n # - u[4] maps to u[4] (which forces u[5] and u[6] to also be fixed, by equivariance)\n # - pol(Pi/3,Pi/6) maps to zero.\n special_quadric := eval(general_quadric):\n rels := simplify(expand({\n op(special_quadric(u[0]) -~ u[0] /~ sqrt(2)), \n op(map(coeffs,simplify(map(rem,expand(\n special_quadric(u[0] +~ t *~ v[0]) -~ special_quadric(u[0]) -~ t *~ ([-1,2,-1]/~sqrt(2))),t^2,t)),t)),\n op(map(coeffs,simplify(map(rem,expand(\n special_quadric(u[0] +~ t *~ w[0]) -~ special_quadric(u[0]) -~ t *~ ([-1,0,1]*~sqrt(3/2))),t^2,t)),t)),\n op(special_quadric(u[4]) -~ u[4] /~ sqrt(2)),\n op(special_quadric(pol(Pi/3,Pi/6)))\n })):\n sol := solve(rels,{seq(a[i],i=7..15)}):\n special_quadric := unapply(expand(subs(sol,special_quadric(x))),x):\n special_quadric0 := unapply(special_quadric(x)[1],x);\nend:\n\nmake_sextic := proc()\n global general_sextic0,general_sextic,sextic_point_rels,sextic_point_sol,\n hband_sextic,vband_sextic;\n local B,x;\n \n B := homogeneous_basis(6,x);\n general_sextic0 := unapply(add(a[i] * B[i],i=1..nops(B)),x):\n general_sextic := extend_cyclic(general_sextic0);\n\n sextic_point_rels := [\n op(general_sextic(u[0]) -~ u[0]),\n op(general_sextic(u[1]) +~ u[1])\n ]:\n\n hband_sextic := \n map(collect,combine(simplify(expand(general_sextic(hband(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n vband_sextic[0] := \n map(collect,combine(simplify(expand(general_sextic(vband(0)(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n vband_sextic[Pi/6] := \n map(collect,combine(simplify(expand(general_sextic(vband(Pi/6)(t,0))))),{seq(cos(k*t),k=1..10),seq(sin(k*t),k=1..10)}):\n\n sextic_point_sol := solve(sextic_point_rels);\nend:\n\ncheck_sextic := proc()\n local x,xx;\n xx := [x[1],x[2],x[3]];\n \n _ASSERT(\n general_sextic(-~xx) -~ general_sextic(xx) = [0$3],\n \"general_sextic is Z/2-equivariant\"\n );\n \n _ASSERT(\n general_sextic(rot(xx)) -~ rot(general_sextic(xx)) = [0$3],\n \"general_sextic is Z/3-equivariant\"\n );\nend:\n\nmake_quadric():\nmake_sextic():\n\nrefine_sextic_a := proc()\n global sextic_a0,sextic_a;\n local sextic_rels,sextic_sol;\n \n sextic_rels := [op(sextic_point_rels),\n seq(coeff(combine(expand(dp(u[0],hband_sextic))),f,1), f in [cos(2*t),sin(4*t),cos(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(v[0],hband_sextic))),f,1), f in [cos(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(w[0],hband_sextic))),f,1), f in [sin(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(u[0],vband_sextic[0]))),f,1), f in [sin(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(v[0],vband_sextic[0]))),f,1), f in [sin(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(w[0],vband_sextic[0]))),f,1), f in [cos(2*t),sin(4*t),cos(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(u[0],vband_sextic[Pi/6]))),f,1), f in [sin(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(v[0],vband_sextic[Pi/6]))),f,1), f in [sin(4*t),sin(6*t),cos(6*t)]),\n seq(coeff(combine(expand(dp(w[0],vband_sextic[Pi/6]))),f,1), f in [cos(2*t),sin(4*t),cos(4*t),sin(6*t),cos(6*t)])\n ]:\n\n sextic_sol := solve(sextic_rels);\n sextic_a0 := unapply(simplify(expand(subs(sextic_sol,general_sextic0(x)))),x);\n sextic_a := unapply(simplify(expand(subs(sextic_sol,general_sextic(x)))) ,x);\nend:\n\nrefine_sextic_b := proc()\n global sextic_b0,sextic_b;\n local sextic_rels,sextic_sol;\n \n sextic_rels := [op(sextic_point_rels),\n op(map(coeffs,expand(simplify(expand(map(convert,map(series,expand(general_sextic(hband(t,s)) -~ triangle_mobius(t,s)),s=0,2),polynom,s)))),{sin(t),cos(t),s}))\n ]:\n\n sextic_sol := solve(sextic_rels);\n sextic_b0 := unapply(simplify(expand(subs(sextic_sol,general_sextic0(x)))),x);\n sextic_b := unapply(simplify(expand(subs(sextic_sol,general_sextic(x)))) ,x);\nend:\n\ncompare_terms := (u,v) -> \n abs(subs({x[1]=1,x[2]=1,x[3]=1},u)) < abs(subs({x[1]=1,x[2]=1,x[3]=1},v));\n\nsort_terms := proc(p)\n local T;\n T := `if`(type(p,`+`),[op(p)],[p]);\n return sort(T,compare_terms);\nend:\n\n# Precompute coefficients for approximate integration over S2 using the\n# triangulation T.\nint_setup := proc(T)\n local a,b,c,d,f;\n T[\"face_area\"] := table():\n T[\"face_centre\"] := table():\n T[\"face_centre_be\"] := table():\n for f in T[\"faces\"] do\n a,b,c := op(map(i -> T[\"embedding\"][i],f));\n d := a +~ b +~ c;\n d := d /~ `norm_2/R`(3)(d);\n T[\"face_centre\"][f] := d;\n T[\"face_centre_be\"][f] := bef(d);\n T[\"face_area\"][f] := spherical_triangle_area(a,b,c);\n od:\nend:\n\n# Integration over S2, normalised to have total area 1.\nsphere_int := proc(g,T)\n local u,f;\n u := 0;\n for f in T[\"faces\"] do \n u := u + (g(T[\"face_centre\"][f]) * T[\"face_area\"][f]);\n od:\n u := evalf(u / (4*Pi));\n return u;\nend:\n\nsphere_int_be := proc(g,T)\n local u,f;\n u := [0,0,0];\n for f in T[\"faces\"] do \n u := u +~ (g(T[\"face_centre\"][f]) * T[\"face_area\"][f]) *~ T[\"face_centre_be\"][f];\n od:\n u := evalf(u / (4*Pi));\n return u;\nend:\n\n# Symbolic integration over the sphere, again normalised to have area 1\nsint0 := proc(u) \n option remember;\n local v;\n v := subs({x[1]=sin(s)*cos(t),x[2]=sin(s)*sin(t),x[3]=cos(s)},u) * sin(s)/(4*Pi);\n v := expand(convert(v,exp));\n v := int(v,t=0..2*Pi);\n v := int(v,s=0..Pi);\n return v;\nend:\n\nsint := apply_linear(sint0,realcons):\n\nips := (u,v) -> evalf(sint(expand(u*v))):\n\n# Faster symbolic integration for polynomials\nsintp0 := proc(u)\n local c,d,i;\n c := 1;\n for i from 1 to 3 do \n d[i] := degree(u,x[i]);\n od:\n if u <> x[1]^d[1] * x[2]^d[2] * x[3]^d[3] then\n error(\"Argument is not monomial\");\n fi:\n if modp(d[1],2) = 1 or modp(d[2],2) = 1 or modp(d[3],2) = 1 then\n return 0;\n fi;\n\n return doublefactorial(d[1]-1) * \n doublefactorial(d[2]-1) * \n doublefactorial(d[3]-1) /\n doublefactorial(d[1]+d[2]+d[3]+1);\nend:\n\nsintp := apply_linear(sintp0,realcons):\n\nipsp := (u,v) -> evalf(sintp(expand(u*v))):\n\nmake_orthonormal := proc(B,T)\n local Y,i,j;\n\n Y := table():\n for i from 1 to nops(B) do \n Y[i] := B[i]:\n for j from 1 to i-1 do \n Y[i] := expand(Y[i] - sphere_int(unapply(Y[i]*Y[j],x),T) * Y[j]);\n od:\n Y[i] := expand(Y[i] / sqrt(sphere_int(unapply(Y[i]^2,x),T0))):\n od:\n\n return eval(Y):\nend:\n\nmake_immersion := proc(p,T_)\n local pp,T,s,t;\n\n pp := p;\n if not(type(pp,function)) then pp := unapply(pp,x); fi;\n if not(type(pp(x),list)) then\n pp := unapply([pp([x[1],x[2],x[3]]),\n pp([x[2],x[3],x[1]]),\n pp([x[3],x[1],x[2]])],x);\n fi;\n \n if nargs > 1 then T := eval(T_) else T := table(): fi;\n T[\"map\"] := eval(pp);\n T[\"map0\"] := unapply(pp(x)[1],x);\n\n pp := T[\"map0\"](pol(s,t));\n pp := combine(expand(simplify(evalf(expand(pp)))));\n T[\"pol_map0\"] := unapply(pp,s,t);\n T[\"pol_map\"] :=\n unapply(evalf([pp(s,t),pp(s+2*Pi/3,t),pp(s,t-2*Pi/3)]),s,t);\n\n return eval(T);\nend:\n\nmake_plots := proc(T)\n local opts,p;\n opts := style=patchnogrid,scaling=constrained,axes=none;\n T[\"plot\"] := plot3d(T[\"pol_map\"](s,t),t=0..2*Pi,s=0..Pi,opts,numpoints=8000);\n T[\"hband_plot\"] := plot3d(T[\"map\"](hband(t,s)),t=0..2*Pi,s=-0.2..0.2,opts,numpoints=8000);\n T[\"vband_plot\"] := table():\n for p in [0,Pi/6] do \n T[\"vband_plot\"][p] := plot3d(T[\"map\"](vband(p)(t,s)),t=0..2*Pi,s=-0.2..0.2,opts,numpoints=8000);\n od:\n \n return T[\"plot\"];\nend:\n\north_proj := (x) -> <\n ,\n <-x[1]*x[2]|x[1]^2+x[3]^2|-x[2]*x[3]>,\n <-x[1]*x[3]|-x[2]*x[3]|x[1]^2+x[2]^2>\n>;\n\nsegment_max := proc(f)\n local T,N,s_step,t_step,m0,s0,t0,i,j,sol;\n T := f(pol(s,t));\n N := 6;\n s_step := evalf(Pi/(2*N)):\n t_step := evalf(2*Pi/(3*N)):\n m0 := 0;\n s0 := 0;\n t0 := 0;\n for i from 0 to N-1 do \n for j from 0 to N-1 do\n try \n sol := \n NLPSolve(T,[],s=i*s_step..(i+1)*s_step,t=j*t_step..(j+1)*t_step,\n maximize=true,method=sqp);\n if sol[1] > m0 then\n m0 := sol[1];\n s0 := subs(sol[2],s);\n t0 := subs(sol[2],t);\n fi;\n catch:\n end try:\n od:\n od:\n\n return [m0,s0,t0]\nend:\n\n# If p : R^3 -> R^3 then jac(p)(x) is a 3x3 positive semidefinite\n# matrix with 0 as one eigenvalue. The map p is immersive at a\n# point x in S2 iff the other two eigenvalues of jac(p)(x) are\n# strictly positive. If p(x) is a homogeneous polynomial of degree\n# d in the variables x[i], then jac(p)(x) is homogeneous of degree\n# 2 in the coefficients of p, and homogeneous of degree 2d in the\n# variables x[i].\n\njac := proc(p)\n local J0,P,J,x;\n J0 := Matrix([seq([seq(diff(p(x)[i],x[j]),j=1..3)],i=1..3)]):\n P := orth_proj(x);\n J := map(expand,P . Transpose(J0) . J0 . P);\n return unapply(J,x);\nend:\n\njac_det := proc(p)\n local J,f,t,x;\n J := jac(p)(x);\n f := Determinant(t * IdentityMatrix(3) - J);\n return unapply(coeff(f,t,1),x);\nend:\n\njac_det_min := proc(p)\n local f,m0,s0,t0;\n f := unapply(-jac_det(p)(x),x);\n m0,s0,t0 := op(segment_max(f));\n return [-m0,s0,t0];\nend:\n\njac_det_plot := proc(T)\n local p;\n p := T[\"map\"];\n \n T[\"jac_det_plot\"] := \n display(\n plot3d(0,s=0..Pi/2,t=0..2*Pi/3,colour=grey,style=patchnogrid),\n plot3d(jac_det(p)(pol(s,t)),s=0..Pi/2,t=0..2*Pi/3)\n );\n return T[\"jac_det_plot\"];\nend:\n\n# This returns a function of x measuring the failure of p to be\n# locally isometric at x. It is easy to evaluate and integrate,\n# but does not strongly penalise points where the Jacobian becomes\n# singular. If p is homogeneous quadric, then jac_dev_a(p)\njac_dev_a := proc(p)\n local J,P,E;\n J := jac(p)(x);\n P := orth_proj(x);\n E := add(add((J[i,j] - P[i,j])^2,j=1..3),i=1..3);\n return unapply(E,x);\nend:\n\n# This is a different measure of the failure of p to be a local\n# isometry. It is less easy to compute but strongly penalises\n# points where the Jacobian becomes singular.\njac_dev_b := proc(p)\n local J,f,c1,c2,x;\n J := jac(p)(x);\n f := Determinant(t * IdentityMatrix(3) - J);\n c1 := - coeff(f,t,2);\n c2 := coeff(f,t,1);\n return unapply(c1*(1+1/c2),x);\nend:\n\njac_dev_a_max := (p) -> segment_max(jac_dev_a(p));\n\njac_dev_b_max := (p) -> segment_max(jac_dev_b(p));\n\n# This takes a polynomial map p : R3 -> R3 (which may depend linearly\n# on some parameters) and another polynomial map p_start : R3 -> R3\n# (with no parameters). It specialises the parameters in p to make it\n# as close as possible (as measured by coefficients) to p_start.\n# Starting from there, it adjusts the parameters to minimize the\n# value of jac_dev_b_max.\noptimise_immersion := proc(p,p_start)\n global F,F_n,F_vars,F_best,F_vals;\n local pp,pp_start,p0,err,sol,aa0;\n\n pp := maybe_extend_cyclic(p);\n pp_start := maybe_extend_cyclic(p_start);\n\n F_vars := indets(pp(x)) minus {x[1],x[2],x[3]};\n F_n := nops(F_vars);\n p0 := unapply(subs({seq(F_vars[i] = a[i],i=1..F_n)},pp(x)),x);\n F_vals := table():\n F_best := NULL:\n\n err := evalf(expand(p0(x)[1] - pp_start(x)[1]));\n err := [coeffs(err,{x[1],x[2],x[3]})];\n err := expand(add(t^2,t in err));\n sol := solve({seq(diff(err,a[i]),i=1..F_n)}):\n aa0 := subs(sol,[seq(a[i],i=1..F_n)]);\n\n F := proc(aa)\n local p1,m;\n global F_vals,F_best;\n p1 := unapply(evalf(subs({seq(a[i]=aa[i],i=1..F_n)},p0(x))),x);\n m := jac_dev_b_max(p1);\n F_vals := [op(F_vals),[convert(aa,list),m]];\n if F_best = NULL or m[1] < F_best[2][1] then\n F_best := [convert(aa,list),m];\n fi;\n print(m[1]);\n return m[1];\n end:\n\n NLPSolve(F_n,F,initialpoint=Vector(aa0),method=nonlinearsimplex);\n return unapply(evalf(subs({seq(a[i] = F_best[1][i],i=1..F_n)},p0(x))),x); \nend:\n\nsextics := table():\n\nsextics[1] := make_immersion(\n 0.264790817514485*x[2]*x[3]^5 + \n 0.310873678789934*x[2]^5*x[3] + \n 0.314356886190530*x[1]^6 + \n(-0.367461017219878)*x[1]^3*x[2]^3 + \n 0.520593122199589*x[1]^3*x[3]^3 +\n 0.576919957376212*x[3]^6 + \n 0.916070813636660*x[1]^4*x[2]*x[3] + \n 1.08011357291557*x[1]*x[2]^4*x[3] + \n(-1.29574375446066)*x[1]^2*x[2]^4 + \n(-1.50136425744714)*x[2]^4*x[3]^2 +\n 1.75322964015665*x[2]^3*x[3]^3 + \n 1.83297848992403*x[1]^4*x[3]^2 + \n 1.97193642230680*x[1]^3*x[2]^2*x[3] + \n 3.00614990897844*x[1]^2*x[2]*x[3]^3 + \n 3.14671754019206*x[2]^2*x[3]^4 + \n(-3.31538823843401)*x[1]^3*x[2]*x[3]^2 + \n 3.47953011385635*x[1]*x[2]^3*x[3]^2 +\n(-3.48258924201893)*x[1]^2*x[2]^2*x[3]^2 + \n 3.68883801947675*x[1]^2*x[3]^4 + \n(-3.70117135607353)*x[1]*x[2]^2*x[3]^3 + \n 5.13825301199981*x[1]^2*x[2]^3*x[3]):\n\nquadrics := table():\n\n# This map is nice and simple and is equivariant for the full symmetry\n# group of the tetrahedron. There are double points on the intersections\n# of the coordinate planes with S2, and the points +/- e[i] are all\n# sent to the origin. The map is not an immersion because the Jacobian\n# is zero at [+/-1,+/-1,0]/sqrt(2) and permutations of that. \nquadrics[0] := make_immersion(\n sqrt(2)*x[2]*x[3]*(-2*x[1]^2+x[2]^2+x[3]^2)+(3*sqrt(3))*x[1]^2*x[2]*x[3]\n);\n\nquadrics[\"singular\"] := eval(quadrics[0]);\n\n# This is fitted to the original Boys embedding. The pictures are nice but\n# the minimal Jacobian determinant is very small.\nquadrics[1] := make_immersion(\n 2.22504534947546*x[1]^2*x[2]*x[3]+\n 0.458129331010717*x[2]*x[3]^3+\n 0.189460510525367*x[1]*x[2]*x[3]^2+\n 0.707682203241314*x[2]^3*x[3]+\n 0.188439848721650*x[1]*x[2]^2*x[3]+\n 0.259985777619243*x[1]^3*x[3]+\n (-0.287042815821211)*x[1]*x[3]^3+\n 1.76981740175627*x[1]^2*x[3]^2+\n 0.118256474175355*x[2]^2*x[3]^2+\n (-0.478109121568119)*x[1]^3*x[2]+\n 0.279208660926366*x[1]*x[2]^3+\n (-1.02732331413132)*x[1]^2*x[2]^2+\n (-0.127292231262611)*x[2]^4+\n 0.812016127928750*x[3]^4+\n 0.348555338251230*x[1]^4):\n\nquadrics[\"boys\"] := eval(quadrics[1]);\n\n# This is chosen for simplicity. The pictures are again nice and the minimal\n# Jacobian determinant is a bit bigger than for quadric1, but still small.\nquadrics[2] := make_immersion(\n x[1]^2*x[3]*(x[2]+x[3])+(1/2)*(-1+3*sqrt(3))*x[2]*x[3]*(x[2]^2+x[3]^2)+\n sqrt(3)*x[3]^4-(1+sqrt(3))*x[1]^2*x[2]^2):\n\nquadrics[\"simple\"] := eval(quadrics[2]);\n\n# The map quadric3 is a special case of special_quadric0 with\n# max(jac_dev_b) minimized.\n\nquadrics_a[3] :=\n [0.439109301326211, 1.00088884489061, 0.276971768183746,\n 0.804297719366554, -0.228929556357166, -0.0920206086999537]:\n\nquadrics[3] := make_immersion(\n evalf(sqrt(2) * subs({seq(a[i] = quadrics_a[3][i],i=1..6)},special_quadric0(x))));\n\nquadrics[3][\"a\"] := quadrics_a[3];\n\nquadrics[\"best\"] := eval(quadrics[3]);\n\n# This is Apery's quadric, up to linear changes of variables in the\n# domain and codomain. It sends u[0] to itself, and u[1] to u[6]\n# to the origin.\nquadrics[4] := make_immersion((\n (2 + 20*sqrt(2)) * x[1]^4 + \n (2 - 10*sqrt(2)) * (x[2]^4 + x[3]^4) + \n (10*sqrt(2) + 13) * x[1]^2 * (x[2]^2 + x[3]^2) + \n 27 * x[1] * x[2] * x[3] * (x[1]+x[2]+x[3]) +\n (13 - 20*sqrt(2)) * x[2]^2 * x[3]^2 + \n 9 * x[1]^3 * (x[2] + x[3]) + \n 9 * x[2] * x[3] * (x[2]^2 + x[3]^2) + \n 9 * x[1] * (x[2]^3 + x[3]^3) + \n (9 + 20*sqrt(2)) * x[2] * x[3] * (x[2]^2 - x[3]^2) + \n (10 * sqrt(2) - 9) * x[1] * (x[2]^3-x[3]^3) + \n (10 * sqrt(2) - 9) * (-x[1]^3) * (x[2] - x[3])) / (20 * sqrt(3)));\n\nquadrics[\"apery\"] := eval(quadrics[4]);\n\n# This is optimised in a similar way to quadric3 but with slightly\n# different constraints\nquadrics[5] := make_immersion(\n 3.25245542513966246*x[1]^2*x[2]*x[3]+\n 0.567045610094270236*x[1]^2*x[3]^2+\n 0.506746342124321902*x[2]^3*x[3]+\n 1.43695065673601552*x[2]*x[3]^3+\n 0.506586664999783221*x[3]^4+\n (-1.07154585120271717)*x[1]^2*x[2]^2+\n (-0.137651281752026899)*x[2]^2*x[3]^2+\n (-0.0475300936088673548)*x[2]^4+\n (-0.0729799939799069125)*x[1]*x[3]^3+\n (0.600907939705055405)*x[1]*x[2]*x[3]^2+\n (-0.121589626981102178)*x[1]*x[2]^2*x[3]+\n (0.0173511518008154855)*x[1]*x[2]^3+\n 0.194569620961009104*x[1]^3*x[3]+\n (-0.618259091505870884)*x[1]^3*x[2]+\n 0.183094951469558120*x[1]^4);\n\nfind_double_direction := proc(T,x0,x1)\n local v0,v1,w0,w1,pv0,pv1,pw0,pw1,n0,n1,nn;\n v0 := evalf(u[0] -~ dp(u[0],x0) *~ x0);\n v0 := v0 /~ sqrt(dp(v0,v0));\n w0 := evalf(cross_product(x0,v0));\n v1 := evalf(u[0] -~ dp(u[0],x1) *~ x1);\n v1 := v1 /~ sqrt(dp(v1,v1));\n w1 := evalf(cross_product(x1,v1));\n pv0 := evalf(subs(t = 0,map(diff,T[\"map\"](x0 +~ t *~ v0),t)));\n pw0 := evalf(subs(t = 0,map(diff,T[\"map\"](x0 +~ t *~ w0),t)));\n pv1 := evalf(subs(t = 0,map(diff,T[\"map\"](x1 +~ t *~ v1),t)));\n pw1 := evalf(subs(t = 0,map(diff,T[\"map\"](x1 +~ t *~ w1),t)));\n n0 := cross_product(pv0,pw0);\n n1 := cross_product(pv1,pw1);\n nn := cross_product(n0,n1);\n nn := nn /~ sqrt(dp(nn,nn));\n return nn;\nend:\n\nfind_double_point := proc(T,x0,y0,u0,d0)\n local pp,eqs,start,sol,xyz;\n\n pp := T[\"map\"];\n eqs := {\n x[1]^2 + x[2]^2 + x[3]^2 - 1,\n y[1]^2 + y[2]^2 + y[3]^2 - 1,\n op(pp(x) -~ pp(y)),\n dp(pp(x),u0) - d0\n };\n start := {\n seq(x[i] = x0[i],i=1..3),\n seq(y[i] = y0[i],i=1..3)};\n sol := fsolve(eqs,start);\n xyz := evalf(subs(sol,\n [[x[1],x[2],x[3]],[y[1],y[2],y[3]],pp(x)]));\n if not(type(T[\"double_points\"],list)) then\n T[\"double_points\"] := []:\n fi:\n T[\"double_points\"] := [op(T[\"double_points\"]),xyz];\n return xyz;\nend:\n\ndouble_point_step := proc(T,e)\n local p,q,x0,y0,u0,d0;\n p := T[\"double_points\"][-2];\n q := T[\"double_points\"][-1];\n x0 := 2 *~ q[1] -~ p[1];\n y0 := 2 *~ q[2] -~ p[2];\n u0 := q[3] -~ p[3];\n u0 := evalf(u0 /~ sqrt(dp(u0,u0)));\n d0 := dp(q[3],u0) + e;\n return find_double_point(T,x0,y0,u0,d0);\nend:\n\nfind_seam := proc(T,xyz0,u0,e_min,e_max)\n local pp,z0,z01,z02,r0,r1,c0,c1,dc0,dc1,N,M,F,i,aa,bb,a,b;\n \n pp := T[\"map\"];\n\n N := 240:\n F := proc(e)\n local i;\n T[\"double_points\"] := evalf([xyz0]):\n find_double_point(T,xyz0[1],xyz0[2],u0,e):\n for i from 1 to N do double_point_step(T,e); od:\n return table([\"err\" = dp(T[\"double_points\"][N+1][3],u0)]);\n end:\n\n T[\"double_point_step_length\"] := \n brent_fsolve(F,e_min,e_max,false,false,10^(-7),10^(-7))[1];\n\n aa := T[\"double_points\"][1];\n bb := T[\"double_points\"][240];\n \n if evalf(`d_2/R`(3)(bb[1],aa[2])) < evalf(`d_2/R`(3)(bb[1],-~aa[2])) then \n T[\"double_points_alt\"] := [\n seq(T[\"double_points\"][i][1],i=1..240),\n seq(T[\"double_points\"][i][2],i=1..240),\n seq(-~ T[\"double_points\"][i][1],i=1..240),\n seq(-~ T[\"double_points\"][i][2],i=1..240),\n T[\"double_points\"][1][1]]:\n else\n T[\"double_points_alt\"] := [\n seq(T[\"double_points\"][i][1],i=1..240),\n seq(-~ T[\"double_points\"][i][2],i=1..240),\n seq(-~ T[\"double_points\"][i][1],i=1..240),\n seq(T[\"double_points\"][i][2],i=1..240),\n T[\"double_points\"][1][1]]:\n fi;\n \n M := 20:\n for i from 0 to M do\n a[i] := add(T[\"double_points_alt\"][j+1][1] * evalf(cos(Pi * (2 * i + 1) * j/480)),j=0..959)/480;\n b[i] := add(T[\"double_points_alt\"][j+1][1] * evalf(sin(Pi * (2 * i + 1) * j/480)),j=0..959)/480;\n od:\n\n T[\"seam0\"] := unapply(\n add(a[i] * cos((2 * i + 1) * t) + b[i] * sin((2 * i + 1) * t),i=0..M),t):\n\n T[\"seam\"] := unapply([T[\"seam0\"](t),T[\"seam0\"](t+2*Pi/3),T[\"seam0\"](t-2*Pi/3)],t):\n\n return NULL:\nend:\n\ndouble_points_plot := proc(T)\n local L;\n L := T[\"double_points\"];\n display(\n usphere_plot,\n seq(point(x[1],colour=red),x in L),\n seq(point(x[2],colour=blue),x in L),\n seq(point(-~ x[1],colour=magenta),x in L),\n seq(point(-~ x[2],colour=cyan),x in L),\n axes=none,scaling=constrained\n );\nend:\n\nseam_plot := proc(T)\n spacecurve(T[\"seam\"](t),t=0..2*Pi,colour=red,scaling=constrained,axes=none)\nend:\n", "meta": {"hexsha": "895355e89d1e9a67a9105b575386379fc9941127", "size": 45620, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/geometry/boys_extra.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/geometry/boys_extra.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/geometry/boys_extra.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": 32.2630834512, "max_line_length": 161, "alphanum_fraction": 0.5836694432, "num_tokens": 18558, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7718434978390746, "lm_q2_score": 0.5156199157230156, "lm_q1q2_score": 0.3979778793071412}} {"text": "\n# Konvertierung Vektor zu symmetrischer Matrix\n# Einleitung\n# Generiere die Umwandlung von Vektor mit oberem rechten Teil einer Symmetrischen Matrix zur Matrix selbst f\u00fcr die Dimensionen des Roboters.\n# Diese Umwandlung verursacht weniger Rechenoperationen als die Verwendung der numerischen Funktion vec2symmat in Matlab, da dort jedes Mal die Indizes beim Zusammenbauen der Matrix getestet werden m\u00fcssen.\n# Autor\n# Tim Job (Studienarbeit bei Moritz Schappler), 2019-4\n# Moritz Schappler, moritz.schappler@imes.uni-hannover.de\n# (C) Institut f\u00fcr Mechatronische Systeme, Universit\u00e4t Hannover\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.\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_vector2mat\":\nread \"../robot_codegen_definitions/robot_env_par\":\nread sprintf(\"../codeexport/%s/tmp/para_definitions\", robot_name):\nprintf(\"Generiere Symmat2Vector-Funktionen f\u00fcr %s\\n\", robot_name):\ncodegen_opt := 0: # Soll nicht von Einstellung in robot_env \u00fcberschrieben werden.\n;\n# Funktion symmat2vector f\u00fcr den Roboter definieren\n# Erstelle eine Dummy-Variable (mv), die als tempor\u00e4re Variable in Matlab dient (zum Zusammensetzen der Matrix).\nclear('mv'):\nM_NX:= vec2mat(mv, NX):\n# Warnungen bei Code-Generierung unterdr\u00fccken. Die Meldung das der Ausdruck mv() in Matlab nicht bekannt ist, spielt keine Rolle, da diese Variable nach dem Einsetzen des Codes vorher definiert sein wird.\ninterface(warnlevel=0):\nMatlabExport(M_NX, sprintf(\"../codeexport/%s/tmp/vec2mat_%d_matlab.m\", robot_name, NX), codegen_opt):\n\n", "meta": {"hexsha": "da2b59813024c426e17fdd104b9a055c1d66d9d8", "size": 1834, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "helper/robot_gen_symmat2vector_parrob.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": "helper/robot_gen_symmat2vector_parrob.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": "helper/robot_gen_symmat2vector_parrob.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": 52.4, "max_line_length": 205, "alphanum_fraction": 0.7977099237, "num_tokens": 504, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7490872131147275, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.3979221490809678}} {"text": "p := 5;\n\n# b(i) is the image in H_{2i}(QS^0) of the standard generator of H_{2i}(BC_p)\n# This is zero unless i is divisible by p-1. An expression like b(8,4,6)\n# represents the circle product of b(8), b(4) and b(6).\n\nb := proc()\n if map(mods,{0,args},p-1) <> {0} or min(0,args) < 0 then\n return(0);\n fi;\n 'b'(op(sort([args]))); \nend:\n\n# Signature of permutations of {1,...,n}, represented as lists of values.\n# Sends non-permutations to zero.\nsignature := proc(s)\n local i,j,x;\n x := 1; \n for i from 1 to nops(s)-1 do\n for j from i+1 to nops(s) do\n if op(i,s) > op(j,s) then\n x := -x;\n elif op(i,s) = op(j,s) then\n return(0);\n fi;\n od;\n od;\n x;\nend:\n\n# a(i) is the image in H_{2i+1}(QS^0) of the standard generator of H_{2i+1}(BC_p)\n# This is zero unless i+1 is divisible by p-1. An expression like a(11,3,7)\n# represents the circle product of a(11), a(3) and a(7).\na := proc()\n if map(modp,{-1,args},p-1) <> {p-2} or min(0,args) < 0 then\n return(0);\n fi;\n signature([args]) * 'a'(op(sort([args]))); \nend:\n\n\n# The elements b(i) satisfy \\sum b(i,j) s^i t^j=\\sum b(i,j) s^i (s+t)^j. \n# By expanding this out we see that b_rel(i,j) = 0 for all i and j,\n# where b_rel(i, j) is as defined below.\n\nb_rel := proc(i,j)\n add(mods(binomial(i+j-u,j),p) * b(u,i+j-u),u=0..i-1);\nend:\n\nb_rels := proc(d) [seq(b_rel(i,d-i),i=0..d)]; end:\n\n# The elements a(i) satisfy \\sum a(i,j) s^i t^j=\\sum a(i,j) s^i (s+t)^j. \n# By expanding this out we see that a_rel(i,j) = 0 for all i and j,\n# where a_rel(i, j) is as defined below.\n\na_rel := proc(i,j)\n add(mods(binomial(i+j-u,j),p) * a(u,i+j-u),u=0..i-1);\nend:\n\na_rels := proc(d) [seq(a_rel(i,d-i),i=0..d)]; end:\n\n\n# Degree function for expressions in a's, b's, P's and Q's.\n# Should be refactored to use apply_deg\n# Not sure what the P's and Q's are\ndeg := proc(x) \n local d,n;\n if type(x,`+`) then\n d := map(deg,{op(x)});\n if nops(d) = 1 then\n return(op(1,d));\n else\n error(\"inhomogeneous sum\");\n fi;\n elif type(x,`*`) then\n return(`+`(op(map(deg,[op(x)]))));\n elif type(x,function) and op(0,x) = o then\n return(`+`(op(map(deg,[op(x)]))));\n elif type(x,integer) then\n return(0);\n elif type(x,function) and op(0,x) = a then\n return(`+`(op(map(i->2*i+1,[op(x)]))));\n elif type(x,function) and op(0,x) = b then\n return(`+`(op(map(i->2*i,[op(x)]))));\n elif type(x,function) and op(0,x) = P then\n n := nops(x)/2;\n return( -2*(p-1)*add(op(2*i,x),i=1..n) - add(op(2*i-1,x),i=1..n));\n elif type(x,function) and op(0,x) = Q then\n n := nops(x)/2;\n return( 2*(p-1)*add(op(2*i,x),i=1..n) - add(op(2*i-1,x),i=1..n));\n fi;\nend:\n\n# Circle product. Shoud be refactored to use apply_*\no := proc()\n local xx;\n xx := map(mods,[args],p);\n if member(0,xx) then\n return(0);\n else\n return('o'(op(xx)));\n fi; \nend:\n\n# Bockstein operation. Recognises star and circle products, a's, b's and Q's\nbeta := proc(x) \n local xx,n,s,y,i,j;\n if type(x,`+`) then\n return(map(beta,x));\n elif type(x,`*`) then\n xx := [op(x)];\n n := nops(xx);\n s := 1;\n y := 0;\n for i from 1 to n do\n y := y + s * mul(xx[j],j=1..(i-1)) * beta(xx[i]) * mul(xx[j],j=i+1..n);\n s := s * (-1)^deg(xx[i]);\n od;\n return(mods(expand(y),p));\n elif type(x,function) and op(0,x) = o then\n xx := [op(x)];\n n := nops(xx);\n s := 1;\n y := 0;\n for i from 1 to n do\n y := y + s * o(seq(xx[j],j=1..(i-1)),beta(xx[i]),seq(xx[j],j=i+1..n));\n s := s * (-1)^deg(xx[i]);\n od;\n return(mods(expand(y),p));\n elif type(x,integer) then\n return(0);\n elif type(x,function) and op(0,x) = a then\n return(0);\n elif type(x,function) and op(0,x) = b then\n xx := [op(x)];\n n := nops(xx);\n y := 0;\n for i from 1 to n do \n if xx[i] > 0 then\n y := y + o(a(xx[i]-1),b(seq(xx[j],j=1..i-1),seq(xx[j],j=i+1..n)));\n fi;\n od;\n return(mods(expand(y),p));\n elif type(x,function) and op(0,x) = Q then\n if nops(x) = 0 or op(1,x) = 1 then return(0); fi;\n return(Q(1,op(2..-1,x))); \n else \n return('beta'(x));\n fi; \nend:\n\n# Dyer-Lashof operation. Only knows linearity and the Cartan rule\nQQ := proc(i,x)\n local y,z;\n if type(x,`+`) then\n return(map2(QQ,i,x));\n elif type(x,`*`) then\n y := op(1,x);\n z := `*`(op(2..-1,x));\n if type(y,integer) then \n return(mods(expand(y*QQ(i,z)),p));\n else \n return(mods(expand(add(QQ(j,y)*QQ(i-j,z),j=0..i)),p));\n fi;\n elif type(x,integer) then\n if i = 0 then\n return(x);\n else\n return(0);\n fi;\n else\n return('QQ'(i,x));\n fi;\nend:\n\n# Steenrod operation. Knows the Cartan rule for star and circle products,\n# and behaviour on a's, b's and Q's.\nPP := proc(i,x)\n local y,z,j,s;\n if i<0 then \n return(0);\n elif i=0 then\n return(x);\n elif type(x,`+`) then\n return(map2(PP,i,x));\n elif type(x,`*`) then\n y := op(1,x);\n z := `*`(op(2..-1,x));\n if type(y,integer) then \n return(mods(expand(y*PP(i,z)),p));\n else \n return(mods(expand(add(PP(j,y)*PP(i-j,z),j=0..i)),p));\n fi;\n elif type(x,function) and op(0,x) = o then\n y := op(1,x);\n z := o(op(2..-1,x));\n if type(y,integer) then \n return(mods(expand(y * PP(i,z)),p));\n else \n return(mods(expand(add(o(PP(j,y),PP(i-j,z)),j=0..i)),p));\n fi;\n elif type(x,integer) then\n if i = 0 then\n return(x);\n else\n return(0);\n fi;\n elif type(x,function) and op(0,x) = b then\n j := op(1,x);\n if nops(x) = 1 then\n return(mods(binomial(j-(p-1)*i,i),p)*b(j-(p-1)*i));\n else \n z := b(op(2..-1,x));\n return(mods(expand(add(binomial(j-(p-1)*k,k)*o(b(j-(p-1)*k),PP(i-k,z)),k=0..j/(p-1))),p));\n fi;\n elif type(x,function) and op(0,x) = a then\n j := op(1,x);\n if nops(x) = 1 then\n return(mods(binomial(j-(p-1)*i,i),p)*a(j-(p-1)*i));\n else\n z := a(op(2..-1,x));\n return(mods(expand(add(binomial(j-(p-1)*k,k)*o(a(j-(p-1)*k),PP(i-k,z)),k=0..j/(p-1))),p));\n fi;\n elif type(x,function) and op(0,x) = Q then\n if nops(x) = 0 then\n if i=0 then return(x) else return(0); fi;\n fi;\n s := op(2,x);\n y := Q(op(3..-1,x));\n if op(1,x) = 0 then\n return(add((-1)^(i+k)*binomial((s-i)*(p-1),i-p*k)*oQ(Q(0,s-i+k),PP(k,y)),k=0..i/p));\n else\n return(zap(\n add((-1)^(i+k)*binomial((s-i)*(p-1)-1,i-p*k)*oQ(Q(1,s-i+k),PP(k,y)),k=0..i/p) + \n add((-1)^(i+k)*binomial((s-i)*(p-1)-1,i-p*k-1)*oQ(Q(0,s-i+k),PP(k,beta(y))),k=0..i/p)\n ));\n fi;\n else\n return('PP'(i,x));\n fi;\nend:\n\n# Length function for Steenrod or Dyer-Lashof words.\nlen := proc(x) \n if type(x,function) and (op(0,x) = P or op(0,x) = Q) then\n return(nops(x)/2);\n else\n return('len'(x));\n fi; \nend:\n\n# Excess for Dyer-Lashof words\nexcess := proc(x)\n local n;\n if type(x,function) and op(0,x) = Q then\n n := nops(x)/2;\n if n = 0 then return(0); fi; \n return(2*op(2,x) - op(1,x) - add(2*(p-1)*op(2*i,x)-op(2*i-1,x),i=2..n));\n else\n return('excess'(x));\n fi;\nend:\n\n# Admissibility criterion for Dyer-Lashof words\nis_admissible := proc(x)\n local i,n;\n if type(x,function) and op(0,x) = Q then\n n := nops(x)/2;\n if n = 0 then\n return(true);\n fi;\n if op(2,x) < op(1,x) then\n return(false);\n fi;\n for i from 2 to n do\n if p*op(2*i,x) - op(2*i-1,x) < op(2*i-2,x) then\n return(false);\n fi;\n od;\n return(true);\n else\n return('is_admissible'(x));\n fi;\nend:\n\nQ_adem := proc() \n local i,j,u,ep,r,dl,s,v;\n if nargs = 0 then\n return(Q());\n fi;\n if args[2] < args[1] then\n # (we must have args[1] = 1, args[2] = 0)\n if nargs = 2 then\n# error(\"naked beta\");\n return(Q(1,0));\n fi;\n if args[3] = 1 then\n return(0);\n else\n return(Q(1,args[4..-1]));\n fi;\n fi;\n for i from 2 to nargs/2 do\n u := args[1..2*i-4];\n ep := args[2*i-3];\n r := args[2*i-2];\n dl := args[2*i-1];\n s := args[2*i ];\n v := args[2*i+1..-1];\n if r > p*s-dl then\n if dl = 0 then \n return(\n mods(add(\n (-1)^(r+j)*binomial((p-1)*(j-s)-1,p*j-r)*\n Q(u,ep,r+s-j,0,j,v),\n j=ceil(r/p)..(r-(p-1)*s-1)\n ),p)\n );\n else\n if ep = 0 then\n return(mods(add(\n (-1)^(r+j)*binomial((p-1)*(j-s),p*j-r)*\n Q(u,1,r+s-j,0,j,v),\n j=ceil(r/p)..(r-(p-1)*s)\n ),p) - \n mods(add(\n (-1)^(r+j)*binomial((p-1)*(j-s)-1,p*j-r-1)*\n Q(u,0,r+s-j,1,j,v),\n j = ceil((r+1)/p)..(r-(p-1)*s)\n ),p));\n else \n return(mods(add(\n (-1)^(r+j+1)*binomial((p-1)*(j-s)-1,p*j-r-1)*\n Q(u,1,r+s-j,1,j,v),\n j = ceil((r+1)/p)..(r-(p-1)*s)\n ),p));\n fi;\n fi;\n fi;\n od;\n return(Q(args));\nend:\n\nQ_exc0 := proc()\n if excess(Q(args)) < 0 then\n return(0);\n else\n return(Q(args));\n fi;\nend:\n\nQ_comp := proc(a,b) \n local aa,bb,n,m,i,d;\n aa := a;\n bb := b;\n if type(aa,`*`) then\n aa := select(type,a,specfunc(integer,Q));\n fi;\n if type(bb,`*`) then\n bb := select(type,b,specfunc(integer,Q));\n fi;\n if not(type([aa,bb],[specfunc(integer,Q)$2])) then\n error(\"invalid arguments\");\n fi;\n n := nops(aa)/2;\n m := nops(bb)/2;\n for i from 1 to min(n,m) do\n d := 2*op(2*i,aa) - op(2*i-1,aa) - 2*op(2*i,bb) + op(2*i-1,bb);\n if d < 0 then\n return(true);\n elif d > 0 then\n return(false);\n fi;\n od; \n if n1 then\n return(expand(n*oQ(aa,b)));\n fi;\n fi;\n if type(b,`*`) then\n n,bb := selectremove(type,b,integer);\n if n<> 1 then\n return(expand(n*oQ(a,bb)));\n fi;\n fi;\n if type(a,integer) or type(b,integer) then\n return(expand(a*b)); \n fi;\n if type(a,specfunc(integer,Q)) and type(b,specfunc(integer,Q)) then\n return(Q(op(a),op(b)));\n fi;\nend:\n\nzap := proc(x) mods(eval(subs(Q=Q_exc0,eval(subs(Q = Q_adem,x)))),p); end:\n\n", "meta": {"hexsha": "a3f9be4aa7b2cc348414117a681b7ab33f5e2408", "size": 9993, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/dyer_lashof/dyer_lashof.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/dyer_lashof/dyer_lashof.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/dyer_lashof/dyer_lashof.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": 22.7113636364, "max_line_length": 93, "alphanum_fraction": 0.5454818373, "num_tokens": 3991, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7549149978955811, "lm_q2_score": 0.5234203489363239, "lm_q1q2_score": 0.39513787161576935}} {"text": "program typeconv;\r\n var i : integer; b : boolean; c : char;\r\nbegin\r\n i := integer(false);\r\n while i <= integer(true) do begin\r\n writeln( boolean(i), ' : ', i);\r\n i := i + 1;\r\n end;\r\n writeln;\r\n i := integer(' ');\r\n while i < 127 do begin\r\n if i div 16 * 16 = i then writeln;\r\n write(char(i), ' ');\r\n i := i + 1;\r\n end;\r\n writeln\r\nend.\r\n ", "meta": {"hexsha": "e8ed684c436a604a006c9e753280403977fa697c", "size": 361, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "data/sample35.mpl", "max_stars_repo_name": "naru380/SoftwareExperience5", "max_stars_repo_head_hexsha": "89020bf73d9fc6b58f8d564c7aaed52a0e02f371", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2022-02-10T01:27:36.000Z", "max_stars_repo_stars_event_max_datetime": "2022-02-10T01:27:36.000Z", "max_issues_repo_path": "task3_sample/sample35.mpl", "max_issues_repo_name": "shouth/LanguageProcessing", "max_issues_repo_head_hexsha": "7d4f751b5babb97857310990e746740f884fa5e5", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 14, "max_issues_repo_issues_event_min_datetime": "2020-10-04T11:15:32.000Z", "max_issues_repo_issues_event_max_datetime": "2021-01-20T02:11:14.000Z", "max_forks_repo_path": "samples/program3/sample35.mpl", "max_forks_repo_name": "Hiroya-W/lang-processing", "max_forks_repo_head_hexsha": "c93ef2d5757e560c4df2335f07ac25552750140c", "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": 20.0555555556, "max_line_length": 41, "alphanum_fraction": 0.5041551247, "num_tokens": 113, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6039318337259583, "lm_q2_score": 0.6513548782017746, "lm_q1q2_score": 0.393373945998746}} {"text": "read \"print_comp.mpl\":\nall_var_set:=[ \n [DPH,0,dn] , [dg,2,dn] , \n [met,2,dn], [invmet,2,up], [DDL,2,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 ];\ns:=\"\";\nfor i from 1 to nops(all_var_set) do\n s:=cat(s,print_comp(all_var_set[i][1],[x,theta,phi],all_var_set[i][2],diag=true,tp=all_var_set[i][3])):\nend do:\nFP:=fopen(\"allequations.mpl\",WRITE);\nwriteline(FP,s);\nfclose(FP);\n", "meta": {"hexsha": "63dc3e618cb243c3528c31dc349cd5eacc0149e7", "size": 484, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "archive/write_all_comp.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": "archive/write_all_comp.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": "archive/write_all_comp.