data/code/maple/0.35-0.40.jsonl

{"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 <x[2]^2+x[3]^2|-x[1]*x[2]|-x[1]*x[3]>,\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 für 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 müssen.\n# Autor\n# Tim Job (Studienarbeit bei Moritz Schappler), 2019-4\n# Moritz Schappler, moritz.schappler@imes.uni-hannover.de\n# (C) Institut für Mechatronische Systeme, Universität Hannover\n# Initialization\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(ArrayTools):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools):\n# Einstellungen für Code-Export: Optimierungsgrad (2=höchster) 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 für %s\\n\", robot_name):\ncodegen_opt := 0: # Soll nicht von Einstellung in robot_env überschrieben werden.\n;\n# Funktion symmat2vector für den Roboter definieren\n# Erstelle eine Dummy-Variable (mv), die als temporäre Variable in Matlab dient (zum Zusammensetzen der Matrix).\nclear('mv'):\nM_NX:= vec2mat(mv, NX):\n# Warnungen bei Code-Generierung unterdrücken. 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 n<m then return(true); fi;\n return(false);\nend:\n\nQ_terms := proc(x) \n if type(x,specfunc(integer,Q)) then\n  return([x]);\n elif type(x,`*`) then\n  return(select(type,[op(x)],specfunc(integer,Q)));\n elif type(x,`+`) then\n  return(map(op,map(Q_terms,[op(x)])));\n else\n  return([]);\n fi;\nend:\n\nQ_bot := proc(x)\n local t;\n t := sort(Q_terms(x),Q_comp);\n if t = [] then\n  return(0);\n else\n  return(t[1]);\n fi;\nend:\n\nQ_top := proc(x)\n local t;\n t := sort(Q_terms(x),Q_comp);\n if t = [] then\n  return(0);\n else\n  return(t[nops(t)]);\n fi;\nend:\n\noQ := proc(a,b)\n local n,aa,bb;\n if type(a,`+`) then\n  return(map(oQ,a,b));\n elif type(b,`+`) then\n  return(map2(oQ,a,b));\n fi;\n if type(a,`*`) then\n  n,aa := selectremove(type,a,integer);\n  if n<>1 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": "\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 für allgemeinen Roboter\n# chain -> Berechnung für eine serielle Struktur (nicht: Baumstruktur)\n# fixb -> fixed base. Kein Floating base Modell. Dort ist diese Form der Minimalparameterform nicht möglich.\n# rotmat -> Kinematik wird mit Rotationsmatrizen berechnet\n# NewtonEuler -> Berechnung der Newton Euler Bewegungsgleichung\n# regressor -> Regressorform (parameterlinear)\n# \n# Initialisierung\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\ninterface(rtablesize=100): # Zur Anzeige von größeren 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 für %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 Abschätzen der Komplexität\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: # Standardmäßig aus\n  else # mit kinematischen Zwangsbedingungen\n    use_simplify := 1: # standardmäßig simplify-Befehle anwenden\n  end if:\nelse # Benutzer-Einstellungen:\n  use_simplify := simplify_options(10): # zehnter Eintrag ist für 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 Vorwärtsrekursive für Fixed-Base Modelle generiert. Erkenne welche Basis-Modellierung aktiv ist\nif base_method_name=\"twist\" then # Basis-Methode \"twist\" wird (hier) nur für 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 Verfügung. \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. Länge: %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. Länge: %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. Länge: %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_Schnittkräfte\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. Länge: %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-Ausdrücke 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": "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": "`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 := <IdentityMatrix(nx)|Matrix(nx,n1-nx)>;\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 := <SubMatrix(L,1..n2,1..nx)|Matrix(n2,n2-nx)>;\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,<M0|V0>,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": "#!/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 ≥ 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 ≥ 0 and k ≥ 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": "#######################################################################\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<nops(pw),\n                                   op(i,pw),\n                                   subs(pw=op(i,pw), e)),\n                              i=1..nops(pw)));\n          return termize(pw, var, kb);\n        end if;\n      else\n        # Yay, the conditions don't depend on var.\n        # So just map into the piecewise.