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": 24.2, "max_line_length": 105, "alphanum_fraction": 0.5392561983, "num_tokens": 215, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6926419831347361, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.3920482007092462}} {"text": "var $g_i8_u \nvar $g_i8 = 8\nvar $g_u8_u \nvar $g_u8 = 8\n\nvar $g_i16_u \nvar $g_i16 = 16\nvar $g_u16_u \nvar $g_u16 = 16\n\nvar $g_i32_u \nvar $g_i32 = 32\nvar $g_u32_u \nvar $g_u32 = 32\n\nvar $g_i64_u \nvar $g_i64 = 0x123456789a\nvar $g_u64_u \nvar $g_u64 = 0x123456789a\n\nvar $g_f32_u \nvar $g_f32 = 1.2f\n\nvar $g_f64_u \nvar $g_f64 = 2.4\n\n# i8/u8\nfunc $add_i8_u () i8 { \n return (\n add i32(dread i32 $g_i8_u, constval i32 0))}\n\nfunc $add_i8 () i8 { \n return (\n add i32(dread i32 $g_i8, constval i32 0))}\n\t \nfunc $add_u8_u () u8 { \n return (\n add u32(dread u32 $g_u8_u, constval u32 0))}\n\nfunc $add_u8 () u8 { \n return (\n add u32(dread u32 $g_u8, constval u32 0))}\n\t \n# i16/u16\nfunc $add_i16_u () i16 { \n return (\n add i32(dread i32 $g_i16_u, constval i32 0))}\n\nfunc $add_i16 () i16 { \n return (\n add i32(dread i32 $g_i16, constval i32 0))}\n\t \nfunc $add_u16_u () u16 { \n return (\n add u32(dread u32 $g_u16_u, constval u32 0))}\n\nfunc $add_u16 () u16 { \n return (\n add u32(dread u32 $g_u16, constval u32 0))}\n\t \n# i32/u32\nfunc $add_i32_u () i32 { \n return (\n add i32(dread i32 $g_i32_u, constval i32 0))}\n\nfunc $add_i32 () i32 { \n return (\n add i32(dread i32 $g_i32, constval i32 0))}\n\t \nfunc $add_u32_u () u32 { \n return (\n add u32(dread u32 $g_u32_u, constval u32 0))}\n\nfunc $add_u32 () u32 { \n return (\n add u32(dread u32 $g_u32, constval u32 0))}\n\t \n# i64/u64\nfunc $add_i64_u () i64 { \n return (\n add i64(dread i64 $g_i64_u, constval i64 0))}\n\nfunc $add_i64 () i64 { \n return (\n add i64(dread i64 $g_i64, constval i64 0))}\n\t \nfunc $add_u64_u () u64 { \n return (\n add u64(dread u64 $g_u64_u, constval u64 0))}\n\nfunc $add_u64 () u64 { \n return (\n add u64(dread u64 $g_u64, constval u64 0))}\n\t \n# # f32\n# func $add_f32_u () f32 { \n # return (\n # add f32(dread f32 $g_f32_u, constval f32 0.0f))}\n\n# func $add_f32 () f32 { \n # return (\n # add f32(dread f32 $g_f32, constval f32 0.0f))}\n\t \n# # f64\n# func $add_f64_u () f64 { \n # return (\n # add f64(dread f64 $g_f64_u, constval f64 0))}\n\n# func $add_f64 () f64 { \n # return (\n # add f64(dread f64 $g_f64, constval f64 0))}\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "37e344e4952365c8ef1546107276b9eb9e6356ac", "size": 2380, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0038-mapleall-irbuild-edge-global/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/I0038-mapleall-irbuild-edge-global/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/I0038-mapleall-irbuild-edge-global/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": 20.6956521739, "max_line_length": 55, "alphanum_fraction": 0.5966386555, "num_tokens": 1036, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6513548782017746, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.39093561564405377}} {"text": "\n# Base Parameter Regressor for Robot based on MDH frames\n# Einleitung\n# Erstellung einer parameterlinearen Regressorform in Newton Euler Bewegungsgleichung\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# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# NewtonEuler -> Berechnung der Newton Euler Bewegungsgleichung\n# regressor -> Regressorform (parameterlinear)\n# \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:\ncodeexport_grav := true: \ncodeexport_corvec := true:\ncodeexport_cormat := true:\ncodeexport_inertia := true:\ncodeexport_inertiaD := true:\ncodeexport_invdyn := true:\ncodeexport_act:= true:\ncodegen_dynpar := 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 Regressorform f\u00fcr %s\\n\", robot_name, codegen_dynpar):\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# Term-Vereinfachungen einstellen\nif not assigned(simplify_options) or simplify_options(10)=-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(10): # zehnter Eintrag ist f\u00fcr Dynamik-Regressor\n\nend if:\n# Ergebnisse der Newton Euler- Bewegungsgleichung laden\nread sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_linkframe_par%d_maple.m\", robot_name, base_method_name, codegen_dynpar):\nf_i_i := f_i_i:\nm_i_i := m_i_i:\ntau_B := tau_B:\ntau_J := tau_J:\n# Mit diesem Arbeitsblatt werden die Vorw\u00e4rtsrekursive f\u00fcr Fixed-Base Modelle generiert. Erkenne welche Basis-Modellierung aktiv ist\nif base_method_name=\"twist\" then # Basis-Methode \"twist\" wird (hier) nur f\u00fcr fixed Base benutzt\n expstring:=\"fixb\":\nelif base_method_name=\"eulxyz\" then \n expstring:=\"floatb_eulxyz\":\nelse\n printf(\"Nicht behandelte Basis-Methode: %s\\n\", base_method_name):\nend if:\n# Die kinetischen und potentiellen Energien aus (2) und (3) stehen ab hier durch T_fixb und U_fixb zur Verf\u00fcgung. \n# Der Parametervektor 'PV2_vec' aus (13) wurde in 'robot_tree_floatb_twist_definitions.mw' aufgestellt. \n\n# Parameterlinearisierung\n# Parameterlinearisierung auf Basis von [HRL_IDR] (14) und (15)\n# Linearisierung_Gelenkmomente\ntauJ_regressor := Matrix(NQJ, 10*(NL-1)):\n\nfor i from 1 to NQJ do \n for j from 1 to 10*(NL-1) do\n tauJ_regressor[i,j] := diff(tau_J(i,1),PV2_vec[10+j,1]):\n end do:\nend do:\n# Terme vereinfachen\nif use_simplify>=1 then\n tmp_t1:=time():\n tmp_l1 := length(tauJ_regressor):\n tauJ_regressor := simplify2(tauJ_regressor):\n tmp_t2:=time():\n tmp_l2 := length(tauJ_regressor):\n printf(\"%s: Gelenkmoment-Regressor vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\n\n# Linearisierung_Gelenkmomente(base)\n# \ntauB_regressor := Matrix(6,10*NL):\nfor i from 1 to 6 do \n for j from 1 to 10*NL do\n tauB_regressor[i,j] := diff(tau_B(i,1),PV2_vec[j,1]):\n end do:\nend do:\n# Terme vereinfachen\nif use_simplify>=1 then\n tmp_t1:=time():\n tmp_l1 := length(tauB_regressor):\n tauB_regressor := simplify2(tauB_regressor):\n tmp_t2:=time():\n tmp_l2 := length(tauB_regressor):\n printf(\"%s: Basis-Kraft/Moment-Regressor vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\n\n\n# Linearisierung_Schnittmomente\nm_regressor := Matrix(3*NL,10*NL):\n\nm_i_i_vec := Matrix(3*(NL),1):\nfor i from 1 to NL do\n for j from 1 to 3 do\n m_i_i_vec[3*(i-1)+j] := m_i_i[j,i]:\n end do:\nend do:\n\nfor i from 1 to 3*NL do \n for j from 1 to 10*NL do\n m_regressor[i,j] := diff~(m_i_i_vec(i,1),PV2_vec[j,1]):\n end do:\nend do:\n\n# Terme vereinfachen\nif use_simplify>=1 then\n tmp_t1:=time():\n tmp_l1 := length(m_regressor):\n m_regressor := simplify2(m_regressor):\n tmp_t2:=time():\n tmp_l2 := length(m_regressor):\n printf(\"%s: Schnittmoment-Regressor vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\n\n# Linearisierung_Schnittkr\u00e4fte\nf_regressor := Matrix(3*NL,10*NL):\nf_i_i_vec := Matrix(3*(NL),1):\nfor i from 1 to NL do\n for j from 1 to 3 do \n f_i_i_vec[3*(i-1)+j] := f_i_i[j,i]:\n end do:\nend do:\n\nfor i from 1 to 3*NL do \n for j from 1 to 10*NL do\n f_regressor[i,j] := diff~(f_i_i_vec(i,1),PV2_vec[j,1]):\n end do:\nend do:\n# Terme vereinfachen\nif use_simplify>=1 then\n tmp_t1:=time():\n tmp_l1 := length(f_regressor):\n f_regressor := simplify2(f_regressor):\n tmp_t2:=time():\n tmp_l2 := length(f_regressor):\n printf(\"%s: Schnittkraft-Regressor vereinfacht. L\u00e4nge: %d->%d. Rechenzeit %1.1fs.\\n\", \\\n FormatTime(\"%Y-%m-%d %H:%M:%S\"), tmp_l1, tmp_l2, tmp_t2-tmp_t1):\nend if:\n\n# Export\n# Maple Export\nsave tauJ_regressor, sprintf(\"../codeexport/%s/tmp/fixb_NewtonEuler_tauJ_regressor_maple.m\", robot_name):\nsave tauB_regressor, sprintf(\"../codeexport/%s/tmp/fixb_NewtonEuler_tauB_regressor_maple.m\", robot_name):\nsave m_regressor, sprintf(\"../codeexport/%s/tmp/fixb_NewtonEuler_m_regressor_maple.m\", robot_name):\nsave f_regressor, sprintf(\"../codeexport/%s/tmp/fixb_NewtonEuler_f_regressor_maple.m\", robot_name):\nprintf(\"Maple-Ausdr\u00fccke exportiert. %s\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n# Matlab Export\nif codegen_act then\n MatlabExport(convert_t_s(tauJ_regressor), sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_tauJ_regressor_matlab.m\", robot_name, expstring), codegen_opt):\n MatlabExport(convert_t_s(tauB_regressor), sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_tauB_regressor_matlab.m\", robot_name, expstring), codegen_opt):\n MatlabExport(convert_t_s(m_regressor), sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_m_regressor_matlab.m\", robot_name, expstring), codegen_opt):\n MatlabExport(convert_t_s(f_regressor), sprintf(\"../codeexport/%s/tmp/invdyn_%s_NewtonEuler_f_regressor_matlab.m\", robot_name, expstring), codegen_opt):\nend if\n;\n\n", "meta": {"hexsha": "83778725921eaa95383641125a0edbb32a336664", "size": 6858, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_dynamics/robot_chain_fixb_rotmat_NewtonEuler_regressor.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_chain_fixb_rotmat_NewtonEuler_regressor.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_chain_fixb_rotmat_NewtonEuler_regressor.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": 37.6813186813, "max_line_length": 159, "alphanum_fraction": 0.7423447069, "num_tokens": 2228, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702761768248, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.3906929160345561}} {"text": " func $foo (\n var %i i32 \n#var %i1 i32, var %j1 i32, var %k1 i32\n ) i32 { \n return (\n neg i32(dread i32 %i))}\n\n func $foo1 (\n var %i i32, var %j i32, var %k i32, \n var %i1 i32, var %j1 i32, var %k1 i32\n ) i32 { \n return (\n neg i32(dread i32 %i))}\n\n func $foo2 (\n var %i i32, var %j i32, var %k i32\n ) i32 { \n return (\n neg i32(constval i32 0x111111111))}\n\n func $foo3 (\n var %i i64, var %j i64, var %k i32\n ) i64 { \n return (\n neg i64(dread i64 %i))}\n\n\n func $foo5 (\n var %i i64, var %j i64, var %k i32\n ) i64 { \n return (\n neg i64(constval i64 0x11111))}\n\n func $foo6 (\n var %i f64\n ) f64 { \n return (\n neg f64(dread f64 %i))}\n\n func $foo7 (\n var %i f32\n ) f32 { \n return (\n neg f32(dread f32 %i))}\n\n func $foo8 (\n var %i f64\n ) f64 { \n return (\n neg f64(constval f64 -1.24))}\n\n func $foo9 (\n var %i f32\n ) f32 { \n return (\n neg f32(constval f32 -1.24f))}\n# todo float neg\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "c06bc9c2dc1ae05dea9f5f4fe868265d9c01833e", "size": 1049, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0059-mapleall-irbuild-edge-neg/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/I0059-mapleall-irbuild-edge-neg/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/I0059-mapleall-irbuild-edge-neg/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": 17.1967213115, "max_line_length": 43, "alphanum_fraction": 0.5414680648, "num_tokens": 445, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300573952052, "lm_q2_score": 0.5544704649604272, "lm_q1q2_score": 0.38953216757259507}} {"text": "LogText:= proc(text, target)\n\t# must pass text as sprintf(text)!!!\n\tUpdateLog(text, target);\nend proc:\n\nLogExpression:= proc(text, target)\n\t# must pass text as sprintf(\"%q\\n\", text)!!!\n\tUpdateLog(text, target);\nend proc:\n\n#LogTextSIAN := ()->UpdateLog(sprintf(_passed), \"LogAreaSIAN\");\n#LogExpressionSIAN := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"SIAN\");\n\n#LogTextME := ()->UpdateLog(sprintf(_passed), \"LogAreaME\");\n#LogExpressionME := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"LogAreaME\");\n\n#LogTextSE := ()->UpdateLog(sprintf(_passed), \"LogAreaSE\");\n#LogExpressionSE := ()->UpdateLog(sprintf(\"%q\\n\", _passed), \"LogAreaSE\");\n\nUpdateLog := proc(s, target)\nlocal logsofar;\n\n\tlogsofar := DocumentTools:-GetProperty(target, value);\n\tif logsofar <> \"\" then\n\t\tlogsofar := logsofar, \"\\n\";\n\tend if;\n\t\n\tDocumentTools:-SetProperty(target, value, cat(logsofar,s), 'refresh');\n\nend proc:\n\nexamples := table([ \n \t\"Biohydrogenation\" = [ \"Taken from R. Munoz-Tamayo, L. Puillet, J.B. Daniel, D. Sauvant, O. Martin, M. Taghipoor, P. Blavy\\n Review: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?\\ndoi.org/10.1017/S1751731117002774\\nSystem (3) in Supplementary Material 2, initial conditions are assumed to be unknown\",\n \t[\n \"dx4/dt = - k5 * x4 / (k6 + x4);\\n\",\n \"dx5/dt = k5 * x4 / (k6 + x4) - k7 * x5/(k8 + x5 + x6);\\n\",\n \"dx6/dt = k7 * x5 / (k8 + x5 + x6) - k9 * x6 * (k10 - x6) / k10;\\n\",\n \"dx7/dt = k9 * x6 * (k10 - x6) / k10;\\n\",\n \"y1 = x4;\\n\",\n \"y2 = x5\"]],\n\n \t\"Chemical Reaction Network\" = [\"Taken from Conradi, C., Shiu, A., Dynamics of post-translational modification systems: recent progress and future directions Eq. 3.4\",\n\t[\n \"dx1/dt = -k1 * x1 * x2 + k2 * x4 + k4 * x6;\\n\",\n \"dx2/dt = k1 * x1 * x2 + k2 * x4 + k3 * x4;\\n\",\n \"dx3/dt = k3 * x4 + k5 * x6 - k6 * x3 * x5;\\n\",\n \"dx4/dt = k1 * x1 * x2 - k2 * x4 - k3 * x4;\\n\",\n \"dx5/dt = k4 * x6 + k5 * x6 - k6 * x3 * x5;\\n\",\n \"dx6/dt = -k4 * x6 - k5 * x6 + k6 * x3 * x5;\\n\",\n \"y1 = x3;\\n\"\n \"y2 = x2;\\n\" ]],\n\n\t\"DAISY Ex. 3\" = [\"DAISY Example 3\", [\n \"dx1/dt = -1 * p1 * x1 + p2 * x2 + u(t);\\n\",\n \"dx2/dt = p3 * x1 - p4 * x2 + p5 * x3;\\n\",\n \"dx3/dt = p6 * x1 - p7 * x3;\\n\",\n \"y1 = x1;\\n\"]],\n\n\t\"DAISY_mamil3\" = [\"DAISY mamil 3\",\n\t[\n \"dx1/dt = -(a21 + a31 + a01) * x1 + a12 * x2 + a13 * x3 + u(t);\\n\",\n \"dx2/dt = a21 * x1 - a12 * x2;\\n\",\n \"dx3/dt = a31 * x1 - a13 * x3;\\n\",\n \"y = x1\"]],\n \n\t\"DAISY_mamil4\" = [\"DAISY mamil 4\", [\n \"dx1/dt = -k01 * x1 + k12 * x2 + k13 * x3 + k14 * x4 - k21 * x1 - k31 * x1 - k41 * x1 + u(t);\\n\",\n \"dx2/dt = -k12 * x2 + k21 * x1;\\n\",\n \"dx3/dt = -k13 * x3 + k31 * x1;\\n\",\n \"dx4/dt = -k14 * x4 + k41 * x1;\\n\",\n \"y = x1\"]],\n\n\t\"HIV\" = [\"Example (with initial conditions assumed being unknown) from Section IV of 'DAISY: an Efficient Tool to Test Global Identifiability. Some Case Studies' by G. Bellu, M.P. Saccomani\",\n\t[\n \"dx1/dt = -b * x1 * x4 - d * x1 + s;\\n\",\n \"dx2/dt = b * q1 * x1 * x4 - k1 * x2 - mu1 * x2;\\n\",\n \"dx3/dt = b * q2 * x1 * x4 + k1 * x2 - mu2 * x3;\\n\",\n \"dx4/dt = -c * x4 + k2 * x3;\\n\",\n \"y1 = x1;\\n\",\n \"y2 = x4\"]],\n\n\t\"HIV2\" = [\"The system is taken from Wodarz, D., Nowak, M.\\nSpecific therapy regimes could lead to long-term immunological control of HIV\\nhttps://doi.org/10.1073/pnas.96.25.14464\\nPage 1\",\n\t[\n \"dx/dt = lm - d * x - beta * x * v;\\n\",\n \"dy/dt = beta * x * v - a * y;\\n\",\n \"dv/dt = k * y - u * v;\\n\",\n \"dw/dt = c * x * y * w - c * q * y * w - b * w;\\n\",\n \"dz/dt = c * q * y * w - h * z;\\n\",\n \"y1 = w;\\n\",\n \"y2 = z\"]],\n\n\t\"Lipolysis\" = [\"Taken from R. Munoz-Tamayo, L. Puillet, J.B. Daniel, D. Sauvant, O. Martin, M. Taghipoor, P. Blavy\\nReview: To be or not to be an identifiable model. Is this a relevant question in animal science modelling?\\ndoi.org/10.1017/S1751731117002774\\nSystem (1) in Supplementary Material 2, initial conditions are assumed to be unknown\\nbrought to the rational function form by introducing new state variable x5 = k1 e^(-k3 t)\",\n\t[\n \"dx1/dt = -x1 * x5 / (k2 + x1);\\n\",\n \"dx2/dt = 2 * x1 * x5 / ((k2 + x1) * 3) - k4 * x2;\\n\",\n \"dx3/dt = k4*(x2)/2 - k4*x3;\\n\",\n \"dx4/dt = x1 * x5 / (3 * (k2 + x1)) + k4 * (x2)/2 + k4 * x3;\\n\",\n \"dx5/dt = -k3 * x5;\\n\",\n \"y1 = x1;\\n\",\n \"y2 = x2 + x3;\\n\",\n \"y3 = x4\"]],\n\n \t\"LV\" = [\"Lotka-Volterra System\",[\n \t\"dx1/dt = a*x1 - b*x1*x2;\\n\", \n \t\"dx2/dt = -c*x2 + d*x1*x2;\\n\",\n \t\"y = x1;\\n\"]],\n\t\"OralGlucose\" = [\"Example (with initial conditions assumed being unknown) from Section III of 'DAISY: an Efficient Tool to Test Global Identifiability. Some Case Studies'\\nby G. Bellu, M.P. Saccomani\",\n\t[\n \"dG/dt = -(p1 + X) * G + p1 * Gb + v * R;\\n\",\n \"dX/dt = -p2 * X + p3 * (u(t) - Ib);\\n\",\n \"dR/dt = k;\\n\",\n \"dIb/dt = 0;\\n\",\n \"dGb/dt = 0;\\n\",\n \"y1 = G;\\n\",\n \"y2 = Ib;\\n\",\n \"y3 = Gb;\\n\"]],\n\n\t\"SEIR\" = [\"Taken from N. Tuncer, T. Le\\n'Structural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.2) with prevalence observations\",\n[\n \"dS/dt = -b * S * In / N;\\n\",\n \"dE/dt = b * S * In / N - nu * E;\\n\",\n \"dIn/dt = nu * E - a * In;\\n\",\n \"dN/dt = 0;\\n\",\n \"y1 = In;\\n\",\n \"y2 = N;\\n\"]],\n\n\t\"SEIR2\" = [\"Taken from N. Tuncer, T. Le\\n'Structural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.2) with cumulative incidence observations\",\n\t[\n \"dS/dt = -b * S * In / N;\\n\",\n \"dE/dt = b * S * In / N - nu * E;\\n\",\n \"dIn/dt = nu * E - a * In;\\n\",\n \"dN/dt = 0;\\n\",\n \"dCu/dt = nu * E;\\n\",\n \"y1 = Cu;\\n\",\n \"y2 = N\"]],\n\n\t\"SIR_R0\" = [\"SIR R0\",[\n \"dS/dt = -b * In * S;\\n\",\n \"dIn/dt = b * In * S - g * In;\\n\",\n \"dR/dt = g * In;\\n\",\n \"daux/dt = 0;\\n\",\n \"y1 = In;\\n\",\n \"y2 = b / g + aux;\"]],\n\n\t\"SIRSForced\" = [\"Taken from Capistran M., Moreles M., Lara B.\\n'Parameter Estimation of Some Epidemic Models.\\n The Case of Recurrent Epidemics Caused by Respiratory Syncytial Virus'\\ndoi.org/10.1007/s11538-009-9429-3\\nEquations (7)-(11)\",\n[\n \"ds/dt = mu - mu * s - b0 * (1 + b1 * x1) * i * s + g * r;\\n\",\n \"di/dt = b0 * (1 + b1 * x1) * i * s - (nu + mu) * i;\\n\",\n \"dr/dt = nu * i - (mu + g) * r;\\n\",\n \"dx1/dt = -M * x2;\\n\",\n \"dx2/dt = M * x1;\\n\",\n \"y1 = i;\\n\",\n \"y2 = r;\\n\"]],\n\n\t\"SlowFast\" = [\"Taken from Vajda S., Rabitz H.\\n'Identifiability and Distinguishability of First-Order Reaction Systems', p. 701\\nWe added an extra output x_C\",\n\t[\n \"dxA/dt = -k1 * xA;\\n\",\n \"dxB/dt = k1 * xA - k2 * xB;\\n\",\n \"dxC/dt = k2 * xB;\\n\",\n \"deA/dt = 0;\\n\",\n \"deC/dt = 0;\\n\",\n \"y1 = eA * xA + eB * xB + eC * xC;\\n\",\n \"y2 = xC;\\n\",\n \"y3 = eA;\\n\",\n \"y4 = eC\"]],\n\t\n\t\"Treatment\" = [\"Taken from N. Tuncer, T. Le\\nStructural and practical identifiability analysis of outbreak models'\\nhttps://doi.org/10.1016/j.mbs.2018.02.004\\nEquation (2.3) with observed treatment\",\n\t[\n \"dS/dt = -b * S * In / N - d * b * S * Tr / N;\\n\",\n \"dIn/dt = b * S * In / N + d * b * S * Tr / N - (a + g) * In;\\n\",\n \"dTr/dt = g * In - nu * Tr;\\n\",\n \"dN/dt = 0;\\n\",\n \"y1 = Tr;\\n\",\n \"y2 = N\"]],\n\n\t\"Tumor\" = [\"Example (with initial conditions assumed being unknown) from Section 3 of\\n'Examples of testing global identifiability of biological and biomedical models with the DAISY software'\\nby M.P. Saccomani, S. Audoly, G. Bellu, L. D'Angio\",\n[ \"dx1/dt = -(k3 + k7) * x1 + k4 * x2;\\n\",\n \"dx2/dt = k3 * x1 - (k4 + a * k5 + b * d1 * k5) * x2 + k6 * x3 + k6 * x4 + k5 * x2 * x3 + k5 * x2 * x4;\\n\",\n \"dx3/dt = a * k5 * x2 - k6 * x3 - k5 * x2 * x3;\\n\",\n \"dx4/dt = b * d1 * k5 * x2 - k6 * x4 - k5 * x2 * x4;\\n\",\n \"dx5/dt = k7 * x1;\\n\",\n \"da/dt = 0;\\n\",\n \"db/dt = 0;\\n\",\n \"dd1/dt = 0;\\n\",\n \"y1 = x5;\\n\",\n \"y2 = a;\\n\",\n \"y3 = b;\\n\",\n \"y4 = d1;\\n\"]]\n]):\n\n# Setup\n\ntimed_SIAN:=proc(sigma, params_to_assess, p, output_targets_sian, count_solutions, char)\n\tlocal output, data, start, finish:\n\tstart:= time():\n\toutput := IdentifiabilityODE(sigma, params_to_assess, p, output_targets_sian, count_solutions, char):\n\tfinish:= time():\n\tDocumentTools:-SetProperty(output_targets_sian[runningtime], value, convert(finish-start, string), 'refresh'): # time\n\treturn output:\nend proc:\n\ntimed_Multi:=proc(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets_multi)\n\tlocal start, output, finish, data, bound, generators:\n\tstart:=time():\n\tbound, generators := op(MultiExperimentIdentifiableFunctions(model, simplified_generators, no_bound, simplify_bound, max_perms, output_targets_multi)):\n\tfinish:=time():\n\tDocumentTools:-SetProperty(output_targets_multi[runningtime], value, convert(finish-start, string), 'refresh'):\n\treturn [bound, finish-start, generators]: #table([output=bound, runtime=finish-start]):\nend proc:\n\ntimed_Single:=proc(model, output_targets_single)\n\tlocal start, output, finish, data:\n\tstart:=time():\n\toutput := SingleExperimentIdentifiableFunctions(model, output_targets_single):\n\tfinish:=time():\n\tDocumentTools:-SetProperty(output_targets_single[runningtime], value, convert(finish-start, string), 'refresh'):\n\treturn output:\nend proc:\n\nwith(StringTools):\n\nsigmaParser := proc(sigma)\n\tlocal states, state_eqs, outputs, output_eqs;\n\tif SearchText(\"diff\", sigma)>0 then\n\t\tsigma := [map(x->parse(x), Split(sigma, \";\"))]:\n\telse\n\t\tLogExpression(sprintf(\"%q \\n\", Split(sigma, \";\")), \"LogAreaSIAN\"):\n\t\tsigma := Split(sigma, \";\"):\n\t\t\n\t\tstates := map(x->Trim(RegSubs(\"d([a-zA-Z0-9]+)/dt(.*)\" = \"\\\\1\", x)), select(x->SearchText(x, \"/dt\")>0, sigma)):\n\t\tstate_eqs := select(x->Has(x, \"/dt\"), sigma):\n\t\t\n\t\toutputs := map(x->Trim(Split(x, \"=\")[1]), select(x->not Has(x, \"/dt\"), sigma)):\n\t\toutput_eqs := select(x->not SearchText(x, \"/dt\")>0, sigma):\n\t\t\n\t\tstate_eqs := map(x->convert(subs({seq(parse(states[i])=parse(cat(states[i],\"(t)\")), i=1..nops(states))}, parse(x)), string), state_eqs):\n\t\tstate_eqs := map(x->parse(RegSubs(\"d([a-zA-Z0-9]+)/dt(.*)\" = \"diff(\\\\1(t), t)\\\\2\", x)), state_eqs):\n\t\n\t\toutput_eqs := map(x->parse(Subs({seq(outputs[i]=cat(outputs[i],\"(t)\"), i=1..nops(outputs))}, x)), output_eqs):\t\n\t\toutput_eqs := map(x->subs({seq(parse(states[i])=parse(cat(states[i],\"(t)\")), i=1..nops(states))}, x), output_eqs):\n\t\t\n\t\tsigma := [op(state_eqs), op(output_eqs)]:\n\tend if:\n\treturn sigma;\nend proc:\n\n\nDocumentTools:-SetProperty(\"RunningTimeSingle\", value, \"\"):\nDocumentTools:-SetProperty(\"RunningTimeMulti\", value, \"\"):\nDocumentTools:-SetProperty(\"RunningTimeSIAN\", value, \"\"):\n\nDocumentTools:-SetProperty(\"run_system\", enabled, true):\nDocumentTools:-SetProperty(\"Meter_sian\", visible, true):\nDocumentTools:-SetProperty(\"Meter_sian\", value, 0):\nDocumentTools:-SetProperty(\"sigma\", enabled, true):\nDocumentTools:-SetProperty(\"p\", value, \"0.99\"):\nDocumentTools:-SetProperty(\"params\", value, \"\"):\nDocumentTools:-SetProperty(\"replicas\", value, \"1\"):\n\nDocumentTools:-SetProperty(\"p\", enabled, true):\nDocumentTools:-SetProperty(\"params\", enabled, true):\nDocumentTools:-SetProperty(\"replicas\", enabled, true):\nDocumentTools:-SetProperty(\"LogAreaSE\", value, \"\"):\nDocumentTools:-SetProperty(\"LogAreaSIAN\", value, \"\"):\nDocumentTools:-SetProperty(\"LogAreaME\", value, \"\"):\n\nDocumentTools:-SetProperty(\"printSolutions\", enabled, true):\nDocumentTools:-SetProperty(\"printSolutions\", value, true):\n\nDocumentTools:-SetProperty(\"GlobalParams1\", expression, NULL):\nDocumentTools:-SetProperty(\"LocalParams1\", expression, NULL):\nDocumentTools:-SetProperty(\"NoIDParams1\", expression, NULL):\n\nDocumentTools:-SetProperty(\"Parameters\", value, \"\"):\n\nDocumentTools:-SetProperty(\"Bound\", expression, NULL):\nDocumentTools:-SetProperty(\"MultiFunctions\", expression, NULL):\nDocumentTools:-SetProperty(\"SingleFunctions\", expression, NULL):\n\nDocumentTools:-SetProperty(\"use_char\", enabled, true):\nDocumentTools:-SetProperty(\"use_char\", value, false):\nDocumentTools:-SetProperty(\"p_label\", enabled, true):\n\nDocumentTools:-SetProperty(\"ComputeId\", enabled, true):\nDocumentTools:-SetProperty(\"ComputeId\", value, false):\nDocumentTools:-SetProperty(\"bypass\", enabled, false):\n\nDocumentTools:-SetProperty(\"bypass\", value, true):\nDocumentTools:-SetProperty(\"SimplifiedGen\", enabled, false):\nDocumentTools:-SetProperty(\"SimplifiedGen\", value, true):\nDocumentTools:-SetProperty(\"SkipSingle\", enabled, false):\nDocumentTools:-SetProperty(\"SkipSingle\", value, false):\nDocumentTools:-SetProperty(\"Refine\", enabled, false):\nDocumentTools:-SetProperty(\"NoBound\", enabled, false):\nDocumentTools:-SetProperty(\"NoBound\", value, false):\nDocumentTools:-SetProperty(\"UsingUpTo\", enabled, false):\nDocumentTools:-SetProperty(\"MaxPermutations\", enabled, false):\nDocumentTools:-SetProperty(\"Permutations\", enabled, false):\nDocumentTools:-SetProperty(\"RunSIAN\", enabled, true):\nDocumentTools:-SetProperty(\"RunSIAN\", value, true):\nDocumentTools:-SetProperty(\"being_refined\", caption, \"\");\nDocumentTools:-SetProperty(\"sigma\", value, \"dx1/dt = a*x1 + x2*b + u(t);\\ndx2/dt = x2*c + x1;\\ny=x2\"):\nDocumentTools:-SetProperty(\"example_box\", value, \"Custom\"):\nDocumentTools:-SetProperty(reference, value, \"\"):\nDocumentTools:-SetProperty(\"LocalLabel\" , caption, \"Locally Identifiable Paramters\");\nDocumentTools:-SetProperty(TxtOutput, visible, false);\nDocumentTools:-SetProperty(TxtOutput, value, \"\");\nDocumentTools:-SetProperty(SaveOutputLabel, visible, false);\n\nreadyToSave:=false:\ncounter:=0:\nexname:=\"Custom\":", "meta": {"hexsha": "19cae8246242eac432e189911720a8c2cfbd3e12", "size": 13144, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "src/default_startup_.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/default_startup_.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/default_startup_.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": 42.1282051282, "max_line_length": 437, "alphanum_fraction": 0.624771759, "num_tokens": 4772, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6370307944803831, "lm_q2_score": 0.6113819732941511, "lm_q1q2_score": 0.3894691441785575}} {"text": "######################################################################\n\n`is_element/ICP` := (N::posint) -> (A::set) -> proc(Q)\n local i,U,V;\n\n global reason;\n\n if not `is_element/ACP`(N)(A)(Q) then\n reason := [convert(procname,string),\"Q in ACP(N)(A)\",reason];\n return false;\n fi;\n\n if not `is_separated/preord`(A)(Q[N]) then\n reason := [convert(procname,string),\"Q[N] is not separated\",Q[N]];\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/ICP` := (N::posint) -> (A::set) -> proc(Q1,Q2)\n global reason;\n\n if Q1 <> Q2 then\n reason := [convert(procname,string),\"Q1 <> Q2\",Q1,Q2];\n return false;\n fi;\n\n return true;\nend:\n\n`is_leq/ICP` := (N::posint) -> (A::set) -> proc(Q1,Q2)\n local i;\n\n for i from 1 to N do \n if Q2[i] minus Q1[i] <> {} then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n######################################################################\n\n`random_element/ICP` := (N::posint) -> (A::set) -> proc()\n local i,j,n,pi,Q,R,S,B,C;\n\n if nops(A) = 0 then\n return FAIL;\n fi;\n\n R := `random_element/total_preord`(A)();\n Q := [R];\n for i from 2 to N do \n pi := `block_partition/preord`(A)(R);\n R := {};\n for B in pi do\n if i < N then\n S := `random_element/total_preord`(B)();\n else\n C := `random_element/ord`(B)();\n n := nops(C);\n S := {seq(seq([C[i],C[j]],j=i..n),i=1..n)};\n fi;\n \n R := R union S;\n od;\n Q := [op(Q),R];\n od;\n\n return Q;\nend:\n\n######################################################################\n\n`build/ICP` := (N::posint) -> (A::set) -> proc(Ru)\n local R,u,n,i,j,p,a,b,aa,bb,Q;\n R,u := op(Ru);\n n := nops(A);\n aa := table():\n bb := table():\n for i from 1 to n do\n for p from 1 to N do\n a := i;\n while a > 1 and u[a-1] > p do a := a - 1; od;\n aa[i,p] := a;\n b := i;\n while b < n and u[b] >= p do b := b + 1; od;\n bb[i,p] := b;\n od:\n od:\n Q := [seq(\n {seq(seq([R[i],R[j]],j=aa[i,p]..bb[i,p]),i=1..n)}\n ,p=1..N)];\n\n return Q;\nend:\n\n######################################################################\n\n`list_elements/ICP` := (N::posint) -> proc(A::set)\n local U,u,n,i,j,RR,R;\n \n U := [[]];\n n := nops(A);\n for i from 1 to n-1 do\n U := [seq(seq([op(u),j],j=1..N),u in U)];\n od:\n\n RR := `list_elements/ord`(A);\n\n [seq(seq(`build/ICP`(N)(A)([R,u]),u in U),R in RR)];\nend:\n\n`count_elements/ICP` := (N::posint) -> (A::set) ->\n nops(A)! * N^(nops(A) - 1);\n\n######################################################################\n\n`list_ordered_elements/ICP` := (N::posint) -> proc(A::{set,list})\n local U,u,n,i,j,R,A0;\n \n U := [[]];\n n := nops(A);\n for i from 1 to n-1 do\n U := [seq(seq([op(u),j],j=1..N),u in U)];\n od:\n\n R := [op(A)];\n A0 := {op(A)};\n\n [seq(`build/ICP`(N)(A0)([R,u]),u in U)];\nend:\n\n`count_ordered_elements/ICP` := (N::posint) -> (A::set) ->\n N^(nops(A) - 1);\n\n######################################################################\n\n# Note that we omit the rank of Q[N], because it is always equal to N here.\n\n`rank_vector/ICP` := (N) -> (A) -> proc(Q)\n local i;\n return [seq(`rank/preord`(A)(Q[i])-1,i=1..N-1)];\nend;\n\n`rank/ICP` := (N) -> (A) -> proc(Q)\n return `+`(op(`rank_vector/ICP`(N)(A)(Q)));\nend;\n\n######################################################################\n\n`phi/SEM/ICP` := (N::posint) -> (A::set) -> proc(eta)\n local A2,a,b,i;\n\n A2 := {seq(seq([a,b],b in A),a in A)};\n\n return [seq(select(ab -> `is_preceq/E`(N)(eta[op(ab)],epsilon^i),A2),i=0..N-1)];\nend;\n\n`psi/ICP/SEM` := (N::posint) -> (A::set) -> proc(Q)\n local eta,a,b,i;\n\n eta := table();\n for a in A do\n for b in A do \n if a = b then \n eta[a,b] := 0;\n else\n i := 1;\n while (i < N and member([a,b],Q[i]) and member([b,a],Q[i])) do \n i := i+1;\n od;\n if member([a,b],Q[i]) then\n eta[a,b] := epsilon^(i-1);\n else \n eta[a,b] := -epsilon^(i-1);\n fi;\n fi;\n od;\n od;\n\n return eval(eta);\nend:\n\n######################################################################\n\n`totalise/ICP/ord` := (N::posint) -> (A::set) -> proc(Q)\n local R,T,r,i,a;\n\n R := `id/autorel`(A);\n for i from 1 to N do\n R := R union (Q[i] minus `op/autorel`(A)(Q[i]));\n od:\n\n T := table():\n for a in A do\n r := nops(select(x -> member([x,a],R),A));\n T[r] := a;\n od:\n\n return [seq(T[i],i=1..nops(A))];\nend:\n \n`res/ICP` := (N::posint) -> (A::set,B::set) -> proc(Q)\n local BB;\n\n BB := `top/autorel`(B);\n\n return(map(`intersect`,Q,BB));\nend;\n\n######################################################################\n\n`is_fibre_sphere/ICP` := (N::posint) -> (A::set) -> (a,b,Q) -> proc(P)\n local B,i,U,V,L;\n\n if not(member(a,A)) then error(\"a not in A\"); fi;\n B := A minus {a};\n\n if not(`is_equal/ICP`(N)(B)(`res/ICP`(N)(A,B)(P),Q)) then\n return false;\n fi;\n\n i := 1;\n while i < N and member([a,b],P[i]) and member([b,a],P[i]) do\n i := i+1;\n od;\n\n U := select(x -> member([x,a],P[i]),B);\n V := select(x -> member([a,x],P[i]),B);\n\n if U intersect V <> {} then return false; fi;\n if member(b,U) then\n L := select(x -> not(member([x,b],P[i])),U);\n if L <> {} then return false; fi;\n fi;\n if member(b,V) then\n L := select(x -> not(member([b,x],P[i])),V);\n if L <> {} then return false; fi;\n fi;\n\n return true;\nend;\n\n######################################################################\n# Each of the subsets S_b(Q) is isomorphic to ICP_N({a,b})\n\n`f/fibre_sphere/ICP` := (N::posint) -> (A::set) -> (a,b,Q) -> proc(R)\n local i,e;\n\n i := 1;\n while member([a,b],R[i]) and member([b,a],R[i]) do\n i := i+1;\n od;\n if member([a,b],R[i]) then\n e := -1;\n else\n e := +1;\n fi;\n\n return `f_alt/fibre_sphere/ICP`(N)(A)(a,b,Q)([i,e]);\nend:\n\n`f_alt/fibre_sphere/ICP` := (N::posint) -> (A::set) -> (a,b,Q) -> proc(ie)\n local i,e,PT,j,x,L,U;\n\n i,e := op(ie);\n \n PT := table();\n for j from 1 to i-1 do\n PT[j] := {[a,a]} union Q[j];\n for x in Q[j] do\n if x[1] = b then PT[j] := {op(PT[j]),[a,x[2]]}; fi;\n if x[2] = b then PT[j] := {op(PT[j]),[x[1],a]}; fi;\n od;\n od;\n PT[i] := Q[i] union {[a,a]};\n L := select(x -> member([x,b],Q[i]),A);\n U := select(x -> member([b,x],Q[i]),A);\n if e = -1 then\n L := L minus U;\n else \n U := U minus L;\n fi;\n PT[i] := PT[i] union {seq([x,a],x in L)}\n union {seq([a,x],x in U)};\n for j from i+1 to N do\n PT[j] := Q[j] union {[a,a]};\n od;\n\n return [seq(PT[j],j=1..N)];\nend:\n\n`g/fibre_sphere/ICP` := (N::posint) -> (A::set) -> (a,b,Q) -> proc(P)\n if not(`is_fibre_sphere/ICP`(N)(A)(a,b,Q)(P)) then\n return FAIL;\n fi;\n return `res/ICP`(N)(A,{a,b})(P);\nend:\n\n`g_alt/fibre_sphere/ICP` := (N::posint) -> (A::set) -> (a,b,Q) -> proc(P)\n local R,i,e;\n \n R := `g/fibre_sphere/ICP`(N)(A)(a,b,Q)(P);\n if R = FAIL then return FAIL; fi;\n i := 1;\n while member([a,b],R[i]) and member([b,a],R[i]) do\n i := i+1;\n od;\n if member([a,b],R[i]) then\n e := -1;\n else\n e := +1;\n fi;\n return [i,e];\nend:\n\n######################################################################\n# This function provides a point of intesection between\n# S_b(Q) and S_b1(Q), where b1 is the successor of b in the total\n# order induced by Q.\n\n`m/fibre_sphere/ICP` := (N::posint) -> (A::set) -> proc(a,b,Q)\n local B,L,n,r,b1,i,R;\n\n B := A minus {a};\n L := `totalise/ICP/ord`(N)(B)(Q);\n n := nops(B);\n r := table();\n for i from 1 to n do\n r[L[i]] := i;\n od;\n if not(r[b] < n) then\n return FAIL;\n fi;\n b1 := L[r[b]+1];\n i := 0;\n while i < N and member([b1,b],Q[i+1]) do\n i := i+1;\n od;\n R := [{[a,a],[a,b],[b,a],[b,b]}$i,\n {[a,a],[b,a],[b,b]},\n {[a,a],[b,b]}$(N-i-1)];\n return `f/fibre_sphere/ICP`(N)(A)(a,b,Q)(R);\nend:\n\n######################################################################\n\n`bump/ICP` := (N::posint) -> (A::set) -> proc(Q)\n local r,n,i,j,R,E,Q1;\n\n r := `rank_vector/ICP`(N)(A)(Q);\n n := nops(A);\n i := N-1;\n while i > 0 and r[i] = n-1 do \n i := i - 1;\n od;\n if i = 0 then\n return FAIL;\n fi;\n R := `bump/striped_preord`(A)(Q[i]);\n E := R intersect `op/autorel`(A)(R);\n Q1 := [seq(Q[j],j=1..i-1),\n R,\n seq(Q[j] intersect E,j=i+1..N)];\n return Q1;\nend:\n\n######################################################################\n\n`describe/ICP` := eval(`describe/ACP`):\n\n", "meta": {"hexsha": "417fae9edd479521997fb5b4903bf8663d87d6ac", "size": 7988, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/chains/ICP.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/chains/ICP.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/chains/ICP.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": 21.3013333333, "max_line_length": 81, "alphanum_fraction": 0.4500500751, "num_tokens": 2869, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.672331699179286, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.3882684401435392}} {"text": "Foo:=module()\n export fun1,fun2;\n `fun1`:=proc()\n fun11:=proc()\n \n end proc:\n return fun11;\n end proc:\n fun2:=proc()\n return module() \n end module:\n end proc:\nend module:\n\nA[B]:=proc()\n \nend proc:\n\nA[1]:=proc()\n \nend proc:\n\nA[\"fadfa\"]:=proc()\n \nend proc:\n\n:-C[D]:=proc()\n\n\nend proc:\n\n:-U['V']:=proc()\n \nend proc:\n\nA:-B:-C:=proc()\n \nend proc:\n\nU[V][W]:=proc()\n fadfa:=proc()\n \n end proc:\n \nend proc:\n\njkladfjakdflkja:=proc()\n \nend proc:\n\n(*\n OptMethods.mpl\n*)\n\n# Maple \u7b26\u53f7\u7ebf\u6027\u89c4\u5212\nOpt[SLP]:=proc(A,b)\n uses LinearAlgebra;\n local E,x,FF,AA,BB,m,n;\n n:=RowDimension(A);\n m:=ColumnDimension(A);\n E:=IdentityMatrix(n);\n FF:=Vector([[0$m][],[1$n][]]);\n AA:=<,<-A|-E>>;\n BB:=convert(,Vector);\n x:=Opt[Simplex](FF,AA,BB);\n x:=x[1..m];\n return x;\nend proc:\n\n# Maple \u5355\u7eaf\u5f62\u6cd5\u77e9\u9635\u63a5\u53e3\n# min f*x\n# A*x<=b\nOpt[Simplex]:=proc(f,A,b)\n uses LinearAlgebra;\n local m,n,v,V,x,AA,CC;\n m:=RowDimension(A);\n n:=ColumnDimension(A);\n V:=Vector([seq(v[k],k=1..n)]);\n AA:=A.V;\n CC:=map(k->(AA[k]<=b[k]),{seq(1..m)});\n x:=simplex[minimize](f^%T.V,CC,UNRESTRICTED);\n x:=map(k->rhs(k),[x[]]);\n return Vector(x);\nend proc:\n\n# Maple \u8fdb\u884c\u6574\u6570\u7ebf\u6027\u89c4\u5212\nOpt[NILP]:=proc(A,b)\n uses LinearAlgebra,Optimization;\n local E,x,FF,AA,BB,m,n;\n n:=RowDimension(A);\n m:=ColumnDimension(A);\n E:=IdentityMatrix(n);\n FF:=Vector([[0$m][],[1$n][]]);\n AA:=<,<-A|-E>>;\n # \u6839\u636e\u5e2e\u52a9\u6587\u6863\u7684\u8bf4\u6cd5\uff0csparse \u77e9\u9635\u66f4\u5feb\n # \u5b9e\u9645\u4e0a\u5e76\u4e0d\u662f -_-||\n # AA:=Matrix(AA,storage=sparse); \n BB:=convert(,Vector);\n x:=LPSolve(FF,[AA,BB],integervariables=[seq(1..m)]);\n x:=map(round,x[2][1..m]);\n return x;\nend proc:\n\n# Matlab \u6574\u6570\u7ebf\u6027\u89c4\u5212\n# \u8c03\u7528\u4ee3\u4ef7\u7ea6\u4e3a 0.02 \u79d2\nOpt[MatlabILP]:=proc(A,b)\n uses Matlab;\n local x;\n setvar(\"A\",A);\n setvar(\"b\",b);\n # \u76f4\u63a5\u8fd0\u884c\u5177\u4f53\u4ee3\u7801\uff0c\u907f\u514d\u4ea7\u751f\u8def\u5f84\u95ee\u9898\n evalM(\"[n,m]=size(A);E=eye(n);AA=[A,-E;-A,-E];BB=[b;-b];f=[zeros(m,1);ones(n,1)];x=intlinprog(f,1:m,AA,BB,[],[],[],[],optimoptions('intlinprog','Display','off'));x=x(1:m);\");\n x:=getvar(\"x\");\n if type(x,float) then\n x:=Vector([round(x)]);\n else\n x:=map(round,x);\n end if;\n return x;\nend proc:\n\n# Mathematica \u7b26\u53f7\u7ebf\u6027\u89c4\u5212\n# \u8c03\u7528\u4ee3\u4ef7\u7ea6\u4e3a 0.7 \u79d2\nOpt[mmaSLP]:=proc(A,b)\n uses LinearAlgebra;\n local E,x,FF,AA,BB,m,n;\n n:=RowDimension(A);\n m:=ColumnDimension(A);\n E:=IdentityMatrix(n);\n FF:=Vector([[0$m][],[1$n][]]);\n AA:=<,<-A|-E>>;\n BB:=convert(,Vector);\n x:=Opt[mmaLP](FF,-AA,-BB);\n x:=x[1..m];\n return x;\nend proc:\n\nOpt[mmaLP]:=proc(f,A,b)\n uses FileTools;\n local cmd,fd,r;\n cmd:=sprintf(\"Print[LinearProgramming[%s,%s,%s,-Infinity,Method->\\\"Simplex\\\"]];\",\n mmaVec(f),mmaMat(A),mmaVec(b));\n fd:=Text[Open](\"LP.wl\",create,overwrite);\n Text[WriteString](fd,cmd);\n Text[Close](fd);\n r:=ssystem(\"wolframscript -file LP.wl\")[2];\n try\n r:=parse(cat(\"[\",r[2..-2],\"]\"));\n catch :\n error r;\n finally\n Remove(\"LP.wl\");\n end try;\n return Vector(r);# end proc\nend proc:# proc\n\n(*\nmmaVec:=proc(x)\n uses StringTools;\n local k,n,buffer,fmt;\n n:=numelems(x);\n buffer:=StringBuffer();\n buffer:-clear();\n buffer:-append(\"{\");\n for k from 1 to n do\n buffer:-append(sprintf(\"%d\",x[k]));\n if k simplify_factor_assuming > eval_factor > hack_Beta > Loop:-graft\n# but Loop:-intssums does not seem to even be used anywhere...\n\n # A debugging utility that's like `and` except it calls `userinfo` if there is disagreement\n and_info := proc(e :: {list,set})\n local s, r;\n s, r := selectremove(evalb, e);\n if nops(r) = 0 then return true end if;\n if nops(s) > 0 then userinfo(op([_rest, s, r])) end if;\n return false;\n end proc;\n\n hack_Beta_pw := proc(pw::specfunc(piecewise), x::name, bounds::range, $)\n local i, cond, via, dif, ineq, k;\n # Remove a particular superfluous inequality\n for i from 1 by 2 to nops(pw)-1 do\n cond := op(i,pw);\n if cond :: 'specfunc(And)' and membertype('{`<=`,`<>`}', cond) then\n for via in select(has, select(type, cond, `=`), x) do\n dif := lhs(via)-rhs(via)+rhs(bounds)-x; # known nonnegative\n for k from 1 to nops(cond) do\n ineq := op([k,1],cond)-op([k,2],cond);\n if op(k,cond) :: `<=`\n and Testzero(dif+ineq)\n or op(k,cond) :: `<>`\n and (Normalizer(dif+ineq) :: negative\n or Normalizer(dif-ineq) :: negative)\n then\n return subsop(i=bool_And(op(subsop(k=NULL,cond))), pw);\n end if;\n end do;\n end do;\n end if;\n end do;\n return pw;\n end proc;\n\n hack_Beta := proc(e :: specfunc(Beta), kb :: t_kb,\n loops :: list([identical(product,Product,sum,Sum),\n name=range]),\n $)\n local x, bounds, res, s1, r1, s2, r2, sg, rg;\n # Temporary hack to show desired output for examples/{dice_predict,gmm_gibbs,naive_bayes_gibbs}.hk\n if nops(loops) > 0 and e :: 'specfunc(`+`, Beta)' and has(e, piecewise) then\n x, bounds := op(op([-1,2],loops));\n res := subsindets(e, 'specfunc(piecewise)', hack_Beta_pw, x, bounds);\n s1, r1 := selectremove(has, op(1,res), piecewise);\n s2, r2 := selectremove(has, op(2,res), piecewise);\n sg := graft_pw(combine(combine(s1+s2), 'sum'));\n rg := Loop:-graft(r1+r2);\n if and_info([rg = eval(r2,x=x-1), sg = combine(eval(s2,x=x-1))],\n 3, 'procname',\n \"Telescoping match! ALMOST\") then\n elif and_info([rg = eval(r1,x=x-1), sg = combine(eval(s1,x=x-1))],\n 3, 'procname',\n \"Telescoping match, but swap Beta arguments! ALMOST\") then\n s1, s2 := s2, s1;\n r1, r2 := r2, r1;\n else\n # No telescoping match -- bail out\n return FAIL;\n end if;\n # At this point we know that e = Beta(s1+r1, s2+r2)\n # and that s2 = eval(s2, x=rhs(bounds)+1) + sum(s1, x=x+1..rhs(bounds)+1)\n # and that r2 = eval(r2, x=rhs(bounds)+1) + sum(r1, x=x+1..rhs(bounds)+1)\n # So our remaining job is to express\n # product(Beta(s1+r1, eval(s2+r2, x=rhs(bounds)+1) + sum(s1+r1, x=x+1..rhs(bounds)+1)), x=bounds)\n # in terms of\n # product(Beta( r1, eval( r2, x=rhs(bounds)+1) + sum( r1, x=x+1..rhs(bounds)+1)), x=bounds)\n res := wrap('Beta'(r1, eval(r2, x=rhs(bounds)+1) + 'sum'(r1, x=x+1..rhs(bounds)+1)), loops)\n * Loop:-graft(wrap(GAMMAratio(s1, r1), loops)\n * wrap(eval('GAMMAratio'(s1 (* + s2 *), r1 + r2), x=rhs(bounds)+1),\n # Unsound HACK: assuming eval(s2, x=rhs(bounds)+1) = 0\n # (Discharging this assumption sometimes requires checking idx(w,k) < size(word_prior) for symbolic k)\n eval(subsop(-1=NULL, loops), x=rhs(bounds)+1)))\n / wrap(eval('GAMMAratio'(s2, r2), x=lhs(bounds)-1),\n eval(subsop(-1=NULL, loops), x=lhs(bounds)-1));\n return eval_factor(res, kb, `*`, []);\n end if;\n # Temporary hack to show desired output for the \"integrate BetaD out of\n # BetaD-Bernoulli\" test\n return hackier_Beta(loops, e)\n\n # return FAIL;\n end proc;\n\n hackier_Beta := proc(loops,e)\n local s1, r1, s2, r2;\n\n if nops(loops) = 0 and e :: 'specfunc(And(`+`, Not(`+`(Not(idx({[1,0],[0,1]}, anything))))), Beta)' then\n s1, r1 := selectremove(type, op(1,e), 'idx({[1,0],[0,1]}, anything)');\n s2, r2 := selectremove(type, op(2,e), 'idx({[1,0],[0,1]}, anything)');\n if s1 :: 'idx([1,0], anything)' and s2 :: 'idx([0,1], anything)' and op(2,s1) = op(2,s2) then\n return Beta(r1, r2) * idx([r1, r2], op(2,s1)) / (r1 + r2);\n elif s1 :: 'idx([0,1], anything)' and s2 :: 'idx([1,0], anything)' and op(2,s1) = op(2,s2) then\n return Beta(r1, r2) * idx([r2, r1], op(2,s1)) / (r1 + r2);\n end if\n end if;\n\n FAIL\n\n end proc;\n\n\n\n # GAMMAratio(s, r) = GAMMA(s+r) / GAMMA(r)\n GAMMAratio := proc(s, r, $)\n local var;\n if s :: t_piecewiselike then\n map_piecewiselike(GAMMAratio,\n `if`(s :: 'specfunc(piecewise)' and nops(s) :: even, 'piecewise'(op(s), 0), s),\n r)\n elif s :: 'numeric' then\n product(var+r, var=0..s-1)\n else\n var := 'j';\n if has(r, var) then var := gensym(var) end if;\n Product(var+r, var=0..s-1) # inert so as to not become GAMMA\n end if\n end proc;\n\n\n\n\n # Rewrite piecewise(i<=j-1,1,0) + piecewise(i=j,1,0) + ...\n # to piecewise(i<=j,1,0) + ...\n # and rewrite piecewise(And(i<=j-1,a `if`(c=jcond, subsop(0=`<=`,icond), c)), op([j,1],terms)), terms);\n break\n end do\n end do;\n `+`(op(terms))\n end proc)\n end proc;\n\n\n wrap := proc(e, loops :: list([identical(product,Product,sum,Sum),\n name=range]), $)\n local res, loop;\n res := e;\n for loop in loops do\n res := op(1,loop)(res, op(2,loop));\n end do;\n res\n end proc;\n", "meta": {"hexsha": "fdf8045852d9d4cac92fe7f34240cd88013d8062", "size": 7673, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Beta.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/Beta.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/Beta.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": 45.4023668639, "max_line_length": 156, "alphanum_fraction": 0.5124462401, "num_tokens": 2406, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7248702880639791, "lm_q2_score": 0.5350984286266115, "lm_q1q2_score": 0.38787695210115447}} {"text": "`cartesian_product/sets` := proc()\n local A,P,a,p;\n if nargs = 0 then\n return {[]};\n else\n A := args[1];\n if not type(A,set) then\n error \"Argument is not a set\";\n fi;\n P := `cartesian_product/sets`(args[2..-1]);\n return {seq(seq([a,op(p)],p in P),a in A)};\n fi;\nend:\n\n`cartesian_product/lists` := proc()\n local A,P,a,p;\n if nargs = 0 then\n return [[]];\n else\n A := args[1];\n if not type(A,list) then\n error \"Argument is not a list\";\n fi;\n P := `cartesian_product/lists`(args[2..-1]);\n return [seq(seq([a,op(p)],p in P),a in A)];\n fi;\nend:\n\n", "meta": {"hexsha": "26cc7b36a09707cb4403bf40ae1685fd1208f463", "size": 556, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/cartesian_product.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/cartesian_product.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/cartesian_product.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": 19.1724137931, "max_line_length": 46, "alphanum_fraction": 0.5827338129, "num_tokens": 193, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6261241772283034, "lm_q2_score": 0.6187804267137442, "lm_q1q2_score": 0.38743338556112156}} {"text": "#@ Not autoload\n\nwith(LinearAlgebra):\n\np := 2;\nadams_n_max := 5;\nadams_s_max := 20;\n\nunprotect('t');\nunassign('t');\n\nxi[0] := 1;\n\nprotect('t');\n\nHH_vars := plex(seq(xi[i],i=1..adams_n_max));\n\n# The cobar complex involves variables xi[n,s] corresponding to the copy of\n# xi[n] in the s'th tensor factor. We use the ordering with\n# xi[1,1] >> xi[2,1] >> xi[3,1] >> ... >> xi[1,2] >> xi[2,2] >> xi[3,2] >> ...\n# so the variables from each tensor factor dominate those from the next tensor\n# factor. It is not clear whether this is the best choice.\nH_cobar_vars :=\n plex(seq(seq(xi[i,j],i=1..adams_n_max),j=1..adams_s_max));\n\nHH_cmp := (a,b) -> TestOrder(a,b,HH_vars):\nH_cobar_cmp := (a,b) -> TestOrder(a,b,H_cobar_vars):\n\nH_degree_rule := {\n seq(xi[n] = e^(2^n-1) * xi[n],n=1..adams_n_max),\n seq(seq(xi[n,i] = e^(2^n-1) * xi[n,i],n=1..adams_n_max),i=1..adams_s_max)\n}:\n\nH_degree := (u) -> degree(subs(H_degree_rule,u),e);\n\nH_bidegree := proc(u)\n local s,t;\n t := H_degree(u);\n s := adams_s_max;\n while s > 0 and not(has(u,{seq(xi[i,s],i=1..adams_n_max)})) do\n s := s-1;\n od;\n return [s,t];\nend:\n\n# Basis for Z[xi[i] : i >= n] in degree d\nT_basis := proc(d::integer,n::posint := 1)\n option remember;\n local m,r,i;\n m := 2^n-1;\n r := floor(d/m);\n if d < 0 then\n return [];\n elif d = 0 then\n return [1];\n elif r = 0 then\n return [];\n else\n map(op,[seq(xi[n]^i *~ T_basis(d-m*i,n+1),i=0..r)]);\n fi;\nend:\n\n# Basis for Z[v[i] : i >= n] in degree <= d\nT_lower_basis := proc(d::integer,n::posint := 1)\n option remember;\n local m,r,i;\n m := 2^n-1;\n r := floor(d/m);\n if d < 0 then\n return [];\n elif r = 0 then\n return [1];\n else\n map(op,[seq(xi[n]^i *~ T_lower_basis(d-m*i,n+1),i=0..r)]);\n fi;\nend:\n\n# Basis for the s-fold tensor power of Z[t_1,t_2,...] in degree d\n# The copy of xi[i] in the j'th tensor factor is represented by xi[i,j]\nT_power_basis := proc(s::nonnegint,d::integer)\n local B,m,R1,R2,u,v;\n if s = 0 then return `if`(d = 0,[1],[]); fi;\n\n R1 := {seq(xi[n] = xi[n,1],n=1..adams_n_max)};\n R2 := {seq(seq(xi[n,i] = xi[n,i+1],i=1..s-1),n=1..adams_n_max)};\n B := NULL;\n \n for u in subs(R1,T_lower_basis(d)) do\n m := d - H_degree(u);\n for v in subs(R2,T_power_basis(s-1,m)) do\n B := B,(u*v);\n od;\n od;\n return [B];\nend:\n\n# Basis for the s-fold tensor power of the augmentation ideal in\n# Z[t_1,t_2,...] in degree d\nT_reduced_power_basis := proc(s::nonnegint,d::integer)\n local B,m,R1,R2,u,v;\n if s = 0 then return `if`(d = 0,[1],[]); fi;\n\n R1 := {seq(xi[n] = xi[n,1],n=1..adams_n_max)};\n R2 := {seq(seq(xi[n,i] = xi[n,i+1],i=1..s-1),n=1..adams_n_max)};\n B := NULL;\n \n for u in subs(R1,T_lower_basis(d)) do\n if u <> 1 then \n m := d - H_degree(u);\n for v in subs(R2,T_reduced_power_basis(s-1,m)) do\n B := B,(u*v);\n od;\n fi;\n od;\n return [B];\nend:\n\nH_cobar_basis := (s,d) -> T_reduced_power_basis(s,d);\n\n# Hopf algebroid coproduct on the generators xi[n]\npsi_xi := proc(n)\n local a,b;\n option remember;\n if n = 0 then return 1; fi;\n\n return xi[n,1] + xi[n,2] + add(xi[n-i,1]^(2^i)*xi[i,2],i=1..n-1);\nend:\n\nd_H_cobar_rule := proc(s,i)\n local R0,R1,R2,R3;\n if i = 0 then\n R0 := {seq(xi[j]=xi[j,1],j=1..adams_n_max)};\n R1 := {seq(xi[j]=xi[j,2],j=1..adams_n_max)};\n R2 := {seq(seq(xi[j,k]=xi[j,k+1],k=1..s),j=1..adams_n_max)};\n return {op(R1),op(R2)};\n else\n R0 := {seq(xi[j,1]=xi[j,i],j=1..adams_n_max),\n seq(xi[j,2]=xi[j,i+1],j=1..adams_n_max)};\n R1 := {seq(seq(xi[j,k]=xi[j,k+1],k=i+1..s),j=1..adams_n_max)};\n R2 := {seq(xi[j,i] = subs(R0,psi_xi(j)),j=1..adams_n_max)};\n if i = 1 then\n R3 := {seq(xi[j] = modp(expand(subs(R0,psi_xi(j))),2),j=1..adams_n_max)};\n else\n R3 := {seq(xi[j] = xi[j,1],j=1..adams_n_max)};\n fi;\n return {op(R1),op(R2),op(R3)};\n fi;\nend:\n\nd_H_cobar := (s) -> (u) ->\n modp(expand(add(subs(d_H_cobar_rule(s,i),u),i=0..s+1)),2);\n\n\nd_H_cobar_matrix := proc(s,d)\n local B1,B2,cf;\n B1 := H_cobar_basis(s,d);\n B2 := H_cobar_basis(s+1,d);\n cf := proc(u)\n local sol;\n sol := solve({coeffs(u - add(c[i]*B2[i],i=1..nops(B2)),indets(B2))});\n subs(sol,[seq(c[i],i=1..nops(B2))]);\n end;\n Transpose(Matrix(map(cf,map(d_H_cobar(s),B1))));\nend:\n\nmu_H_cobar := (s1,s2) -> proc(a,b)\n local i,b0;\n b0 := b;\n for i from 0 to s1-1 do\n b0 := modp(expand(subs(d_H_cobar_rule(s2+i,0),b0)),2);\n od:\n return modp(expand(a * b0),2);\nend:\n\nanalyse_H_cobar := proc(s::nonnegint,d::integer)\n local i,R,R0,B1,B2,n1,n2,M,L0,P0,x,x1,L,P,Q,nx,LB2,y,HB,HE,T,U,L1,K,Ki;\n global H_cobar_data;\n \n if d + s >= 2*(p^(adams_n_max + 1) - 1) then\n error(\"adams_n_max is too small\");\n fi;\n\n if s > adams_s_max then\n error(\"adams_s_max is too small\");\n fi;\n \n R := table():\n\n if s = 0 then\n if d = 0 then\n R[\"chain_basis\"] := [1];\n R[\"chain_rank\"] := 1;\n R[\"cycle_basis\"] := [1];\n R[\"cycle_rank\"] := 1;\n R[\"boundary_basis\"] := [];\n R[\"boundary_rank\"] := 0;\n R[\"pivot_data\"] := [[1,infinity]];\n R[\"non_cycle_basis\"] := [];\n R[\"homology_basis\"] := [1];\n R[\"homology_exponents\"] := [infinity];\n else\n R[\"chain_basis\"] := H_cobar_basis(0,d);\n R[\"chain_rank\"] := nops(R[\"chain_basis\"]);\n R[\"cycle_basis\"] := [];\n R[\"cycle_rank\"] := 0;\n R[\"boundary_basis\"] := [];\n R[\"boundary_rank\"] := 0;\n R[\"pivot_data\"] := [];\n R[\"non_cycle_basis\"] := R[\"chain_basis\"];\n R[\"homology_basis\"] := [];\n R[\"homology_exponents\"] := [];\n fi;\n\n H_cobar_data[s,d] := eval(R);\n return eval(R);\n fi;\n\n if type(H_cobar_data[s-1,d+1],table) then\n R0 := H_cobar_data[s-1,d+1];\n B1 := R0[\"non_cycle_basis\"];\n else\n B1 := H_cobar_basis(s-1,s+d):\n fi;\n\n B2 := H_cobar_basis(s,s+d):\n n1 := nops(B1);\n n2 := nops(B2);\n R[\"chain_basis\"] := B2;\n R[\"chain_rank\"] := n2;\n\n if n2 = 0 then\n R[\"cycle_basis\"] := [];\n R[\"cycle_rank\"] := 0;\n R[\"boundary_basis\"] := [];\n R[\"boundary_rank\"] := 0;\n R[\"pivot_data\"] := [];\n R[\"non_cycle_basis\"] := [];\n R[\"homology_basis\"] := [];\n R[\"homology_exponents\"] := [];\n H_cobar_data[s,d] := eval(R);\n return eval(R);\n fi;\n \n M := Transpose(Matrix(map(coeff_list,map(d_H_cobar(s-1),B1),B2)));\n L0,P0,x := op(Zpl_reduce(Transpose(M),p)):\n L := Transpose(L0):\n P := Transpose(P0):\n nx := nops(x):\n R[\"cycle_rank\"] := nx;\n \n LB2 := convert(L0.Vector(B2),list):\n R[\"boundary_basis\"] := [seq(LB2[i],i=1..nx)];\n R[\"cycle_basis\"] := [seq(LB2[i]/p^xi[i][2],i=1..nx)];\n R[\"pivot_data\"] := x;\n\n y := sort([op({seq(i,i=1..n2)} minus {seq(xi[i][1],i=1..nx)})]);\n R[\"non_cycle_basis\"] := [seq(B2[i],i in y)];\n \n HB := [];\n HE := [];\n \n for i from 1 to nx do\n if xi[i][2] > 0 then\n HB := [op(HB),R[\"cycle_basis\"][i]];\n HE := [op(HE),p^xi[i][2]];\n fi;\n od;\n\n R[\"homology_basis\"] := HB;\n R[\"homology_exponents\"] := HE;\n \n T := ;\n U := Matrix(nx,n2):\n for i from 1 to nx do U[i,xi[i][1]] := 1; od:\n L1 := U.L.Transpose(T);\n Q := P.Transpose(T).(1/L1).U;\n K := ;\n y := sort([op({seq(i,i=1..n2)} minus {seq(xi[i][1],i=1..nx)})]);\n for i from 1 to n2 - nx do \n K[y[i],nx+i] := 1;\n od:\n Ki := 1/K;\n\n H_cobar_data[s,d] := eval(R);\n return eval(R);\nend:\n\nsave_H2_data := proc()\n local file;\n file := sprintf(\"%s/H_2.m\",data_dir);\n save(adams_n_max,adams_s_max,psi_xi,H_basis,H_lower_basis,file);\nend:\n\nload_H2_data := proc(p)\n local file;\n file := sprintf(\"%s/H_2.m\",data_dir,p);\n load(file);\nend:\n\nsave_H2_cobar_data := proc()\n local file;\n file := sprintf(\"%s/H_cobar_data_2.m\",data_dir);\n save(H_cobar_data,file);\nend:\n\nload_H2_cobar_data := proc()\n local file;\n file := sprintf(\"%s/H_cobar_data_2.m\",data_dir);\n load(file);\nend:\n\nadams_representative := proc(u)\n local a,b,c,sa,sb,v,i;\n if type(u,integer) then\n return modp(u,2); \n elif type(u,`+`) then\n return modp(map(adams_representative,u),2);\n elif type(u,`*`) then\n c,v := selectremove(type,u,integer);\n if modp(c,2) = 0 then\n return 0;\n else\n v := sort([op(v)]);\n a := adams_representative(v[1]);\n b := adams_representative(mul(v[i],i=2..nops(v)));\n sa := H_bidegree(a)[1];\n sb := H_bidegree(b)[1];\n return modp(mu_H_cobar(sa,sb)(a,b),2)\n fi;\n elif type(u,`^`) and type(op(2,u),posint) then\n a := adams_representative(op(1,u));\n b := a;\n sa := H_bidegree(a)[1];\n for i from 2 to op(2,u) do\n b := modp(mu_H_cobar(sa,(i-1)*sa)(a,b),2);\n od;\n return b;\n else\n return procname(args);\n fi;\nend:\n\nadams_assassin := proc(err)\n local s,t,B0,B1,M0,V0,MV,sol;\n s,t := op(H_bidegree(err));\n B0 := H_cobar_basis(s-1,t);\n B1 := H_cobar_basis(s,t);\n M0 := d_H_cobar_matrix(s-1,t);\n V0 := Vector(coeff_list(err,B1));\n MV := LinearAlgebra[Modular][Mod](2,,integer[]):\n sol := LinearAlgebra[Modular][LinearSolve](2,MV,1,inplace=false):\n return ([sol][1] . Vector(B0));\nend:\n\nadams_representative(h[0]) := xi[1,1];\nadams_representative(h[1]) := xi[1,1]^2;\nadams_representative(h[2]) := xi[1,1]^4;\nadams_representative(h[3]) := xi[1,1]^8;\nadams_representative(c[0]) := xi[1,1]^2*xi[1,2]^7*xi[1,3]^2+xi[1,1]^2*xi[1,2]^4*xi[1,3]^2*xi[2,2]-xi[1,2]^4*xi[1,3]^4*xi[2,1]+xi[1,1]^2*xi[1,2]^3*xi[2,3]^2+xi[1,1]^2*xi[1,2]*xi[1,3]^2*xi[2,2]^2+xi[1,1]^2*xi[1,2]*xi[1,3]^2*xi[2,3]^2+xi[1,1]^2*xi[1,3]^2*xi[3,2]+xi[1,1]^2*xi[2,2]*xi[2,3]^2;\n\nadams_relations := [\n [h[0]*h[1],xi[1,1]^3+xi[2,1]],\n [h[0]^2*h[2]+h[1]^3,xi[1,1]^2*xi[1,2]*xi[2,1]+xi[1,1]^2*xi[1,2]*xi[2,2]+xi[2,1]*xi[2,2]],\n [h[1]*h[2],xi[1,1]^6+xi[2,1]^2],\n [h[0]*h[2]^2,xi[1,1]^5*xi[1,2]^4+xi[1,1]^2*xi[1,2]^7+xi[1,1]^2*xi[1,2]^4*xi[2,1]+xi[1,1]^2*xi[1,2]^4*xi[2,2]+xi[1,2]^6*xi[2,1]+xi[1,1]^2*xi[1,2]*xi[2,2]^2+xi[1,1]^2*xi[3,2]+xi[2,1]*xi[2,2]^2],\n [h[0]^4*h[3],xi[1,1]^2*xi[1,2]^5*xi[1,3]^3*xi[1,4]^2+xi[1,1]^2*xi[1,2]^3*xi[1,3]^2*xi[1,4]^5+xi[1,1]^2*xi[1,2]^2*xi[1,3]^5*xi[1,4]^3+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[1,4]^6+xi[1,1]^6*xi[1,2]*xi[1,3]*xi[1,4]*xi[2,1]+xi[1,1]^4*xi[1,2]^3*xi[1,3]^2*xi[2,4]+xi[1,1]^4*xi[1,2]^3*xi[1,3]*xi[1,4]*xi[2,2]+xi[1,1]^4*xi[1,2]^3*xi[1,3]*xi[1,4]*xi[2,3]+xi[1,1]^2*xi[1,2]^5*xi[1,3]*xi[1,4]*xi[2,2]+xi[1,1]^2*xi[1,2]^4*xi[1,3]^2*xi[1,4]*xi[2,3]+xi[1,1]^2*xi[1,2]^4*xi[1,3]*xi[1,4]^2*xi[2,3]+xi[1,1]^2*xi[1,2]^3*xi[1,3]^3*xi[1,4]*xi[2,3]+xi[1,1]^2*xi[1,2]^3*xi[1,3]^3*xi[1,4]*xi[2,4]+xi[1,1]^2*xi[1,2]^3*xi[1,3]^2*xi[1,4]^2*xi[2,2]+xi[1,1]^2*xi[1,2]^3*xi[1,4]^4*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^4*xi[1,4]*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^4*xi[1,4]*xi[2,4]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^3*xi[1,4]^2*xi[2,2]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^3*xi[1,4]^2*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[1,4]^3*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[1,4]^3*xi[2,4]+xi[1,1]^2*xi[1,3]^4*xi[1,4]^3*xi[2,2]+xi[1,1]^2*xi[1,3]^2*xi[1,4]^5*xi[2,2]+xi[1,2]^4*xi[1,3]^3*xi[1,4]^2*xi[2,1]+xi[1,2]^2*xi[1,3]^2*xi[1,4]^5*xi[2,1]+xi[1,1]^4*xi[1,2]*xi[1,4]*xi[2,2]*xi[2,3]+xi[1,1]^4*xi[1,3]*xi[1,4]*xi[2,2]^2+xi[1,1]^2*xi[1,2]^3*xi[1,3]*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,2]^3*xi[1,4]*xi[2,3]^2+xi[1,1]^2*xi[1,2]^3*xi[1,4]*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[2,1]*xi[2,4]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,2]^2*xi[1,3]^2*xi[2,4]^2+xi[1,1]^2*xi[1,2]^2*xi[1,3]*xi[1,4]*xi[2,1]*xi[2,2]+xi[1,1]^2*xi[1,2]^2*xi[1,3]*xi[1,4]*xi[2,1]*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,3]*xi[1,4]*xi[2,2]^2+xi[1,1]^2*xi[1,2]^2*xi[1,3]*xi[1,4]*xi[2,3]^2+xi[1,1]^2*xi[1,2]^2*xi[1,4]^2*xi[2,2]*xi[2,3]+xi[1,1]^2*xi[1,2]^2*xi[1,4]^2*xi[2,3]^2+xi[1,1]^2*xi[1,2]^2*xi[1,4]^2*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,2]*xi[1,3]^2*xi[1,4]*xi[2,2]*xi[2,3]+xi[1,1]^2*xi[1,2]*xi[1,3]^2*xi[1,4]*xi[2,2]*xi[2,4]+xi[1,1]^2*xi[1,2]*xi[1,3]*xi[1,4]^2*xi[2,2]^2+xi[1,1]^2*xi[1,3]^3*xi[1,4]*xi[2,2]^2+xi[1,1]^2*xi[1,3]^3*xi[1,4]*xi[2,2]*xi[2,3]+xi[1,1]^2*xi[1,3]^3*xi[1,4]*xi[2,2]*xi[2,4]+xi[1,1]^2*xi[1,3]^2*xi[1,4]^2*xi[2,2]*xi[2,3]+xi[1,1]^2*xi[1,4]^4*xi[2,2]*xi[2,3]+xi[1,2]^4*xi[1,3]*xi[1,4]*xi[2,1]^2+xi[1,2]^4*xi[1,3]*xi[1,4]*xi[2,1]*xi[2,2]+xi[1,2]^2*xi[1,3]^3*xi[1,4]*xi[2,1]*xi[2,3]+xi[1,2]^2*xi[1,3]^3*xi[1,4]*xi[2,1]*xi[2,4]+xi[1,2]^2*xi[1,3]^2*xi[1,4]^2*xi[2,1]*xi[2,2]+xi[1,2]^2*xi[1,4]^4*xi[2,1]*xi[2,3]+xi[1,1]^2*xi[1,2]*xi[1,3]*xi[1,4]*xi[3,1]+xi[1,1]^2*xi[1,2]*xi[1,3]*xi[1,4]*xi[3,2]+xi[1,1]^2*xi[1,2]*xi[2,2]*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,3]^2*xi[1,4]*xi[3,2]+xi[1,1]^2*xi[1,3]*xi[1,4]^2*xi[3,2]+xi[1,1]^2*xi[1,3]*xi[2,2]*xi[2,3]*xi[2,4]+xi[1,1]^2*xi[1,4]*xi[2,1]*xi[2,2]*xi[2,3]+xi[1,1]^2*xi[1,4]*xi[2,2]^2*xi[2,3]+xi[1,1]^2*xi[1,4]*xi[2,2]*xi[2,3]*xi[2,4]+xi[1,2]^3*xi[1,3]*xi[1,4]*xi[3,1]+xi[1,2]^2*xi[1,3]*xi[2,1]*xi[2,3]*xi[2,4]+xi[1,2]^2*xi[1,4]*xi[2,1]^2*xi[2,3]+xi[1,2]^2*xi[1,4]*xi[2,1]*xi[2,3]^2+xi[1,2]^2*xi[1,4]*xi[2,1]*xi[2,3]*xi[2,4]+xi[1,2]*xi[1,3]^2*xi[2,1]^2*xi[2,4]+xi[1,2]*xi[1,3]*xi[1,4]*xi[2,1]^3+xi[1,2]*xi[1,3]*xi[1,4]*xi[2,1]^2*xi[2,2]+xi[1,2]*xi[1,3]*xi[1,4]*xi[2,1]^2*xi[2,3]+xi[1,3]^2*xi[1,4]*xi[2,1]*xi[2,2]*xi[2,3]+xi[1,3]^2*xi[1,4]*xi[2,1]*xi[2,2]*xi[2,4]+xi[1,3]*xi[1,4]^2*xi[2,1]*xi[2,2]^2+xi[1,2]*xi[1,4]*xi[2,3]*xi[3,1]+xi[1,3]*xi[1,4]*xi[2,1]*xi[3,2]+xi[2,1]*xi[2,2]*xi[2,3]*xi[2,4]],\n[h[1]^2*h[3]+h[2]^3,xi[1,1]^4*xi[1,2]^2*xi[2,1]^2+xi[1,1]^4*xi[1,2]^2*xi[2,2]^2+xi[2,1]^2*xi[2,2]^2],\n[h[0]*c[0],xi[1,1]^2*xi[1,2]^5*xi[1,3]^2*xi[2,3]+xi[1,1]^2*xi[1,2]^4*xi[1,3]^3*xi[2,3]+xi[1,1]^2*xi[1,2]^4*xi[2,3]^2+xi[1,1]^2*xi[1,2]^3*xi[1,3]*xi[2,2]^2+xi[1,1]^2*xi[1,2]*xi[1,3]^3*xi[2,2]^2+xi[1,1]^2*xi[1,3]^4*xi[2,2]^2+xi[1,2]^4*xi[1,3]^2*xi[2,1]*xi[2,3]+xi[1,1]^2*xi[1,2]*xi[1,3]^2*xi[3,2]+xi[1,1]^2*xi[1,2]*xi[2,2]^2*xi[2,3]+xi[1,1]^2*xi[1,3]^3*xi[3,2]+xi[1,1]^2*xi[1,3]*xi[2,2]^3+xi[1,1]^2*xi[1,3]*xi[2,2]^2*xi[2,3]+xi[1,3]^3*xi[2,1]*xi[2,2]^2+xi[1,3]^2*xi[2,1]*xi[3,2]+xi[2,1]*xi[2,2]^2*xi[2,3]]\n]:\n\n`is_admissible/Steenrod2` := proc(u)\n local v;\n \n if type(u,`+`) or type(u,list) or type(u,set) then\n return `and`(op(map(`is_admissible/Steenrod2`,[op(u)])));\n elif type(u,`*`) then\n v := select(type,[op(u)],specfunc(nonnegint,Sq));\n if nops(v) = 0 then\n return true;\n elif nops(v) = 1 then\n return `is_admissible/Steenrod2`(v[1]);\n else\n return FAIL;\n fi;\n elif type(u,specfunc(nonnegint,Sq)) then\n return `and`(true,seq(evalb(op(j,u) >= 2*op(j+1,u)),j=1..nops(u)-1));\n else\n return true;\n fi;\nend:\n\nadem_relation := proc(k::nonnegint,j::nonnegint)\n Sq(k,j) + add(modp(binomial(j-m-1,k-2*m),2) * Sq(j+k-m,m),m=0..floor(k/2));\nend:\n\n`reduce_Sq` := proc()\n option remember;\n local a,r,m,n,u,v,j,k;\n\n a := select(i -> i > 0,[args]);\n r := nops(a);\n \n if `is_admissible/Steenrod2`(Sq(op(a))) then\n return Sq(op(a));\n fi;\n\n n := 1;\n while n < r and a[n] >= 2*a[n+1] do\n n := n+1;\n od:\n\n u := seq(a[i],i=1..n-1);\n k := a[n];\n j := a[n+1];\n v := seq(a[i],i=n+2..r);\n return\n modp(add(modp(binomial(j-m-1,k-2*m),2) * reduce_Sq(u,j+k-m,m,v),m=0..floor(k/2)),2);\nend:\n\n`reduce/Steenrod2` := (u) -> modp(expand(eval(subs(Sq=reduce_Sq,u))),2);\n\n`mu0/Steenrod2` := proc(u,v)\n if type(u,specfunc(nonnegint,Sq)) and type(v,specfunc(nonnegint,Sq)) then\n return reduce_Sq(op(u),op(v));\n else\n return FAIL;\n fi;\nend:\n\n`mu/Steenrod2` := apply_linear_assoc_mod(`mu0/Steenrod2`,Sq(),2);", "meta": {"hexsha": "843bdf300e3234f47a3cb1a5df451d76f0b37362", "size": 14782, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/chromatic/H2.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/chromatic/H2.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/chromatic/H2.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": 34.376744186, "max_line_length": 3283, "alphanum_fraction": 0.5572994182, "num_tokens": 7437, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7401743620390163, "lm_q2_score": 0.523420348936324, "lm_q1q2_score": 0.387422322852183}} {"text": "#!/bin/bash maple\n# Use `maple -q symengine_bench.mpl -D n=15` to run\n\ne := sin(cos(x+1)):\nst := time[real]():\nf := series(e, x=0,n):\n1000*(time[real]()-st);\n\ndone\n", "meta": {"hexsha": "9d53895939df81892295397c6d11c5d010fbd175", "size": 164, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarks/symengine_bench.mpl", "max_stars_repo_name": "jmig5776/symengine", "max_stars_repo_head_hexsha": "03babc5c56b047b2fe81ef6f8391d1845e6bb66c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 808, "max_stars_repo_stars_event_min_datetime": "2015-10-24T14:47:34.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T02:59:22.000Z", "max_issues_repo_path": "benchmarks/symengine_bench.mpl", "max_issues_repo_name": "HQSquantumsimulations/symengine", "max_issues_repo_head_hexsha": "95d6af92dc6a759d9320d6bdadfa51d038c81218", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1226, "max_issues_repo_issues_event_min_datetime": "2015-10-12T19:28:02.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T06:22:58.000Z", "max_forks_repo_path": "benchmarks/symengine_bench.mpl", "max_forks_repo_name": "HQSquantumsimulations/symengine", "max_forks_repo_head_hexsha": "95d6af92dc6a759d9320d6bdadfa51d038c81218", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 253, "max_forks_repo_forks_event_min_datetime": "2015-10-24T14:49:40.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-13T06:44:29.000Z", "avg_line_length": 16.4, "max_line_length": 51, "alphanum_fraction": 0.5853658537, "num_tokens": 64, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7185943805178139, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.3873103135795625}} {"text": "\nwith(LinearAlgebra);\ncdir := \"/home/scott/wDocuments/research/software/hqca/hqca/maple/\";\ndata := readdata(cat(cdir, \"temp.rdm\"), 6);\nwith(ArrayTools);\n# \nRearrange := proc(x) local n, a, i, j, k, l; `local`(a, n, i, j, k, l); `description`(\"convert chemists to numpy and flatten an array to form a matrix\"); n := Size(x); a := Array(1 .. n[1], 1 .. n[2], 1 .. n[3], 1 .. n[4], datatype = float[8]); for i to n[1] do for j to n[2] do for k to n[3] do for l to n[4] do a[i, k, j, l] := x[i, j, k, l]; end do; end do; end do; end do; return a; end proc;\nFlatten := proc(x) local n, a, i, j, k, l; `local`(a, n, i, j, k, l); `description`(\"convert chemists to numpy and flatten an array to form a matrix\"); n := Size(x); a := Array(1 .. n[1]*n[2], 1 .. n[3]*n[4], datatype = float[8]); for i to n[1] do for j to n[2] do for k to n[3] do for l to n[4] do a[(i - 1)*n[1] + j, (k - 1)*n[3] + l] := x[i, k, j, l]; end do; end do; end do; end do; return a; end proc;\nNew := Array(1 .. 3, 1 .. 3, 1 .. 3, 1 .. 3, datatype = float[8]);\nnewdata := data[3 .. ()];\nfor i in newdata do\n New[round(i[1]), round(i[2]), round(i[4]), round(i[3])] := i[5];\nend do;\nNew[1, 2];\nwith(QuantumChemistry);\n\nmol := [[\"H\", 1.00000000, 0, 0], [\"H\", -1.00000000, 0, 0]];\n\nh2 := Variational2RDM(mol, basis = \"STO-3G\", return_rdm = \"rdm1_and_rdm2\");\n\n\n\nh2[rdm2];\n\npure := Purify2RDM(h2[rdm2], spin_free = true, electron_number = 2, conv_tol = 0.10000000, conditions = \"DQG\");\n^2 D ^{i,j}_{k,l} = < i j l k > -> A[1..r,1..r,1..r,1..r] <=> A[i,j,k,l] \n;\n\nG := Flatten(h2[rdm2]);\n\nEigenvalues(G);\nF := Flatten(pure[rdm2]);\n\n\nEigenvalues(F);\n\n\n", "meta": {"hexsha": "1f6c17361c4905457e093f0d090bbed6f88d61a0", "size": 1615, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "hqca/maple/old/purification_scheme.mpl", "max_stars_repo_name": "damazz/HQCA", "max_stars_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "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": "hqca/maple/old/purification_scheme.mpl", "max_issues_repo_name": "damazz/HQCA", "max_issues_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "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": "hqca/maple/old/purification_scheme.mpl", "max_forks_repo_name": "damazz/HQCA", "max_forks_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-10T00:20:09.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-10T00:20:09.000Z", "avg_line_length": 42.5, "max_line_length": 406, "alphanum_fraction": 0.5684210526, "num_tokens": 676, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6926419958239132, "lm_q2_score": 0.5583269943353745, "lm_q1q2_score": 0.38672072367882043}} {"text": "\n# Slider_Crank\n\n# Autor\n# Abderahman Bejaoui\n# Studienarbeit bei: Moritz Schappler, moritz.schappler@imes.uni-hannover.de, 2018-08\n# (C) Institut fuer mechatronische Systeme, Leibniz Universitaet Hannover\n# Quellen\n# TODO\n# \n# Initialisierung\n# Import \nrestart:\nkin_constraints_exist := true: # F\u00fcr Speicherung\n;\nwith(StringTools): # F\u00fcr Zeitausgabe\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\n#with(ListTools):\ncodegen_act := true:\ncodegen_opt := 1: # Geringerer Optimierungsgrad. Sonst zu lange.\ncodegen_debug := 0: # Zur Code-Generierung auch f\u00fcr Nicht-Inert-Ausdr\u00fccke\n;\nread \"../helper/proc_MatlabExport\":\nread \"../transformation/proc_rotx\":\nread \"../transformation/proc_roty\":\nread \"../transformation/proc_rotz\":\nread \"../helper/proc_convert_s_t\":\nread \"../helper/proc_convert_t_s\":\nread \"../robot_codegen_constraints/proc_subs_kintmp_exp\":\nwith(RealDomain): # Schr\u00e4nkt alle Funktionen auf den reellen Bereich ein. Muss nach Definition von MatlabExport kommen. Sonst geht dieses nicht.\n;\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\",robot_name):\n# Ergebnisse von Trigonometrischer Elimination lesen\nread sprintf(\"../codeexport/fourbarprisTE/tmp/kinematic_constraints_maple_inert.m\"):\nkin_constraints_exist := kin_constraints_exist:\nkintmp_qs := kintmp_qs:\nkintmp_qt := kintmp_qt:\nkintmp_subsexp := kintmp_subsexp:\n# Variable entfernen\nkintmp_subsexp:= Matrix(2*RowDimension(kintmp_s),2):\n# Export\nkintmp_qt := convert_s_t(kintmp_qs):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple\", robot_name):\nsave kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_subsexp_maple.m\", robot_name):\n#printf(\"Ausdr\u00fccke f\u00fcr kintmp_subsexp gespeichert (Maple). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\nfor i from 1 to RowDimension(kintmp_s) do\n tmp := kintmp_qs(i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d\",robot_name, i):\n save tmp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert_kintmpq_%d.m\", robot_name, i):\nend do:\nsave kin_constraints_exist, kintmp_qs, kintmp_qt,kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert\" ,robot_name):\nsave kin_constraints_exist, kintmp_qs, kintmp_qt, kintmp_subsexp, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_maple_inert.m\", robot_name):\nsave kintmp_qs, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_kintmp_qs_maple_inert\", robot_name):\n#printf(\"Ausdr\u00fccke mit Inert-Arctan exportiert (Matlab). %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n# Liste mit abh\u00e4ngigen konstanten Kinematikparametern erstellen (wichtig f\u00fcr Matlab-Funktionsgenerierung)\nread \"../helper/proc_list_constant_expressions\";\nkc_symbols := Matrix(list_constant_expressions( kintmp_qs ));\n#kc_symbols :=Transpose(kc_symbols);\nsave kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name):\nMatlabExport(kc_symbols, sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_matlab.m\",robot_name),2);\n#printf(\"Fertig. %s. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n\n", "meta": {"hexsha": "ff3d87b0567626faf634b491cc40183992400fac", "size": 3263, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "systems/fourbarpris/codegen/fourbarprisDE_kinematic_constraints.mpl", "max_stars_repo_name": "SchapplM/robsynth-serhybroblib", "max_stars_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/fourbarpris/codegen/fourbarprisDE_kinematic_constraints.mpl", "max_issues_repo_name": "SchapplM/robsynth-serhybroblib", "max_issues_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": "systems/fourbarpris/codegen/fourbarprisDE_kinematic_constraints.mpl", "max_forks_repo_name": "SchapplM/robsynth-serhybroblib", "max_forks_repo_head_hexsha": "8e4d39cf919a85a5d3d54391b699ae51ada191a1", "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": 49.4393939394, "max_line_length": 146, "alphanum_fraction": 0.7799570947, "num_tokens": 972, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.731058578630005, "lm_q2_score": 0.5273165233795671, "lm_q1q2_score": 0.38549926806998214}} {"text": "#!/bin/bash maple\n# Use `maple -q expand7.mpl -D n=20` to run\n\ne := (1 + sqrt(3) * x + sqrt(5) * y) ^ n:\nf := e * (e + sqrt(7)):\n\nst := time[real]():\nf := expand(f):\n1000*(time[real]() - st);\n\ndone\n", "meta": {"hexsha": "dc4d750719fbdc2aa3da568ae21e683be8f0adb2", "size": 198, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "benchmarks/expand7.mpl", "max_stars_repo_name": "jmig5776/symengine", "max_stars_repo_head_hexsha": "03babc5c56b047b2fe81ef6f8391d1845e6bb66c", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 808, "max_stars_repo_stars_event_min_datetime": "2015-10-24T14:47:34.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T02:59:22.000Z", "max_issues_repo_path": "benchmarks/expand7.mpl", "max_issues_repo_name": "HQSquantumsimulations/symengine", "max_issues_repo_head_hexsha": "95d6af92dc6a759d9320d6bdadfa51d038c81218", "max_issues_repo_licenses": ["MIT"], "max_issues_count": 1226, "max_issues_repo_issues_event_min_datetime": "2015-10-12T19:28:02.000Z", "max_issues_repo_issues_event_max_datetime": "2022-03-30T06:22:58.000Z", "max_forks_repo_path": "benchmarks/expand7.mpl", "max_forks_repo_name": "HQSquantumsimulations/symengine", "max_forks_repo_head_hexsha": "95d6af92dc6a759d9320d6bdadfa51d038c81218", "max_forks_repo_licenses": ["MIT"], "max_forks_count": 253, "max_forks_repo_forks_event_min_datetime": "2015-10-24T14:49:40.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-13T06:44:29.000Z", "avg_line_length": 16.5, "max_line_length": 43, "alphanum_fraction": 0.5, "num_tokens": 83, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.7577943712746407, "lm_q2_score": 0.5078118642792044, "lm_q1q2_score": 0.38481697241726287}} {"text": "BinomSums := module()\n\noption package;\n\nlocal\n gfdict, gfdictcomp, gfnames, multinomial, packvars, geomsum, solvecons,\n linearorder, slopes, asylt, inorout_base, ratres2, geomsum_, simpfacts,\n simpfacts0, SimpleImpl, isconvergent, asy, inorout, sumtores0 ;\n\nexport\n sumtores, addnewgf, rser, computesum, hermitered, ratres, geomred, \n geomredall, sumtoct, `BinomSums/version`;\n\n `BinomSums/version` := 0.11;\n\n # This module provides a simple implementation of the computation of integral\n # representation of binomial sums.\n SimpleImpl := module()\n \n export sumtores;\n\n # Input :\n # - U a binomial sum, as a Maple expression\n # - v a name\n # - num an integer (default: 1)\n # Output :\n # A rational function R(v[num],...,v[num+k]) such that U = res R.\n sumtores := proc(U, v :: name, num :: integer := 1)\n local L, first, rest, rat_first, num_first, i;\n if type(U, `+`) then\n return normal(map(sumtores, U, v, num));\n elif type(U, `*`) or type(U, `^`(anything, posint)) then\n first := op(1, U); # the first factor\n if type(U, `*`) then\n rest := subsop(1=1, U); # the rest of the product\n else\n rest := first^(op(2, U) - 1);\n end if;\n rat_first := sumtores(first, v, num);\n num_first := max(num, op(map(op, indets(rat_first, specindex(v)))));\n return normal(rat_first*sumtores(rest, v, num_first + 1));\n elif type(U, specfunc(Delta)) then\n return v[num]^op(U);\n elif type(U, specfunc(Binomial)) then\n return (1+v[num])^op(1, U)/v[num]^(op(2, U)+1); \n elif type(U, specfunc(Sum)) then\n return normal(sum(expand(sumtores(op(1, U), v, num)), op(2, U)));\n else\n return U/v[num];\n end if;\n end proc;\n\n end module:\n\n\n#### SUM TO PERIOD\n\ngfdict := table();\ngfdictcomp := table();\ngfnames := {};\n\n# Input :\n# - name, a name\n# - a function gf such that name(n) stands for res( gf(n) )\n# - a function comp such that comp( n ) = res( gf(n) )\n#\n# Effect :\n# Add 'name' as a basic block for constructing binomial sums\naddnewgf := proc(name :: name, gf, comp)\n #global gfdict, gfdictcomp, gfnames;\n gfdict[name] := gf;\n gfdictcomp[name] := comp;\n gfnames := gfnames union {name};\nend proc;\n\n# There are different definitions of the binomial.\n# Binomial(n,k) = coeff of x^k in the power series (1+x)^n\n# It is non-zero only if k \u2265 0. \naddnewgf(Binomial,\n ((v,n,k) -> (1+v[1])^n/v[1]^(k)),\n (n,k) -> `if`(k>=0, binomial(n,k), 0));\n\n# binomial2(n, k) = binomial(n, n-k)\n# If Binomial2(n,k) and Binomial(n,k) are both non zero, their value coincide.\n# Maple's binomial evaluated at (n,k) is the non-zero element of {Binomial(n,k),Binomial2(n,k)}, if any.\naddnewgf(Binomial2,\n ((v,n,k) -> (1+v[1])^n*v[1]^k/v[1]^n),\n (n,k) -> `if`(n-k>=0, binomial(n,n-k), 0));\n\n# Binomial3(n,k) = Binomial2(n,k)\n# alternative definition.\naddnewgf(Binomial3,\n ((v,n,k) -> 1/(1-v[1])^(k+1)/v[1]^(n-k)),\n (n,k) -> `if`(n-k>=0, binomial(n,n-k), 0));\n\n# natbinomial(n,k) = binomial(n,k) if n \u2265 0 and k \u2265 0 and 0 otherwise.\naddnewgf(NatBinomial,\n ((v,n,k) -> 1/(1-v[1]-v[2])/v[1]^k/v[2]^(n-k)),\n (n,k) -> `if`(n >=0 and k >= 0, binomial(n,k), 0));\n\naddnewgf(Multinomial,\n ((v,L) -> 1/(1-add(v[i],i=1..nops(L)))/mul(v[i]^(L[i]),i=1..nops(L))),\n (L ->multinomial(L)));\n\naddnewgf(Catalan,\n ((v,n) -> (1+v[1])^(2*n)*(1-v[1])/v[1]^(n)),\n (n -> 1/(n+1)*binomial(2*n,n) ));\n\naddnewgf(H,\n ((v,n) -> v[1]^(-n)/(1-v[1])),\n n -> `if`(n >= 0, 1, 0));\n\naddnewgf(Delta,\n ((v,n) -> v[1]^n),\n n -> `if`(n = 0, 1, 0));\n\n#addnewgf(CT,\n# ( (R, v) -> CT(R,v) ),\n# (R, v) -> residue(R/v,v=0));\n\nmultinomial := proc( x :: list(numeric))\n if nops(x) <= 1 then\n if x[1] < 0 then\n return 0;\n else\n return 1;\n end if;\n elif x[1] < 0 then\n return 0;\n else\n return binomial(`+`(op(x)), x[1])*multinomial(x[2..-1]);\n end if;\nend;\n\n\n# Outputs a list of sets s[1],...,s[nops(L)] such that the substitutions\n# subs(s[i], L[i]) guarantees that the variables of the elements of L does not\n# overlap and and are numbered consecutively.\n#\n# Example : packvars([ 1/(x[4]+x[6]), x[7] ], x);\n# => [{x[4] = x[1], x[6] = x[2]}, {x[7] = x[3]}]\npackvars := proc(L :: list, v :: name)\n local Lv, Ls, i, j, l;\n Lv := map2(select, has, map(indets, L, name), v);\n Ls := NULL;\n i := 0;\n for l in Lv do\n Ls := Ls, {seq(l[j]=v[i+j], j=1..nops(l))};\n i := i + nops(l);\n end do;\n return [Ls];\nend proc;\n\n#\n# (Alternative implementation)\ngeomsum_ := proc(S, bounds)\n local T, svar, infb, supb, ret, prim:\n T := expand(normal(S));\n if type(T, `+`) then\n return normal(map(geomsum_, T, bounds));\n fi;\n \n svar := op(1, bounds);\n infb := op([2, 1], bounds);\n supb := op([2, 2], bounds);\n\n ASSERT(infb <> -infinity);\n if supb = infinity then\n T := _W[_||svar]^svar*T;\n fi;\n\n prim := SumTools[Hypergeometric][Gosper](T, svar);\n ret := -subs(svar=infb, prim);\n \n if supb <> infinity then \n ret := ret + subs(svar=supb+1, prim);\n fi;\n \n return normal(ret);\nend proc;\n\n# Input :\n# - S, an expression of the form P(k)*A^k, where P is a polynomial\n# - bounds, an expression in the form k=a..b, where b can be infinity\n#\n# Returns an expression T without k such that\n# T = sum(S(k), k=a..b)\n#\n# If the upper bound b is `infinity' then it marks the sum\n# with the extra variable _W[_k].\ngeomsum := proc(S, bounds)\n local T, svar, infb, supb, ret, prim, den, opT, denother, dendep:\n \n svar := op(1, bounds);\n infb := op([2, 1], bounds);\n supb := op([2, 2], bounds);\n\n T := normal(S);\n \n if infb = -infinity or supb = -infinity then\n error \"Summation bounds cannot be -infinity.\";\n fi;\n\n if supb = infinity then\n T := _W[_||svar]^svar*T;\n fi;\n\n # dendep (resp. denother) contains the factors of the denominator of T that\n # depends (resp. do not depend) on the summation variable.\n den := factor(denom(T));\n if type(den, `*`) then\n dendep, denother := selectremove(has, den, svar);\n elif has(den, svar) then\n dendep, denother := den, 1;\n else\n dendep, denother := 1, den;\n end if;\n\n T := expand(numer(T));\n if type(T, `+`) then\n opT := [op(T)];\n else\n opT := [T];\n end if;\n opT := map(`*`, opT, 1/dendep);\n \n # Factor simplification, to rewrite things like\n # A := -(-1+u[1])^(-n-1+j)*(-1+u[2])^(-n+j-1)*(1-u[1])^(-j)*(1-u[2])^(-j)*u[1]^(-n)*u[2]^(-n)\n # which actually does not depend on j.\n # On such an input, SumTools[IndefiniteSummation](A, j) does not work.\n opT := map(simpfacts, opT);\n opT := map(SumTools[IndefiniteSummation], opT, svar);\n\n ret := -convert(subs(svar=infb, opT),`+`);\n \n if supb <> infinity then \n ret := ret + convert(subs(svar=supb+1, opT), `+`);\n fi;\n \n return (ret/denother);\nend proc;\n\n\n# Input:\n# - P, a product of expressions of the form F^a, where `F' is a polynomial\n# and `a' an expression that may depend on variables.\n#\n# Returns an equivalent product (when the variables in the exponent are\n# integers) with the garantee that for any two factors F^a and G^b, F is not\n# proportional to G.\nsimpfacts := proc(P)\n local t, i, ret;\n t := simpfacts0(P);\n ret := 1;\n for i in indices(t) do\n if op(i) = -1 then\n ret := ret*op(i)^(t[op(i)] mod 2);\n else\n ret := ret*op(i)^t[op(i)];\n end if;\n end do;\nend proc;\n\n# Input:\n# - same input as simpfacts\n#\n# Return an associative array T such that\n# P = mul(F^a, (F, a) in T)\nsimpfacts0 := proc(P)\n local t, t1, ind, f, i, lc;\n if type(P, `^`) then\n t := simpfacts0(op(1, P));\n for f in indices(t) do\n t[op(f)] := t[op(f)]*op(2, P);\n end do;\n return t;\n elif type(P, `*`) then\n t := table();\n ind := {};\n for f in [op(P)] do\n t1 := simpfacts0(f);\n for i in indices(t1) do\n if not (i in ind) then\n ind := ind union {i};\n t[op(i)] := 0;\n end if;\n t[op(i)] := t[op(i)] + t1[op(i)];\n end do;\n end do;\n return t;\n else\n f := normal(expand(P));\n lc := lcoeff(f);\n f := normal(expand(f/lc));\n return table([ lc = 1, f = 1 ]);\n end if;\nend proc;\n\n# Given a binomial sum, returns an expression such that the binomial sum equal\n# the constant term of the expression.\n#\n# The output may contains extravariables _W[_k] to track infinite summations\nsumtoct := proc(S, v :: name)\n local L;\n #global gfdict, gfnames;\n if type(S, specfunc(Sum)) then\n return geomsum(sumtoct(op(1, S), v), op(2, S));\n elif type(S, `+`) then\n return map(sumtoct, S, v);\n elif type(S, `*`) then\n L := map(sumtoct, convert(S, list), v);\n return convert(zip(subs, packvars(L, v), L), `*`);\n elif type(S, `^`(anything, posint)) then\n L := [sumtoct(op(1, S), v) $ op(2, S)];\n return convert(zip(subs, packvars(L, v), L), `*`);\n elif type(S, specfunc(CT)) then\n return subs(op(2,S)=v[1], op(1, S));\n elif type(S, specfunc(gfnames)) then\n return eval(gfdict[op(0,S)](v, op(S)));\n else\n return S;\n end if;\nend proc;\n\n\n\n#### INFINITE SUMS\n\n# Input :\n# - cons, a set of Laurent monomials\n# - G, a directed graph whose vertices are variables and edges are domination\n# relation.\n# - params, set of `small' variables\n#\n# If possible, returns a directed acyclic graph H extending G such that if the\n# variables are ordered according to H, then every monomials in cons is greater\n# than 1 (lexicographic ordering).\n#\n# Raises an error if not possible.\nsolvecons := proc(cons :: set, G := false, params := {})\n local cons1, rcons, u, v, H;\n uses GraphTheory;\n\n if G = false then\n H := GraphTheory[Digraph]({seq([1, v], v in indets(cons)), seq(seq([v, u], u in params), v in indets(cons) minus params)});\n return solvecons(cons, H);\n elif not IsAcyclic(G) then error \"inconsistent\";\n elif nops(cons) = 0 then return G;\n end if;\n \n cons1 := cons[1];\n rcons := cons minus {cons1};\n for v in indets(numer(cons1)) do\n try\n H := CopyGraph(G);\n AddArc(H, {seq([w, v], w in indets(denom(cons1)))});\n return solvecons(rcons, H);\n catch \"inconsistent\" :\n end;\n end do;\n\n error \"inconsistent\";\nend proc;\n\n# Returns a linear order compatible with the DAG G.\nlinearorder := proc(G)\n local racines, H, rest;\n uses GraphTheory;\n\n if nops(Vertices(G)) = 0 then\n return [];\n end if;\n\n racines := select(v -> InDegree(G, v) = 0, Vertices(G));\n H := DeleteVertex(G, racines);\n rest := linearorder(H);\n\n return [op(rest),op(racines)];\nend proc;\n\n# Input :\n# - R, a rational function\n# - params, a list of variables\n#\n# Assume that R is a Laurent formal series w.r.t. variables _W[1],...,_W[r]\n# Let T = sum of coefficients of this series\n#\n# If there exist an order such that T is convergent, then returns T and that order.\n# If not, fails\n#\n# params is an indication on the way the parameters should be ordered.\nisconvergent := proc(R :: ratpoly, params :: list(name) := [])\n local svars, L, ct, co, mord, res, cons, G, ord, den, facts, f; \n \n svars := indets(R, specindex(_W));\n L := [ op(params), op(indets(R) minus svars minus convert(params, set)) ];\n mord := plex(op(L));\n cons := {};\n\n facts := map2(op, 1, factors(denom(normal(R)))[2]);\n for f in facts do\n ct := subs(map(`=`, svars, 0), f);\n co := remove(`=`, [coeffs(collect(normal(f/ct-1), svars, distributed, normal), svars)], 0);\n cons := cons union {seq( Groebner[TrailingTerm](numer(c), mord)[2]/Groebner[TrailingTerm](denom(c), mord)[2], c in co)};\n end do;\n\n G := solvecons(cons, false, {});\n ord := remove(`=`, linearorder(G), 1);\n\n mord := plex(op(ord));\n res := not `or`(\n seq( Groebner[TestOrder](\n Groebner[TrailingTerm](numer(c), mord)[2],\n Groebner[TrailingTerm](denom(c), mord)[2],\n mord ), c in co ) );\n\n if res then\n return normal(subs(map(`=`, svars, 1), R)), ord;\n else\n return FAIL;\n end if;\nend proc;\n\n\n# Input :\n# - S, a binomial sum\n# - name, a name\n#\n# Output : R, L\n# - R, a rational function\n# - L, a list of variables\n#\n# The list L gives an order on the variables.\n# S is the residue of R with respect to the variables in L that are not\n# parameters\nsumtores0 := proc(S, name)\n local R, vars, x;\n R := sumtoct(S, name);\n vars := select(has, indets(R), name);\n return isconvergent(normal(R/mul(x, x in vars)));\nend proc;\n\n\n\n# Input :\n# - R, a rational function\n# - vars, a list of variables\n# - ord, a positive integer\n#\n# Returns the first `ord' terms of res_{vars[2..-1]}(R), computed in the Laurent series field\n# K((vars[-1]))...((vars[1])).\n#\n# Very useful to check the consistency of an integral representation.\nrser :=\n (R, vars, ord) ->\n map2(foldl, residue, map(normal, series(R, vars[1], ord)), seq(v=0,v in select(member, vars, indets(R))[2..-1])):\n\n# Replaces infinity by maxn in the expression S, replaces Sum by add, Binomial\n# by binomial, etc and evaluates.\ncomputesum := (S, maxn) -> eval(subs([Sum=add, infinity=maxn, op(op(op(gfdictcomp)))], S));\n\n\n\n\n###### GEOMETRIC REDUCTION OF PERIODS\n\ninorout_base := proc(S, i)\n\tlocal minx, maxx, miny, left, right, dom, middle, ret;\n\tminx := min(map2(op, 1, S)); \n\tmaxx := max(map2(op, 1, S));\n\n\tif minx=maxx then return {}; end if;\n \tif nops(S[1]) <= 1 or i <= 1 then return {-1} end if;\n\n \tminy := min(map2(op, 2, S));\n \tmiddle := map2(subsop, 2=NULL, select(m -> m[2] = miny, S));\n\n \tleft := min(map2(op, 1, middle));\n \tright := max(map2(op, 1, middle));\n\tret := inorout_base(middle, i-1);\n\n\tif left > minx then ret := ret union {1}; end if;\n\tif right < maxx then ret := ret union {-1}; end if;\n\n\treturn ret;\nend proc;\n\n\ninorout := proc(P, T, ord)\n local S, vars;\n vars := remove(has, ord, T);\n coeffs(collect(P, [T, op(vars)], distributed), [T, op(vars)], 'mon');\n S := map2(map2, degree, {mon}, [T, op(vars)]);\n\n return inorout_base(S, ListTools[Search](T, ord));\nend proc;\n\n\n# Hermite reduction\n# Input :\n# - R, a rational function\n# - v, a name\n# - cert, a boolean (default: false)\n#\n# Output :\n# A rational function S such that R - S = T' for some rational function T'\n# and such that S has poles of order at most 1 w.r.t. v (including at infinity)\n#\n# If cert=true, then it also returns T.\nhermitered := proc(R, v :: name, cert := false)\n local a, d, g, dm, ds, dm2, dms, b, c, k;\n a := numer(R);\n d := denom(R);\n \n g := 0;\n dm := gcd(d, diff(d, v));\n dm := normal(dm);\n ds := normal(d/dm);\n\n while degree(dm, v) > 0 do\n dm2 := gcd(dm, diff(dm, v));\n dms := normal(dm/dm2);\n gcdex(-normal(ds*diff(dm,v)/dm), dms, a, v, 'b', 'c');\n a := normal(c - diff(b,v)*ds/dms);\n g := g + b/dm;\n dm := dm2;\n end do;\n \n if cert then\n return normal(a/ds/dm), g;\n else\n return normal(a/ds/dm);\n end if;\nend proc;\n\n# Input:\n# - R, rational function\n# - v, symbol\n# - ord, list of symbols containing v\n#\n# Returns FAIL or a rational function without v which is the sum of the\n# residues of R at `small' poles.\n#\n# [Implementation using hermitered and Rothstein-Tragger resutant\n# for the residue computation]\nratres := proc(R :: ratpoly, v :: name, ord :: list(name))\n local Rn, F, tot, f, ioo, Q, res, n;\n\n if type(R, `+`) then\n return map(ratres, R, v, ord);\n end if;\n\n Rn := hermitered(normal(R), v);\n F := map2(op, 1, select(has, factors(denom(Rn))[2], v));\n \n tot := 0;\n for f in F do\n if type(f, `+`) then\n ioo := inorout(f, v, ord);\n\n if ioo = {1} then\n Q := normal(Rn*f/diff(f, v));\n res := collect(resultant(numer(Q)-Z_*denom(Q), f, v), Z_);\n n := degree(res, Z_);\n tot := tot - normal(coeff(res, Z_, n-1)/coeff(res, Z_, n));\n elif nops(ioo) > 1 then\n return FAIL;\n end if;\n else # f = v\n tot := tot + normal(subs(v=0,normal(v*Rn)));\n end if;\n end do;\n\n return normal(tot);\nend proc;\n\n# Idem\n#\n# [Implementation using maple's residue(R, v=infinity)]\nratres2 := proc(R, v, ord)\n local terms, F, tot, f, ioo, Q, res, n;\n\n terms := convert(R, parfrac, v);\n if type(terms, `+`) then\n terms := [op(terms)];\n else\n terms := [terms];\n end if;\n\n tot := 0;\n for F in terms do\n f := denom(F);\n if eval(f, v=0) = 0 then\n tot := tot + residue(F, v=0);\n elif degree(f, v) > 0 then\n ioo := inorout(f, v, ord);\n if ioo = {1} then\n tot := tot - residue(F, v=infinity);\n elif nops(ioo) > 1 then\n return FAIL;\n end if;\n end if;\n end do;\n\n return normal(tot);\nend proc;\n\n\ngeomred := proc(R :: ratpoly, ord :: list, params :: set)\n local S, red, v;\n S := R;\n for v in indets(R) minus params do\n red := ratres(S, v, ord);\n if red <> FAIL then S := red; end if;\n end do;\n return collect(factor(S), params, factor, distributed);\nend proc;\n\ngeomredall := proc(R :: ratpoly, ord :: list, params :: set)\n local tbl, cur, ivars, st, red, v, nst, all, deg;\n\n tbl := table([ {} = normal(R) ]);\n cur := { {} };\n ivars := indets(R) minus params;\n\n while nops(cur) > 0 do\n st := cur[1];\n red := tbl[st];\n if red <> FAIL then\n for v in ivars minus st do\n nst := st union {v};\n if type(tbl[nst], indexed) then\n tbl[nst] := factor(ratres(red, v, ord));\n end if;\n cur := cur union {nst};\n end do;\n end if;\n cur := cur minus {st};\n end do;\n \n all := remove(`=`, map(op, [entries(tbl)]), FAIL);\n cur := min(map(nops@indets, all));\n all := select(f -> nops(indets(f))=cur, all);\n deg := f -> degree(denom(f), ivars) + min(0, degree(numer(f),ivars)-degree(denom(f),ivars) +nops(ivars)+1);\n cur := min(map(deg, all));\n all := select(f -> deg(f)=cur, all);\n\n return map(f -> collect(factor(f), params, factor, distributed), all);\nend proc;\n\n# Input :\n# - S, a binomial sum\n# - name, a name\n#\n# Output : R, L\n# - R, a rational function\n# - L, a list of variables\n#\n# The list L gives an order on the variables.\n# S is the residue of R with respect to the variables in L that are not\n# parameters\nsumtores := proc(S, name)\n local R, ord, params, flag;\n\n R, ord := sumtores0(S, name);\n params := indets(R) intersect indets(S);\n \n flag := true;\n hasoption([_rest], 'geomred' = boolean, 'flag');\n if flag then\n R := geomred(R, ord, params);\n ord := select(has, ord, indets(R));\n end if;\n\n return op(subs(packvars([ord], name)[1], [R,ord]));\nend proc;\n\n\nend module:\n\n\n", "meta": {"hexsha": "1f92d15264161fd1a648b1f1cbd818946bfddf7a", "size": 18251, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "src/binomsums.mpl", "max_stars_repo_name": "lairez/binomsum", "max_stars_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2015-10-28T00:00:41.000Z", "max_stars_repo_stars_event_max_datetime": "2021-05-27T07:47:59.000Z", "max_issues_repo_path": "src/binomsums.mpl", "max_issues_repo_name": "lairez/binomsum", "max_issues_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "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/binomsums.mpl", "max_forks_repo_name": "lairez/binomsum", "max_forks_repo_head_hexsha": "95086f8a51dc450cedc8556c54e40cc7ba04e927", "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": 26.7609970674, "max_line_length": 127, "alphanum_fraction": 0.5833652951, "num_tokens": 6255, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6334102775181399, "lm_q2_score": 0.6039318337259584, "lm_q1q2_score": 0.38253663040239844}} {"text": "######################################################################\n\n`is_element/SCP` := (N::posint) -> (A::set) -> proc(Q)\n local i,U,V;\n\n global reason;\n\n if not `is_element/ACP`(N)(A)(Q) then\n reason := [convert(procname,string),\"Q in ACP(N)(A)\",reason];\n return false;\n fi;\n\n if nops(Q[N]) = nops(A)^2 then\n reason := [convert(procname,string),\"Q[N] has only one block\",Q[N]];\n return false;\n fi;\n\n return true;\nend:\n\n`is_equal/SCP` := (N::posint) -> (A::set) -> proc(Q1,Q2)\n global reason;\n\n if Q1 <> Q2 then\n reason := [convert(procname,string),\"Q1 <> Q2\",Q1,Q2];\n return false;\n fi;\n\n return true;\nend:\n\n`is_leq/SCP` := (N::posint) -> (A::set) -> proc(Q1,Q2)\n local i;\n\n for i from 1 to N do \n if Q2[i] minus Q1[i] <> {} then\n return false;\n fi;\n od;\n\n return true;\nend:\n\n`list_elements/SCP` := (N::posint) -> proc(A::set)\n local X,n;\n n := nops(A);\n X := `list_elements/ACP`(N)(A);\n X := select(Q -> nops(Q[N]) < n^2,X);\n return X;\nend:\n\n`count_elements/SCP` := (N::posint) -> proc(A::set)\n local d;\n return add(Stirling2(nops(A),d)*d!*N^(d-1),d=2..nops(A)); \nend:\n\n`random_element/SCP` := (N::posint) -> (A::set) -> proc()\n local i,n,pi,Q,R,S,B,C,ok;\n\n if nops(A) <= 1 then\n return FAIL;\n fi;\n\n ok := false;\n\n while not ok do \n Q := `random_element/ACP`(N)(A)();\n if nops(Q[N]) < nops(A)^2 then\n ok := true;\n fi;\n od;\n\n return Q;\nend:\n\n\n`res/SCP` := (N::posint) -> (A::set,B::set) -> proc(Q)\n return map(`intersect`,Q,`top/autorel`(B));\nend:\n\n######################################################################\n\n`gamma/SCP` := (N::posint) -> (A::set) -> proc(Q)\n local i;\n [seq(`op/autorel`(A)(Q[i]) minus Q[i],i=1..N)];\nend:\n\n######################################################################\n\n`mu/SW/SCP` := (N::posint) -> (A::set) -> proc(x) \n return `mu/W/ACP`(N)(A)(x);\nend:\n\n`sigma/SCP/SW` := (N::posint) -> (A::set) -> proc(Q)\n return `bottom_normalise/SW`(N)(A)(`sigma/ACP/W`(N)(A)(Q));\nend;\n\n######################################################################\n\n`describe/SCP` := eval(`describe/ACP`):\n\n", "meta": {"hexsha": "6d3a4efe43743c009c39349eb308f3642a696af7", "size": 2049, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/chains/SCP.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/chains/SCP.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/chains/SCP.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": 20.0882352941, "max_line_length": 70, "alphanum_fraction": 0.4831625183, "num_tokens": 680, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7217431943271999, "lm_q2_score": 0.5273165233795671, "lm_q1q2_score": 0.3805871120054824}} {"text": "$ifndef _CLASSIFYER_\n$define _CLASSIFYER_\n\n$include \"Basic.mpl\"\n$include \"Condition.mpl\"\n$include \"Fetch.mpl\"\n$include \"InvOrder.mpl\"\n$include \"InvSimplify.mpl\"\n$include \"InvSol.mpl\"\n$include \"Logout.mpl\"\n$include \"Utils.mpl\"\n\nClassifyHolder:=module()\n option object;\n export \n cid, # \u5f53\u524d\u4e0d\u53d8\u91cf\u65b9\u7a0b\u4e2d\u7684\u5e38\u6570\u9879\u4e0b\u6807\n ieqCode, # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7f16\u53f7\n sols, # \u5f53\u524d\u6240\u6709\u89e3\n usols, # \u4e0a\u4e00\u4e2a\u5168\u96f6\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u89e3\n oldSols; # \u4e0a\u4e00\u6b21getSols\u7684\u89e3\nend module:\n\n# \u72b6\u6001\u91cd\u7f6e\nreset:=proc()\n ClassifyHolder:-cid:=0;\n ClassifyHolder:-ieqCode:=0;\n ClassifyHolder:-sols:={};\n ClassifyHolder:-usols:=table();\n ClassifyHolder:-oldSols:={};\nend proc:\n\n# \u65b0\u589e\u89e3\naddSol:=proc(sol)\n ClassifyHolder:-sols:=ClassifyHolder:-sols union {sol};\n return;\nend proc:\n\n# \u83b7\u53d6\u65b0\u589e\u7684\u4ee3\u8868\u5143\n# \u65b0\u7684\u4ee3\u8868\u5143\u53ea\u80fd\u83b7\u53d6\u4e00\u6b21\ngetNewSols:=proc()\n local res;\n res:=sort([ (ClassifyHolder:-sols minus ClassifyHolder:-oldSols)[] ],'key'=(x->x:-ieqCode));\n ClassifyHolder:-oldSols:=ClassifyHolder:-sols;\n return res;\nend proc:\n\ngetCname:=proc()\n ClassifyHolder:-cid:=ClassifyHolder:-cid+1;\n return c[ClassifyHolder:-cid];\nend proc:\n\ngetIeqCode:=proc()\n ClassifyHolder:-ieqCode:=ClassifyHolder:-ieqCode+1;\n return ClassifyHolder:-ieqCode;\nend proc:\n\nclassify:=proc(A,As,eqs)\n local sol;\n reset();\n sol:=Object(InvSol):\n sol:-stateCode:=1:\n sol:-oeq:=eqs:\n sol:-As:=As:\n sol:-A:=A:\n sol:-nvars:=LinearAlgebra[RowDimension](A):\n sol:-vars:=[seq(a[i],i=1..sol:-nvars)]:\n resolve(sol);\n return;\nend proc:\n\n# \u6682\u65f6\u6ca1\u505a\u91cd\u590d\u4ee3\u8868\u5143\u7684\u5904\u7406\ngetSols:=proc()\n ClassifyHolder:-oldSols:=ClassifyHolder:-sols;\n return sort([ClassifyHolder:-sols[]],'key'=(x->[x:-ieqCode,convert(getDesc(x),`global`)]));\nend proc:\n\nresolve:=proc(sol::InvSol)\n local spos,pos,nDelta,_usols,_usol,oldDeltas,oldSol;\n \n if (sol:-stateCode=1) then\n # \u5c1d\u8bd5\u6c42\u89e3\u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\n # \u5982\u679c\u6240\u6709\u65b9\u7a0b\u7ec4\u4e3a\u7a7a\uff0c\u5219\u505c\u6b62\u6c42\u89e3\n if (sol:-oeq={}) then\n return;\n end if;\n nDelta:=getInvariants(sol:-oeq);\n # \u6c42\u89e3\u5931\u8d25\n if (indets(nDelta,name) intersect {seq(a[i],i=1..sol:-nvars)} = {}) then\n # \u6c42\u89e3\u5931\u8d25\u4e0d\u6dfb\u52a0\u89e3\n # \u4e0d\u8003\u8651\u4e0d\u80fd\u6c42\u89e3\u4e0d\u53d8\u91cf\u7684\u60c5\u51b5\n return \"\u65b0\u4e0d\u53d8\u91cf\u6c42\u89e3\u5931\u8d25\";\n end if;\n # \u8bbe\u7f6e\u65b0\u7684\u4e0d\u53d8\u91cf\n spos:=numelems(sol:-Delta)+1;\n oldDeltas:={sol:-Delta[]};\n oldSol:=Object(sol);\n if (sol:-Delta<>[]) then\n sol:-Delta:=[sol:-Delta[],nDelta[]]:\n # \u6574\u4f53\u5316\u7b80\u4e0d\u53d8\u91cf\n if (1>=LogLevelHolder:-logLevel) then\n flogf[1](\"-----------------------------------------------\");\n flogf[1](\"\u5bf9\u65b0\u589e\u4e0d\u53d8\u91cf\u6309\u7167\u539f\u4e0d\u53d8\u91cf\u8fdb\u884c\u5316\u7b80\");\n flogf[1](\"\u5316\u7b80\u524d\");\n printDeltas(sol:-Delta);\n sol:-Delta:=simplifyInvariants(sol:-Delta);\n flogf[1](\"\u5316\u7b80\u540e\");\n printDeltas(sol:-Delta);\n end if;\n else\n sol:-Delta:=[sol:-Delta[],nDelta[]]:\n end if;\n sol:-orders:=findInvariantsOrder~(sol:-Delta):# \u8ba1\u7b97\u4e0d\u53d8\u91cf\u9636\u6570\n # \u6839\u636e\u65b0\u7684\u4e0d\u53d8\u91cf\u662f\u5426\u6709\u7ea6\u675f\u6765\u51b3\u5b9a\u662f\u5426\u6c42\u89e3\u4e0a\u4e00\u4e2a\u5168\u96f6\u65b9\u7a0b\n nDelta:=remove(x->(x in oldDeltas),sol:-Delta);\n if ( `union`(findDomain~(nDelta)[]) <> {} ) and (sol:-Delta<>[]) then\n solveRestAllZeroIeqs(oldSol);\n end if;\n # \u5efa\u7acb\u548c\u6c42\u89e3\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7ec4\n for pos from spos to numelems(sol:-Delta) do\n buildInvEqs(sol,pos);\n end do;\n # \u751f\u6210\u65b0\u7684\u4e0d\u53d8\u91cf\n genInvariants(sol);\n elif (sol:-stateCode=2) then\n # \u6c42\u89e3\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7ec4\n solveInvEqs(sol);\n elif (sol:-stateCode=3) then\n # \u53d6\u4ee3\u8868\u5143\n fetchRep(sol);\n elif (sol:-stateCode=4) then\n # \u6c42\u89e3\u53d8\u6362\u65b9\u7a0b\n solveTransEq(sol);\n end if;\n return;\nend proc:\n\n# \u5efa\u7acb\u4e0d\u53d8\u91cf\u7684\u65b9\u7a0b\u7ec4\nbuildInvEqs:=proc(_sol::InvSol,pos::posint)\n global sols,cid;\n local sol,rs,i,n,x,xpos,eqs;\n n:=numelems(_sol:-Delta);\n # \u5206\u5947\u5076\u8ba8\u8bba\n if type((_sol:-orders[pos]),even) then\n xpos:=[1,-1,0];\n else\n xpos:=[1,0];\n end if;\n # \u751f\u6210\u65b9\u7a0b\u53f3\u7aef\n cid:=0;\n rs:=Array(1..n,x->\n if (x>pos) then\n getCname()\n else\n 0\n end if);\n # \u9010\u4e2a\u65b9\u7a0b\u6c42\u89e3\n for x in xpos do\n # \u5bf9\u4e8eDelta[pos]=0\uff0c\u6784\u5efa\u4e0b\u4e00\u4e2a\u65b9\u7a0b\u8fdb\u884c\u6c42\u89e3\n # \u4e0d\u6c42\u89e3\u5168\u96f6\u65b9\u7a0b\n if (x=0) then\n # \u8fd9\u91cc\u662f\u6bcf\u4e2a\u5168\u96f6\u65b9\u7a0b\u90fd\u8fdb\u884c\u6c42\u89e3\u7684\u610f\u601d\n # \u5426\u5219\u76f4\u63a5next\u5c31\u597d\u4e86\n if (pos<>n) then\n next;\n else\n # \u8fd9\u91cc\u662f\u76f4\u63a5\u6c42\u89e3\n # solveAllZero(_sol);\n \n # \u8fd9\u91cc\u662f\u5ef6\u540e\u6c42\u89e3\n ClassifyHolder:-usols[getUsolsKey(_sol)]:=_sol;\n return;\n end if;\n\n # next;\n end if;\n rs[pos]:=x;\n eqs:=[seq(_sol:-Delta[i]=rs[i],i=1..n)];\n sol:=Object(_sol);\n sol:-ieqCode:=getIeqCode();\n sol:-ieq:=eqs;\n sol:-stateCode:=2;\n resolve(sol);\n end do;\n return;\nend proc:\n\n# \u751f\u6210\u65b0\u7684\u4ee3\u8868\u5143\ngenInvariants:=proc(_sol::InvSol)\n local isols,isol,sol;\n sol:=Object(_sol);\n isols:=ieqsolve(sol:-Delta,[seq(a[i],i=1..sol:-nvars)]);\n # \u5168\u90e8\u6c42\u89e3\u5931\u8d25\uff0c\u5219\u6c42\u89e3\u4e0a\u4e00\u4e2a\u5168\u96f6\u65b9\u7a0b\n if andmap(isol->(subsOeq(sol,isol)=\"\u65b0\u4e0d\u53d8\u91cf\u6c42\u89e3\u5931\u8d25\"),isols) then\n solveRestAllZeroIeqs(sol);\n end if;\nend proc:\n\n# \u751f\u6210\u65b0\u7684\u4e0d\u53d8\u91cf\u65b9\u7a0b\n# \u8fd9\u4e48\u5199\u4f1a\u5bfc\u81f4\u548c\u975e\u81ea\u7531\u53d8\u91cf\u6709\u5173\u7684\u504f\u5bfc\u90fd\u53d8\u62100\nsubsOeq:=proc(_sol::InvSol,isol)\n local oeq,sol,v,vv,vars,Delta;\n flogf[1](\"--------------------------------------------------------------\");\n flogf[1](\"\u6c42\u89e3\u65b0\u7684\u4e0d\u53d8\u91cf\");\n flog[1]({seq(Delta[i]=0,i=1..numelems(_sol:-Delta))});\n flog[2](getDisplayDelta(_sol));\n flogf[1](\"\u53d6\u89e3\");\n flog[1](isol);\n oeq:=_sol:-oeq;\n vars:=_sol:-vars;\n v,vv:=selectremove(x->(lhs(x)<>rhs(x)),isol);\n vv:=lhs~(vv);# \u65b9\u7a0b\u4e2d\u7684\u5269\u4f59\u81ea\u7531\u53d8\u91cf\n oeq:=PDETools:-dsubs(phi(vars[])=phi(vv[]),oeq);\n oeq:=eval(subs(v[],oeq)) minus {0};\n sol:=Object(_sol);\n sol:-oisol:=isol;\n sol:-stateCode:=1;\n sol:-oeq:=oeq;\n sol:-vars:=vv;\n return resolve(sol);\nend proc:\n\n# \u6c42\u89e3\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7ec4\nsolveInvEqs:=proc(_sol::InvSol)\n local isols,icons,n,vars,sol,i;\n n:=_sol:-nvars;\n vars:=[seq(a[i],i=1..n)];\n isols:=ieqsolve(_sol:-ieq,vars);\n icons:=findSolutionDomain~(isols);\n n:=numelems(isols);\n for i from 1 to n do\n sol:=Object(_sol);\n sol:-stateCode:=3;\n sol:-isol:=isols[i];\n sol:-icon:=icons[i];\n resolve(sol);\n end do;\n return;\nend proc:\n\n# \u5bf9\u4e0d\u53d8\u91cf\u5168\u4e3a0\u7684\u65b9\u7a0b\u8fdb\u884c\u6c42\u89e3\nsolveAllZero:=proc(_sol)\n local sol,var,isols,icons,i,n,reps,rep,nsol,nnsol;\n sol:=Object(_sol);\n sol:-ieq:=[seq(x=0,x in sol:-Delta)];\n sol:-ieqCode:=getIeqCode();\n var:=[seq(a[i],i=1..sol:-nvars)];\n isols:=ieqsolve(sol:-Delta,var);\n icons:=findSolutionDomain~(isols);\n n:=numelems(isols);\n for i from 1 to n do\n nsol:=Object(sol);\n nsol:-isol:=isols[i];\n nsol:-icon:=icons[i];\n reps:=fetchSolRep(nsol,nonzero);\n for rep in reps do\n nnsol:=Object(nsol);\n nnsol:-stateCode:=4;\n setRep(nnsol,rep);\n flogf[1](\"--------------------------------------------------------------\");\n flogf[1](\"\u6c42\u89e3\u5168\u96f6\u65b9\u7a0b\");\n flog[1](getDisplayIeq(nnsol));\n flog[1](getDisplayDelta(nnsol));\n flogf[1](\"\u53d6\u89e3\");\n flog[1](nnsol:-isol);\n flogf[1](\"\u5177\u6709\u7ea6\u675f\u6761\u4ef6\");\n flog[1](nnsol:-icon);\n flogf[1](\"\u53d6\u7279\u89e3\");\n flog[1](nnsol:-rvec);\n flogf[1](\"\u53d6\u4ee3\u8868\u5143\");\n flog[1](nnsol:-rep);\n resolve(nnsol);\n end do;\n end do;\nend proc:\n\n# \u53d6\u4ee3\u8868\u5143\nfetchRep:=proc(_sol::InvSol)\n local n,_ax;\n flogf[1](\"--------------------------------------------------------------\");\n flogf[1](\"\u5bf9\u4e8e\u4e0d\u53d8\u91cf\u65b9\u7a0b\");\n flog[1](getDisplayIeq(_sol));\n flog[1](getDisplayDelta(_sol));\n flogf[1](\"\u53d6\u89e3\");\n flog[1](_sol:-isol);\n flogf[1](\"\u5177\u6709\u7ea6\u675f\u6761\u4ef6\");\n flog[1](_sol:-icon);\n n:=_sol:-nvars;\n _ax:=fetchSolRep(_sol);\n if (_ax=NULL) then# \u53d6\u7279\u89e3\u5931\u8d25\n addSol(_sol);\n flogf[1](\"\u53d6\u7279\u89e3\u5931\u8d25\");\n return;\n end if;\n setRep(_sol,_ax);\n if (_sol:-rep=0) then\n flogf[1](\"\u4ee3\u8868\u5143\u53d60\");\n return;\n end if;\n _ax:=Matrix(_ax);\n _sol:-stateCode:=4;\n flogf[1](\"\u53d6\u7279\u89e3\");\n flog[1](convert(_ax,list));\n flogf[1](\"\u53d6\u4ee3\u8868\u5143\");\n flog[1](_sol:-rep);\n resolve(_sol);\nend proc:\n\nsolveTransEq:=proc(_sol::InvSol)\n local ax,_ax,n,eq,sol,con;\n n:=_sol:-nvars;\n ax:=Matrix([seq(a[i],i=1..n)]);\n _ax:=_sol:-rvec;\n # a_=a.A\n _sol:-teq[1],_sol:-tsol[1],_sol:-tcon[1]:=solveTeq(_ax,ax,_sol);\n # a=a_.A\n _sol:-teq[2],_sol:-tsol[2],_sol:-tcon[2]:=solveTeq(ax,_ax,_sol);\n if andmap(x->(x=[]),_sol:-tsol) then\n # \u65e0\u89e3\n flogf[1](\"\u53d8\u6362\u65b9\u7a0b\u6c42\u89e3\u5931\u8d25\");\n addSol(_sol);\n else\n # \u6709\u89e3\n flogf[1](\"\u53d8\u6362\u65b9\u7a0b\u6709\u89e3\");\n _sol:-stateCode:=5;\n addSol(_sol);\n # \u5728logLevel\u4e3a1\u65f6\u8f93\u51fa\n if (1>=LogLevelHolder:-logLevel) then\n printTeq(_sol,1);\n printTeq(_sol,2);\n end if;\n end if;\n return;\nend proc:\n\n(*\n \u6c42\u89e3\u53d8\u6362\u65b9\u7a0b\n\n \uff1f \u56e0\u4e3a\u53d8\u6362\u65b9\u7a0b\u53ea\u5173\u5fc3\u5176\u5b58\u5728\u6027\uff0c\u800c\u4e0d\u5728\u4e4e\u5176\u5b8c\u6574\u6027\uff0c\u56e0\u6b64\u4e0d\u7528explicit\u9009\u9879\uff0c\u800c\u91c7\u7528convert/radical\n\n \u662f\u5426\u9009\u62e9explicit\u9009\u9879\u4e5f\u662f\u6709\u5f85\u8861\u91cf\u7684\uff0cexample3\u51fa\u73b0\u4e86\u4e0d\u7528explicit\u9009\u9879\u5219\u6709\u590d\u6742\u7ea6\u675f\u4e0d\u80fd\u7b80\u5355\u6d88\u53bb\u7684\u60c5\u51b5\u3002\n \u4f46\u662f\u9009\u62e9explicit\u9009\u9879\u4e4b\u540e\uff0c\u4f1a\u9762\u4e34\u89e3\u8fc7\u591a\u7684\u95ee\u9898\n \u4e24\u5bb3\u53d6\u5176\u8f7b\uff0c\u8fd8\u662f\u53d6\u5427\n\n \u8be5\u4e8c\u6b21\u6c42\u89e3\u7b97\u6cd5\u7684\u6c42\u89e3\u80fd\u529b\u503c\u5f97\u80af\u5b9a\uff0c\u6d4b\u8bd5\u662f\u5426\u53ef\u4ee5\u8f6c\u5316\u4e5f\u4f9d\u8d56\u4e8e\u8be5\u7b97\u6cd5\uff0c\u6700\u597d\u4e0d\u8981\u4fee\u6539\u3002\n \u5f53\u7136\u4e5f\u51fa\u73b0\u8fc7\u89e3\u7684\u7684\u89e3\u4e0d\u6ee1\u8db3\u65b9\u7a0b\u7684\u60c5\u51b5\uff0c\u81f3\u4e8e\u662f\u5426\u8981\u52a0\u4ee5\u9a8c\u8bc1\uff0c\u8fd8\u6709\u5f85\u8003\u8651\u3002\n*)\nsolveTeq:=proc(a,b,sol)\n local var,teq,tsol,tcon,scon,eqs,eq,_eq,_con,_sol;\n teq:=convert((a-b.sol:-A),list);\n teq:=subs(sol:-isol[],teq);\n var:=[seq(epsilon[i],i=1..sol:-nvars)];\n tsol:=teqsolve(teq,var);\n if (tsol=[]) then\n # \u6c42\u89e3\u5931\u8d25\uff0c\u5c1d\u8bd5\u4e8c\u6b21\u6c42\u89e3\u6cd5\u65b9\u6cd5\n # \u9996\u6b21\u6c42\u89e3\n eqs:=teqsolve(teq);\n # \u4e8c\u6b21\u6c42\u89e3\n tsol:=[];\n tcon:=[];\n for eq in eqs do\n _eq:=select(eqOfEpsilon,eq);\n _con:=remove(eqOfEpsilon,eq);\n _con:=remove(x->type(x,`=`) and (lhs(x)=rhs(x)),_con);\n _sol:=teqsolve(_eq,var,_explicit);\n _con:=map(x->clearConditions(findSolutionDomain(x)) union _con,_sol);\n tsol:=[tsol[],_sol[]];\n tcon:=[tcon[],_con[]];\n end do;\n else\n # \u6c42\u89e3\u6210\u529f\uff0c\u76f4\u63a5\u8ba1\u7b97\u7ea6\u675f\n tcon:=map(x->clearConditions(findSolutionDomain(x)),tsol);\n end if;\n # \u6e05\u7406\u77db\u76fe\u89e3\n tsol:=zip((s,c)->if (undefined in rhs~(c)) then NULL else s end if,tsol,tcon);\n tcon:=remove(c->(undefined in rhs~(c)),tcon);\n return teq,tsol,tcon;\nend proc:\n\neqOfEpsilon:=proc(eq)\n return ormap(x->type(x,specindex(epsilon)),indets(eq,name));\nend proc:\n\n# \u4fdd\u7559\u548ca,c\u6709\u5173\u7684\u7ea6\u675f\nclearConditions:=proc(con)\n return select(has,con,{a,c});\nend proc:\n\n# \u6c42\u89e3\u5269\u4f59\u5168\u96f6\u4e0d\u53d8\u91cf\u65b9\u7a0b\nsolveRestAllZeroIeqs:=proc(sol::InvSol)\n solveAllZero( ClassifyHolder:-usols[getUsolsKey(sol)] );\nend proc:\n\n# \u83b7\u53d6\u5168\u96f6\u4e0d\u53d8\u91cf\u65b9\u7a0b\u5728usols\u4e2d\u7684key\ngetUsolsKey:=proc(sol)\n return convert([seq(Delta[i],i=1..numelems(sol:-Delta))],`global`);\nend proc:\n\n# \u81ea\u5b9a\u4e49\u4e0d\u53d8\u91cf\u65b9\u7a0b\u6c42\u89e3\u51fd\u6570\n# \n# \u91c7\u7528set\u7684\u65b9\u5f0f\u6307\u5b9a\u53d8\u91cf\u76f8\u6bd4\u4e8elist\u65b9\u5f0f\u6307\u5b9a\u53d8\u91cf\uff0c\u89e3\u53ef\u80fd\u66f4\u7b80\u6d01\u3002\n# \u4ee5\u4e3alist\u65b9\u5f0f\u6307\u5b9a\u53d8\u91cf\u4f1a\u4f18\u5148\u7528\u540e\u9762\u7684\u53d8\u91cf\u8868\u793a\u524d\u9762\u7684\u53d8\u91cf\uff0c\u6709\u65f6\u8fd9\u662f\u4e0d\u597d\u7684\u3002\n#\n# \u91c7\u7528set\u6c42\u89e3\u65f6\uff0cexample3\u51fa\u73b0\u4e86\u6ca1\u6709\u5bfc\u51faa[4]=0\u7684\u89e3\u7684\u60c5\u51b5\uff0c\u4f8b\u5b50\u5e76\u4e0d\u5b8c\u6574\u3002\n# \u91c7\u7528list\u6c42\u89e3\u65f6\uff0cexample\u5305\u542b\u4e86a[3]a[4]\u7684\u7ea6\u675f\uff0c\u4e5f\u6ca1\u6c42\u89e3\u5b8c\u6574\u3002\n#\n# \u53ef\u80fd\u53ef\u4ee5\u901a\u8fc7\u81ea\u5b9a\u4e49\u8865\u5168\u89e3\u7684\u7b97\u6cd5\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002\n# \u4e0d\u8fc7\u76ee\u524d\u53ea\u80fd\u60f3\u5230\u5904\u7406\u4e0d\u7b49\u4e8e0\u7684\u7ea6\u675f\uff0c\u81f3\u4e8e\u5927\u4e8e0\u5c0f\u4e8e0\u7684\u7ea6\u675f\u5219\u8fd8\u6ca1\u60f3\u6cd5\u3002\n# \u4e0d\u7b49\u4e8e0\u7684\u7ea6\u675f\uff0c\u53ef\u4ee5\u76f4\u63a5\u53d6\u4e3a0\u4e4b\u540e\u518d\u8fdb\u884c\u6c42\u89e3\nieqsolve:=proc(eq,vars)\n # return convert~([RealDomain:-solve(eq,convert(vars,set),explicit)],list);\n return RealDomain:-solve(eq,vars,explicit);\nend proc:\n\n# \u81ea\u5b9a\u4e49\u53d8\u6362\u65b9\u7a0b\u6c42\u89e3\u51fd\u6570\nteqsolve:=proc({_explicit::boolean:=false})\n if _explicit then\n if _nrest=1 then\n return [RealDomain:-solve(_rest,explicit)];\n elif _nrest=2 then\n return RealDomain:-solve(_rest,explicit);\n else\n error \"\u672a\u77e5\u8c03\u7528\u65b9\u5f0f\";\n end if;\n else\n if _nrest=1 then\n return convert~([RealDomain:-solve(_rest)],radical);\n elif _nrest=2 then\n return convert~(RealDomain:-solve(_rest),radical);\n else\n error \"\u672a\u77e5\u8c03\u7528\u65b9\u5f0f\";\n end if;\n end if;\nend proc:\n\n# \u8f93\u51faDelta\nprintDeltas:=proc(ds)\n map(i->print(Delta[i]=ds[i]),[seq(x,x=1..numelems(ds))]);\nend proc:\n\n$endif", "meta": {"hexsha": "72cbdc1ead12da7a45ca1510c5a5cecfeedca5d5", "size": 11592, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "old/Classifyer.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/Classifyer.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/Classifyer.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": 26.3454545455, "max_line_length": 96, "alphanum_fraction": 0.5545203589, "num_tokens": 4387, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6791787121629466, "lm_q2_score": 0.5583269943353744, "lm_q1q2_score": 0.3792038089785083}} {"text": "#######################################################################\n# This file is part of the crlibm library, and is distributed under\n# the LGPL.\n# To use:\n# restart; read \"exp-td.mpl\";\nDigits := 120:\n\ninterface(quiet=true):\n\nread \"common-procedures.mpl\":\nread \"triple-double.mpl\":\nmkdir(\"TEMPEXPM1\"):\n\n\nprintPolynomialIntoFile := proc(fd,s,p) \nlocal i, hi, mi, lo:\nfor i from 0 to degree(p(x),x) do\n\t(hi,mi,lo) := hi_mi_lo(coeff(p(x),x,i)):\n\tif ((abs(hi) = 1.0) and (mi = 0) and (lo = 0)) then \n\t\tprintf(\n\t\t\"Coefficient %d of the polynomial is exactly %f and will not be stored in the table\\n\",i,hi): \n\telse \n\tif ((abs(hi) = 0.5) and (mi = 0) and (lo = 0)) then \n\t\tprintf(\n\t\t\"Coefficient %d of the polynomial is exactly %f and will not be stored in the table\\n\",i,hi): \n\telse \n\tif (hi <> 0) then\n \t\tfprintf(fd,\"#define %s%dh %1.50e\\n\",s,i,hi):\n\tend if:\n\tif (mi <> 0) then\n\t \tfprintf(fd,\"#define %s%dm %1.50e\\n\",s,i,mi):\n\tend if:\n\tif (lo <> 0) then\n\t \tfprintf(fd,\"#define %s%dl %1.50e\\n\",s,i,lo):\n\tend if:\n\tend if:\n\tend if:\nod:\nend proc:\n\n\n# First, we compute special values \n\nReturnXBound := convert((ieeehexa(2^(-54)))[1],decimal,hex):\n\nLargest := 2^(1023) * ((2^(53) - 1) / 2^(52)):\n\nSmallest := 2^(-1023) * 1 * 2^(-51):\n\nOverflowBound := nearest(log(Largest + 1)):\n\nMinusOneBound := nearest(log(2^(-54))):\n\nSimpleOverflowBound := convert(ieeehexa(OverflowBound)[1],decimal,hex):\n\nDirectIntervalBound := convert((ieeehexa(0.25))[1],decimal,hex):\n\nMinusOnePlusOneUlp := -1 + 2^(-53): # Attention: it's 2^(-53) because we are at a binade boundary\n\n# Second, we have the computation of the values for the direct interval\n\n# The function, that we approximate is \n\ndirectF := unapply(exp(x) - 1,x):\n\n# The domain is \n\ndirectA := -2^(-5):\ndirectB := 2^(-5):\n\n# The polynomials are\n\nquickDirectpoly := X -> X+1/2*X^2+(3360682229480701/1180591620717411303424*X^6+3660136839517697/147573952589676412928*X^5+7320130809407439/36893488147419103232*X^4+3202559734508631/2305843009213693952*X^3+4803839602572223/576460752303423488*X^2+6004799503160665/144115188075855872*X+6004799503160661/36028797018963968)*X^3:\n\naccuDirectpoly := X -> X+1/2*X^2+(3786738884990361/4951760157141521099596496896*X^12+7100145222887513/618970019642690137449562112*X^11+6212541673969101/38685626227668133590597632*X^10+5047690109993399/2417851639229258349412352*X^9+3785767582868083/151115727451828646838272*X^8+5205430426443615/18889465931478580854784*X^7+29303968161043118891149009244865/10633823966279326983230456482242756608*X^6+65933928362347017505024866986963/2658455991569831745807614120560689152*X^5+65933928362347017505149159875899/332306998946228968225951765070086144*X^4+28846093658526820158502757550845/20769187434139310514121985316880384*X^3+21634570243895115118877068038417/2596148429267413814265248164610048*X^2+27043212804868893898596335048021/649037107316853453566312041152512*X+243583606221817153033947472119380503276473908509/1461501637330902918203684832716283019655932542976)*X^3:\n\n\n# Truncate the quick phase direct interval polynomial to degree specialDegree \n# for special interval |x| <= specialBound (speed-up)\n\nspecialDegree := 5:\nspecialBound := 2^(-12):\n\nspecialPoly := unapply(sum(coeff(quickDirectpoly(x),x,i) * x^i,i=0..specialDegree),x):\n\nprintf(\"Special polynomial is the direct polynomial truncated to degree %d used in |x| < 2^(%f)\\n\",\n\tspecialDegree, evalf(log[2](specialBound))):\n\n# Compute the relative errors\n\nerrDirectQuick := numapprox[infnorm](quickDirectpoly(x)/directF(x) -1,x=directA..directB):\nerrDirectAccu := numapprox[infnorm](accuDirectpoly(x)/directF(x) -1,x=directA..directB):\n\nerrSpecialPoly := numapprox[infnorm](specialPoly(x)/directF(x) -1,x=-specialBound..specialBound):\n\nerrDirectAccuSpecial := numapprox[infnorm](accuDirectpoly(x)/directF(x) -1,x=2^(-12)..2^(-12)):\n\nprintf(\"The relative approximation error of the direct interval quick polynomial is 2^(%f)\\n\",\n\tevalf(log[2](abs(errDirectQuick)))):\nprintf(\"The relative approximation error of the direct interval accurate polynomial is 2^(%f)\\n\",\n\tevalf(log[2](abs(errDirectAccu)))):\nprintf(\"The relative approximation error of the special interval special polynomial is 2^(%f)\\n\",\n\tevalf(log[2](abs(errSpecialPoly)))):\nprintf(\"The relative approximation error of the direct interval accurate polynomial in special domain is 2^(%f)\\n\",\n\tevalf(log[2](abs(errDirectAccuSpecial)))):\n\n\n\n# Third, we have the computation of the values for the common interval\n\n# The function, that we approximate is \n\ncommonF := unapply(exp(x),x):\n\n# The domain is \n\ncommonA := -log(2)*2^(-12) * (1/2 + 2^(-19)):\ncommonB := log(2)*2^(-12) * (1/2 + 2^(-19)):\n\n\nquickCommonpoly := X -> 1+X+1/2*X^2+(6004799504593679/144115188075855872*X+6004799504235425/36028797018963968)*X^3:\n\naccuCommonpoly := X -> 1+X+1/2*X^2+(3660068549402285/18446744073709551616*X^4+6405119471061623/4611686018427387904*X^3+4803839602528529/576460752303423488*X^2+54086425609737787796676993069745/1298074214633706907132624082305024*X+54086425609737787797192670135537/324518553658426726783156020576256)*X^3:\n\n# Compute the relative errors\n\nerrCommonQuick := numapprox[infnorm](quickCommonpoly(x)/commonF(x) -1,x=commonA..commonB):\nerrCommonAccu := numapprox[infnorm](accuCommonpoly(x)/commonF(x) -1,x=commonA..commonB):\n\nprintf(\"The relative approximation error of the common interval quick polynomial is 2^(%f)\\n\",\n\tevalf(log[2](abs(errCommonQuick)))):\nprintf(\"The relative approximation error of the common interval accurate polynomial is 2^(%f)\\n\",\n\tevalf(log[2](abs(errCommonAccu)))):\n\nepsilonApproxRmAccurate := numapprox[infnorm]( ((1+x)/(exp(x)))-1, x=commonA*2^(-52)..commonB*2^(-52)):\nepsilonApproxRlAccurate := numapprox[infnorm]( ((1+x)/(exp(x)))-1, x=commonA*2^(-105)..commonB*2^(-105)):\n\nprintf(\"The approximation rel error for approximating exp(rm) by 1 + rm is 2^(%2f)\\n\", \n\tlog2(abs(epsilonApproxRmAccurate))):\nprintf(\"The approximation rel error for approximating exp(rl) by 1 + rl is 2^(%2f)\\n\", \n\tlog2(abs(epsilonApproxRlAccurate))):\n\n\n\n# Compute the constants for argument reduction and the tables in the common path\n\nMsLog2Div2L := evalf(-log(2)/(2^(12))):\n\nmsLog2Div2Lh, msLog2Div2Lm, msLog2Div2Ll := hi_mi_lo(MsLog2Div2L):\n\nepsMsLog2Div2L := evalf(abs(((msLog2Div2Lh + msLog2Div2Lm + msLog2Div2Ll) - MsLog2Div2L)/MsLog2Div2L)):\nepsDDMsLog2Div2L := evalf(abs(((msLog2Div2Lh + msLog2Div2Lm) - MsLog2Div2L)/MsLog2Div2L)):\n\nprintf(\"The error made by storing MsLog2Div2L as a double-double is 2^(%f)\\n\",log[2](epsDDMsLog2Div2L)):\nprintf(\"The error made by storing MsLog2Div2L as a triple-double is 2^(%f)\\n\",log[2](epsMsLog2Div2L)):\n\ngap := -floor(-log[2](abs(msLog2Div2Lm/msLog2Div2Lh))):\n\nprintf(\"Information: |msLog2Div2Lm| <= 2^(%f) * |msLog2Div2Lh|\\n\",gap):\n\n\nlog2InvMult2L := nearest(2^(12) / (log(2))):\n\nshiftConst := 2^(52) + 2^(51):\n\nindexmask1 := 2^((12)/2) - 1:\nindexmask2 := indexmask1 * 2^((12)/2):\n\nfor i from 0 to 2^(12/2) - 1 do\n\ttwoPowerIndex1hi[i], twoPowerIndex1mi[i], twoPowerIndex1lo[i] := hi_mi_lo(evalf(2^(i/(2^12)))):\n\ttwoPowerIndex2hi[i], twoPowerIndex2mi[i], twoPowerIndex2lo[i] := hi_mi_lo(evalf(2^(i/(2^(12/2))))):\nod: \n\n# Estimate the error of the two quick phases \n\n# ATTENTION: C EST PIFOMETRIQUE POUR L INSTANT\n\nepsQuickDirectOverall := 2^(-62):\nepsQuickCommonOverall := 2^(-62):\n\n\n\n# Write the tables\n\nprintf(\"Write tables...\\n\"):\n\nfilename:=\"TEMPEXPM1/expm1.h\":\nfd:=fopen(filename, WRITE, TEXT):\n\nfprintf(fd, \"#include \\\"crlibm.h\\\"\\n#include \\\"crlibm_private.h\\\"\\n\"):\n\nfprintf(fd, \"\\n/* File generated by maple/expm1.mpl */\\n\"):\n\nfprintf(fd, \"\\#define log2InvMult2L %1.50e\\n\",log2InvMult2L):\nfprintf(fd, \"\\#define msLog2Div2Lh %1.50e\\n\",msLog2Div2Lh):\nfprintf(fd, \"\\#define msLog2Div2Lm %1.50e\\n\",msLog2Div2Lm):\nfprintf(fd, \"\\#define msLog2Div2Ll %1.50e\\n\",msLog2Div2Ll):\nfprintf(fd, \"\\#define shiftConst %1.50e\\n\",shiftConst):\nfprintf(fd, \"\\#define INDEXMASK1 0x%08x\\n\",indexmask1):\nfprintf(fd, \"\\#define INDEXMASK2 0x%08x\\n\",indexmask2):\nfprintf(fd, \"\\#define RETURNXBOUND 0x%08x\\n\",ReturnXBound):\nfprintf(fd, \"\\#define OVERFLOWBOUND %1.50e\\n\",OverflowBound):\nfprintf(fd, \"\\#define LARGEST %1.50e\\n\",Largest): \nfprintf(fd, \"\\#define SMALLEST %1.50e\\n\",Smallest): \nfprintf(fd, \"\\#define MINUSONEBOUND %1.50e\\n\",MinusOneBound):\nfprintf(fd, \"\\#define SIMPLEOVERFLOWBOUND 0x%08x\\n\",SimpleOverflowBound):\nfprintf(fd, \"\\#define DIRECTINTERVALBOUND 0x%08x\\n\",DirectIntervalBound):\nfprintf(fd, \"\\#define SPECIALINTERVALBOUND 0x%08x\\n\",convert((ieeehexa(specialBound))[1],decimal,hex)):\nfprintf(fd, \"\\#define ROUNDCSTDIRECTRN %1.50e\\n\",compute_rn_constant(epsQuickDirectOverall)):\nfprintf(fd, \"\\#define ROUNDCSTDIRECTRD %1.50e\\n\",epsQuickDirectOverall):\nfprintf(fd, \"\\#define ROUNDCSTCOMMONRN %1.50e\\n\",compute_rn_constant(epsQuickCommonOverall)):\nfprintf(fd, \"\\#define ROUNDCSTCOMMONRD %1.50e\\n\",epsQuickCommonOverall):\nfprintf(fd, \"\\#define MINUSONEPLUSONEULP %1.50e\\n\",MinusOnePlusOneUlp):\n\n\n\nfprintf(fd,\"\\n\\n\"):\n\nprintPolynomialIntoFile(fd,\"quickDirectpolyC\",quickDirectpoly):\nfprintf(fd,\"\\n\"):\nprintPolynomialIntoFile(fd,\"accuDirectpolyC\",accuDirectpoly):\nfprintf(fd,\"\\n\"):\nprintPolynomialIntoFile(fd,\"quickCommonpolyC\",quickCommonpoly):\nfprintf(fd,\"\\n\"):\nprintPolynomialIntoFile(fd,\"accuCommonpolyC\",accuCommonpoly):\n\n\nfprintf(fd,\"\\n\\n\"):\n\n# Print the tables\nfprintf(fd, \"typedef struct tPi_t_tag {double hi; double mi; double lo;} tPi_t; \\n\"):\nfprintf(fd, \"static const tPi_t twoPowerIndex1[%d] = {\\n\", 2^(12/2)):\nfor i from 0 to 2^(12/2)-1 do\n fprintf(fd, \" { \\n\"): \n fprintf(fd, \" %1.50e, /* twoPowerIndex1hi[%d] */ \\n\", twoPowerIndex1hi[i], i):\n fprintf(fd, \" %1.50e, /* twoPowerIndex1mi[%d] */ \\n\", twoPowerIndex1mi[i], i):\n fprintf(fd, \" %1.50e, /* twoPowerIndex1lo[%d] */ \\n\", twoPowerIndex1lo[i], i):\n fprintf(fd, \" } \"):\n if(i<2^(12/2)-1) then fprintf(fd, \", \\n\"): fi\nod:\nfprintf(fd, \"}; \\n \\n\"):\nfprintf(fd, \"static const tPi_t twoPowerIndex2[%d] = {\\n\", 2^(12/2)):\nfor i from 0 to 2^(12/2)-1 do\n fprintf(fd, \" { \\n\"): \n fprintf(fd, \" %1.50e, /* twoPowerIndex2hi[%d] */ \\n\", twoPowerIndex2hi[i], i):\n fprintf(fd, \" %1.50e, /* twoPowerIndex2mi[%d] */ \\n\", twoPowerIndex2mi[i], i):\n fprintf(fd, \" %1.50e, /* twoPowerIndex2lo[%d] */ \\n\", twoPowerIndex2lo[i], i):\n fprintf(fd, \" } \"):\n if(i<2^(12/2)-1) then fprintf(fd, \", \\n\"): fi\nod:\nfprintf(fd, \"}; \\n \\n\"):\n\nfprintf(fd, \"\\n\\n\"):\n\nfclose(fd):\n\nprintf(\" ...done\\n\"):", "meta": {"hexsha": "73f4bb657881a470e2bf6c75c896e459053b4708", "size": 10419, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "crlibm/maple/expm1.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/expm1.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/expm1.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": 40.5408560311, "max_line_length": 865, "alphanum_fraction": 0.7099529705, "num_tokens": 3664, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7025300698514777, "lm_q2_score": 0.5389832206876841, "lm_q1q2_score": 0.37865191967849315}} {"text": "# Step 3 of 3: from Maple LO (linear operator) back to Hakaru\nfromLO := module()\n export ModuleApply :=\n proc(lo :: LO(name, anything), {_ctx :: t_kb := empty}, $)\n local h;\n h := gensym(op(1,lo));\n _Env_HakaruSolve := false;\n unintegrate(h, eval(op(2,lo), op(1,lo) = h), _ctx)\n end proc;\n\n export\n unintegrate := proc(h :: name, e, kb :: t_kb_mb, $)\n local x, c, lo, hi, make, m, mm, w, w0, w1, recognition, subintegral,\n i, kb1, kb2, loops, subst, hh, pp, t, bnds, br;\n if kb :: t_not_a_kb then return Msum(); end if;\n if e :: 'And'('specfunc({Int,int})',\n 'anyfunc'('anything','name'='range'('freeof'(h)))) then\n (lo, hi) := op(op([2,2],e));\n x, kb1 := genLebesgue(op([2,1],e), lo, hi, kb);\n subintegral := eval(op(1,e), op([2,1],e) = x);\n (w, m) := unweight(unintegrate(h, subintegral, kb1));\n recognition := recognize_continuous(w, x, lo, hi, kb1);\n if recognition :: 'Recognized(anything, anything)' then\n (w, w0) := factorize(op(2,recognition), x, kb1);\n weight(w0, bind(op(1,recognition), x, weight(w, m)))\n else error \"recognize_continuous is never supposed to fail\" end if\n elif e :: 'And'('specfunc({Sum,sum})',\n 'anyfunc'('anything','name'='range'('freeof'(h)))) then\n (lo, hi) := op(op([2,2],e));\n x, kb1 := genType(op([2,1],e), HInt(closed_bounds(lo..hi)), kb);\n subintegral := eval(op(1,e), op([2,1],e) = x);\n (w, m) := unweight(unintegrate(h, subintegral, kb1));\n recognition := recognize_discrete(w, x, lo, hi, kb1);\n if recognition :: 'Recognized(anything, anything)' then\n (w, w0) := factorize(op(2,recognition), x, kb1);\n weight(w0, bind(op(1,recognition), x, weight(w, m)))\n else error \"recognize_discrete is never supposed to fail\" end if\n elif e :: 'And'('specfunc({Ints,ints,Sums,sums})',\n 'anyfunc'('anything', 'name', 'range'('freeof'(h)),\n 'list(name=range)')) then\n loops := op(4,e);\n bnds := op(3,e);\n if op(0,e) in {Ints,ints} then\n t := HReal(open_bounds(bnds));\n make := Int;\n else\n t := HInt(closed_bounds(bnds));\n make := Sum;\n end if;\n x, kb1 := genType(op(2,e), mk_HArray(t, loops), kb);\n if nops(op(4,e)) > 0 then\n kb1 := assert(size(x)=op([4,-1,2,2],e)-op([4,-1,2,1],e)+1, kb1);\n ASSERT(type(kb1,t_kb), \"unintegrate{Ints,Sums}: integral bounds invalid\");\n end if;\n subintegral := eval(op(1,e), op(2,e) = x);\n (w, m) := unweight(unintegrate(h, subintegral, kb1));\n w := simplify_factor_assuming(peel(w), kb1); # for \"Don't be confused by extra iterations\" tests\n bnds, loops, kb2 := genLoop(bnds, loops, kb, 'Integrand'(x,[w,m]));\n w, pp := unproducts(w, x, loops, kb2);\n hh := gensym('ph');\n subintegral := make(pp * applyintegrand(hh,x), x=bnds);\n (w1, mm) := unweight(unintegrate(hh, subintegral, kb2));\n mm := foldl(((mmm,loop) ->\n Plate(op([2,2],loop) - op([2,1],loop) + 1,\n op(1,loop),\n eval(mmm, op(1,loop) = op(1,loop) - op([2,1],loop)))),\n mm, op(loops));\n w := w * foldl(product, w1, op(loops));\n w := simplify_factor_assuming(w, kb1);\n (w, w0) := factorize(w, x, kb1);\n weight(simplify_factor_assuming(w0, kb),\n bind(mm, x, weight(simplify_factor_assuming(w, kb1), m)))\n elif e :: 'applyintegrand'('identical'(h), 'freeof'(h)) then\n Ret(op(2,e))\n elif e = 0 then\n Msum()\n elif e :: `+` then\n map2(unintegrate, h, Msum(op(e)), kb)\n elif e :: `*` then\n (subintegral, w) := selectremove(depends, e, h);\n if subintegral :: `*` then error \"Nonlinear integral %1\", e end if;\n (w0, w) := op(Domain:-Extract:-Shape(w));\n w0 := Domain:-Shape:-toConstraints(w0);\n kb1 := foldr(assert, kb, op(w0));\n if kb1 :: t_kb then\n m := weight(w, unintegrate(h, subintegral, kb1));\n if m :: Weight(anything, anything) then\n m := weight(simplify_factor_assuming(op(1,m), kb1), op(2,m));\n end if;\n piecewise_And(w0, m, Msum())\n else # if the domain is empty\n Msum()\n end if;\n elif e :: t_pw and not Partition:-ConditionsDepend(Partition:-PWToPartition(e), h) then\n m := kb_piecewise(e, kb, ((lhs, kb)-> lhs), ((rhs, kb)-> unintegrate(h, rhs, kb)), 'no_split_disj');\n if m :: t_pw and nops(m) = 2 then\n piecewise(op(m), Msum());\n else\n m;\n end if;\n elif e :: Partition and not Partition:-ConditionsDepend(e, h) then\n kb_Partition(e, kb, ((lhs, kb)-> lhs), ((rhs, kb)-> unintegrate(h, rhs, kb)));\n elif e :: t_case then\n subsop(2=map(proc(b :: Branch(anything, anything))\n eval(subsop(2='toLO:-unintegrate'(x,op(2,b),c),b),\n {x=h, c=kb})\n end proc,\n op(2,e)),\n e);\n elif e :: 'Context(anything, anything)' then\n kb1 := assert(op(1,e),kb);\n if kb1 :: t_kb then\n subsop(2=unintegrate(h, op(2,e), kb1), e);\n else# A contradictory `Context' implies anything, so produce 'anything'\n # In particular, 42 :: t_Hakaru = false, so a term under a false\n # assumption should never be inspected in any way.\n 42\n end if;\n\n elif e :: 'toLO:-integrate'('freeof'(h), 'anything', identical([])) then\n x := mk_sym('x', op(2,e));\n # If we had HType information for op(1,e),\n # then we could use it to tell kb about x.\n (w, m) := unweight(unintegrate(h, applyintegrand(op(2,e), x), kb));\n (w, w0) := factorize(w, x, kb);\n weight(w0, bind(op(1,e), x, weight(w, m)))\n elif e :: identical('undefined') then\n undefined\n else\n # Failure: return residual LO\n LO(h, e)\n end if\n end proc;\n\n export\n recognize_continuous := proc(weight0, x, lo, hi, kb, $)\n local Constant, de, Dx, f, w, res, rng;\n res := FAIL;\n # gfun[holexprtodiffeq] contains a test for {radfun,algfun} that seems like\n # it should test for {radfun(anything,x),algfun(anything,x)} instead.\n # Consequently, it issues the error \"expression is not holonomic: %1\" for\n # actually holonomic expressions such as exp(x*sum(g(i,j),j=1..n)).\n # Moreover, mysolve has trouble solve-ing constraints involving sum, etc.\n # To work around these weaknesses, we wrap sum(...), etc. in Constant[...].\n # Unlike sum(...), Constant[sum(...)] passes the type test {radfun,algfun},\n # which we need to handle exp(x*sum(...)) using gfun[holexprtodiffeq].\n # Like sum(...i...), Constant[sum(...i...)] depends on i, which we need so\n # that product(sum(...i...),i=1..m) doesn't simplify to ...^m.\n w := subsindets[flat](weight0,\n And(function, Not(specfunc({exp, And, Or, Not})),\n 'freeof'(x)),\n proc(e) Constant[e] end);\n w := subsindets[flat](w, {`^`, specfunc(exp)},\n proc(e)\n applyop(proc(e)\n subsindets[flat](e,\n And({`^`, specfunc(exp)},\n Not(radfun), Not(algfun), 'freeof'(x)),\n proc(e) Constant[e] end)\n end,\n -1, e)\n end);\n de := get_de(w, x, Dx, f);\n if de :: 'Diffop(anything, anything)' then\n res := recognize_de(op(de), Dx, f, x, lo, hi, kb)\n end if;\n if res = FAIL then\n res := Recognized(Lebesgue(lo, hi), w);\n rng := hi - lo;\n if not (rng :: 'SymbolicInfinity') then\n w := simplify_factor_assuming(w * rng, kb);\n # w could be piecewise and simplify will hide the problem\n if not (w :: {'SymbolicInfinity', 'undefined'}) then\n res := Recognized(Uniform(lo, hi), w)\n end if\n end if\n end if;\n # Undo Constant[...] wrapping\n res := subsindets[flat](res, 'specindex'(anything, Constant), x -> op(1,x));\n res\n end proc;\n\n export\n recognize_discrete := proc(w, k, lo, hi, kb, $)\n local se, Sk, f, a0, a1, lambda, r, s, res;\n res := FAIL;\n if lo = 0 and hi = infinity then\n se := get_se(w, k, Sk, f);\n if se :: 'Shiftop(anything, anything, identical(ogf))' and\n ispoly(op(1,se), 'linear', Sk, 'a0', 'a1') then\n lambda := normal(-a0/a1*(k+1));\n if not depends(lambda, k) then\n res := Recognized(PoissonD(lambda), eval(w,k=0)/exp(-lambda));\n end if;\n if ispoly(lambda, 'linear', k, 'b0', 'b1') then\n r := b0/b1;\n res := Recognized(NegativeBinomial(r, b1), eval(w,k=0)/(1-b1)^r);\n end if\n end if;\n elif lo = 0 and not(hi :: 'SymbolicInfinity') then\n s, r := factorize(simplify_factor_assuming(w, kb), k, kb);\n if s <> 1 then\n s := simplify_factor_assuming(s, kb);\n res := ary(hi+1, k, s);\n if res :: 'list' and nops(convert(res,'set')) = 1 then\n res := Recognized(Counting(lo, hi+1), res[1]);\n else\n res := Recognized(Categorical(res), r);\n end if;\n end if;\n end if;\n if res = FAIL then\n res := Recognized(Counting(lo, hi+1), w);\n end if;\n applyop(simplify_assuming, 1,\n applyop(simplify_factor_assuming, 2, res, kb), kb)\n end proc;\n\n local\n get_de := proc(dens, var, Dx, f, $)\n :: Or(Diffop(anything, set(function=anything)), identical(FAIL));\n local de, init;\n try\n de := gfun[holexprtodiffeq](dens, f(var));\n de := gfun[diffeqtohomdiffeq](de, f(var));\n if not (de :: set) then\n de := {de}\n end if;\n init, de := selectremove(type, de, `=`);\n if nops(de) = 1 then\n if nops(init) = 0 then\n # TODO: Replace {0, 1/2, 1} by PyMC's distribution-specific \"testval\"\n init := map(proc (val)\n try f(val) = eval(dens, var=val)\n catch: NULL\n end try\n end proc,\n {0, 1/2, 1})\n end if;\n return Diffop(DEtools[de2diffop](de[1], f(var), [Dx, var]), init)\n end if\n catch: # do nothing\n end try;\n FAIL\n end proc;\n\n local\n get_se := proc(dens, var, Sk, u, $)\n :: Or(Shiftop(anything, set(function=anything), name), identical(FAIL));\n local x, de, re, gftype, init, f;\n try\n # ser := series(sum(dens * x^var, var=0..infinity), x);\n # re := gfun[seriestorec](ser, f(var));\n # re, gftype := op(re);\n _EnvFormal := true;\n de := gfun[holexprtodiffeq](sum(dens*x^var, var=0..infinity), f(x));\n re := gfun[diffeqtorec](de, f(x), u(var));\n re := gfun[rectohomrec](re, u(var));\n if not (re :: set) then\n re := {re}\n end if;\n init, re := selectremove(type, re, `=`);\n if nops(re) = 1 then\n if nops(init) = 0 then\n init := {u(0) = eval(rens, var=0)};\n end if;\n re := map(proc(t)\n local s, r;\n s, r := selectremove(type, convert(t, 'list', `*`),\n u(polynom(nonnegint, var)));\n if nops(s) <> 1 then\n error \"rectohomrec result nonhomogeneous\";\n end if;\n s := op([1,1],s) - var;\n if s :: nonnegint and r :: list(polynom(anything, var)) then\n `*`(op(r), Sk^s);\n else\n error \"unexpected result from rectohomrec\"\n end if\n end proc,\n convert(re[1], 'list', `+`));\n return Shiftop(`+`(op(re)), init, 'ogf')\n end if\n catch: # do nothing\n end try;\n FAIL\n end proc;\n\n local\n recognize_de := proc(diffop, init, Dx, f, var, lo, hi, kb, $)\n local dist, ii, constraints, w, a0, a1, a, b0, b1, c0, c1, c2, loc, nu;\n dist := FAIL;\n if lo = -infinity and hi = infinity\n and ispoly(diffop, 'linear', Dx, 'a0', 'a1') then\n a := normal(a0/a1);\n if ispoly(a, 'linear', var, 'b0', 'b1') then\n dist := Gaussian(-b0/b1, sqrt(1/b1))\n elif ispoly(numer(a), 'linear', var, 'b0', 'b1') and\n ispoly(denom(a), 'quadratic', var, 'c0', 'c1', 'c2') then\n loc := -c1/c2/2;\n if Testzero(b0 + loc * b1) then\n nu := b1/c2 - 1;\n if Testzero(nu - 1) then\n dist := Cauchy(loc, sqrt(c0/c2-loc^2))\n else\n dist := StudentT(nu, loc, sqrt((c0/c2-loc^2)/nu))\n end if\n end if\n end if;\n elif lo = 0 and hi = 1\n and ispoly(diffop, 'linear', Dx, 'a0', 'a1')\n and ispoly(normal(a0*var*(1-var)/a1), 'linear', var, 'b0', 'b1') then\n dist := BetaD(1-b0, 1+b0+b1)\n # elif not evalb((hi - lo) :: 'SymbolicInfinity')\n # and ispoly(diffop, 'linear', Dx, 'a0', 'a1')\n # and ispoly(a0 - 2*var, 'linear', var, 'b0', 'b1') then\n # c0 := (lo*b1 + hi + lo + b0) / (hi - lo);\n # c1 := -(hi*b1 + hi + lo + b0) / (hi - lo);\n # if c0 = 1 and c1 = 1 then\n # dist := Uniform(lo, hi)\n # else\n # dist := bind(BetaD(c0, c1),x,lo+(hi-lo)*x)\n # end if\n elif lo = 0 and hi = infinity\n and ispoly(diffop, 'linear', Dx, 'a0', 'a1')\n and ispoly(normal(a0*var/a1), 'linear', var, 'b0', 'b1') then\n # if Testzero(b1-1/2) then\n # dist := ChiSquared(2*(1-b0))\n # else\n dist := GammaD(1-b0, 1/b1)\n # end if;\n end if;\n if dist <> FAIL then\n try\n ii := map(convert, init, 'diff');\n constraints := eval(ii, f = (x -> w*density[op(0,dist)](op(dist))(x)));\n w := eval(w, mysolve(constraints, w));\n if not (has(w, 'w')) then\n return Recognized(simplify_assuming(dist, kb),\n simplify_factor_assuming(w, kb));\n end if\n catch: # do nothing\n end try;\n WARNING(\"recognized %1 as %2 but could not solve %3\", f, dist, init)\n end if;\n FAIL\n end proc;\n\n\n # (s,r):=factorize(e,var,kb) expresses e in the context kb as s*r,\n # where r doesn't depend on var and s is as simple as possible\n # (and non-negative if possible).\n local\n factorize := proc(e, var, kb, $)\n local res, x, y, kb1, s, r;\n if not depends(e, var) then\n return 1, e;\n end if;\n if e :: `*` then\n res := map(`[]`@factorize, list_of_mul(e), var, kb);\n return `*`(op(map2(op,1,res))),\n `*`(op(map2(op,2,res)));\n end if;\n if e :: 'anything^freeof(var)' then\n s, r := factorize(op(1,e), var, kb);\n return s^op(2,e),\n r^op(2,e);\n end if;\n if e :: 'And(specfunc({product,Product}),\n anyfunc(anything, name=range(freeof(var))))' then\n x, kb1 := genType(op([2,1],e), HInt(closed_bounds(op([2,2],e))), kb, var);\n s, r := factorize(eval(op(1,e), op([2,1],e)=x), var, kb1);\n return op(0,e)(s, x=op([2,2],e)),\n op(0,e)(r, x=op([2,2],e));\n end if;\n if e :: 'And(specfunc({product,Product}),\n anyfunc(anything, name=range))'\n and not depends(subsop([2,2,2]=undefined,e), var) then\n s, r := termize(op([2,2,2],e), var, kb);\n x := op([2,1],e);\n y := `if`(depends(r,x), gensym(x), x);\n return op(0,e)(eval(op(1,e),x=r+1+y), y=0..s-1),\n op(0,e)(op(1,e), x=op([2,2,1],e)..r);\n end if;\n e, 1;\n end proc;\n\n\n\n\n # (s,r):=termize(e,var,kb) expresses e in the context kb as s+r,\n # where r doesn't depend on var and s is as simple as possible.\n local\n termize := proc(e, var, kb, $)\n local res, x, y, kb1, s, r, i, conds, pw;\n if not depends(e, var) then\n return 0, e;\n end if;\n if e :: `+` then\n res := map(`[]`@termize, [op(e)], var, kb);\n return `+`(op(map2(op,1,res))),\n `+`(op(map2(op,2,res)));\n end if;\n if e :: `*` then\n s, r := selectremove(depends, e, var);\n if r <> 1 then return op(map(`*`, [termize(s, var, kb)], r)) end if;\n end if;\n if e :: 'And(specfunc({sum,Sum}),\n anyfunc(anything, name=range(freeof(var))))' then\n x, kb1 := genType(op([2,1],e), HInt(closed_bounds(op([2,2],e))), kb, var);\n s, r := termize(eval(op(1,e), op([2,1],e)=x), var, kb1);\n return op(0,e)(s, x=op([2,2],e)),\n op(0,e)(r, x=op([2,2],e));\n end if;\n if e :: 'And(specfunc({sum,Sum}),\n anyfunc(anything, name=range))'\n and not depends(subsop([2,2,2]=undefined,e), var) then\n s, r := termize(op([2,2,2],e), var, kb);\n x := op([2,1],e);\n y := `if`(depends(r,x), gensym(x), x);\n return op(0,e)(eval(op(1,e),x=r+1+y), y=0..s-1),\n op(0,e)(op(1,e), x=op([2,2,1],e)..r);\n end if;\n if e :: 'specfunc(piecewise)' then\n conds := [seq(op(i,e), i=1..nops(e)-1, 2)];\n if depends(conds, var) then\n # Too bad the conditions depend on var.\n # But maybe the conditions depend on var only in certain cases\n # (whose conditions in turn do not depend on var)?\n pw := select(proc(pw, $)\n local i;\n if not depends(pw, var) then return false end if;\n for i from 1 by 2 to nops(pw)-1 do\n if depends(op(i,pw), var) then return false end if;\n end do;\n for i from 2 by 2 to nops(pw)-1 do\n if not depends(op(i,pw), var) then return true end if;\n end do;\n return not depends(op(-1,pw), var);\n end proc,\n indets(conds, 'specfunc(piecewise)'));\n if nops(pw) > 0 then\n pw := op(1, pw); # Pick any eligible piecewise to lift\n pw := piecewise(seq(`if`(i::odd and i cond),\n ((ee, kb) -> [termize(ee, var, kb)]));\n if res :: 'specfunc(piecewise)'\n and [seq(op(i,res), i=2..nops(res)-1, 2), op(-1,res)]\n :: 'list([anything, anything])' then\n return piecewise(seq(op(`if`(i::odd and i unweight(mi)[1]), m)));\n (total, map((mi -> weight(1/total, mi)), m))\n else\n (1, m)\n end if;\n end proc;\n\nend module; # fromLO\n", "meta": {"hexsha": "54168b4fce53d32b0d8d5f99ba341ea9ebd160fd", "size": 19166, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/From.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/From.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/From.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": 39.5991735537, "max_line_length": 108, "alphanum_fraction": 0.504800167, "num_tokens": 6055, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7122321720225278, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.37834440579671635}} {"text": " func $landi32 (\n var %i i32, var %j i32\n ) i32 { \n return (\n land i32(dread i32 %i, dread i32 %j))}\n\n func $landi64 (\n var %i i64, var %j i64\n ) i32 { \n return (\n land i64(dread i64 %i, dread i64 %j))}\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "a69899900b708d617827eb390e793be96bb06431", "size": 321, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0050-mapleall-irbuild-edge-land/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/I0050-mapleall-irbuild-edge-land/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/I0050-mapleall-irbuild-edge-land/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": 21.4, "max_line_length": 43, "alphanum_fraction": 0.5825545171, "num_tokens": 131, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6548947425132315, "lm_q2_score": 0.5774953651858118, "lm_q1q2_score": 0.37819867848594685}} {"text": "\n # Like simplify_assuming, but does a lot of hack-y things\n simplify_factor_assuming := module ()\n\n export ModuleApply;\n local graft_pw, GAMMAratio, wrap, and_info,\n hack_Beta_pw, hack_Beta, hackier_Beta,\n eval_piecewise, bounds_are_simple, eval_loop, eval_factor;\n\n$include \"NewSLO/Beta.mpl\"\n$include \"NewSLO/Piecewise.mpl\"\n\n bounds_are_simple := proc(bounds :: range, $)\n local bound, term, i;\n if `-`(op(bounds)) :: integer then return true end if;\n for bound in bounds do\n for term in convert(bound, 'list', `+`) do\n if term :: `*` then term := remove(type, term, integer) end if;\n if term :: 'specfunc(piecewise)' then\n for i from 2 by 2 to nops(term)-1 do\n if not(op(i,term) :: integer) then return false end if\n end do;\n if not(op(-1,term) :: integer) then return false end if\n elif not(term :: integer) then return false end if\n end do\n end do;\n true\n end proc;\n\n eval_loop := proc(e :: And(specfunc({product,Product,sum,Sum}),\n anyfunc(anything, name=range)),\n kb :: t_kb,\n mode :: identical(`*`,`+`),\n loops, $)\n local o, body, x, bounds, res, go, y, kb1;\n o := op(0,e);\n body, bounds := op(e);\n x, bounds := op(bounds);\n bounds := map(eval_factor, bounds, kb, `+`, []);\n if bounds_are_simple(bounds) then\n # Expand {product,sum} to {mul,add}\n if o=Product then o:=product elif o=Sum then o:=sum end if;\n bounds := lift_piecewise(bounds,\n 'And(range, Not(range(Not(specfunc(piecewise)))))');\n res := `if`(bounds :: 'specfunc(piecewise)', map_piecewiselike, apply)\n ((b -> o(go(x), x=b)), bounds);\n # Work around this bug:\n # > product(Sum(f(j),j=0..n-1),j=0..0)\n # Sum(f(0),0=0..n-1)\n res := eval(res, go = (i -> eval(body, x=i)));\n return eval_factor(res, kb, mode, loops);\n end if;\n y, kb1 := genType(x, HInt(closed_bounds(bounds)), kb);\n return eval_factor(subs(x=y,body), kb1, mode, [[o,y=bounds],op(loops)]);\n end proc;\n\n # eval_factor is a simplifier. It maintains the following invariants:\n # eval_factor(e, kb, mode, []) = e\n # eval_factor(e, kb, `*` , [...,[product,i=lo..hi]])\n # = product(eval_factor(e, kb, `*`, [...]), i=lo..hi)\n # eval_factor(e, kb, `+` , [...,[sum ,i=lo..hi]])\n # = sum (eval_factor(e, kb, `+`, [...]), i=lo..hi)\n # It recursively traverses e while \"remembering\" the loops traversed,\n # as ``context'' information, to help with transformations.\n eval_factor := proc(e, kb :: t_kb, mode :: identical(`*`,`+`), loops, $)\n local res, i, j, k, s, r;\n if not (loops :: 'list'([`if`(mode=`*`, 'identical(product,Product)',\n 'identical(sum ,Sum )'),\n 'name=range'])) then\n error \"invalid input: mode=%1, loops=%2\", mode, loops;\n end if;\n if e :: mode then\n # Transform product(a*b,...) to product(a,...)*product(b,...)\n # (where e=a*b and loops=[[product,...]])\n return map(eval_factor, e, kb, mode, loops);\n end if;\n if e = mode () then\n return e;\n end if;\n if e :: And(specfunc(`if`(mode=`*`, '{product,Product}', '{sum,Sum}')),\n 'anyfunc(anything, name=range)') then\n return eval_loop(e, kb, mode, loops);\n end if;\n if e :: 'specfunc(piecewise)' then\n return eval_piecewise(e, kb, mode, loops);\n end if;\n if e :: `*` then\n # If we're here, then mode=`+` (else \"e :: mode\" above would be true)\n s, r := selectremove(depends, e, map2(op,[2,1],loops));\n # Transform sum(a*b(i),i=...) to a*sum(b(i),i=...)\n if r <> 1 then\n return eval_factor(s, kb, `+`, loops)\n * maptype(`*`, eval_factor, r, kb, `+`, []);\n end if;\n end if;\n if mode = `*` then\n i := map2(op,[2,1],loops);\n if e :: '`^`' then\n # Transform product(a(i)^b,i=...) to product(a(i),i=...)^b\n if not depends(op(2,e), i) then\n return eval_factor(op(1,e), kb, `*`, loops)\n ^ eval_factor(op(2,e), kb, `+`, []);\n end if;\n end if;\n if e :: 'exp(anything)' or e :: '`^`' and not depends(op(1,e), i) then\n # Transform product(a^((b(i)+c(i))^2),i=...)\n # to a^ sum(b(i)^2 ,i=...)\n # * a^(2*sum(b(i)*c(i),i=...))\n # * a^ sum(c(i)^2 ,i=...)\n return mul(subsop(-1=j,e),\n j in convert(eval_factor(expand(op(-1,e)), kb, `+`,\n map2(subsop,1=sum,loops)),\n 'list', `+`));\n end if;\n # Rewrite ... * idx([p,1-p],i)\n # to ... * p^idx([1,0],i) * (1-p)^idx([0,1],i)\n # because the latter is easier to integrate and recognize with respect to p\n if e :: 'idx(list, anything)' and not depends(op(1,e), i) then\n return mul(op([1,j],e)\n ^ eval_factor(idx([seq(`if`(k=j,1,0), k=1..nops(op(1,e)))],\n op(2,e)),\n kb, `+`, map2(subsop,1=sum,loops)),\n j=1..nops(op(1,e)));\n end if;\n end if;\n\n # Try not to use hack_beta for now...\n\n if mode = `*` and e :: 'specfunc(Beta)' then\n res := hack_Beta(e, kb, loops);\n if res <> FAIL then\n userinfo(3, 'hack_Beta',\n printf(\"Beta hack was applied to %a, %a, %a\\n\"\n \"\\tto produce %a\\n\", e, kb, loops, res));\n return res\n end if;\n end if;\n\n if nops(loops) > 0 then\n # Emit outermost loop as last resort\n return op([-1,1],loops)(eval_factor(e, kb, mode, loops[1..-2]),\n op([-1,2],loops));\n end if;\n # In the remainder of this function, assume loops=[] and recur in\n if e :: '{specfunc({GAMMA, Beta, exp, And, Or, Not}), relation, logical}' then\n return map(eval_factor, e, kb, `+`, []);\n end if;\n if e :: `^` then\n return eval_factor(op(1,e), kb, mode, [])\n ^ eval_factor(op(2,e), kb, `+` , []);\n end if;\n if e :: `+` then\n return map(eval_factor, e, kb, mode, []);\n end if;\n return e;\n end proc;\n\n ModuleApply := proc(e, kb::t_kb, $)\n simplify_assuming(eval_factor(convert(Partition:-PartitionToPW_mb(e), 'Beta'), kb, `*`, []), kb);\n end proc;\n end module; # simplify_factor_assuming\n", "meta": {"hexsha": "50cc2d2c530e5a4bec16f5932388a3cf7819f79e", "size": 6768, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Factor.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/Factor.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/Factor.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": 41.7777777778, "max_line_length": 103, "alphanum_fraction": 0.4867021277, "num_tokens": 1922, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7310585903489892, "lm_q2_score": 0.5156199157230157, "lm_q1q2_score": 0.37694836874433246}} {"text": "\n# Berechnung und Projektion der Dynamikgleichungen\n# Einleitung\n# Berechnung und Projektion der Dynamikgleichungen\n# \n# Dateiname:\n# robot -> Berechnung f\u00fcr allgemeinen Roboter\n# para -> Berechnung f\u00fcr einen parallelen Roboter\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# projection -> Die Dynamikgleichungen werden auf EE-Koordinaten projiziert\n# dynamics -> Berechnung der Dynamik\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):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools): # F\u00fcr Zeitausgabe\n;\n# Einstellungen f\u00fcr Code-Export: Optimierungsgrad (2=h\u00f6chster).\n#codegen_act := true: # noch nicht implementiert\ncodegen_debug := false:\ncodegen_opt := 2:\ncodeexport_invdyn := true:\ncodeexport_actcoord := false: # Generierung der Dynamik in Antriebskoordinaten nicht standardm\u00e4\u00dfig (hoher Rechenaufwand)\n;\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_simplify2\":\nread \"../robot_codegen_definitions/robot_env_par\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_definitions\", leg_name):\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 zus\u00e4tzlichen Definitionen f\u00fcr parallele Roboter laden\nread \"../robot_codegen_definitions/robot_env_par\":\nread sprintf(\"../codeexport/%s/tmp/para_definitions\", robot_name):\n# Ergebnisse der Plattform-Dynamik laden (aus robot_para_plattform_rotmat_dynamics.mw)\n\nread \"../robot_codegen_definitions/robot_env_par\":\ndynamicsfile := sprintf(\"../codeexport/%s/tmp/floatb_platform_dynamic_maple.m\", robot_name):\nif FileTools[Exists](dynamicsfile) then\n read dynamicsfile:\nelse\n printf(\"%s. PKM-Dynamik konnte nicht geladen werden. Abbruch der Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\n# Neu-Definition der geladenen Variablen\nMME:=MME:\ncvecE:=cvecE:\ngE:=gE:\ntauE:=tauE:\nH:=H:\ndH:=dH:\n\n# Ergebnisse der Kinematik f\u00fcr parallelen Roboter laden\n\nread \"../robot_codegen_definitions/robot_env_par\":\nkinematicsfile := sprintf(\"../codeexport/%s/tmp/kinematics_%s_platform_maple.m\", robot_name, base_method_name):\nif FileTools[Exists](kinematicsfile) then\n read kinematicsfile:\nelse\n printf(\"%s. PKM-Kinematik konnte nicht geladen werden. Abbruch der Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\nread \"../robot_codegen_definitions/robot_env_par\": # Nochmal laden, um Standard-Einstellungen \u00fcberschreiben zu k\u00f6nnen.\n# Neu-Definition der von dieser Datei gelesenen Variablen, damit sie im Workspace erscheinen\npivotMat := pivotMat:\npivotMatMas := pivotMatMas:\nJinv := Jinv:\nJBinv_i := JBinv_i:\nU_i := U_i:\n\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)):\nread(sprintf(\"%s/transformation/maple/proc_eul%sjac\", robotics_repo_path, \"zyx\")): # TODO: Muss hier die Winkelkonvention eingesetzt werden? Wird das hier gebraucht?\n# TODO: Euler-Funktion mit \"parse\"-Befehl hier definieren\n# Alle Basisgeschwindigkeiten und -winkel aus Berechnung der seriellen Kette zu null setzen.\nomegaxs_base := 0:\nomegays_base := 0:\nomegazs_base := 0:\nalphaxs_base := 0:\nbetays_base := 0:\ngammazs_base := 0:\nvxs_base := 0:\nvys_base := 0:\nvzs_base := 0:\n# Startzeit messen zur Beurteilung der Zeitdauer einzelner Schritte\nst := time():\n# Physikalische Parameter der durch Koppelgelenke bewegten K\u00f6rper zu Null setzen.\nNQ := NQ - (NQJ-NQJ_parallel):\nfor i from NQJ_parallel+1 to NQJ do\n\tXXC||i := 0:\n\tXYC||i := 0:\n\tXZC||i := 0:\n\tYYC||i := 0:\n\tYZC||i := 0:\n\tZZC||i := 0:\n\tXX||i := 0:\n\tXY||i := 0:\n\tXZ||i := 0:\n\tYY||i := 0:\n\tYZ||i := 0:\n\tZZ||i := 0:\n\tSX||i := 0:\n\tSY||i := 0:\n\tSZ||i := 0:\n\tMX||i := 0:\n\tMY||i := 0:\n\tMZ||i := 0:\n\tM||i := 0:\nend do:\n# Ergebnisse G-Vektor der Beinkette laden.\n# Die Rotation der Basis wird nur in der Jacobi-Matrix der inverse Kinematik ber\u00fccksichtigt. Deshalb muss der Gravitationsvektor ebenfalls an die Rotation angepasst werden.\n\ng1 := gtmp1:\ng2 := gtmp2:\ng3 := gtmp3:\n\ndynamicsfile_leg := sprintf(\"../codeexport/%s/tmp/gravload_par%d_maple.m\", leg_name, codegen_dynpar):\nif FileTools[Exists](dynamicsfile_leg) then\n read dynamicsfile_leg:\nelse\n printf(\"%s. Beinketten-Dynamik (g) konnte nicht geladen werden. Abbruch der Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\nG := simplify2(Matrix(taug_s(7..NQ,1))):\nunassign('g1','g2','g3'):\ng := :\nRmat := Transpose(parse(sprintf(\"eul%s2r\",angleConvLeg))(frame_A_i(1..3,1))):\ngtmp1 := (Rmat.g)(1):\ngtmp2 := (Rmat.g)(2):\ngtmp3 := (Rmat.g)(3):\nG := G:\n\n\n# Ergebnisse C-Vektor der Beinkette laden\ndynamicsfile_leg := sprintf(\"../codeexport/%s/tmp/coriolisvec_par%d_maple.m\", leg_name, codegen_dynpar):\nif FileTools[Exists](dynamicsfile_leg) then\n read dynamicsfile_leg:\nelse\n printf(\"%s. Beinketten-Dynamik (c) konnte nicht geladen werden. Abbruch der Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\nCvec := simplify2(Matrix(tauCC_s(7..NQ,1))):\nCvec := Cvec:\n\n# Ergebnisse M-Matrix der Beinkette laden\n\ndynamicsfile_leg := sprintf(\"../codeexport/%s/tmp/inertia_par%d_maple.m\", leg_name, codegen_dynpar):\nif FileTools[Exists](dynamicsfile_leg) then\n read dynamicsfile_leg:\nelse\n printf(\"%s. Beinketten-Dynamik (M) konnte nicht geladen werden. Abbruch der Berechnung.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n quit: # Funktioniert in GUI nicht richtig...\n robot_name := \"\": # ...Daher auch L\u00f6schung des Roboternamens.\nend if:\nMM := simplify(MM_s(7..NQ,7..NQ)):\nMM := simplify(MM):\nMME := simplify(MME):\n# Ausdruck f\u00fcr Gravitationsterme der Plattform nochmal vereinfachen.\ngE := simplify2(gE):\n# Ergebnisse der Kinematik f\u00fcr parallen Roboter laden (wurde oben schon gemacht.\n#read sprintf(\"../codeexport/%s/tmp/kinematics_%s_platform_maple.m\", robot_name, base_method_name):\nprintf(\"%s. Alle Daten geladen. Generiere Dynamik f\u00fcr PKM %s mit Parametersatz %d\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), robot_name, codegen_dynpar, base_method_name):\n\n# Berechne Dynamik-Matrizen f\u00fcr alle Beine\n# Dupliziere alle berechneten Matrizen. i steht f\u00fcr den Index des jeweiligen Beines\n\nfor i to N_LEGS do\n MM||i := Copy(MM):\n Cvec||i := Copy(Cvec):\n G||i := Copy(G):\nend do:\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 NQJ_parallel do\n \t\tfor l to 3 do\n \t \t\tCvec||k(i,1):=subs({frame_A_i(l,1)=frame_A_i(l,k)},Cvec||k(i,1)):\n \t \t\tG||k(i,1):=subs({frame_A_i(l,1)=frame_A_i(l,k)},G||k(i,1)):\n \t\tend do:\n \t\tfor m to NQJ_parallel do #alpha\n \t\tn := (m + (k-1)*NQJ_parallel):\n \t\tCvec||k(i,1):=subs({qJD||m||s=qJ||D||n||s,qJ||m||s=qJ||n||s},Cvec||k(i,1)):\n \t\tG||k(i,1):=subs({qJ||m||s=qJ||n||s},G||k(i,1)):\n \t\tend do:\n \t\tfor j to NQJ_parallel do\n \t\t\tfor l to 3 do\n \t \t\t\tMM||k(i,j):=subs({rame_A_i(l,1)=frame_A_i(l,k)},MM||k(i,j)):\n \t \t\tend do:\n \t\tfor m to NQJ_parallel do #alpha\n \t\t\tn := m + (k-1)*NQJ_parallel:\n \t\t\tMM||k(i,j):=subs({qJ||m||s=qJ||n||s},MM||k(i,j)):\n \t\tend do:\n \t\tend do:\n \tend do:\nend do:\n\n\n# Berechnung, Projektion und Addition der Dynamikgleichungen\n# Berechnung der Kr\u00e4fte/Momente an den Gelenken der jeweiligen Beine und Projektion auf EE-Plattform\n# Abdellatif2007 S.38 (3.27); [Job2018_S759], S. 29\n\nfor i to N_LEGS do\n\n Jtmp := Multiply(Transpose(U_i(..,..,i)),Transpose(JBinv_i(..,..,i))):\n qDtmp := Multiply(JBinv_i(..,..,i),U_i(..,..,i).H.xED_s):\n A||i := simplify(Multiply(JBinv_i(..,..,i),JBD_i(..,..,i))):\n B||i := Multiply(-MM||i,Multiply(A||i,qDtmp)):\n\n # [Job2018_S759], Term in der Summe in Gl. (3.50)\n MMs||i := Jtmp . MM||i . Transpose(Jtmp) . H:\n # [Job2018_S759], Term in der Summe in Gl. (3.51)\n cvecs||i := Jtmp.MM||i.JBinv_i(..,..,i).(U_i(..,..,i).dH + UD_i(..,..,i).H).xED_s + Jtmp.B||i + Jtmp.Cvec||i:\n # [Job2018_S759], Term in der Summe in Gl. (3.52)\n gvecs||i := Jtmp.G||i:\n \n tau||i := Jtmp.MM||i.JBinv_i(..,..,i).(U_i(..,..,i).H.xEDD_s+U_i(..,..,i).dH.xED_s+UD_i(..,..,i).H.xED_s) + Multiply(Jtmp,(B||i+Cvec||i+G||i)):\n\n\n taus||i := MMs||i.xEDD_s + cvecs||i + gvecs||i:\nend do:\n\n# Abdellatif2007 S.40 (3.33); [Job2018_S759], (3.49)\n# Aufsummieren aller Kr\u00e4fte, projiziert auf EE-Plattform\nTmp := 0:\nfor i to N_LEGS do\n Tmp := Tmp + tau||i:\nend do:\n# Addiere Inverse Dynamik der Plattform\ntauGes := Tmp + tauE:\n# Aufsummieren aller Massenmatrizen, projiziert auf EE-Plattform\n# [Job2018_S759], (3.50)\nTmp := 0:\nfor i to N_LEGS do\n Tmp := Tmp + MMs||i:\nend do:\n# Addiere Massenmatrix der Plattform\nMMGes := Tmp + MME:\n# Aufsummieren aller Coriolisvektoren, projiziert auf EE-Plattform\n# [Job2018_S759], (3.51)\nTmp := 0:\nfor i to N_LEGS do\n Tmp := Tmp + cvecs||i:\nend do:\n# Addiere Coriolisvektor der Plattform\ncvecGes := Tmp + cvecE:\n# Aufsummieren aller Gravitiationsvektoren, projiziert auf EE-Plattform\n# [Job2018_S759], (3.52)\nTmp := 0:\nfor i to N_LEGS do\n Tmp := Tmp + gvecs||i:\nend do:\n# Addiere Gravitiationsvektor der Plattform\ngGes := Tmp - gE:\n#tauGes := MMGes.xEDD_s + cvecGes + gGes:\n# Replace Joint Velocities\n# Substituiere die Gelenkgeschwindigkeiten \u00fcber H-, Ui- und JBi-Matrix mit EE-Geschwindikeiten\nTmp := 0:\nfor i to N_LEGS do\n Tmp := Multiply(H,xED_s):\n Tmp := Multiply(U_i(..,..,i),Tmp):\n z||i := Multiply(JBinv_i(..,..,i),Tmp):\nend do:\nfor i to 6 do\n for j to N_LEGS do\n for l to NQJ_parallel do\n tauGes(i,1) := subs({qJD_i_s(l,j)=z||j(l)},tauGes(i,1)):\n cvecGes(i,1) := subs({qJD_i_s(l,j)=z||j(l)},cvecGes(i,1)):\n gGes(i,1) := subs({qJD_i_s(l,j)=z||j(l)},gGes(i,1)):\n for k to 6 do\n MMGes(i,k) := subs({qJD_i_s(l,j)=z||j(l)},MMGes(i,k)):\n end do:\n end do:\n end do:\nend do:\n# Export\n# W\u00e4hle die Eintr\u00e4ge aus Dynamikgleichungen, die f\u00fcr Freiheitsgrade des Roboters relevant sind.\n# (\u00fcber die Auswahl-Matrix \"pivotMat\").\n#Jtestinv := Matrix(6,6,symbol=Jentry):\n#Jtest := MatrixInverse(Jtestinv):\n#Jtest := simplify(Jtest):\n#for i to RowDimension(Jtest) do\n# for j to ColumnDimension(Jtest) do\n# for k to RowDimension(Jtest) do\n# for l to ColumnDimension(Jtest) do\n# Jtest(i,j) := subs(Jentry[k,l]=simplify(Jinv(k,l)),Jtest(i,j)):\n# end do:\n# end do:\n# end do:\n#end do:\n# Dynamik-Terme in Plattform-Koordinaten\ntau_x := pivotMat.tauGes:\nMMGes_x := pivotMat.MMGes.Transpose(pivotMatMas):\ncvecGes_x := pivotMat.cvecGes:\ngGes_x := pivotMat.gGes:\n# Maple-Export (zur eventuellen sp\u00e4teren Verarbeitung in Maple)\nsave tau_x, sprintf(\"../codeexport/%s/tmp/invdyn_para_plfcoord_par%d_maple.m\", robot_name, codegen_dynpar):\nsave MMGes_x, sprintf(\"../codeexport/%s/tmp/inertia_para_plfcoord_par%d_maple.m\", robot_name, codegen_dynpar):\nsave cvecGes_x, sprintf(\"../codeexport/%s/tmp/coriolisvec_para_plfcoord_par%d_maple.m\", robot_name, codegen_dynpar):\nsave gGes_x, sprintf(\"../codeexport/%s/tmp/gravvec_para_plfcoord_par%d_maple.m\", robot_name, codegen_dynpar):\n# Dynamik in Antriebs-Koordinaten umrechnen. Nur machen, wenn die Jacobi-Matrix einfach genug ist. Sonst ist die symbolische Invertierung zu teuer und sollte numerisch gemacht werden\n# [Job2018_S759], S. 30; Gl. 3.53, 3.54\nif RowDimension(Jinv) < 5 and codeexport_actcoord then\n printf(\"%s. Beginn der Matrix-Invertierung. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n J:=MatrixInverse(Jinv): # TODO: Matrix-Invertierung in eigenem Skript (bei der Kinematik; dort mit Platzhalter-Matrix invertieren)\n save J, sprintf(\"../codeexport/%s/tmp/jacobian_maple.m\", robot_name): # TODO: Besseren Namen w\u00e4hlen und dies im Kinematik-Skript machen.\n printf(\"%s. Matrix-Invertierung beendet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n # J:=simplify(J):\n # printf(\"%s. Optimierung beendet. CPU-Zeit bis hier: %1.2fs.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\"), time()-st):\n tau_qa := Transpose(J) . tau_x:\n MMGes_qa := Transpose(J) . MMGes_x:\n cvecGes_qa := Transpose(J) . cvecGes_x:\n gGes_qa := Transpose(J) . gGes_x:\n # Maple-Export (zur eventuellen sp\u00e4teren Verarbeitung in Maple)\n save tau_qa, sprintf(\"../codeexport/%s/tmp/invdyn_para_actcoord_par%d_maple.m\", robot_name, codegen_dynpar):\n save MMGes_qa, sprintf(\"../codeexport/%s/tmp/inertia_para_actcoord_par%d_maple.m\", robot_name, codegen_dynpar):\n save cvecGes_qa, sprintf(\"../codeexport/%s/tmp/coriolisvec_para_actcoord_par%d_maple.m\", robot_name, codegen_dynpar):\n save gGes_qa, sprintf(\"../codeexport/%s/tmp/gravvec_para_actcoord_par%d_maple.m\", robot_name, codegen_dynpar):\nend if:\nprintf(\"%s. Speicherung der Dynamik-Terme in symbolischer Form beendet. Starte Code-Export in Matlab\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n# Matlab Export\nif codeexport_invdyn then\n printf(\"%s. Beginne Code-Export Inverse Dynamik in Plattform-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(tau_x, sprintf(\"../codeexport/%s/tmp/invdyn_para_plfcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Massenmatrix in Plattform-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(MMGes_x, sprintf(\"../codeexport/%s/tmp/inertia_para_plfcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Coriolis-Vektor in Plattform-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(cvecGes_x, sprintf(\"../codeexport/%s/tmp/coriolisvec_para_plfcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Gravitations-Vektor in Plattform-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(gGes_x, sprintf(\"../codeexport/%s/tmp/gravvec_para_plfcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\nend if:\nif codeexport_invdyn and RowDimension(Jinv) < 5 and codeexport_actcoord then\n printf(\"%s. Beginne Code-Export Inverse Dynamik in Antriebs-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(tau_qa, sprintf(\"../codeexport/%s/tmp/invdyn_para_actcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Massenmatrix in Antriebs-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(MMGes_qa, sprintf(\"../codeexport/%s/tmp/inertia_para_actcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Coriolis-Vektor in Antriebs-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(cvecGes_qa, sprintf(\"../codeexport/%s/tmp/coriolisvec_para_actcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\n printf(\"%s. Beginne Code-Export Gravitations-Vektor in Antriebs-Koordinaten.\\n\", FormatTime(\"%Y-%m-%d %H:%M:%S\")):\n MatlabExport(gGes_qa, sprintf(\"../codeexport/%s/tmp/gravvec_para_actcoord_par%d_matlab.m\", robot_name, codegen_dynpar), codegen_opt);\nend if:\n\n", "meta": {"hexsha": "6e6ee5b6e97ca441fc225cc01634c7883b78d0d1", "size": 16075, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_parallel/robot_para_rotmat_projection_dynamics.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_projection_dynamics.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_projection_dynamics.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": 45.154494382, "max_line_length": 198, "alphanum_fraction": 0.7083048212, "num_tokens": 5485, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.7634837527911057, "lm_q2_score": 0.4921881357207956, "lm_q1q2_score": 0.3757776449393711}} {"text": "#\n# These procedures come from the source code of GFun.\n#\ngetname:=proc(yofz::function(name), y, z)\n y:=op(0,yofz);\n if type(y,'procedure') then error `not an unassigned name`,y fi;\n z:=op(yofz)\nend proc:\n\n\n#\n# returns the smallest i such that u(n+i) appears in a recurrence\n#\nminindex := proc(rec,u,n)\n min(op(map(op,indets(rec,'specfunc'('linear'(n),u)))))-n\nend proc:\n\n\n#\n# returns the largest i such that u(n+i) appears in a recurrence\n#\nmaxindex := proc(rec,u,n)\n max(op(map(op,indets(rec,'specfunc'('linear'(n),u)))))-n\nend proc:\n\n\n#\n# A recurrence of the form a(n+d) = p(n)/q(n) a(n) is represented through a record:\n# OneTermRecurrence : record(order, numerator, denominator)\n#\n`type/OneTermRecurrence` := 'record(order, numerator, denominator)':\n\n\n#\n#checkOneTermRecurrence\n# Input: a recurrence rec (either with or without initial conditions).\n# If it has initial conditions, they are ignored.\n# a(n): the name of the sequence and the name of the variable.\n#\n# Output:\n# This procedure checks that rec is a recurrence of the form a(n+d) = p(n)/q(n) a(n)\n# If the check succeeds, it returns the corresponding record. If it fails, an error is\n# returned.\n#\ncheckOneTermRecurrence := proc(rec, aofn)::OneTermRecurrence;\n local r, d, a, n, term1, term2, res;\n\n getname(aofn, a, n):\n if type(rec, 'set') then\n r:=select(has, rec, n);\n if nops(r)>1\n then error `invalid recurrence`, rec\n fi:\n if nops(r)=0\n then error \"%1 does not appear in the recurrence\", n\n fi:\n r := op(r):\n else r:=rec:\n fi:\n if type(r,'`=`')\n then r:=op(1,r)-op(2,r)\n fi:\n if indets(r,'specfunc'('anything',a)) <> indets(r,'specfunc'('linear'(n),a))\n then error \"the recurrence contains elements that are not linear in %1\", n\n fi:\n if nops(r) <> 2\n then error \"the recurrence contains %1 terms (expected 2)\", nops(r)\n fi:\n r := subs(n=n-minindex(r, a, n), r):\n d := maxindex(r, a, n):\n\n term1 := select(has, r, a(n)):\n term2 := select(has, r, a(n+d)):\n\n res := factor( -(term1/a(n)) / (term2/a(n+d)) ):\n\n Record( 'order'=d, 'numerator' = numer(res), 'denominator' = denom(res) )\nend proc:\n\n\n#\n# my_factors factorizes p the same way as factors(p) would do except that the constant part is computed\n# differently. We assume here that p has integer coefficients, and we want to factorize it over polynomials\n# with integer coefficients. my_factors ensures that the factors have integer coefficients.\n#\nmy_factors := proc(p)\n local L, c, fact, i, my_c, my_fact, q:\n L := factors(p):\n c := L[1]: fact := L[2]:\n my_c := c: my_fact := []:\n for i from 1 to nops(fact) do\n q := denom(fact[i][1]):\n my_fact := [ op(my_fact), [ fact[i][1]*q, fact[i][2] ] ]:\n my_c := my_c / (q^fact[i][2]):\n od:\n [ my_c, my_fact]:\nend proc:\n\n\n#\n# This procedure decomposes a one-term recurrence with the following form:\n# a(n+d) = c * s1(n)/s1(n+d) * s2(n+d)/s2(n) * p(n)/q(n) * a(n)\n#\n# Known issue: this procedure assumes that the only variables involved are n and x with their usual meaning.\n#\ndecomposeOneTermRecurrence := proc(formalRec::OneTermRecurrence, res_cste, res_s1, res_s2, res_p, res_q)\n local p, q, cste, s1, s2, d, L, i, tmp, exponent, r, polyring;\n p := formalRec:-numerator:\n q := formalRec:-denominator:\n d := formalRec:-order:\n s1 := 1:\n L := op(2,my_factors(p)): # L contains the non trivial factors of p\n for i from 1 to nops(L) do\n tmp := L[i][1]: exponent := L[i][2]:\n r := gcd(tmp^exponent, subs(n=n-d, q)):\n p := quo(p,r,n): q := quo(q, subs(n=n+d, r),n): s1 := s1 * r:\n od:\n\n s2 := 1:\n L := op(2,my_factors(p)): # L contains the *remaining* non trivial factors of p\n for i from 1 to nops(L) do\n tmp := L[i][1]: exponent := L[i][2]:\n r := gcd(tmp^exponent, subs(n=n+d, q)):\n p := quo(p, r, n): q := quo(q, subs(n=n-d, r), n): s2 := s2 * r:\n od:\n\n # Finally we look for the constant part (with respect to n) of p/q\n cste := op(1, my_factors(p))/op(1, my_factors(q)):\n p := p/op(1, my_factors(p)): q := q/op(1, my_factors(q)):\n polyring := RegularChains[PolynomialRing]([n,x]):\n L := op(2, my_factors(p)):\n for i from 1 to nops(L) do\n if RegularChains[MainVariable](L[i][1], polyring) = x\n then cste := cste * L[i][1]^L[i][2]: p := quo(p,L[i][1]^L[i][2],x):\n fi:\n od:\n L := op(2, my_factors(q)):\n for i from 1 to nops(L) do\n if RegularChains[MainVariable](L[i][1], polyring) = x\n then cste := cste / L[i][1]^L[i][2]: q := quo(q,L[i][1]^L[i][2],x):\n fi:\n od:\n\n res_cste := cste;\n res_s1 := s1;\n res_s2 := s2;\n res_p := simplify(p);\n res_q := simplify(q);\nend proc:\n\n\n#\n#coeffrecToTermsrec\n# Input: a linear recurrence rec (either with or without initial conditions).\n# a(n): the name of the sequence and the name of the variable.\n# x: a value or symbolic name\n#\n# Output:\n# The recurrence satisfied by a(n)*x^n. Note that this recurrence is also denoted by a(n).\n# If initial conditions were provided, corresponding initial conditions are computed.\n#\ncoeffrecToTermsrec := proc(rec, aofn, x)\n local a,n,L,r,cond,d,i,tmp,c,res;\n getname(aofn, a, n):\n if type(rec, 'set') then\n L := selectremove(has, rec, n):\n r := L[1]:\n if nops(r)>1\n then error `invalid recurrence`, rec\n fi:\n if nops(r)=0\n then error \"%1 does not appear in the recurrence\", n\n fi:\n r := op(r):\n cond := L[2]:\n else r := rec:\n fi:\n d := maxindex(r, a, n):\n L := indets(r,'specfunc'('linear'(n),a)):\n if indets(r,'specfunc'('anything',a)) <> L\n then error \"the recurrence contains elements that are not linear in %1\", n\n fi:\n L := map(op, L):\n for i from 1 to nops(L) do\n r := subs(a(op(i,L))=a(op(i,L))*x^(d-op(i,L)+n), r):\n od:\n if cond<>'cond' then\n c := {}:\n for i from 1 to nops(cond) do\n tmp := op(i, cond): # tmp should have the form 'a(k) = cste'\n if not type(tmp,'`=`') then error \"Invalid initial condition: %1\", tmp: fi:\n L := selectremove(has, {op(tmp)}, a):\n if (nops(L[1]) <> 1) or (nops(L[2])<>1)\n then error \"Invalid initial condition: %1\", tmp:\n fi:\n tmp := op(1, L[1]): # tmp has the form 'a(k)'\n c := {op(c), tmp = op(1, L[2])*x^op(tmp)}:\n od:\n res := {r, op(c)}:\n else res := r:\n fi:\n res:\nend proc:\n\n\n#\n# This procedure removes the conditions of the form a(k)=0 from the initial conditions of rec\n# It returns a list L = [L1, L2, ...] where Li = [k, expr] representing the condition a(k)=expr.\n# Moreover, it asserts that the Li are ordered by increasing k.\n#\nremoveTrivialConditions := proc(rec, aofn)\n local a,n,i,L,tmp,c,cond,k:\n getname(aofn, a, n):\n if not type(rec, 'set') then\n error \"%1 is not a recurrence with initial conditions\", rec\n else\n L := selectremove(has, rec, n):\n cond := L[2]:\n if nops(cond)=0\n then error \"%1 does not contain initial conditions\", rec\n fi:\n fi: \n c := []:\n for i from 1 to nops(cond) do\n tmp := op(i, cond): # tmp should have the form 'a(k) = cste'\n if not type(tmp,'`=`') then error \"Invalid initial condition: %1\", tmp: fi:\n L := selectremove(has, {op(tmp)}, a):\n if (nops(L[1]) <> 1) or (nops(L[2])<>1)\n then error \"Invalid initial condition: %1\", tmp:\n fi:\n if op(1, L[2])<>0 then c := [op(c), [op(op(1, L[1])), op(1, L[2])]]: fi:\n od:\n # We check that the conditions are ordered by increasing k.\n if (nops(c)=0) then return c: fi:\n k := c[1][1]:\n for i from 2 to nops(c) do\n if (c[i][1]<=k)\n then error \"Unexpected error in removeTrivialConditions: the conditions are not correctly ordered (%1)\\n\", c\n else k := c[i][1]\n fi:\n od:\n c:\nend proc:\n\n\n#\n# findFixpointOfDifferences: takes a set L of integer and returns the smallest set S\n# containing L and such that for each i, S[i]-S[i-1] \\in S\nfindFixpointOfDifferences := proc(L)\n local res, i:\n res := L:\n for i from 2 to nops(L) do\n res := { op(res), L[i]-L[i-1] }:\n od:\n if (res=L) then return res else return findFixpointOfDifferences(res) fi:\nend proc:\n\n\n#\n# error_counter functions allows one to follow the accumulation of errors in each variable.\n# an error_counter is a list of the form [[var1, c1], [var2, c2], ... ]\n# where the vari are variable names and the ci indicate how many approximation errors\n# are accumulated in vari.\n#\n\n#\n# This procedure initializes the counter associated with variable var to 1 (and creates it if needed.)\n# It returns an up-to-date error_counter.\ninit_error_counter := proc (var, error_counter)\n local i, res:\n res := error_counter:\n for i from 1 to nops(res) do\n if (res[i][1]=var) \n then res[i][2] := 1:\n return res:\n fi\n od:\n res := [op(res), [var, 1]]:\nend:\n\n\n#\n# This procedure adds a given number to the counter associated with variable var.\n# It returns an up-to-date error_counter.\nadd_to_error_counter := proc (var, n, error_counter)\n local i, res:\n res := error_counter:\n for i from 1 to nops(res) do\n if (res[i][1]=var) \n then res[i][2] := res[i][2]+n:\n return res:\n fi\n od:\n res := [op(res), [var, n]]:\nend proc:\n\n#\n# This procedure sets the value of the counter associated with variable var.\n# It returns an up-to-date error_counter.\nset_error_counter := proc(var, n, error_counter)\n local i,err:\n err := error_counter:\n for i from 1 to nops(err) do\n if (err[i][1]=var) \n then err[i][2] := n:\n return err:\n fi\n od:\n err := [op(err), [var, n]]: \nend proc:\n\n#\n# This procedure initializes the counter associated to the multiplication of var2 and var3,\n# putting the result in variable var1. \n# It returns an up-to-date error_counter.\nerror_counter_of_a_multiplication := proc (var1, var2, var3, error_counter)\n local i, res, c2, c3:\n c2 := 0: c3 := 0:\n for i from 1 to nops(error_counter) do\n if (error_counter[i][1]=var2) then c2 := error_counter[i][2] fi:\n if (error_counter[i][1]=var3) then c3 := error_counter[i][2] fi:\n if (error_counter[i][1]=var1)\n then\n res := [ op(error_counter[1..i-1]), op(error_counter[i+1..nops(error_counter)]) ]\n fi:\n od:\n if (res = 'res') then res := error_counter fi:\n res := [op(res), [var1, c2+c3+1]]:\nend:\n\n#\n# Copies the error counter of var2 into var1\nerror_counter_on_copy := proc(var1, var2, error_counter)\n local i, err, c2:\n c2 := 0:\n for i from 1 to nops(error_counter) do\n if (error_counter[i][1] = var2) then c2 := error_counter[i][2] fi:\n if (error_counter[i][1] = var1)\n then\n err := [ op(error_counter[1..i-1]), op(error_counter[i+1..nops(error_counter)]) ]\n fi:\n od:\n if (err = 'err') then err := error_counter fi:\n if (c2 <> 0) then err := [op(res), [var1, c2]] fi:\nend proc:\n\n\n#\n# Returns the value of the error counter associated to a variable\nfind_in_error_counter := proc(var, error_counter) \n local i:\n for i from 1 to nops(error_counter) do\n if (error_counter[i][1] = var) then return error_counter[i][2] fi:\n od:\n return 0:\nend proc:\n\n#\n# generate_multiply_rational(fd, var1, var2, r, error_counter, indent) generates code for performing\n# var1 = var2*r in MPFR\n# fd is the file descriptor in which the code shall be produced.\n# var1 and var2 are strings representing variable names. r is a Maple rational number.\n# error_counter is an error_counter (as described above).\n# indent is an optional argument. It is a string used to correctly indent the code. It is prefixed to any\n# generated line. Hence, if indent=\" \", the generated code will be indented by 2 spaces. \n# An up-to-date error_counter is returned.\ngenerate_multiply_rational := proc(fd, var1, var2, r, error_counter, indent:=\"\")\n local p,q,err:\n err := error_counter:\n if (whattype(r)<>'fraction') and (whattype(r)<>'integer')\n then error \"generate_multiply_rational used with non rational number %1\", r: fi:\n if (abs(r)=1)\n then\n if (var1=var2)\n then\n if (r<>1) then fprintf(fd, \"%sMPFR_CHANGE_SIGN (%s);\\n\", indent, var1) fi:\n return err:\n else \n if (r=1)\n then fprintf(fd, \"%smpfr_set (%s, %s, MPFR_RNDN);\\n\", indent, var1, var2):\n else fprintf(fd, \"%smpfr_neg (%s, %s, MPFR_RNDN);\\n\", indent, var1, var2):\n fi:\n return error_counter_on_copy(var1, var2, err):\n fi\n fi:\n # Now, r is a rational number different from 1.\n p := numer(r): q := denom(r):\n if (abs(p)<>1)\n then\n fprintf(fd, \"%smpfr_mul_si (%s, %s, %d, MPFR_RNDN);\\n\", indent, var1, var2, p):\n err := error_counter_of_a_multiplication(var1, var2, \"\", err):\n if(q<>1)\n then\n fprintf(fd, \"%smpfr_div_si (%s, %s, %d, MPFR_RNDN);\\n\", indent, var1, var1, q):\n err := error_counter_of_a_multiplication(var1, var1, \"\", err):\n fi:\n else\n fprintf(fd, \"%smpfr_div_si (%s, %s, %d, MPFR_RNDN);\\n\", indent, var1, var2, p*q):\n err := error_counter_of_a_multiplication(var1, var2, \"\", err):\n fi:\n return err:\nend proc:\n\n\n#\n# generate_multiply_poly is the same as generate_multiply_rational but when r is a rational fraction.\n# The fraction r must have the form p/q where p and q are polynomials with integer coefficients.\n# Moreover, the gcd of the coefficients of p must be 1. Idem for q.\n# The procedure returned a list [m, d, err] where m is the set of indices k such that\n# a mpfr_mul_sik function is needed and idem for d with mpfr_div_sik.\n# err is an up-to-date error counter.\ngenerate_multiply_poly := proc(fd, var1, var2, r, error_counter, indent:=\"\")\n local p,q,Lp,Lq,n,i,j,var, required_mulsi, required_divsi, err:\n err := error_counter:\n required_mulsi := {}:\n required_divsi := {}:\n p := numer(r): q := denom(r):\n Lp := my_factors(p): Lq := my_factors(q):\n if (Lp[1] <> 1)\n then error \"generate_multiply_poly: an integer can be factored out of %1\", p:\n fi:\n if (Lq[1] <> 1)\n then error \"generate_multiply_poly: an integer can be factored out of %1\", q:\n fi:\n Lp := Lp[2]: Lq := Lq[2]:\n var := var2:\n if (nops(Lp) <> 0)\n then\n n := 0:\n for i from 1 to nops(Lp) do n := n + Lp[i][2] od:\n if (n=1)\n then\n fprintf(fd, \"%smpfr_mul_si (%s, %s\", indent, var1, var):\n else\n required_mulsi := { op(required_mulsi), n }:\n fprintf(fd, \"%smpfr_mul_si%d (%s, %s\", indent, n, var1, var):\n fi:\n for i from 1 to nops(Lp) do\n for j from 1 to Lp[i][2] do\n fprintf(fd, \", %a\", Lp[i][1]):\n od:\n od:\n fprintf(fd, \", MPFR_RNDN);\\n\"):\n err := set_error_counter(var1, n+find_in_error_counter(var, err) , err):\n var := var1:\n fi:\n if (nops(Lq) <> 0)\n then\n n := 0:\n for i from 1 to nops(Lq) do n := n + Lq[i][2] od:\n if (n=1)\n then\n fprintf(fd, \"%smpfr_div_si (%s, %s\", indent, var1, var):\n else\n required_divsi := { op(required_divsi), n }:\n fprintf(fd, \"%smpfr_div_si%d (%s, %s\", indent, n, var1, var)\n fi:\n for i from 1 to nops(Lq) do\n for j from 1 to Lq[i][2] do\n fprintf(fd, \", %a\", Lq[i][1])\n od:\n od:\n fprintf(fd, \", MPFR_RNDN);\\n\"):\n err := set_error_counter(var1, n+find_in_error_counter(var, err) , err):\n var := var1:\n fi:\n if (var1 <> var) then\n fprintf(fd, \"%smpfr_set (%s, %s, MPFR_RNDN);\\n\", indent, var1, var):\n err := set_error_counter(var1, find_in_error_counter(var, err) , err):\n fi:\n return [required_mulsi, required_divsi, err]:\nend proc:\n\n\n#\n# This function generates the code of a procedure mpfr_mul_uin or mpfr_div_uin\n#\ngenerate_muldivsin := proc(op, n)\n local i, var:\n if ((op <> \"mul\") and (op <> \"div\"))\n then error \"Invalid argument to generate_muldivuin (%1). Must be 'mul' or 'div'\", op\n fi:\n if (whattype(n) <> 'integer')\n then error \"Invalid argument to generate_muldivuin (%1). Must be an integer.\", n\n fi:\n\n if (op=\"mul\") then var := \"MUL\" else var := \"DIV\" fi:\n\n printf(\"__MPFR_DECLSPEC void mpfr_div_si%d _MPFR_PROTO((mpfr_ptr, mpfr_srcptr,\\n\", n):\n for i from n to 2 by -2 do\n printf(\" long int, long int,\\n\"):\n od:\n if (i=1)\n then\n printf(\" long int, mpfr_rnd_t));\\n\"):\n else\n printf(\" mpfr_rnd_t));\\n\")\n fi:\n\n printf(\"\\n\\n\\n\"):\n printf(\"void\\n\"):\n printf(\"mpfr_%s_si%d (mpfr_ptr y, mpfr_srcptr x,\\n\", op, n):\n for i from n to 2 by -2 do\n printf(\" long int v%d, long int v%d,\\n\", n-i+1, n-i+2):\n od:\n if (i=1)\n then\n printf(\" long int v%d, mpfr_rnd_t mode)\\n\", n):\n else\n printf(\" mpfr_rnd_t mode)\\n\")\n fi:\n printf(\"{\\n\"):\n printf(\" long int acc = v1;\\n\"):\n printf(\" mpfr_set (y, x, mode);\\n\"):\n for i from 2 to n do\n printf(\" MPFR_ACC_OR_%s (v%d);\\n\", var, i):\n od:\n printf(\" mpfr_%s_si (y, y, acc, mode);\\n\", op):\n printf(\"}\\n\"):\n return:\nend proc:\n", "meta": {"hexsha": "7917be78bbdfde05ea4a127ac88c83a99e2bf207", "size": 16659, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_common.mpl", "max_stars_repo_name": "ekzyis/CrypTool-2", "max_stars_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 12, "max_stars_repo_stars_event_min_datetime": "2021-09-29T14:50:06.000Z", "max_stars_repo_stars_event_max_datetime": "2022-03-31T15:01:21.000Z", "max_issues_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_common.mpl", "max_issues_repo_name": "ekzyis/CrypTool-2", "max_issues_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 15, "max_issues_repo_issues_event_min_datetime": "2021-12-24T22:53:49.000Z", "max_issues_repo_issues_event_max_datetime": "2021-12-25T10:03:13.000Z", "max_forks_repo_path": "LibSource/mpfr/tools/metaMPFR/metaMPFR_common.mpl", "max_forks_repo_name": "ekzyis/CrypTool-2", "max_forks_repo_head_hexsha": "1af234b4f74486fbfeb3b3c49228cc36533a8c89", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 10, "max_forks_repo_forks_event_min_datetime": "2021-10-17T19:46:51.000Z", "max_forks_repo_forks_event_max_datetime": "2022-03-18T02:57:57.000Z", "avg_line_length": 31.9137931034, "max_line_length": 112, "alphanum_fraction": 0.6130019809, "num_tokens": 5409, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.5583269943353745, "lm_q2_score": 0.6688802537704064, "lm_q1q2_score": 0.37345390165791353}} {"text": "`is_element/SW` := eval(`is_element/prime_simplex_boundary`);\n`is_equal/SW` := eval(`is_equal/prime_simplex_boundary`);\n`is_leq/SW` := NULL;\n`random_element/SW` := eval(`random_element/prime_simplex_boundary`);\n`list_elements/SW` := NULL;\n`count_elements/SW` := NULL;\n`phi/nonempty_subsets/SW` := eval(`phi/nonempty_subsets/prime_simplex_boundary`);\n", "meta": {"hexsha": "2e6c16796b1cec9eddfbcbc06e5bf03ae4890cf7", "size": 350, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/scratch/SW.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/SW.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/SW.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": 43.75, "max_line_length": 81, "alphanum_fraction": 0.7571428571, "num_tokens": 102, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.6370307944803831, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.3727274531134735}} {"text": "var nTimes : int := 0;\nprint \"How many times? \";\nread nTimes;\nvar x : int;\nfor x in 0..nTimes-1 do\n print x;\n print \" : Hello, World!\\n\";\nend for;\nassert (x = nTimes);\n", "meta": {"hexsha": "2ab8d438168806314e0a21ba93bb4daebb92e12c", "size": 174, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "loopExample.mpl", "max_stars_repo_name": "jgke/miniplc", "max_stars_repo_head_hexsha": "6b340edd0fc0f69a68e0100dfcf89b18e179e7cc", "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": "loopExample.mpl", "max_issues_repo_name": "jgke/miniplc", "max_issues_repo_head_hexsha": "6b340edd0fc0f69a68e0100dfcf89b18e179e7cc", "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": "loopExample.mpl", "max_forks_repo_name": "jgke/miniplc", "max_forks_repo_head_hexsha": "6b340edd0fc0f69a68e0100dfcf89b18e179e7cc", "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": 17.4, "max_line_length": 31, "alphanum_fraction": 0.5977011494, "num_tokens": 61, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.640635854839898, "lm_q2_score": 0.5813030906443133, "lm_q1q2_score": 0.3724036023959944}} {"text": "with(LinearAlgebra): with(ArrayTools): with(QuantumChemistry):\nloaddata := readdata(cat(cdir,\"_temp.rdm\"), 8):\nFlatten := proc(x) local n, a, i, j, k, l; `local`(a, n, i, j, k, l); `description`(\"convert chemists to numpy and flatten an array to form a matrix\"); n := Size(x); a := Matrix(1 .. n[1]*n[2], 1 .. n[3]*n[4], datatype = float[8]); for i to round(n[1]) do for j to round(n[2]) do for k to round(n[3]) do for l to round(n[4]) do a[(i - 1)*n[1] + j, (k - 1)*n[3] + l] := x[i, j, k, l]; end do; end do; end do; end do; return a; end proc:\nNew := Array(1 .. 4, 1 .. 4, 1 .. 4, 1 .. 4, datatype = float[8]):\nfor i in loaddata[3 .. ()] do\n New[round(i[1]), round(i[2]), round(i[3]), round(i[4])] := i[5]:\nend do:\npure := Purify2RDM(New, spin_free = false, electron_number = 4, conv_tol = 0.10000000):\nExportMatrix(cat(cdir, \"_temp_purified.csv\"), Flatten(pure[rdm2])):\n\n\n\n", "meta": {"hexsha": "014c5bbcb6fc0e81194e082c10f31157d9fb434a", "size": 880, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "hqca/maple/old/spin_input.mpl", "max_stars_repo_name": "damazz/HQCA", "max_stars_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "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": "hqca/maple/old/spin_input.mpl", "max_issues_repo_name": "damazz/HQCA", "max_issues_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "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": "hqca/maple/old/spin_input.mpl", "max_forks_repo_name": "damazz/HQCA", "max_forks_repo_head_hexsha": "b013ba68f86e42350913c4abc2e1c91695a429b7", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2021-08-10T00:20:09.000Z", "max_forks_repo_forks_event_max_datetime": "2021-08-10T00:20:09.000Z", "avg_line_length": 67.6923076923, "max_line_length": 435, "alphanum_fraction": 0.5988636364, "num_tokens": 341, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO\n\n", "lm_q1_score": 0.7490872131147275, "lm_q2_score": 0.49609382947091946, "lm_q1q2_score": 0.37161754416178394}} {"text": " func $liori32 (\n var %i i32, var %j i32\n ) i32 { \n return (\n lior i32(dread i32 %i, dread i32 %j))}\n\n func $liori64 (\n var %i i64, var %j i64\n ) i32 { \n return (\n lior i64(dread i64 %i, dread i64 %j))}\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "900ffdf6706556ad56c9170525f2e0a7f332c8ea", "size": 321, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0051-mapleall-irbuild-edge-lior/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/I0051-mapleall-irbuild-edge-lior/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/I0051-mapleall-irbuild-edge-lior/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": 21.4, "max_line_length": 43, "alphanum_fraction": 0.5825545171, "num_tokens": 133, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.600188359260205, "lm_q2_score": 0.6187804337438501, "lm_q1q2_score": 0.37138481327103934}} {"text": "# Extract a domain from an expression\nexport Extract := module ()\n export ModuleApply := proc(e, kb, $) :: [ HDomain, anything ];\n local b, eb, s, es;\n b, eb := op(Bound(e));\n s, es := op(Shape(eb, kb ));\n [ DOMAIN(b, s), es ];\n end proc;\n\n # Extract a domain bound from an expression\n # This pops off the integration constructors recursively, keeping\n # track of the bounds in a KB (which literally become the DBound).\n export Bound := module ()\n export ModuleApply := proc(e, $) :: [ DomBound, anything ];\n local arg, vars, kb;\n arg, vars := do_extract(e)[];\n vars := Domain:-Bound:-withVarsIxs(DBound(vars));\n [ vars , arg ];\n end proc;\n\n local do_extract_arg := proc(kind, arg_)\n local x0, x, vars, arg := arg_, rng;\n x0 := ExtBound[kind]:-ExtractVar(_rest); # variable name\n rng := ExtBound[kind]:-ExtractRange(_rest); # variable range\n x := DInto(x0, rng, kind); # the variable spec\n arg, vars := do_extract(arg)[];\n [ arg, [ op(vars), x ] ];\n end proc;\n\n local do_extract := proc(arg, $)\n local sub, prod, svars;\n if arg :: `*` then\n sub := map(do_extract, [op(arg)]);\n prod, svars := selectremove(x->op(2,x)=[],sub);\n if nops(svars) = 1 then\n [ `*`(op([1,1],svars),op(map2(op,1,prod)))\n , op([1,2], svars) ];\n else\n [ arg, [] ];\n end if;\n elif Domain:-Has:-Bound(arg) then\n do_extract_arg(op(0,arg), op(arg));\n else\n [ arg, [] ]\n end if;\n end proc;\n end module;\n\n # Extract a domain shape from an expression\n # This extracts the domain shape from individual multiplicands of\n # expressions, and multiplies the subexpressions back together.\n # essentially this assumes a distributive law (of domain shapes over\n # products)\n export Shape := module ()\n export ModuleApply := proc(e) :: [ anything, anything ];\n local ixs, w, e1;\n ixs := [indices(ExtShape, 'nolist')];\n w, e1 := do_gets(ixs, true, e) [];\n if not ('no_simpl' in {_rest}) then\n w := simpl_shape(w);\n end if;\n [ w, e1 ];\n end proc;\n\n local do_get := proc(f, f_ty, e, $)\n local sub, inds, rest;\n if e::`*` then\n sub := map(x->do_get(f, f_ty,x), [op(e)]);\n [ `And`(op(map2(op,1,sub))), `*`(op(map2(op,2,sub))) ]\n elif e::`^` then\n inds, rest := do_get(f, f_ty, op(1,e)) [] ;\n [ inds, subsop(1=rest, e) ]\n elif e:: f_ty then\n f(e,z->ModuleApply(z,'no_simpl'))\n else\n [ true, e ]\n end if\n end proc;\n\n # apply a list of extractors, in order, until all fail to produce\n # any output .\n local do_gets := proc(todo::list, w, e, $)\n local t0, ts, w1, e1;\n if nops(todo) = 0 then\n [ w, e ]\n else\n t0 := op(1, todo);\n ts := op(subsop(1=NULL, todo));\n w1, e1 := do_get(ExtShape[t0]:-MakeCtx\n ,ExtShape[t0]:-MapleType\n ,e) [] ;\n ts := `if`(is(w1), [ts], [ts, t0]);\n do_gets( ts, bool_And(w1, w), e1 );\n end if;\n end proc;\n\n # todo: simplify the shape\n local simpl_shape := proc(e0,$)\n local e := Domain:-simpl_relation(e0);\n e := subsindets(e, specfunc(`Or`) , x->DSum(op(x)));\n e := subsindets(e, specfunc(`And`), x->DConstrain(op(x)));\n e;\n end proc;\n end module;\nend module;\n", "meta": {"hexsha": "045b3b2c98fd3fe9bd86c67faa55fe890d847147", "size": 3935, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/Domain/Extract.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/Extract.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/Extract.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": 37.1226415094, "max_line_length": 75, "alphanum_fraction": 0.4648030496, "num_tokens": 1028, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.679178699175393, "lm_q2_score": 0.5467381519846138, "lm_q1q2_score": 0.37133290685446835}} {"text": "with(Threads):\nid:=Create(int(sin(x)^x,x),res);\nres;\nWait(id);\nres;", "meta": {"hexsha": "fc4ba7bbab2f350911b92e6522063270762290a1", "size": 67, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "Thread/create.mpl", "max_stars_repo_name": "yu961549745/MapleParallel", "max_stars_repo_head_hexsha": "6fe9ceb7766e0803761ab7368caa9b3f856dcf5b", "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": "Thread/create.mpl", "max_issues_repo_name": "yu961549745/MapleParallel", "max_issues_repo_head_hexsha": "6fe9ceb7766e0803761ab7368caa9b3f856dcf5b", "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": "Thread/create.mpl", "max_forks_repo_name": "yu961549745/MapleParallel", "max_forks_repo_head_hexsha": "6fe9ceb7766e0803761ab7368caa9b3f856dcf5b", "max_forks_repo_licenses": ["MIT"], "max_forks_count": null, "max_forks_repo_forks_event_min_datetime": null, "max_forks_repo_forks_event_max_datetime": null, "avg_line_length": 13.4, "max_line_length": 32, "alphanum_fraction": 0.6417910448, "num_tokens": 23, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7122321842389469, "lm_q2_score": 0.519521321952093, "lm_q1q2_score": 0.3700198058926443}} {"text": "$ifndef _INVSOL_\n$define _INVSOL_\n\nInvSol:=module()\n option object;\n export \n # \u516c\u7528\u53d8\u91cf\n As::static, # \u6bcf\u4e2a\u751f\u6210\u5143\u7684\u4f34\u968f\u77e9\u9635\n A::static, # \u603b\u7684\u4f34\u968f\u77e9\u9635\n nvars::static, # \u603b\u7684\u53d8\u91cf\u4e2a\u6570\n # \u5b9e\u4f8b\u53d8\u91cf\n state, # \u72b6\u6001\u4ee3\u7801\uff0c\u4e3b\u8981\u4e3a\u4eba\u5de5\u5e72\u9884\u63d0\u4f9b\u5165\u53e3\n # 0\uff1a\u8fd8\u672a\u751f\u6210\u4e0d\u53d8\u91cf\u65b9\u7a0b\n # 1\uff1a\u4e0d\u53d8\u91cf\u65b9\u7a0b\u6c42\u89e3\u5931\u8d25\n # 2\uff1a\u53d6\u7279\u89e3\u5931\u8d25 \n # 3\uff1a\u53d8\u6362\u65b9\u7a0b\u6c42\u89e3\u5931\u8d25\n # 4\uff1a\u7b49\u5f85\u9009\u62e9\u6700\u4f18\u4ee3\u8868\u5143\n # 5\uff1a\u6c42\u89e3\u5b8c\u6210 \n oeq::static, # \u504f\u5fae\u5206\u65b9\u7a0b\u7ec4\uff0c\n # \u8fed\u4ee3\u8fc7\u7a0b\u4e2doeq\u4fdd\u6301\u4e0d\u53d8\n # \u901a\u8fc7\u53d8\u91cf\u4ee3\u6362\u6765\u83b7\u53d6\u5b9e\u9645\u7684oeq\n Deltas:=[], # \u4e0d\u53d8\u91cf\n orders:=[], # \u4e0d\u53d8\u91cf\u7684\u9636\u6570\n ieq:=[], # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7a0b\u7ec4\uff0c\u6309\u4e0d\u53d8\u91cf\u6392\u5e8f\n ieqCode:=0, # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u7f16\u53f7\n isols:=[], # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7ec4\u7684\u89e3\n icons:=[], # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7ec4\u5bf9\u5e94\u7684\u6761\u4ef6\n isolInd:=1, # \u901a\u89e3\u7684\u4e0b\u6807\n useBranch:=false,# \u4f7f\u7528\u5206\u652f\u6c42\u89e3\u5219\u5047\u8bbe\u6bcf\u4e2a\u7279\u89e3\u90fd\u662f\u4e0d\u7b49\u4ef7\u7684\n rsols:=[], # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u7279\u89e3\n tsols:=[], # TeqSol\u5bf9\u8c61list\n tsolsList, # TsolsList \u5bf9\u8c61\n rep, # \u4ee3\u8868\u5143\n # \u6700\u4f18\u53d8\u6362\u65b9\u7a0b\u7684\u89e3\n teq,\n tInd, \n tsol,\n tcon,\n\n vars, # \u9700\u8981\u6c42\u89e3\u7684\u7cfb\u6570\n # \u6761\u4ef6\u76f8\u5173\n # \u4e0d\u53d8\u91cf\u65b9\u7a0b+\u9644\u52a0\u7ea6\u675f+\u5c55\u793a\u7ea6\u675f\uff0c\u63cf\u8ff0\u4e86\u4ee3\u8868\u5143\u6240\u4ee3\u8868\u7684\u5143\u7d20\u7684\u8303\u56f4\n # \u540e\u671f\u53ea\u7ef4\u62a4\u4ee5\u4e0b\u53d8\u91cf\uff0c\u800c\u4e0d\u4fee\u6539icons,tcons\u7b49\u539f\u59cb\u4fe1\u606f\n addcons:={}, # \u9644\u52a0\u7ea6\u675f\uff0c\u80fd\u591f\u53c2\u4e0e\u8ba1\u7b97\uff0c\u5176\u4e2d\uff0c\n # + \u7b49\u5f0f\u662f\u5bf9\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u6269\u5145\uff0c\u4f8b\u5982a[1]=0\n # + \u4e0d\u7b49\u5f0f\u5f0f\u5bf9\u53d6\u503c\u8303\u56f4\u7684\u63cf\u8ff0\uff0c\u5e76\u80fd\u591f\u8fdb\u884c\u5904\u7406\uff0c\u4f8b\u5982a[1]>0\n discons:={}, # \u5c55\u793a\u7ea6\u675f\uff0c\u4ec5\u7528\u4e8e\u5c55\u793a\u4fe1\u606f\uff0c\u4e0d\u80fd\u53c2\u4e0e\u8ba1\u7b97\uff0c\u5305\u62ec\n # + a[1]*a[3]>0 \u8fd9\u79cd\u4e0d\u80fd\u5904\u7406\u7684\u591a\u53d8\u91cf\u7ea6\u675f\n # \u5bfc\u51fa\u51fd\u6570\n getSubs::static, # \u5728\u6c42\u89e3\u65b0\u7684\u4e0d\u53d8\u91cf\u65f6\u4ee3\u5165\u7684\u6761\u4ef6\n updateVars::static, # \u66f4\u65b0\u6c42\u89e3\u53d8\u91cf \n getRealOeq::static, # \u83b7\u53d6\u4ee3\u6362\u540e\u7684oeq\n getZeroCons::static, # \u83b7\u53d6\u4e3a\u96f6\u7ea6\u675f\n addZeroCons::static, # \u6dfb\u52a0\u4e3a\u96f6\u7ea6\u675f\n getIsolCons::static, # \u8fd4\u56de\u901a\u89e3\u7684\u7ea6\u675f\n displayIeq::static, # \u663e\u793a\u4e0d\u53d8\u91cf\u65b9\u7a0b\n printSol::static,\n getDisplayIeq::static,\n getDisplayCons::static,\n uniqueKey::static,\n ModulePrint::static; # \u663e\u793a\u51fd\u6570\n\n getIsolCons:=proc(s::InvSol)\n return s:-addcons union s:-discons union s:-icons[s:-isolInd];\n end proc:\n\n ModulePrint:=proc(s::InvSol)\n if s:-state<5 then\n return sprintf(\"unsolved %d\",s:-state);\n else\n return s:-rep;\n end if;\n end proc:\n\n uniqueKey:=proc(s::InvSol)\n return ModulePrint(s);\n end proc:\n\n printSol:=proc(s::InvSol)\n if s:-state<5 then\n printf(\"\u6c42\u89e3\u5931\u8d25 %d\",s:-state);\n else\n printf(\"--------------------------------\\n\");\n print(s:-rep);\n print(getDisplayCons(s));\n if s:-isols<>[] then\n print(s:-isols[s:-isolInd]);\n print(s:-tsol);\n print(s:-tcon);\n end if;\n end if;\n end proc:\n\n getDisplayIeq:=proc(s::InvSol)\n return [seq(Delta[i]=rhs(s:-ieq[i]),i=1..numelems(s:-ieq))];\n end proc:\n\n getDisplayCons:=proc(s::InvSol)\n local res:={};\n if s:-isols<>[] then\n res:=res union s:-icons[s:-isolInd];\n end if;\n res:=res union s:-addcons union s:-discons;\n res:=res minus convert(s:-ieq,set);\n return [getDisplayIeq(s)[],res[]];\n end proc:\n \n getSubs:=proc(s::InvSol)\n local r;\n r:=getZeroCons(s);\n r:=[r[]];\n if s:-isols<>[] then\n r:=[r[],s:-isols[s:-isolInd][]];\n end if;\n return remove(x->evalb(lhs(x)=rhs(x)),{r[]});\n end proc:\n\n updateVars:=proc(s::InvSol)\n s:-vars:=s:-vars minus indets(lhs~(getSubs(s)),name);\n end proc:\n\n getRealOeq:=proc(s::InvSol)\n local oeq:=s:-oeq;\n updateVars(s);\n oeq:=PDETools:-dsubs(phi(seq(a[i],i=1..s:-nvars))=phi(s:-vars[]),oeq);\n oeq:=eval(subs(getSubs(s)[],oeq)) minus {0};\n return oeq;\n end proc:\n\n getZeroCons:=proc(s::InvSol)\n return select(type,s:-addcons,equation);\n end proc:\n\n addZeroCons:=proc(s::InvSol,c::set)\n s:-addcons:=s:-addcons union c;\n s:-vars:=s:-vars minus indets(c,name);\n end proc:\n\n displayIeq:=proc(s::InvSol)\n local n;\n n:=numelems(s:-ieq);\n flog[1]([seq(Delta[i]=rhs(s:-ieq[i]),i=1..n)]);\n flog[1]([seq(Delta[i]=s:-Deltas[i],i=1..n)]);\n end proc:\n \nend module:\n\n$endif\n", "meta": {"hexsha": "d6f1ab926ec796383e4699fa2fabbee0b94dc68b", "size": 4513, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/InvSol.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/InvSol.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/InvSol.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": 30.288590604, "max_line_length": 78, "alphanum_fraction": 0.446931088, "num_tokens": 1544, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.7279754489059774, "lm_q2_score": 0.5078118642792044, "lm_q1q2_score": 0.3696745698584351}} {"text": "#struct aa{\n# double b;\n# float *x;\n#};\n\n#struct bb {\n# struct aa b1;\n# struct aa *pa;\n# double x1[10];\n# double dx;\n#};\n\n#typedef struct ss {\n# int f1;\n# char f2:3;\n# struct aa a3;\n# struct aa *pa1;\n# char f3:5;\n# struct bb *b3;\n# struct bb *b2;\n# struct aa xt[23];\n# struct aa(* funcc)(int, int, double);\n#}SS;\n\ntype $unname1 }>\ntype $unname2 }>,\n @pa <* }>>, \n @x1 <[10] f64>,\n @dx f64}>\ntype $SS }>,\n @pa1 <* } >>,\n @f3:5 i32,\n @b3 <* }>,\n @pa <* }>>,\n @x1 <[10] f64>,\n @dx f64}>>,\n @b2 <* $unname2>,\n @xt <[23] }>>,\n @funcc }>>}>\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": "8ec155e6f829f1a086a61fa49f3f0df909bddc44", "size": 1732, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0073-mapleall-irbuild-edge-struct_type/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/I0073-mapleall-irbuild-edge-struct_type/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/I0073-mapleall-irbuild-edge-struct_type/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": 31.4909090909, "max_line_length": 74, "alphanum_fraction": 0.2990762125, "num_tokens": 459, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6297745935070808, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.3684818415488637}} {"text": " func $cvtu64tof64 (\n var %i u64\n ) f64 { \n return (\n cvt f64 u64(dread u64 %i))}\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "8cfabdb80ae05938b81b862982b79bb3bcdccb07", "size": 192, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0021-mapleall-irbuild-edge-cvtllutof64/Main.mpl", "max_stars_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_stars_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 796, "max_stars_repo_stars_event_min_datetime": "2019-08-30T16:20:33.000Z", "max_stars_repo_stars_event_max_datetime": "2021-12-25T14:45:06.000Z", "max_issues_repo_path": "test/testsuite/irbuild_test/I0021-mapleall-irbuild-edge-cvtllutof64/Main.mpl", "max_issues_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_issues_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 16, "max_issues_repo_issues_event_min_datetime": "2019-08-30T18:04:08.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-19T05:02:58.000Z", "max_forks_repo_path": "test/testsuite/irbuild_test/I0021-mapleall-irbuild-edge-cvtllutof64/Main.mpl", "max_forks_repo_name": "harmonyos-mirror/OpenArkCompiler-test", "max_forks_repo_head_hexsha": "1755550ea22eb185cbef8cc5864fa273caebf95a", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 326, "max_forks_repo_forks_event_min_datetime": "2019-08-30T16:11:29.000Z", "max_forks_repo_forks_event_max_datetime": "2021-11-26T12:31:17.000Z", "avg_line_length": 21.3333333333, "max_line_length": 43, "alphanum_fraction": 0.6145833333, "num_tokens": 80, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.5660185498374789, "lm_q2_score": 0.647798211152541, "lm_q1q2_score": 0.3666658040638742}} {"text": "$ifndef _TEST_H_\n$define _TEST_H_\nsign:=proc(x)\n if x>0 then\n 1\n elif x<0 then\n -1\n else\n 0\n end if;\nend proc:\n$endif", "meta": {"hexsha": "ca775b3c1715d795dd4bcff1e0a2432f1a794986", "size": 150, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/test2.mpl", "max_stars_repo_name": "yu961549745/VSCodeHighlightForMaple", "max_stars_repo_head_hexsha": "4636e7754a48f621e7750ae61f26e70eacc52267", "max_stars_repo_licenses": ["Apache-2.0"], "max_stars_count": 8, "max_stars_repo_stars_event_min_datetime": "2016-10-13T19:09:27.000Z", "max_stars_repo_stars_event_max_datetime": "2021-09-10T10:04:02.000Z", "max_issues_repo_path": "test/test2.mpl", "max_issues_repo_name": "yu961549745/VSCodeHighlightForMaple", "max_issues_repo_head_hexsha": "4636e7754a48f621e7750ae61f26e70eacc52267", "max_issues_repo_licenses": ["Apache-2.0"], "max_issues_count": 5, "max_issues_repo_issues_event_min_datetime": "2017-11-19T03:21:15.000Z", "max_issues_repo_issues_event_max_datetime": "2021-09-22T08:18:42.000Z", "max_forks_repo_path": "test/test2.mpl", "max_forks_repo_name": "yu961549745/VSCodeHighlightForMaple", "max_forks_repo_head_hexsha": "4636e7754a48f621e7750ae61f26e70eacc52267", "max_forks_repo_licenses": ["Apache-2.0"], "max_forks_count": 1, "max_forks_repo_forks_event_min_datetime": "2018-09-12T22:47:10.000Z", "max_forks_repo_forks_event_max_datetime": "2018-09-12T22:47:10.000Z", "avg_line_length": 12.5, "max_line_length": 17, "alphanum_fraction": 0.5266666667, "num_tokens": 55, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.546738151984614, "lm_q2_score": 0.6688802603710085, "lm_q1q2_score": 0.3657023574542326}} {"text": "$ifndef _CLASSIFY_HOLDER_\n$define _CLASSIFY_HOLDER_\n\n$include \"Utils.mpl\"\nClassifyHolder:=module()\n local ieqCode,sols,unsolvedSols;\n export reset, # \u91cd\u7f6e\u72b6\u6001\n addSol, # \u65b0\u589e\u89e3\n getSols, # \u83b7\u53d6\u89e3\n addUnsolvedSol,\n getUnsolvedSols,\n getIeqCode; # \u83b7\u53d6\u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u7f16\u53f7\n \n reset:=proc()\n ieqCode:=0;\n sols:={};\n unsolvedSols:={};\n return;\n end proc:\n\n addSol:=proc(s::InvSol)\n flogf[1](\"\u6dfb\u52a0\u4ee3\u8868\u5143\");\n flog[1](s:-rep);\n sols:=sols union {s};\n return;\n end proc:\n\n getSols:=proc()\n local res:=sols;\n res:=uniqueObj(res,InvSol:-uniqueKey);\n res:=sort(res,'key'=(x->x:-ieqCode));\n return res;\n end proc:\n\n getIeqCode:=proc()\n ieqCode:=ieqCode+1;\n return ieqCode;\n end proc:\n\n addUnsolvedSol:=proc(s)\n unsolvedSols:=unsolvedSols union {s};\n return;\n end proc:\n\n getUnsolvedSols:=proc()\n return unsolvedSols;\n end proc:\n\nend module:\n\n$endif\n", "meta": {"hexsha": "81788bace9590fdcc5cdd870afd0596e364e687e", "size": 1042, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "InvClassify/ClassifyHolder.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/ClassifyHolder.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/ClassifyHolder.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": 20.0384615385, "max_line_length": 46, "alphanum_fraction": 0.5393474088, "num_tokens": 325, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.603931819468636, "lm_q2_score": 0.6039318337259583, "lm_q1q2_score": 0.36473365117714773}} {"text": "# Step 2 of 3: computer algebra\n\nimprove := proc(lo :: LO(name, anything), {_ctx :: t_kb := empty}, opts := [], $)\nlocal r, `&context`;\n userinfo(5, improve, \"input: \", print(lo &context _ctx));\n _Env_HakaruSolve := true;\n r:= LO(op(1,lo), reduce(op(2,lo), op(1,lo), _ctx, opts));\n userinfo(5, improve, \"output: \", print(r));\n r\nend proc;\n\n# Walk through integrals and simplify, recursing through grammar\n# h - name of the linear operator above us\n# kb - domain information\nreduce := proc(ee, h :: name, kb :: t_kb, opts := [], $)\n local e, elim, subintegral, w, ww, x, c, kb1, with_kb1, dom_specw, dom_specb\n , body, dom_spec, ed, mkDom, vars, rr\n , do_domain := evalb( not ( \"no_domain\" in {op(opts)} ) ) ;\n e := ee;\n\n if do_domain then\n rr := reduce_Integrals(e, h, kb, opts);\n if rr <> FAIL then return rr end if;\n end if;\n if e :: 'applyintegrand(anything, anything)' then\n map(simplify_assuming, e, kb)\n elif e :: `+` then\n map(reduce, e, h, kb, opts)\n elif e :: `*` then\n (subintegral, w) := selectremove(depends, e, h);\n if subintegral :: `*` then error \"Nonlinear integral %1\", e end if;\n subintegral := convert(reduce(subintegral, h, kb, opts), 'list', `*`);\n (subintegral, ww) := selectremove(depends, subintegral, h);\n simplify_factor_assuming(`*`(w, op(ww)), kb)\n * `*`(op(subintegral));\n elif e :: Or(Partition,t_pw) then\n if e :: t_pw then e := PWToPartition(e); end if;\n e := Partition:-Simpl(e);\n e := kb_Partition(e, kb, simplify_assuming,\n ((rhs, kb) -> %reduce(rhs, h, kb, opts)));\n e := eval(e, %reduce=reduce);\n # big hammer: simplify knows about bound variables, amongst many\n # other things\n Testzero := x -> evalb(simplify(x) = 0);\n e := Partition:-Simpl(e);\n if ee::t_pw and e :: Partition then\n e := Partition:-PartitionToPW(e);\n end if;\n e;\n elif e :: t_case then\n subsop(2=map(proc(b :: Branch(anything, anything))\n eval(subsop(2='reduce'(op(2,b),x,c,opts),b),\n {x=h, c=kb})\n end proc,\n op(2,e)),\n e);\n elif e :: 'Context(anything, anything)' then\n kb1 := assert(op(1,e), kb);\n # A contradictory `Context' implies anything, so produce 'anything'\n # In particular, 42 :: t_Hakaru = false, so a term under a false\n # assumption should never be inspected in any way.\n if kb1 :: t_not_a_kb then\n return 42\n end if;\n applyop(reduce, 2, e, h, kb1, opts);\n elif e :: 'toLO:-integrate(anything, Integrand(name, anything), list)' then\n x := gensym(op([2,1],e));\n # If we had HType information for op(1,e),\n # then we could use it to tell kb about x.\n subsop(2=Integrand(x, reduce(subs(op([2,1],e)=x, op([2,2],e)), h, kb, opts)), e)\n else\n simplify_assuming(e, kb)\n end if;\nend proc;\n\n# \"Integrals\" refers to any types of \"integrals\" understood by domain (Int,\n# Sum currently)\nreduce_Integrals := module()\n export ModuleApply;\n local\n # The callbacks passed by reduce_Integrals to Domain:-Reduce\n reduce_Integrals_body, reduce_Integrals_into\n # tries to evaluate a RootOf\n , try_eval_Root\n # tries to evaluate Int/Sum/Ints/Sums\n , elim_intsum;\n\n reduce_Integrals_body := proc(h,opts,x,kb1) reduce(x,h,kb1,opts) end proc;\n reduce_Integrals_into := proc(h,opts,kind,e,vn,vt,kb,$)\n local rr;\n rr := elim_intsum(Domain:-Apply:-do_mk(args[3..-1]), h, kb,opts);\n rr := subsindets(rr, specfunc(RootOf), x->try_eval_Root(x,a->a));\n return rr;\n end proc;\n\n ModuleApply := proc(expr, h, kb, opts, $)\n local rr;\n rr := Domain:-Reduce(expr, kb\n ,curry(reduce_Integrals_into,h,opts)\n ,curry(reduce_Integrals_body,h,opts)\n ,(_->:-DOM_FAIL));\n rr := kb_assuming_mb(Partition:-Simpl)(rr, kb, x->x);\n if has(rr, :-DOM_FAIL) then\n return FAIL;\n elif has(rr, FAIL) then\n error \"Something strange happened in reduce_Integral(%a, %a, %a, %a)\\n%a\"\n , expr, kb, kb, opts, rr;\n end if;\n rr;\n end proc;\n\n try_eval_Root := proc(e0::specfunc(`RootOf`),on_fail := (_->FAIL), $)\n local ix,e := e0;\n try\n if nops(e)=2 or nops(e)=3\n and op(-1,e) :: `=`(identical(index),{specindex(real),nonnegint}) then\n ix := op([2,-1],e);\n if ix :: specindex(real) then ix := op(ix); end if;\n e := op(0,e)(op(1,e));\n else\n ix := NULL;\n end if;\n e := convert(e, 'radical', ix);\n if e :: specfunc(RootOf) then return on_fail(e) end if;\n return e;\n catch: return on_fail(e0); end try;\n end proc;\n\n # Try to find an eliminate (by evaluation, or simplification) integrals which\n # are free of `applyintegrand`s.\n elim_intsum := module ()\n export ModuleApply := proc(inert0, h :: name, kb :: t_kb, opts, $)\n local ex, e, inert := inert0;\n ex := extract_elim(inert, h, kb);\n e[0] := apply_elim(h, kb, ex);\n e[1] := check_elim(inert, e[0]);\n if e[1] = FAIL then inert\n else\n e[2] := reduce(e[1],h,kb,opts);\n if has(e[2], {csgn}) then\n WARNING(\"Throwing away an eliminated result result containing csgn (this \"\n \"could be a bug!):\\n%1\\n(while running %2)\", e[2], ex);\n inert;\n else e[2] end if;\n end if\n end proc;\n\n local known_tys := table([Int=int_assuming,Sum=sum_assuming,Ints=ints,Sums=sums]);\n local extract_elim := proc(e, h::name, kb::t_kb,$)\n local t, intapps, var, f, e_k, e_args, vs, blo, bhi;\n vs := {op(KB:-kb_to_variables(kb))};\n t := 'applyintegrand'('identical'(h), 'anything');\n intapps := indets(op(1,e), t);\n if intapps = {} then\n return FAIL;\n end if;\n e_k := op(0,e); e_args := op([2..-1],e);\n if Domain:-Has:-Bound(e) and assigned(known_tys[e_k]) then\n var := Domain:-ExtBound[e_k]:-ExtractVar(e_args);\n ASSERT(var::DomBoundVar);\n blo, bhi := Domain:-ExtBound[e_k]:-SplitRange\n (Domain:-ExtBound[e_k]:-ExtractRange(e_args));\n if ormap(b->op(1,b) in map((q-> (q,-q)), vs) and op(2,b)::SymbolicInfinity\n ,[[blo,bhi],[bhi,blo]]) then\n return FAIL end if;\n if var :: list then var := op(1,var) end if;\n if not depends(intapps, var) then\n f := known_tys[e_k];\n else\n return FAIL;\n end if;\n end if;\n [ op(1,e), f, var, [e_args] ];\n end proc;\n\n local apply_elim := proc(h::name,kb::t_kb,todo::{list,identical(FAIL)})\n local body, f, var, rrest;\n if todo = FAIL then return FAIL; end if;\n body, f, var, rrest := op(todo);\n banish(body, h, kb, infinity, var,\n proc (kb1,g,$) do_elim_intsum(kb1, f, g, op(rrest)) end proc);\n end proc;\n\n local check_elim := proc(e, elim,$)\n if has(elim, {MeijerG, undefined, FAIL}) or e = elim or elim :: SymbolicInfinity then\n return FAIL;\n end if;\n return elim;\n end proc;\n\n local do_elim_intsum := proc(kb, f, ee, v::{name,name=anything})\n local w, e, x, g, t, r;\n w, e := op(Domain:-Extract:-Shape(ee));\n w := Domain:-Shape:-toConstraints(w);\n e := piecewise_And(w, e, 0);\n e := f(e,v,_rest,kb);\n x := `if`(v::name, v, lhs(v));\n g := '{sum, sum_assuming, sums}';\n if f in g then\n t := {'identical'(x),\n 'identical'(x) = 'Not(range(Not({SymbolicInfinity, undefined})))'};\n else\n g := '{int, int_assuming, ints}';\n t := {'identical'(x),\n 'identical'(x) = 'anything'};\n if not f in g then g := {f} end if;\n end if;\n for r in indets(e, 'specfunc'(g)) do\n if 1 module()\n option record;\n export MakeKB := (`if`(kind=Sum,KB:-genSummation,KB:-genLebesgue));\n export ExtractVar := (e->op(1,e));\n export ExtractRange := (e->op(2,e));\n export MakeRange := `..`;\n export SplitRange := (e->op(e));\n export Constrain := `if`(kind=Sum,`<=`,`<`);\n export DoMk := ((e,v,t)->kind(e,v=t));\n export Min := `min`; export Max := `max`;\n export VarType := 'name';\n export RangeType := 'range';\n export MapleType := 'And'('specfunc'(kind), 'anyfunc(anything,name=range)');\n export BoundType := `if`(kind=Sum,'integer','real');\n export RecogBound := `if`(kind=Sum,\n (proc(k,b)\n if k = `<=` then (x->subsop(2=b,x))\n elif k = `>=` then (x->subsop(1=b,x))\n elif k = `<` then (x->subsop(2=(b-1),x))\n elif k = `>` then (x->subsop(1=b+1,x))\n end if;\n end proc),\n (proc(k,b)\n if k in {`<=`,`<`} then (x->subsop(2=b,x))\n elif k in {`>=`,`>`} then (x->subsop(1=b,x))\n end if;\n end proc));\nend module;\n\n# Ints( .., var::name, var_ty::range, dims::list(name=range) ) ==\n# [ var , map(lhs,dims) ] :: list(name) &X\n# [ var_ty, map(rhs,dims) ] :: list(range)\nisBound_IntsSums := kind -> module()\n option record;\n export MakeKB := proc(vars, lo, hi, kb, $)\n local var, dims, ty, rngs, x, kb1;\n var := op(1, vars);\n rngs := zip(`..`,lo,hi);\n ty := op(1, rngs);\n dims := subsop(1=NULL,zip(`=`,vars,rngs));\n x, kb1 := genType(var,\n mk_HArray(`if`(kind=Ints,\n HReal(open_bounds(ty)),\n HInt(closed_bounds(ty))),\n dims),kb);\n if nops(dims) > 0 then\n kb1 := assert(size(x)=op([-1,2,2],dims)-op([-1,2,1],dims)+1, kb1);\n end if;\n x, kb1;\n end proc;\n export ExtractVar := ((v,t,d)->[v,map(lhs,d)[]]);\n export ExtractRange := ((v,t,d)->[t,map(rhs,d)[]]);\n export MakeRange := ((a,b)->zip(`..`,a,b));\n export SplitRange := (rs->(map(x->op(1,x),rs), map(x->op(2,x),rs)));\n export Constrain := ((a,b)->zip(`if`(kind=Ints, `<`, `<=`),a,b)[]);\n export DoMk := ((e,v,t)->kind( e,op(1,v),op(1,t), subsop(1=NULL,zip(`=`,v,t)) ));\n export Min := ((a,b)->zip(`min`,a,b));\n export Max := ((a,b)->zip(`max`,a,b));\n export VarType := 'And(list(name),satisfies(x->x<>[]))';\n export RangeType := 'And(list(range),satisfies(x->x<>[]))';\n export MapleType := 'And'('specfunc'(kind),'anyfunc'('anything', 'name', 'range', 'list(name=range)'));\n export BoundType := TopProp;\n export RecogBound := (_->NULL);\nend module;\n", "meta": {"hexsha": "73fe2cd1fe9cd611776630861e1cbc77cae78f0f", "size": 10796, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/NewSLO/Improve.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/Improve.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/Improve.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": 37.3564013841, "max_line_length": 108, "alphanum_fraction": 0.5529825861, "num_tokens": 3438, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6893056295505783, "lm_q2_score": 0.5273165233795671, "lm_q1q2_score": 0.3634822481205748}} {"text": "interface(screenwidth=9999):\nif not (NewSLO :: `module`) then\n WARNING(\"loading NewSLO failed\");\n `quit`(3);\nend if;\n\nwith(Hakaru):\nwith(NewSLO):\n\n#####################################################################\n#\n# Dirichlet conjugacy tests \n#\n#####################################################################\n\n(dice_index, dice_index_t) := Concrete(\"examples/dice_index.hk\"):\ndice_index := value(eval(dice_index)):\n\n(gmm_gibbs, gmm_gibbs_t) := Concrete(\"examples/gmm_gibbs.hk\"):\ngmm_gibbs := value(eval(gmm_gibbs)):\n\n(naive_bayes_gibbs, naive_bayes_gibbs_t) := Concrete(\"examples/naive_bayes/naive_bayes_gibbs.hk\"):\nnaive_bayes_gibbs := value(eval(naive_bayes_gibbs)):\n\n#####################################################################\nTestEfficient( dice_index, dice_index_t, KB:-empty, label=\"dice index\" ):\nTestEfficient( gmm_gibbs, gmm_gibbs_t, KB:-empty, label=\"gmm gibbs\" ):\nTestEfficient( naive_bayes_gibbs, naive_bayes_gibbs_t, KB:-empty, label=\"naive bayes gibbs\" ):\n\n", "meta": {"hexsha": "370fc6b1ba258df6305d6cbdd51ba3a65b96005b", "size": 994, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "maple/PlateT2.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/PlateT2.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/PlateT2.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": 33.1333333333, "max_line_length": 98, "alphanum_fraction": 0.5905432596, "num_tokens": 280, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6334102498375401, "lm_q2_score": 0.5736784074525098, "lm_q1q2_score": 0.3633737833908963}} {"text": "(*\n \u4ee5\u4ee3\u8868\u5143\u4e3a\u6838\u5fc3\u7684\u5bf9\u8c61\n \u4e3b\u8981\u4ee5con\u5212\u5206\u5bf9\u8c61\uff0cisol\u548ctsol\u4ec5\u505a\u53c2\u8003\u4f5c\u7528\n \u4fdd\u8bc1RepSol\u5bf9\u8c61\u7684\u6240\u6709\u5c5e\u6027\u7684\u76f8\u5173\u53d8\u91cf\u90fd\u662fglobal\u7684\u3002\n*)\n$ifndef _REPSOL_\n$define _REPSOL_\n\nRepSol:=module()\n option object;\n local \n # \u5c40\u90e8\u51fd\u6570 \n getDisplayDcon::static, # \u5408\u5e76\u663e\u793a\u6210\u7acb\u6761\u4ef6\n apList::static, # \u62d3\u5c55list\n rmlist::static; # \u53bb\u9664\u4e00\u5c42\u5d4c\u5957list\n export \n # \u5bfc\u51fa\u53d8\u91cf\n rep, # \u4ee3\u8868\u5143\n dcon:=[], # \u4e0d\u53d8\u91cf\u65b9\u7a0b\n acon:=[], # \u9644\u52a0\u7ea6\u675f \n isol:=[], # \u4ee3\u8868\u5143\u7684\u901a\u89e3\n tsol:=[], # \u4ee3\u8868\u5143\u901a\u89e3\u548c\u7279\u89e3\u7684\u8f6c\u5316\n osol:=[], # \u5bf9\u5e94\u7684InvSol\u5bf9\u8c61\n sid:=1, # \u9009\u62e9\u7684\u6700\u7b80\u6761\u4ef6 \n # \u5bfc\u51fa\u51fd\u6570\n ## \u8bbe\u7f6e\u76f8\u5173\n appendSol::static, # \u6269\u5145\u4e00\u4e2aRepSol\u5bf9\u8c61\u6210\u7acb\u7684\u6761\u4ef6\n getCon::static, # \u83b7\u53d6\u4e00\u4e2aRepSol\u5bf9\u8c61\u6210\u7acb\u7684\u6761\u4ef6\n sortCon::static, # \u5bf9\u6210\u7acb\u6761\u4ef6\u8fdb\u884c\u6392\u5e8f\n selectCon::static, # \u9009\u62e9\u6700\u7b80\u6210\u7acb\u6761\u4ef6\n rmCon::static, # \u5220\u9664\u67d0\u4e2a\u6210\u7acb\u6761\u4ef6\u7684\u4e00\u90e8\u5206\n ## \u8f93\u51fa\u76f8\u5173\n printRep::static, # \u7b80\u8981\u663e\u793a\u4ee3\u8868\u5143\u548c\u6240\u6709\u53ef\u80fd\u7684\u6210\u7acb\u6761\u4ef6\n fullPrintRep::static, # \u663e\u793a\u4ee3\u8868\u5143\u548c\u5b8c\u6574\u7684\u6210\u7acb\u6761\u4ef6\u4ee5\u53ca\u5bf9\u5e94\u7684\u4e0d\u53d8\u91cf\u65b9\u7a0b\u548c\u53d8\u6362\u65b9\u7a0b\u7684\u89e3\n ModulePrint::static, # \u7b80\u8981\u663e\u793a\u4ee3\u8868\u5143\n uniqueAndSort::static; # \u5220\u53bb\u91cd\u590d\u6761\u4ef6\n\n # \u7528\u4e8e\u62d3\u5c55\u4e00\u4e2a\u4ee3\u8868\u5143\u5bf9\u8c61\u6240\u80fd\u4ee3\u8868\u7684\u533a\u57df\n appendSol:=proc(r::RepSol,s::InvSol)\n local ieq,sieq,isol,icon,tsols,tcons,i,n;\n if not assigned(r:-rep) then\n r:-rep:=getRep(s);\n end if;\n ieq:=s:-ieq;\n sieq:={ieq[]};\n isol:=s:-isol;\n icon:=s:-icon;\n tsols:=rmlist(s:-tsol);\n tcons:=rmlist(s:-tcon);\n n:=numelems(tsols);\n for i from 1 to n do\n apList(r:-dcon,ieq);\n apList(r:-acon,classifySolve({icon[],tcons[i][]}) minus sieq);\n apList(r:-isol,isol);\n apList(r:-tsol,tsols[i]);\n apList(r:-osol,s);\n end do;\n return;\n end proc:\n\n # \u62d3\u5c55list\n apList:=proc(lst::evaln)\n lst:=[eval(lst)[],_rest];\n return;\n end proc:\n\n # \u83b7\u53d6\u4e00\u4e2aRepSol\u5bf9\u8c61\u6210\u7acb\u7684\u6761\u4ef6\n getCon:=proc(r::RepSol)\n return zip((x,y)->[getDisplayDcon(x)[],y[]],r:-dcon,r:-acon);\n end proc:\n\n # \u4e0d\u53d8\u91cf\u65b9\u7a0b\u7684\u7b80\u5316\u663e\u793a\n getDisplayDcon:=proc(dcon)\n local n;\n n:=numelems(dcon);\n return [seq(Delta[i]=rhs(dcon[i]),i=1..n)];\n end proc:\n\n # \u53bb\u6389\u4e00\u5c42\u5d4c\u5957list\n rmlist:=proc(x)\n return map(y->y[],x);\n end proc:\n\n # \u5bf9\u6210\u7acb\u6761\u4ef6\u8fdb\u884c\u6392\u5e8f\n sortCon:=proc(r::RepSol)\n local con,ind;\n con:=getCon(r);\n ind:=sortByComplexity(con,index);\n r:-dcon:=r:-dcon[ind];\n r:-acon:=r:-acon[ind];\n r:-isol:=r:-isol[ind];\n r:-tsol:=r:-tsol[ind];\n r:-osol:=r:-osol[ind];\n end proc:\n\n # \u9009\u62e9\u6700\u7b80\u6210\u7acb\u6761\u4ef6\n selectCon:=proc(r::RepSol,sid)\n r:-sid:=sid;\n return;\n end proc:\n\n # \u5220\u9664\u67d0\u4e2a\u6210\u7acb\u6761\u4ef6\u7684\u4e00\u90e8\u5206\n rmCon:=proc(r::RepSol,id::posint,con::set)\n r:-acon[id]:=r:-acon[id] minus con;\n end proc:\n\n # \u7b80\u8981\u663e\u793a\u4ee3\u8868\u5143\u548c\u6240\u6709\u53ef\u80fd\u7684\u6210\u7acb\u6761\u4ef6\n printRep:=proc(r::RepSol)\n print(r:-rep);\n print~(getCon(r));\n return ;\n end proc:\n\n # \u663e\u793a\u4ee3\u8868\u5143\u548c\u5b8c\u6574\u7684\u6210\u7acb\u6761\u4ef6\u4ee5\u53ca\u5bf9\u5e94\u7684\u4e0d\u53d8\u91cf\u65b9\u7a0b\u548c\u53d8\u6362\u65b9\u7a0b\u7684\u89e3\n fullPrintRep:=proc(r::RepSol)\n local i,n,con;\n print(r:-rep);\n con:=getCon(r);\n n:=numelems(con);\n for i from 1 to n do\n printf(\"[%d]------------------------------------------------------\",i);\n print(con[i]);\n print(r:-isol[i]);\n print(r:-tsol[i]);\n end do;\n return;\n end proc:\n\n # \u5220\u53bb\u91cd\u590d\u6761\u4ef6\n uniqueAndSort:=proc(r::RepSol)\n local id,con,fun,ind;\n fun:=(x,y,z)->[x,y,z];\n con:=getCon(r);\n id:=fun~(con,r:-isol,r:-tsol);\n ind:=uniqueObj(id,key=(x->x),'index');\n r:-dcon:=r:-dcon[ind];\n r:-acon:=r:-acon[ind];\n r:-isol:=r:-isol[ind];\n r:-tsol:=r:-tsol[ind];\n r:-osol:=r:-osol[ind];\n sortCon(r);\n return r;\n end proc:\n\n # \u7b80\u8981\u663e\u793a\u4ee3\u8868\u5143\n ModulePrint:=proc(r::RepSol)\n return r:-rep;\n end proc:\nend module:\n\n$endif", "meta": {"hexsha": "db97cb9fa07704c21627714d9f120436da805ad5", "size": 3992, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "old/RepSol.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/RepSol.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/RepSol.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": 26.4370860927, "max_line_length": 83, "alphanum_fraction": 0.4716933868, "num_tokens": 1406, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.640635841117624, "lm_q2_score": 0.5660185351961015, "lm_q1q2_score": 0.3626117603835199}} {"text": "func $switchfunc ( var %n i32) i32 {\n var %alocal i32\n switch (dread i32 %n) @labdft {\n -3: goto @lab0\n 1: goto @lab1\n 9: goto @lab9 }\n@lab0\n return (constval i32 -3)\n@labdft\n return (constval i32 100)\n@lab9\n return (constval i32 9)\n@lab1\n return (constval i32 1) }\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "8750d119201ac691f3c2c067808eb86ec0f2c23b", "size": 374, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0076-mapleall-irbuild-edge-switch/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/I0076-mapleall-irbuild-edge-switch/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/I0076-mapleall-irbuild-edge-switch/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": 20.7777777778, "max_line_length": 43, "alphanum_fraction": 0.6550802139, "num_tokens": 156, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.5698526368038304, "lm_q2_score": 0.6334102775181399, "lm_q1q2_score": 0.360950516822358}} {"text": "# typedef struct ss {\n# int f1;\n# char f2:3;\n# char f3:5;\n# } SS;\n# SS foo(SS x) {\n# x.f2 = 32;\n# return x;\n# }\ntype $SS \nfunc $foo (\n\tvar %x <$SS>) i32 {\n dassign %x 2 ( constval i32 32 )\n return ( dread i32 %x 2 ) }\n # EXEC: %irbuild Main.mpl\n # EXEC: %irbuild Main.irb.mpl\n # EXEC: %cmp Main.irb.mpl Main.irb.irb.mpl\n", "meta": {"hexsha": "972dfaabacc967135306ac668068391c9d282ad7", "size": 370, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "test/testsuite/irbuild_test/I0072-mapleall-irbuild-edge-struct/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/I0072-mapleall-irbuild-edge-struct/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/I0072-mapleall-irbuild-edge-struct/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": 20.5555555556, "max_line_length": 47, "alphanum_fraction": 0.5567567568, "num_tokens": 161, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES\n\n", "lm_q1_score": 0.546738151984614, "lm_q2_score": 0.6584175072643413, "lm_q1q2_score": 0.3599819711560221}} {"text": "f1(){\n\t[x, y] = stack(), stack();\n\tx*7-y; // return value\n}\nf2()inline{\n\t[x, y] = stack(), stack();\n\tx*7-y; // return value\n}\nf3()inline, CRPL{swap 7 mul swap sub}\nf4()CRPL{swap 7 mul swap sub}\n\nmain()inline{\n\tShowTraceLog();\n\tClearTraceLog();\n\t\n\tTrace(\"f1 \" $ f1(1, 2));\n\tTrace(\"f2 \" $ f2(1, 2));\n\tTrace(\"f3 \" $ f3(1, 2));\n\tTrace(\"f4 \" $ f4(1, 2));\n}", "meta": {"hexsha": "600dd9a5cd3bf4e9ad63a33151e88f93d3733792", "size": 351, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "examples/functions.mpl", "max_stars_repo_name": "Arin112/mplLang", "max_stars_repo_head_hexsha": "e7d41648305462d70acb6c3716283f311dd89b42", "max_stars_repo_licenses": ["MIT"], "max_stars_count": 1, "max_stars_repo_stars_event_min_datetime": "2019-07-22T19:04:29.000Z", "max_stars_repo_stars_event_max_datetime": "2019-07-22T19:04:29.000Z", "max_issues_repo_path": "examples/functions.mpl", "max_issues_repo_name": "Arin112/mplLang", "max_issues_repo_head_hexsha": "e7d41648305462d70acb6c3716283f311dd89b42", "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/functions.mpl", "max_forks_repo_name": "Arin112/mplLang", "max_forks_repo_head_hexsha": "e7d41648305462d70acb6c3716283f311dd89b42", "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": 17.55, "max_line_length": 37, "alphanum_fraction": 0.5384615385, "num_tokens": 152, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.658417500561683, "lm_q2_score": 0.5467381519846138, "lm_q1q2_score": 0.359981967491423}} {"text": "with(StringTools):\nDiagLatex := proc(spart, size:=0)\n\tlocal phis, thetas, phithetas, zeds, Lambda, string, cercle, triangle, triangle_cercle, boite, part, endline, k;\n\tphis:= spart[2];\n\tphis:= map( x-> [x,\"c\"], phis);\n\tthetas:= spart[3];\n\tthetas:= map(x-> [x,\"b\"], thetas);\n\tphithetas:= spart[1];\n\tphithetas:= map(x-> [x,\"d\"], phithetas);\n\tzeds:= spart[4];\n\tzeds:= map(x-> [x,\"a\"], zeds);\n\tLambda:= sort([op(phithetas),op(phis), op(thetas), op(zeds)]);\n\n\tstring:=\"\";\n\t\n\tcercle:= \"\\\\yC\";\n\ttriangle:= \"\\\\yT\";\n\ttriangle_cercle:= \"\\\\yTC\"; \n\tboite:= \"\\\\,\";\n\tfor k from 1 to nops(Lambda) do\n\t\tpart:= Lambda[k];\n\t\tprint(Lambda);\n\t\tprint(part);\n\t\tif k = 1 then endline:=\"\"; else endline:=\"\\\\\\\\ \\n\"; end if:\n\t\tif part[2] = \"c\" then\n\t\t\tstring:= cat(cat(Repeat(cat(boite, \"& \"), part[1]), triangle, endline), string);\n\t\telif part[2] = \"b\" then\n\t\t\tstring:= cat(cat(Repeat(cat(boite, \"& \"), part[1]), cercle, endline), string);\n\t\telif part[2] = \"a\" then\n\t\t\tstring:= cat(cat(Repeat(cat(boite, \"& \"), part[1]-1), boite, endline), string);\n\t\telif part[2] = \"d\" then \n\t\t\tstring:= cat(cat(Repeat(cat(boite, \"& \"), part[1]), triangle_cercle, endline), string);\n\t\tend if;\n\tend do:\n\tif size = 0 then\n\t\tstring:= cat(\"{\\\\, \\\\superYsmall{\", string, \"}}\");\n\telif size = 1 then\n\t\tstring:= cat(\"{\\\\, \\\\superY{\", string, \"}}\");\n\telif size = 2 then\n\t\tstring:= cat(\"\\\\superRusse{{\\\\superY{\", string, \"}}}\");\n\tend if;\n\treturn string;\nend proc:\n\nsuperLatex := proc(expr,initial_term:=0, wipe:=0)\n\tlocal sparts, astring, spart, spart_string, fd, basetype, terms, thecoeff, latexsparts, latex_terms, k, ou;\n\tif wipe <> 0 then \n\t\tfd:= fopen(\"out.txt\", WRITE);\n\t\tfprintf(fd, \"\");\n\t\tfclose(fd);\n\telse\n\t\tfd:=fopen(\"out.txt\", APPEND);\n\t\tfprintf(fd,\"new \\n \\\\begin{gather*} \\n\");\n\t\tfclose(fd);\n\tend if;\n\tbasetype:= \"m\";\n\tterms:= [op(indets(expr, 'superindexed'))];\n\tterms:= sort(terms, list_sort); \n\t#print(terms);\n\tsparts:= map(x-> [op(x)], terms); \n\t#print(sparts);\n\tthecoeff:= map(x-> coeff(expr, x), terms);\n\t#print(thecoeff); \n\t#latexcoeff:= map(x-> latex(x), thecoeff); \n\n\t#Activate following line for diagrams\n\t#latexsparts:= map(x-> DiagLatex(x,0), sparts);\n\t#Activate following line for sparts\n\tlatexsparts:= map(x-> SpartLatex(x),sparts);\n\tlatex_terms:= [];\n\tif initial_term <> 0 then\n\t\tfd:=fopen(\"out.txt\", APPEND);\n\t\tfprintf(fd,cat(initial_term[1],\"\\\\,\",basetype,\"_\",DiagLatex(initial_term[2], 0),\"=\",\"\\n+\"));\n\t\tfclose(fd);\n\tend if;\n\tfor k from 1 to nops(sparts) do\n\t\tfd:= fopen(\"out.txt\", APPEND);\n\t\tfprintf(fd, \"\\t\");\n\t\tfclose(fd);\n\t\tif whattype(thecoeff[k]) = `+` then \n\t\t\tfd:= fopen(\"out.txt\", APPEND);\n\t\t\tfprintf(fd, \"(\");\n\t\t\tfclose(fd);\n\t\tend if;\n\n\t\tlatex(thecoeff[k],\"out.txt\",'append'); \n\n\t\tif whattype(thecoeff[k]) = `+` then \n\t\t\tfd:= fopen(\"out.txt\", APPEND);\n\t\t\tfprintf(fd, \")\");\n\t\t\tfclose(fd);\n\t\tend if;\n\t\tfd:= fopen(\"out.txt\", APPEND);\n\t\tfprintf(fd, cat(basetype,\"_\",latexsparts[k],\"\\n+\"));\n\t\tfclose(fd);\n\tend do:\n\t\tfd:=fopen(\"out.txt\", APPEND);\n\t\tfprintf(fd,\"\\\\end{gather*} \\n\");\n\t\tfclose(fd);\nend proc:\n\nSpartLatex:= proc(spart)\n\tlocal pts, phis, thetas, zeds, pt_string, phi_string, theta_string, zed_string, SpartString;\n\tpts:= spart[1];\n\tphis:= spart[2];\n\tthetas:= spart[3];\n\tzeds:= spart[4];\n\n\tpt_string:= convert(pts, string);\n\tphi_string:= convert(phis, string);\n\ttheta_string:= convert(thetas, string);\n\tzed_string:= convert(zeds, string);\n\n\tpt_string:= Substitute(pt_string, \"[\", \"(\");\n\tpt_string:= Substitute(pt_string, \"]\", \";\\\\,\");\n\tphi_string:= Substitute(phi_string, \"[\", \"\");\n\tphi_string:= Substitute(phi_string, \"]\", \";\\\\,\");\n\ttheta_string:= Substitute(theta_string, \"[\", \"\");\n\ttheta_string:= Substitute(theta_string, \"]\", \";\\\\,\");\n\tzed_string:= Substitute(zed_string, \"[\", \"\");\n\tzed_string:= Substitute(zed_string, \"]\", \")\");\n\n\tSpartString:= cat(pt_string, phi_string, theta_string, zed_string); \n\tSpartString:= cat(\"{\",SpartString, \"}\");\n\treturn SpartString;\nend proc:\n", "meta": {"hexsha": "5756e4ff044dad30ea29b895257fb41af93be4dd", "size": 3873, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/visual.mpl", "max_stars_repo_name": "LAV42/N2-Superpolynomials", "max_stars_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": "lib/visual.mpl", "max_issues_repo_name": "LAV42/N2-Superpolynomials", "max_issues_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": "lib/visual.mpl", "max_forks_repo_name": "LAV42/N2-Superpolynomials", "max_forks_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": 30.4960629921, "max_line_length": 113, "alphanum_fraction": 0.6181254841, "num_tokens": 1271, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6150878555160665, "lm_q2_score": 0.5851011542032312, "lm_q1q2_score": 0.3598886141988408}} {"text": "`is_element/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n local TT1,B,C,P,T,U;\n global reason;\n\n if not(type(Q,table)) then\n reason := [convert(procname,string),\"Q is not a table\",Q]; \n return false;\n fi;\n\n P := sort(map(sort,map(op,{indices(Q)})));\n TT1 := select(T -> nops(T) > 1,TT);\n\n if P <> TT1 then\n reason := [convert(procname,string),\"Q is not indexed by the big sets in TT\",P,TT1]; \n return false;\n fi;\n\n C := children_map(A)(TT);\n \n for T in P do \n if not(`is_element/SCP`(N)(T)(Q[T])) then\n reason := [convert(procname,string),\"Q[T] is not in SCP(N)(T)\",eval(Q[T]),N,T,reason]; \n return false;\n fi;\n\n for U in C[T] do \n if nops(U) > 1 and not(`is_element/SCP2`(N)(T,U)([Q[T],Q[U]])) then\n reason := [convert(procname,string),\"(Q[T],Q[U]) is not in SCP2(N)(T,U)\",eval(Q[T]),eval(Q[U]),N,T,U,reason]; \n return false;\n fi;\n od;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`random_element/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc()\n `mu/tree_Fbar/tree_FFbar`(N)(A)(TT)(`random_element/tree_Fbar`(N)(A)(TT)());\nend;\n\n######################################################################\n\n`is_equal/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(P,Q)\n local T,TT1;\n global reason;\n\n TT1 := select(T -> nops(T) > 1,TT);\n\n for T in TT1 do \n if not(`is_equal/SCP`(N)(T)(P[T],Q[T])) then\n reason := [convert(procname,string),\"P[T] <> Q[T]\",T,P[T],Q[T],reason]; \n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_leq/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(P,Q)\n local T,TT1;\n global reason;\n\n TT1 := select(T -> nops(T) > 1,TT);\n\n for T in TT1 do \n if not(`is_leq/SCP`(N)(T)(P[T],Q[T])) then\n reason := [convert(procname,string),\"P[T] is not <= Q[T]\",T,P[T],Q[T],reason]; \n return false;\n fi;\n od;\n\n return true;\nend;\n\n######################################################################\n\n`is_interior/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n return `is_element/ICP`(N)(A)(Q[A]);\nend;\n\n######################################################################\n\n`inc/ICP/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q0)\n local Q,TT1,T,t;\n \n Q := table();\n TT1 := select(T -> nops(T) > 1,TT);\n for T in TT1 do\n Q[T] := `top/autorel`(T) intersect Q0;\n od;\n\n return eval(Q);\nend:\n\n######################################################################\n\n`res/tree_FFbar/ICP` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n if not(`is_interior/tree_FFbar`(N)(A)(TT)(Q)) then\n return FAIL;\n fi;\n\n return Q[A];\nend;\n\n######################################################################\n\n`res/FFbar/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n local TT1,Q1,T;\n\n TT1 := select(T -> nops(T) > 1,TT);\n\n Q1 := table():\n for T in TT1 do Q1[T] := eval(Q[T]); od;\n\n return eval(Q1);\nend:\n\n######################################################################\n\n`ext/tree_FFbar/FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n local TT1,UU,TU,T,U,m,Q1,i;\n\n TT1 := select(T -> nops(T) > 1,TT);\n UU := `list_elements/big_subsets`(A);\n\n Q1 := table():\n \n for U in UU do \n TU := select(T -> U minus T = {},TT1);\n m := min(op(map(nops,TU)));\n TU := select(U -> nops(U) = m,TU);\n T := TU[1];\n Q1[U] := [seq(`top/autorel`(U) intersect Q[T][i],i=1..N)];\n if not(`is_element/SCP`(N)(U)(Q1[U])) then\n return FAIL;\n fi;\n od;\n\n return eval(Q1);\nend:\n\n######################################################################\n\n`C/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n local L,TT1,T,G,i,ab;\n L := NULL;\n TT1 := select(T -> nops(T) > 1,TT);\n for T in TT1 do\n G := `gamma/SCP`(N)(T)(Q[T]);\n L := L,seq(seq([i,op(ab)],ab in G[i]),i=1..N);\n od; \n return {L};\nend:\n\n######################################################################\n\n`list_elements/tree_FFbar` := NULL;\n`count_elements/tree_FFbar` := NULL;\n\n######################################################################\n\n`mu/tree_Fbar/tree_FFbar` := (N::posint) -> (A::set) -> (TT) -> proc(x)\n local Q,TT1,T;\n \n TT1 := select(T -> nops(T) > 1,TT);\n\n Q := table();\n\n for T in TT1 do\n Q[T] := `mu/W/ACP`(N)(T)(x[T]);\n od;\n\n return eval(Q);\nend;\n\n\n######################################################################\n\n`sigma/tree_FFbar/tree_Fbar` := (N::posint) -> (A::set) -> (TT) -> proc(Q)\n local x,TT1,T;\n \n TT1 := select(T -> nops(T) > 1,TT);\n\n x := table();\n\n for T in TT1 do\n x[T] := `sigma/ACP/W`(N)(T)(Q[T]);\n od;\n\n return eval(x);\nend;", "meta": {"hexsha": "bfafd8d7041515ee74bd6ff05ddb91ce7d8e32a1", "size": 4571, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/chains/tree_FFbar.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/chains/tree_FFbar.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/chains/tree_FFbar.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": 23.441025641, "max_line_length": 115, "alphanum_fraction": 0.4469481514, "num_tokens": 1446, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6442251064863695, "lm_q2_score": 0.5544704649604273, "lm_q1q2_score": 0.3572037943326781}} {"text": "# Class: RealAlgebraicNumber\n#\n# Description:\n# Implementation of real algebraic numbers together with their comparison.\n# This implementation is inspired by the implementation in CGAL 4.7.\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#\nmodule RealAlgebraicNumber()\n option object;\n (* Univariete polynomaial *)\n local poly::polynom;\n (* Lower bound of the range in which exists only one real root of poly. *)\n local a::rational;\n (* Upper bound of the range in which exists only one real root of poly. *)\n local b::rational;\n (* Real algebraic number is rational when a = b and sign of poly at a/b is 0. *)\n local isRational_;\n (* Note that isolating interval has to be open iff a real algebraic number is not rational and\n closed, a = b, otherwise.*)\n\n# Method: ModuleCopy\n# Standard constructor / copy constructor\n#\n# Parameters:\n# self::RealAlgebraicNumber - a new object to be constructed\n# proto::RealAlgebraicNumber - a prototype object from which self is derived\n# poly::polynom - a univariate polynomial\n# a::rational - a lower bound of the range in which exists only one real root of poly \n# b::rational - an upper bound of the range in which exists only one real root of poly \n#\n# Output:\n# An object of type RealAlgebraicNumber.\n#\n# Exceptions:\n# \"Invalid range. A range is valid when: a <= b.\"\n# \"Degree of %1 is invalid.\"\n#\n export ModuleCopy::static := proc( self::RealAlgebraicNumber,\n proto::RealAlgebraicNumber,\n poly::polynom,\n a::rational,\n b::rational, $ )\n local signAtA, signAtB;\n if _passed = 2 then\n self:-poly := proto:-poly;\n self:-a := proto:-a;\n self:-b := proto:-b;\n self:-isRational_ := proto:-isRational_;\n else\n if upperbound( indets( poly ) ) > 1 then\n error \"%1 is not univariate!\", poly;\n end if;\n if a > b then\n error \"Invalid range. A range is valid when: a <= b.\";\n end if;\n if gcd( poly, diff( poly, op( indets( poly ) ) ) ) <> 1 then\n error \"Polynomial: %1 is not square-free.\", poly;\n end if;\n self:-poly := poly;\n if degree(poly) >= 1 then\n signAtA := signum( eval( poly, indets( poly )[1] = a ) );\n signAtB := signum( eval( poly, indets( poly )[1] = b ) );\n self:-a := a;\n self:-b := b;\n self:-isRational_ := evalb( self:-a = self:-b and signAtA = 0 );\n if signAtA = 0 and signAtB <> 0 then\n WARNING(\"Incorrect interval. Sign of univariate polynomial on one side of the interval\"\n \" evaluated to zero but not on the another. Interval fixed.\");\n self:-b := self:-a;\n self:-isRational_ := true:\n elif signAtB = 0 and signAtA <> 0 then \n WARNING(\"Incorrect interval. Sign of univariate polynomial on one side of the interval\"\n \" evaluated to zero but not on the another. Interval fixed.\");\n self:-a := self:-b;\n self:-isRational_ := true:\n elif signAtA = signAtB and self:-a <> self:-b then\n error \"Interval incorrect! No root in the interval: (%1, %2), for %3 .\", self:-a, self:-b,\n self:-poly;\n fi:\n elif degree( poly ) = 0 then\n self:- denom( poly ) * 'a' - numer( poly );\n self:-a := poly;\n self:-b := poly;\n self:-isRational_ := true;\n else\n error \"Degree of %1 is invalid.\", poly;\n end if;\n end if;\n return self;\n end proc:\n\n# Method: ModulePrint\n# Standard printout of an object of type RealAlgebraicNumber.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n export ModulePrint::static := proc( self::RealAlgebraicNumber )\n if(self:-a = self:-b) then\n nprintf( \"( %a, [%a, %a] )\", self:-poly, self:-a, self:-b );\n else\n nprintf( \"( %a, ]%a, %a[ )\", self:-poly, self:-a, self:-b );\n end if;\n end proc;\n\n\n# Method: ModuleApply\n# Define standard constructor.\n#\n export ModuleApply::static := proc()\n Object(RealAlgebraicNumber, args)\n end proc;\n\n\n# Method: ModuleDeconstruct\n# Provides information how to recreate an object after being serialized.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n export ModuleDeconstruct := proc( self::RealAlgebraicNumber )\n ('RealAlgebraicNumber')(self:-poly, self:-a, self:-b)\n end proc;\n\n\n\n# Method: GetPolynomial\n# A getter method to access the univariate polynomial of RealAlgebraicNumber.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# Univariate polynomial stored in self.\n#\n export GetPolynomial::static := proc( self::RealAlgebraicNumber )\n return self:-poly;\n end proc:\n\n# Method: GetInterval\n# A getter method to access the range isolating a root of univariate polynomial.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# The range isolating a root of univariate polynomial -- self:-poly.\n# Upper and lower bounds of a range are rationals. When lower = upper\n# then a real algebraic number is rational.\n#\n export GetInterval::static := proc( self::RealAlgebraicNumber )\n return [ self:-a, self:-b ];\n end proc:\n\n# Method: IsRational\n# A method to check if a real algebraic number is rational.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# True when a real algebraic number is rational, false\n# otherwise. A real algebraic number is meant as rational when a = b and\n# when sign of poly at a/b is zero.\n#\n export IsRational::static := proc( self::RealAlgebraicNumber )\n return self:-isRational_;\n end proc:\n\n# Method: CompareRational\n# A method used to compare a real algebraic number with a\n# rational number.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n# m::rational - a rational number\n#\n# Output:\n# -1 when a real algebraic number is smaller than a rational\n# number, 0 when they are equal and 1 when a real algebraic\n# number is bigger than a rational.\n#\n local CompareRational::static := proc( self::RealAlgebraicNumber, m::rational )\n local refined:\n refined := StrongRefineAt(self,m);\n if evalb( refined:-a < m ) then\n return -1;\n elif evalb( refined:-a > m ) then\n return 1;\n elif evalb( signum( eval( refined:-poly, op( indets( refined:-poly ) ) = m ) ) = 0 ) then\n return 0;\n end if;\n end proc:\n\n# Method: RefineAt\n# A method used to refine a real algebraic number using a rational\n# number for adaptation of a range isolating a root of poly.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n# m::rational - a rational number\n#\n# Output:\n# A RealAlgebraicNumber obtaind from self refined at m.\n#\n# Comment:\n# Not that the type can change to rational.\n#\n local RefineAt::static := proc( self::RealAlgebraicNumber, m::rational )\n local signAtM, f::polynom, g::polynom;\n local var := op( indets( self:-poly ) );\n if self:-isRational_ or m <= self:-a or self:-b <= m then\n return self;\n end if;\n signAtM := signum( eval( self:-poly, var = m ) );\n if evalb( signAtM = 0 ) then\n g := denom( m ) * var - numer( m );\n return Object( RealAlgebraicNumber, g, m, m ); \n elif evalb( signum( eval( self:-poly, var = self:-a ) ) = signAtM ) then\n return Object( RealAlgebraicNumber, self:-poly, m, self:-b );\n elif evalb( signum( eval( self:-poly, var = self:-b ) ) = signAtM ) then\n return Object( RealAlgebraicNumber, self:-poly, self:-a, m );\n else\n return self;\n end if;\n end proc:\n\n\n# Method: BisectRange\n# A method used to compare a real algebraic number with a\n# rational number.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# Refine an isolating range at ( self:-a + self:-b ) / 2\n#\n local BisectRange::static := proc( self::RealAlgebraicNumber )\n return RefineAt( self, ( self:-a + self:-b ) / 2 );\n end proc:\n\n\n# Method: StrongRefineAt\n# A method used to refine a real algebraic number using a rational\n# number for adaptation of a range isolating a root of poly.\n#\n# Parameters:\n# self::RealAlgebraicNumber - a real algebraic number\n# m::rational - a rational number\n#\n local StrongRefineAt::static := proc( self::RealAlgebraicNumber, m::rational )\n local refined:\n if self:-isRational_ or signum( eval( self:-poly, indets( self:-poly )[1] = m ) ) = 0 then\n return self;\n fi:\n refined := self;\n while refined:-a <= m and m <= refined:-b do\n refined := BisectRange(refined);\n od:\n return refined:\n end proc:\n\n export DisjointRanges::static := proc(a::RealAlgebraicNumber, b::RealAlgebraicNumber)\n local ll := a, rr := b, i;\n\n (* No intersection.*)\n if evalb( ll:-b < rr:-a ) or evalb( ll:-a > rr:-b ) then\n return [a,b];\n fi:\n\n for i from 1 while 1 = 1 do\n ll := BisectRange( ll ):\n rr := BisectRange( rr ):\n\n (* No intersection.*)\n if evalb( ll:-b < rr:-a ) or evalb( ll:-a > rr:-b ) then\n return [ll,rr];\n fi:\n od:\n end proc:\n\n# Method: Compare\n# A method used to compare two real algebraic numbers.\n#\n# Parameters:\n# l::RealAlgebraicNumber - a real algebraic number\n# r::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# -1 when l is smaller than r, 0 when they are equal and 1 when l is bigger than r.\n#\n export Compare::static := proc( l::RealAlgebraicNumber, r::RealAlgebraicNumber, $ ) \n local i::integer, a::rational, b::rational, F1::polynom, F2::polynom, G::polynom;\n local ll::RealAlgebraicNumber, rr::RealAlgebraicNumber;\n\n if indets(l:-poly) <> indets(r:-poly) then\n error \"Univariate polynomials have different variables: %1 and %2.\", indets(l:-poly),\n indets(r:-poly);\n fi;\n\n if evalb( l:-poly = r:-poly and l:-a = r:-a and l:-b = r:-b ) then\n return 0;\n end if; \n \n (* When rationals *)\n if r:-isRational_ then\n return CompareRational( l, r:-a );\n elif l:-isRational_ then\n return -CompareRational( r, l:-a );\n end if;\n\n (* Check if there is no intersection of the ranges *)\n if evalb( l:-b < r:-a ) then\n return -1;\n elif evalb( l:-a > r:-b ) then\n return 1;\n end if:\n\n (* Get the intersecting interval *)\n if evalb( l:-a > r:-a ) then\n a := l:-a;\n else\n a := r:-a;\n end if;\n if evalb( l:-b < r:-b ) then\n b := l:-b;\n else\n b := r:-b;\n end if;\n\n (* refine at the intersecting interval *)\n ll := RefineAt( l, a ):\n ll := RefineAt( ll, b ):\n rr := RefineAt( r, a ):\n rr := RefineAt( rr, b ):\n\n (* Refiment can change type to rational. *)\n if rr:-isRational_ then\n return CompareRational( ll, rr:-a );\n elif ll:-isRational_ then\n return -CompareRational( rr, ll:-a );\n end if;\n\n (* Check if there is no intersection after refiment. *)\n if evalb( ll:-b < rr:-a ) then\n return -1;\n elif evalb( ll:-a > rr:-b ) then\n return 1;\n end if;\n\n (* The number of roots of the GCD of two polynomials is equal to the number of common roots.\n use this to simplify the problem in the intersecting range.*)\n G := gcd( ll:-poly, rr:-poly );\n F1 := simplify( ll:-poly / G );\n F2 := simplify( rr:-poly / G );\n \n if evalb( signum( eval( G, op( indets( G ) ) = ll:-a ) ) <> signum( eval( G,\n op( indets( G ) ) = ll:-b ) ) ) then\n ll := Object( ll, G, ll:-a, ll:-b ):\n else\n ll := Object( ll, F1, ll:-a, ll:-b ):\n end if:\n\n if evalb( signum( eval( G, op( indets( G ) ) = rr:-a ) ) <> signum( eval( G,\n op( indets( G ) ) = rr:-b ) ) ) then\n rr := Object( rr, G, rr:-a, rr:-b ):\n else\n rr := Object( rr, F2, rr:-a, rr:-b ):\n end if:\n\n (* Use of GCD can change type to rational. *)\n if rr:-isRational_ then\n return CompareRational( ll, rr:-a );\n elif ll:-isRational_ then\n return -CompareRational( rr, ll:-a );\n end if;\n\n (* Check for equality. *)\n if evalb( signum( eval( G, op( indets( G ) ) = a ) ) <> signum( eval( G,\n op( indets( G ) ) = b ) ) ) then\n return 0;\n end if;\n \n (* Refiment until disjoitness. *)\n for i from 1 while 1 = 1 do\n ll := BisectRange( ll ):\n rr := BisectRange( rr ):\n\n (* Rationals after refiment. *)\n if rr:-isRational_ then\n return CompareRational( ll, rr:-a );\n elif ll:-isRational_ then\n return -CompareRational( rr, ll:-a );\n end if;\n\n (* No intersection after refiment. *)\n if evalb( ll:-b < rr:-a ) then\n return -1;\n elif evalb( ll:-a > rr:-b ) then\n return 1;\n end if: \n end do:\n end proc:\n\n# Method: < operator\n# A method used to compare two real algebraic numbers.\n#\n# Parameters:\n# l::RealAlgebraicNumber - a real algebraic number\n# r::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# true when l is smaller than r and false otherwise.\n#\n export `<`::static := proc( l, r, $ )\n if ( _npassed <> 2 or not l::RealAlgebraicNumber or not r::RealAlgebraicNumber ) then\n return false; \n end if; \n if Compare( l, r ) = -1 then\n return true;\n else\n return false;\n end if;\n end proc:\n\n# Method: <= operator\n# A method used to compare two real algebraic numbers.\n#\n# Parameters:\n# l::RealAlgebraicNumber - a real algebraic number\n# r::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# true when l is smaller or equal to r and false otherwise.\n#\n export `<=`::static := proc( l, r, $ )\n if ( _npassed <> 2 or not l::RealAlgebraicNumber or not r::RealAlgebraicNumber ) then\n return false; \n end if; \n if Compare( l, r ) <= 0 then\n return true;\n else\n return false;\n end if;\n end proc:\n\n# Method: = operator\n# A method used to compare two real algebraic numbers.\n#\n# Parameters:\n# l::RealAlgebraicNumber - a real algebraic number\n# r::RealAlgebraicNumber - a real algebraic number\n#\n# Output:\n# true when l is equal to r and false otherwise.\n#\n export `=`::static := proc( l, r, $ ) \n if Compare( l, r ) = 0 then\n return true;\n else\n return false;\n end if;\n end proc:\n\nend module:\n\n", "meta": {"hexsha": "d3faaa5234efa8695469357154928040ff33a0bf", "size": 15920, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "RealAlgebraicNumber.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": "RealAlgebraicNumber.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": "RealAlgebraicNumber.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": 31.9038076152, "max_line_length": 107, "alphanum_fraction": 0.6206658291, "num_tokens": 4563, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.672331699179286, "lm_q2_score": 0.5312093733737563, "lm_q1q2_score": 0.3571489006203413}} {"text": "\n# \n# Erstelle Liste aller Kinematikparameter\n# Init\n# Dieses Arbeitsblatt erstellt einen Vektor mit allen Kinematikparameter\n# Es werden nur die Kinematikparameter eingetragen, die ungleich Null sind, also z.B. keine MDH-Parameter die L\u00e4nge oder Winkel Null sind.\n# \n# TODO: Liste mit Kinematikparametern muss immer die selbe Reihenfolge haben. Am besten in der Form a,alpha,qoffset,d,b,beta,kc. Momentan scheint die Reihenfolge zuf\u00e4llig, aber reproduzierbar.\n# \n# Moritz Schappler, schappler@irt.uni-hannover.de, 2017-02\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):\ninterface(rtablesize=100): # Damit der ganze Parametervektor ausgegeben werden kann\n;\nwith(LinearAlgebra):\nread \"../helper/proc_MatlabExport\":\nread \"../helper/proc_convert_t_s\":\ncodegen_act := true:\n# Lese Umgebungsvariable f\u00fcr Codegenerierung.\nread \"../robot_codegen_definitions/robot_env\":\nread sprintf(\"../codeexport/%s/tmp/tree_floatb_twist_definitions\", robot_name):\nrobot_name_OL := robot_name: # Zus\u00e4tzliche Variable zur Abgrenzung f\u00fcr implizite Zwangsbedingungen\n;\n# Schalte um zwischen impliziten ZB und normalen Systemen\nif FileTools[Exists](\"../workdir/tbmode\") then\n read \"../workdir/tbmode\": # Datei tbmode wird von Bash-Skripten erstellt und zeigt den aktuellen Modus an\nelse\n tbmode := \"serial\":\nend if:\nif tbmode = \"implicit\" then\n printf(\"Modus f\u00fcr IC ist aktiv. Bestimme Kinematikparameter f\u00fcr System mit impliziten ZB.\\n\"):\n read \"../robot_codegen_definitions/robot_env_IC\":\nend if:\nprintf(\"Generiere Kinematik-Parametervektor f\u00fcr %s\\n\",robot_name):\n# Parameter der Zwangsbedingungen lesen\nkin_constraints_exist := false:\nkc_symbols2 := []:\n# F\u00fcr explizite Zwangsbedingungen\nconstrfile := sprintf(\"../codeexport/%s/tmp/kinematic_constraints_symbols_list_maple\", robot_name_OL):\nif FileTools[Exists](constrfile) then\n read constrfile:\n printf(\"Symbole der expliziten Zwangsbedingungen aus %s gelesen.\\n\", constrfile):\n kc_symbols2 := kc_symbols:\n kin_constraints_exist := true:\nend if:\n# Parameter f\u00fcr implizite Zwangsbedingungen (dadurch k\u00f6nnen auch neue Konstanten hinzugef\u00fcgt werden)\nconstrfile := sprintf(\"../codeexport/%s/tmp/kinematic_implicit_constraints_symbols_list_maple\", robot_name):\n# F\u00fcr implizite Zwangsbedingungen ist \"robot_name\" das System mit IC und nicht mit OL o.\u00e4.\nif FileTools[Exists](constrfile) then\n read constrfile:\n printf(\"Symbole der impliziten Zwangsbedingungen aus %s gelesen.\\n\", constrfile):\n kc_symbols2 := :\n kin_constraints_exist := true:\nend if:\n# Liste der Kinematikparameter erstellen\n# Alle einzelnen MDH-Parametervektoren stapeln\npkin_tmp1 := :\n# Kinematikparameter f\u00fcr kinematische Zwangsbedingungen hinzuf\u00fcgen (falls vorhanden)\nif kin_constraints_exist then\n pkin_tmp1 := :\n np_kc := ColumnDimension(kc_symbols2):\nelse\n np_kc := 0:# Anzahl der Kinematikparameter f\u00fcr die Zwangsbedingungen\nend if:\n# Alle Symbole herausfinden\n# Durch den Befehl fallen die vektoriell angesprochenen Gelenkkoordinaten (qJ) weg.\n# TODO: Liste mit besserer Reihenfolge (siehe Dateikopf)\nnms:=convert(indets(pkin_tmp1,name),list):\n# Laufende Nummer f\u00fcr Parameterliste\nkk := 0:\n# Matrix mit Platz f\u00fcr alle Kinematikparameter (falls alle ungleich Null)\npkin_tmp2 := Matrix(NJ*6+np_kc,1):\n# Terme aus Liste entfernen\nfor i from 1 to ColumnDimension(nms) do\n if nms[i] = Pi then # (wird im Code sowieso automatisch eingesetzt)\n next:\n end if:\n if nms[i] = t then # sollte eigentlich gar nicht drin sein k\u00f6nnen\n next:\n end if:\n # Parameter zur Liste hinzuf\u00fcgen\n kk := kk + 1:\n pkin_tmp2[kk,1] := nms[i]:\nend do:\n# Konstante Winkel, die aus MDH-Definition und nicht aus den ZB kommen umwandeln.\nq_s := Matrix(1,1,0): q_t :=q_s:\npkin_tmp1 := convert_t_s(pkin_tmp1):\n# Konvertierung nochmals durchf\u00fchren (damit nicht delta8 und delta8s als verschiedene Symbole auftauchen)\npkin_tmp2 :=convert_t_s(pkin_tmp2):\n# Ausgabevariable belegen\npkin := Matrix(pkin_tmp2[1..kk,1],kk,1):\n# Symbole nochmals gruppieren\npkin := Transpose(Matrix(convert(indets(pkin,name),list))):\n# Ergebnis speichern\n# F\u00fcr Generierung des Kinematikparametervektors in Matlab\nMatlabExport(pkin, sprintf(\"../codeexport/%s/tmp/parameter_kin_matlab.m\", robot_name), 2):\n# F\u00fcr schnelle Erkennung der Dimension zum Auslesen durch Bash-Skripte\nsave pkin, sprintf(\"../codeexport/%s/tmp/parameter_kin\", robot_name):\n# Zuordnung zwischen Kinematikparametern und MDH-Parametern\n# Mit der Zuordnung kann der Vektor der Kinematikparameter (der an jede Funktion \u00fcbergeben wird) aus den MDH-Parametern bestimmt werden\n# TODO: Dieser Ansatz funktioniert nur, wenn keine Additionen von Variablen in den MDH-Parametern enthalten sind.\n# Schritt 1: pkin_tmp1 nachverarbeiten: Gelenkvariablen und Pi entfernen (damit der solve-Befehl weniger zu verarbeiten hat)\npkin_tmp3 := pkin_tmp1: # Variable, die gestapelt eine nachbearbeitete Version aller MDH-Parameter enth\u00e4lt\n;\nfor i from 1 to RowDimension(pkin_tmp3) do\n # q entfernen\n for j from 1 to RowDimension(qJ_t) do\n pkin_tmp3(i,1) := subs({qJ_t(j,1)=0}, pkin_tmp3(i,1)):\n end do:\n # Term Null setzen, wenn keine Variablen drin stehen (z.B. nur Pi)\n nms:=convert(indets(pkin_tmp3(i),name),list):\n var_da := 0: # Z\u00e4hler, ob Variablen enthalten sind\n for k from 1 to ColumnDimension(nms) do\n if nms[k] = Pi then # Pi ist Konstante und funktioniert sp\u00e4ter nicht im Solve-Befehl\n next:\n end if:\n var_da := 1:\n end do:\n if var_da = 0 then\n pkin_tmp3(i,1) := 0:\n end if:\nend do:\n\npkin_subs_mdh:=copy(pkin): # ohne \"copy\" wird anscheinend verlinkt und der Rest geht nicht\n;\npkt3i := Matrix(RowDimension(pkin_tmp3), 1): # Index-Vektor f\u00fcr pkin_tmp3\n;\nfor i from 1 to RowDimension(pkin_tmp3) do\n pkt3i(i,1):=parse(sprintf(\"pp%03d\", i)): # Hilfsgr\u00f6\u00dfe zum sp\u00e4teren Ersetzen\nend do:\n# Ersetze \n\nfor i from 1 to RowDimension(pkin_tmp3) do\n if pkin_tmp3(i) = 0 then\n next:\n end if:\n for j from 1 to RowDimension(pkin) do\n # printf(\"i=%d, j=%d\\n\", i, j):\n erg := solve({pkin_tmp3(i)=pkt3i(i)}, pkin(j)):\n if ArrayTools:-NumElems(erg) = 0 then\n next:\n end if:\n # printf(\"i=%d\\n\", i):\n pkin_subs_mdh(j) := subs({lhs(erg[1])=rhs(erg[1])}, pkin_subs_mdh(j)):\n break: # Der erste Fund reicht\n end do:\nend do:\n\n# Ergebnis nachverarbeiten\n# Platzhalter (\"ph\") generieren (f\u00fcr die Eingabeargumente der Matlab-Funktion zur Berechnung der Parameter)\nbeta_ph := Matrix(NJ,1):\nb_ph := Matrix(NJ,1):\nalpha_ph := Matrix(NJ,1):\na_ph := Matrix(NJ,1):\ntheta_ph := Matrix(NJ,1):\nd_ph := Matrix(NJ,1):\nqoffset_ph := Matrix(NJ,1):\nfor i from 1 to NJ do\n beta_ph(i) := parse(sprintf(\"beta_mdh(%d)\", i)):\n b_ph(i) := parse(sprintf(\"b_mdh(%d)\", i)):\n alpha_ph(i) := parse(sprintf(\"alpha_mdh(%d)\", i)):\n a_ph(i) := parse(sprintf(\"a_mdh(%d)\", i)):\n theta_ph(i) := parse(sprintf(\"theta_mdh(%d)\", i)):\n d_ph(i) := parse(sprintf(\"d_mdh(%d)\", i)):\n qoffset_ph(i) := parse(sprintf(\"qoffset_mdh(%d)\", i)):\nend do:\n# Platzhalter-Vektor zur Ersetzung der gestapelten MDH-Parameter\npkt1_ph := :\n# Kinematikparameter f\u00fcr kinematische Zwangsbedingungen hinzuf\u00fcgen (falls vorhanden)\n#TODO (aktuell wird das Problem mit der NaN-Ersetzung unten umgangen).\n;\n# Parameter-Indizes mit den Platzhaltern f\u00fcr die Matlab-Funktion ersetzen\nfor i from 1 to RowDimension(pkin_subs_mdh) do\n for j from 1 to RowDimension(pkt1_ph) do\n pkin_subs_mdh(i) := subs( {pkt3i(j)=pkt1_ph(j)}, pkin_subs_mdh(i) ):\n end do:\nend do:\n# Ersetze alle noch nicht ersetzten Kinematikparameter mit NaN. Ansonsten ist der Matlab-Code nicht lauff\u00e4hig und es treten nachgelagerte Probleme auf.\nfor i from 1 to RowDimension(pkin_subs_mdh) do\n for j from 1 to RowDimension(pkt3i) do\n if has(pkin_subs_mdh(i), pkt3i(j)) then\n printf(\"Die Variable %s kommt noch in der Umrechnung mdh->pkin vor. Vermutlich Fehler beim substituieren. Setze NaN.\\n\", String(pkt3i(j))):\n pkin_subs_mdh(i) := subs( {pkt3i(j)=NaN}, pkin_subs_mdh(i) ):\n end if:\n end do:\n for j from 1 to RowDimension(kintmp_s) do\n if has(pkin_subs_mdh(i), kintmp_s(j)) then\n printf(\"Die Variable %s kommt noch in der Umrechnung mdh->pkin vor. Vermutlich Fehler beim substituieren. Setze NaN.\\n\", String(kintmp_s(j))):\n pkin_subs_mdh(i) := subs( {kintmp_s(j)=NaN}, pkin_subs_mdh(i) ):\n end if:\n\n end do:\nend do:\n\n# Folgender Term muss immer erzeugt werden (wird f\u00fcr Bash-Skripte ben\u00f6tigt. Sonst dort Fehler und Abbruch).\ninterface(warnlevel=0): # Unterdr\u00fccke die folgende Warnung (weil MDH-Parameter als Funktionsnamen interpretiert werden. Code funktioniert trotzdem.)\nMatlabExport(pkin_subs_mdh, sprintf(\"../codeexport/%s/tmp/parameter_kin_from_mdh_matlab.m\", robot_name), 2):\ninterface(warnlevel=3):\n\n# Ausgabe\n# MDH-Tabelle ausgeben\ninterface(rtablesize=100):\nTest := < | sigma| mu| beta| b | alpha | a | theta | d | v>:\nTest:=<<\"i\" | \"sigma\" | \"mu\"|\"beta\"|\"b\"|\"alpha\"|\"a\"|\"theta\"|\"d\"|\"v\">,Test>:\nprintf(\"MDH-Tabelle f\u00fcr %s:\\n\", robot_name):\nTest;\nprintf(\"Kinematik-Parameter f\u00fcr %s: %dx%d\\n\", robot_name, RowDimension(pkin), ColumnDimension(pkin)):\nTranspose(pkin);\n\n", "meta": {"hexsha": "0455798975075ef8dde6cdb36b9d2eeb00510443", "size": 9333, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "robot_codegen_definitions/robot_tree_kinematic_parameter_list.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_kinematic_parameter_list.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_kinematic_parameter_list.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": 44.0235849057, "max_line_length": 192, "alphanum_fraction": 0.7424193721, "num_tokens": 2965, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.6859494550081925, "lm_q2_score": 0.5195213219520929, "lm_q1q2_score": 0.35636536765817384}} {"text": "`type/pN2spart` := proc(spart)\n return isSpartValid(spart);\nend proc:\n\n`type/a_indet` := proc(a) local bool;\n\tif convert(a,string)[1] = \"a\" and type(a,indexed) then bool:=true; else bool:=false; end if;\n\treturn bool; \nend proc:\n\n`type/b_indet` := proc(a) local bool;\n\tif convert(a,string)[1] = \"b\" and type(a,indexed) then bool:=true; else bool:=false; end if;\n\treturn bool; \nend proc:\n`type/z_var` := proc(expr) local bool;\n\tbool:=false;\n\tif convert(expr, string)[1]= \"z\" and type(expr, commutative) and nops(indets(expr)) <2 and degree(expr)=1 then bool:=true; end if; \n\treturn bool;\nend proc:\n\n`type/AC_phi` := proc(expr) local bool;\n\tbool:=false; \n\tif convert(expr, string)[1..3] = \"phi\" and type(expr, anticommutative) and nops(indets(expr)) <2 then bool:= true; end if;\n\treturn bool;\nend proc:\n\n`type/AC_theta` := proc(expr) local bool;\n\tbool:=false; \n\tif convert(expr, string)[1..3] = \"the\" and type(expr, anticommutative) and nops(indets(expr)) <2 then bool:= true; end if;\n\treturn bool;\nend proc:\n\n`type/powersum_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"p[\" and type(expr,indexed) then bool := true; else bool:= false; end if;\n return bool;\nend proc:\n\n`type/monomial_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"m[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/homogeneous_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"h[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/elementary_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"e[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n`type/g_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"g[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/schur_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"s[\" and convert(expr,string)[2] <> \"b\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/schurEtoile_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..4] = \"sEt[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/schurbar_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..5] = \"sbar[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n`type/schurbarEtoile_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..7] = \"sbarEt[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/ep_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..3] = \"ep[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/ph_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..3] = \"ph[\" and type(expr, indexed) then bool := true; else bool := false; end if;\n return bool;\nend proc:\n\n`type/jack_symbolic` := proc(expr) local bool;\n\tif convert(expr,string)[1..2] = \"P[\" and type(expr, indexed) then bool := true; else bool := false; end if;\nend proc:\n\n`type/superbase` := proc(expr) local bool;\n\tbool:= type(expr, monomial_symbolic) or type(expr, powersum_symbolic) or type(expr, elementary_symbolic) or type(expr, homogeneous_symbolic) or type(expr, g_symbolic) or type(expr, schur_symbolic) or type(expr, schurEtoile_symbolic) or type(expr, schurbar_symbolic) or type(expr, schurbarEtoile_symbolic) or type(expr, ep_symbolic) or type(expr, ph_symbolic) or type(expr, jack_symbolic);\n\treturn bool; \nend proc:\n\n`type/superindexed`:= proc(expr) local bool;\n\tbool:= type(expr, indexed) and type([op(expr)], pN2spart);\n\treturn bool;\nend proc:\n\n\nsuper_whattype:= proc(expr)\n\tlocal element_of_basis, sample, types, which_one, the_one;\n\telement_of_basis:= indets(expr, superbase);\n\tif nops(element_of_basis) = 0 then return other; end if;\n\tsample:= element_of_basis[1];\n\ttypes:= [\n\t\t\t\tpowersum_symbolic, \n\t\t\t\tmonomial_symbolic, \n\t\t\t\thomogeneous_symbolic, \n\t\t\t\telementary_symbolic, \n\t\t\t\tg_symbolic, \n\t\t\t\tschur_symbolic, \n\t\t\t\tschurEtoile_symbolic, \n\t\t\t\tschurbar_symbolic, \n\t\t\t\tschurbarEtoile_symbolic, \n\t\t\t\tep_symbolic,\n\t\t\t\tph_symbolic,\n\t\t\t\tjack_symbolic\n\t\t\t];\n\twhich_one:= map(x-> type(sample, x), types);\n\tthe_one:= ListTools:-Search(true, which_one);\n\treturn types[the_one]; \nend proc:\n", "meta": {"hexsha": "612cbc535c573201f1dc80fa6b5793ca8796ab16", "size": 4509, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/types.mpl", "max_stars_repo_name": "LAV42/N2-Superpolynomials", "max_stars_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": "lib/types.mpl", "max_issues_repo_name": "LAV42/N2-Superpolynomials", "max_issues_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": "lib/types.mpl", "max_forks_repo_name": "LAV42/N2-Superpolynomials", "max_forks_repo_head_hexsha": "237274e69b04d206f96d2c15f0f066a3677e47e0", "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": 36.6585365854, "max_line_length": 389, "alphanum_fraction": 0.6881791972, "num_tokens": 1343, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.640635854839898, "lm_q2_score": 0.5544704649604273, "lm_q1q2_score": 0.35521366030339907}} {"text": "type $SS \nvar $sconst1 ,\n @f33 i32,\n @f44 i32,\n @f55 f32,\n @f66 f32}> = [ 6=1007.0f, 2= [1=11.11f, 2=22.22f], 3=-273, 4=75, 1=1425926, 5=6023.0f ]\nfunc $printf (var %p1 <* i8>)void\nfunc $main ( ) i32 {\n call &printf (addrof a32 $sconst1)\n return (constval i32 0) }\n\n\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": "0a9dd08bb4ddd3d158e662307d60a75bbb85e4fa", "size": 496, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "testsuite/irbuild_test/I0075-mapleall-irbuild-edge-substructinit/Main.mpl", "max_stars_repo_name": "openmaple/MapleCompiler", "max_stars_repo_head_hexsha": "1648e63144766563f1ec44a25e0b618415648627", "max_stars_repo_licenses": ["MulanPSL-1.0"], "max_stars_count": 5, "max_stars_repo_stars_event_min_datetime": "2019-09-02T04:44:52.000Z", "max_stars_repo_stars_event_max_datetime": "2021-11-08T12:23:51.000Z", "max_issues_repo_path": "testsuite/irbuild_test/I0075-mapleall-irbuild-edge-substructinit/Main.mpl", "max_issues_repo_name": "venshine/OpenArkCompiler", "max_issues_repo_head_hexsha": "264cd4463834356658154f0d254672ef559f245f", "max_issues_repo_licenses": ["MulanPSL-1.0"], "max_issues_count": 2, "max_issues_repo_issues_event_min_datetime": "2020-07-21T01:22:01.000Z", "max_issues_repo_issues_event_max_datetime": "2021-12-06T08:07:16.000Z", "max_forks_repo_path": "testsuite/irbuild_test/I0075-mapleall-irbuild-edge-substructinit/Main.mpl", "max_forks_repo_name": "venshine/OpenArkCompiler", "max_forks_repo_head_hexsha": "264cd4463834356658154f0d254672ef559f245f", "max_forks_repo_licenses": ["MulanPSL-1.0"], "max_forks_count": 4, "max_forks_repo_forks_event_min_datetime": "2019-09-02T04:46:52.000Z", "max_forks_repo_forks_event_max_datetime": "2020-09-10T11:30:03.000Z", "avg_line_length": 23.619047619, "max_line_length": 95, "alphanum_fraction": 0.5322580645, "num_tokens": 212, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. YES", "lm_q1_score": 0.588889130767832, "lm_q2_score": 0.600188359260205, "lm_q1q2_score": 0.3534444011817134}} {"text": "# This defines the chain complex version of the Barratt-Eccles operad.\n# Basis elements of E(A) are represented by expressions T(...), where\n# there is at least one argument, each argument is a list containing\n# each element of A precisely once, and no two adjacent arguments are\n# the same.\n\n`is_element/barratt_eccles` := (A::set) -> proc(x)\n local y,z,i;\n \n if x = 0 then return true; fi;\n \n if type(x,`+`) then\n return `and`(op(map(`is_element/barratt_eccles`(A),[op(x)])));\n fi;\n\n if type(x,`*`) then\n y,z := selectremove(type,[op(x)],integer);\n return (nops(z) = 1 and `is_element/barratt_eccles`(A)(z[1]));\n fi;\n \n if not type(x,specfunc(T)) then return false; fi;\n\n if nops(T) = 0 then return false; fi;\n \n for i from 1 to nops(x) do\n if not(`is_element/ord`(A)(op(i,x))) then\n return false;\n fi;\n od;\n\n for i from 1 to nops(x) - 1 do\n if op(i,x) = op(i+1,x) then return false; fi;\n od;\n\n return true;\nend:\n\n# Auxiliary function feeding into `diff/barratt_eccles`\n\n`diff0/barratt_eccles` := (A::set) -> proc(x)\n local y,n,i;\n \n y := 0;\n n := nops(x);\n\n for i from 1 to n do\n if 1 < i and i < n and op(i-1,x) = op(i,x) then\n continue;\n fi;\n\n y := y + (-1)^(i-1) * T(op(1..i-1,x),op(i+1..n,x));\n od;\n \n return y;\nend:\n\n# Differential on the chain complex\n`diff/barratt_eccles` := (A::set) -> apply_linear(`diff0/barratt_eccles`(A));\n\n# Auxiliary function feeding into `deg/barratt_eccles`\n`deg0/barratt_eccles` := (A) -> (x) -> nops(x) - 1;\n\n# Degree function\n`deg/barratt_eccles` := (A) -> apply_deg(`deg0/barratt_eccles`(A));\n\n# This is the circle product for the operad structure.\n# It is assumed that B is a subset of A and u is in E(A/B) and v is in E(B),\n# where A/B is implemented as A \\ B u {B}.\n\n`o0/barratt_eccles` := (A,B) -> proc(u,v)\n local d,e,SS,x,s,p,w,u0,v0,w0,i;\n \n d := nops(u) - 1;\n e := nops(v) - 1;\n SS := `list_elements/shuffles`(d,e);\n\n x := 0;\n \n for s in SS do \n p := `to_grid_path/shuffles`(d,e)(s);\n w := NULL;\n for i from 0 to d+e do\n u0 := op(p[i][1]+1,u);\n v0 := op(p[i][2]+1,v);\n w0 := subs(B = op(v0),u0);\n w := w,w0;\n od:\n x := x + `sgn/shuffles`(d,e)(s) * T(w);\n od:\n\n return x;\nend:\n\n`o/barratt_eccles` := (A,B) -> apply_bilinear(`o0/barratt_eccles`(A,B));\n\n# We now have various functions related to an interesting filtration\n# of the operad.\n`flip_count/barratt_eccles` := (A::set) -> proc(x)\n local m,a,b,k,rr,i,r0,r1;\n \n m := table():\n for a in A do\n for b in A do\n m[a,b] := 0;\n od;\n od;\n\n k := nops(x);\n rr := map(`rank_table/ord`(A),[op(x)]);\n \n for i from 1 to k-1 do\n r0 := rr[i];\n r1 := rr[i+1];\n \n for a in A do\n for b in A do\n if (r1[b] - r1[a]) * (r0[b] - r0[a]) < 0 then\n m[a,b] := m[a,b] + 1;\n fi;\n od;\n od;\n od;\n\n return eval(m);\nend:\n\n`flip_count_matrix/barratt_eccles` := (A::set) -> proc(u,s_)\n local m;\n m := `flip_count/barratt_eccles`(A)(args);\n return Matrix([seq([seq(m[a,b],b in A)],a in A)]);\nend:\n\n`max_flip_count/barratt_eccles` := (A::set) -> proc(x)\n local m,mm,a,b;\n \n m := `flip_count/barratt_eccles`(A)(x);\n\n mm := 0;\n for a in A do\n for b in A do\n mm := max(mm,m[a,b]);\n od;\n od;\n\n return mm;\nend:\n\n`is_member/barratt_eccles_cells` := (A::set) -> proc(ms)\n local m,s,AA,a,b;\n \n if not(type(ms,list) and nops(ms) = 2) then return false; fi;\n\n m,s := op(ms);\n\n if not(`is_element/ord`(A)(s)) then return false; fi;\n if not(type(m,table)) then return false; fi;\n\n AA := {seq(seq([a,b],b in A),a in A)};\n if {indices(m)} <> AA then return false; fi;\n \n for a in A do\n for b in A do\n if not(type(m[a,b],nonnegint)) then return false; fi;\n od:\n od:\n\n for a in A do\n if m[a,a] <> 0 then return false; fi;\n for b in A do\n if m[a,b] <> m[b,a] then return false; fi;\n od;\n od;\n\n return true;\nend:\n\n`is_cell_member/barratt_eccles` := (A::set) -> (ms) -> proc(x)\n local m0,m1,s,a,b,y,z;\n\n if x = 0 then return true; fi;\n if type(x,`+`) then\n return `and`(seq(`is_cell_member/barratt_eccles`(A)(ms)(y),y in x));\n fi;\n if type(x,`*`) then\n y,z := selectremove(type,[op(x)],integer);\n if nops(z) = 1 then\n return `is_cell_member/barratt_eccles`(A)(ms)(z[1]);\n else\n return false;\n fi;\n fi;\n \n m0,s := op(ms);\n m1 := `flip_count/barratt_eccles`(A)(T(op(x),s));\n\n for a in A do\n for b in A do\n if m1[a,b] > m0[a,b] then return false; fi;\n od;\n od;\n\n return true;\nend:\n\n`filtration0/barratt_eccles` := (A::set) -> proc(x)\n local m,m_max,s,rr,k,i,r0,r1,a,b;\n\n if type(x,integer) then return 0; fi;\n\n return 1 + `max_flip_count/barratt_eccles`(A)(x);\nend:\n\n`filtration/barratt_eccles` := (A::set) ->\n apply_max_deg(`filtration0/barratt_eccles`(A));\n\n", "meta": {"hexsha": "4eb26eb4ac048f1c950cdc003e48d0bc375428f6", "size": 4581, "ext": "mpl", "lang": "Maple", "max_stars_repo_path": "lib/operads/barratt_eccles.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/barratt_eccles.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/barratt_eccles.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": 21.2083333333, "max_line_length": 77, "alphanum_fraction": 0.6005239031, "num_tokens": 1700, "lm_name": "Qwen/Qwen-72B", "lm_label": "1. YES\n2. NO", "lm_q1_score": 0.7799929002541067, "lm_q2_score": 0.44939263446475963, "lm_q1q2_score": 0.3505230643090015}}