\n        res := kb_piecewise(e, kb, ((cond, kb) -> 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<nops(res), i, [i,1]), res),\n                               i=1..nops(res))),\n                 piecewise(seq(op(`if`(i::odd and i<nops(res), i, [i,2]), res),\n                               i=1..nops(res)));\n        elif res :: '[anything, anything]' then\n          return op(res)\n        end if;\n      end if;\n    end if;\n    e, 0;\n  end proc;\n\n  export\n  unweight := proc(m, $)\n    local total, ww, mm;\n    if m :: 'Weight(anything, anything)' then\n      op(m)\n    elif m :: 'specfunc(Msum)' then\n      total := `+`(op(map((mi -> 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": "\n# Berechnung und Projektion der Dynamikgleichungen\n# Einleitung\n# Berechnung und Projektion der Dynamikgleichungen\n# \n# Dateiname:\n# robot -> Berechnung für allgemeinen Roboter\n# para -> Berechnung für 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 für Mechatronische Systeme, Universität 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 strukturunabhängigen Dynamikmodellierung für parallelkinematische Maschinen (2018)\n# Initialization\ninterface(warnlevel=0): # Unterdrücke die folgende Warnung.\nrestart: # Gibt eine Warnung, wenn über Terminal-Maple mit read gestartet wird.\ninterface(warnlevel=3):\nwith(LinearAlgebra):\nwith(codegen):\nwith(CodeGeneration):\nwith(StringTools): # Für Zeitausgabe\n;\n# Einstellungen für Code-Export: Optimierungsgrad (2=höchster).\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 standardmäßig (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, für 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 zusätzlichen Definitionen für 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 Löschung 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 für 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 Löschung des Roboternamens.\nend if:\nread \"../robot_codegen_definitions/robot_env_par\": # Nochmal laden, um Standard-Einstellungen überschreiben zu können.\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 Körper 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 berücksichtigt. 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 Löschung des Roboternamens.\nend if:\nG := simplify2(Matrix(taug_s(7..NQ,1))):\nunassign('g1','g2','g3'):\ng := <g1;g2;g3>:\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 Löschung 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 Löschung des Roboternamens.\nend if:\nMM := simplify(MM_s(7..NQ,7..NQ)):\nMM := simplify(MM):\nMME := simplify(MME):\n# Ausdruck für Gravitationsterme der Plattform nochmal vereinfachen.\ngE := simplify2(gE):\n# Ergebnisse der Kinematik für 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 für 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 für alle Beine\n# Dupliziere alle berechneten Matrizen. i steht für 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 Kräfte/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 Kräfte, 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 über 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# Wähle die Einträge aus Dynamikgleichungen, die für Freiheitsgrade des Roboters relevant sind.\n# (über 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 späteren 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 wählen 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 späteren 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": "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": "# 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<nops(r) and op(2,r)::t then return FAIL end if\n      end do;\n      e\n    end proc;\n  end module; # elim\nend module; # reduce_Integrals\n\nint_assuming := proc(e, v::name=anything, kb::t_kb, $)\n  simplify_factor_assuming('int'(e, v), kb);\nend proc;\n\nsum_assuming := proc(e, v::name=anything, kb::t_kb)\n  simplify_factor_assuming('sum'(e, v), kb);\nend proc;\n\n# Int( .., var=var_ty ) == var &X var_ty\nisBound_IntSum := kind -> 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": "(*\n    以代表元为核心的对象\n    主要以con划分对象，isol和tsol仅做参考作用\n    保证RepSol对象的所有属性的相关变量都是global的。\n*)\n$ifndef _REPSOL_\n$define _REPSOL_\n\nRepSol:=module()\n    option object;\n    local  \n            # 局部函数 \n            getDisplayDcon::static, # 合并显示成立条件\n            apList::static,         # 拓展list\n            rmlist::static;         # 去除一层嵌套list\n    export  \n            # 导出变量\n            rep,                    # 代表元\n            dcon:=[],               # 不变量方程\n            acon:=[],               # 附加约束 \n            isol:=[],               # 代表元的通解\n            tsol:=[],               # 代表元通解和特解的转化\n            osol:=[],               # 对应的InvSol对象\n            sid:=1,                 # 选择的最简条件   \n            # 导出函数\n            ## 设置相关\n            appendSol::static,      # 扩充一个RepSol对象成立的条件\n            getCon::static,         # 获取一个RepSol对象成立的条件\n            sortCon::static,        # 对成立条件进行排序\n            selectCon::static,      # 选择最简成立条件\n            rmCon::static,          # 删除某个成立条件的一部分\n            ## 输出相关\n            printRep::static,       # 简要显示代表元和所有可能的成立条件\n            fullPrintRep::static,   # 显示代表元和完整的成立条件以及对应的不变量方程和变换方程的解\n            ModulePrint::static,    # 简要显示代表元\n            uniqueAndSort::static;      # 删去重复条件\n\n    # 用于拓展一个代表元对象所能代表的区域\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    # 拓展list\n    apList:=proc(lst::evaln)\n        lst:=[eval(lst)[],_rest];\n        return;\n    end proc:\n\n    # 获取一个RepSol对象成立的条件\n    getCon:=proc(r::RepSol)\n        return zip((x,y)->[getDisplayDcon(x)[],y[]],r:-dcon,r:-acon);\n    end proc:\n\n    # 不变量方程的简化显示\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    # 去掉一层嵌套list\n    rmlist:=proc(x)\n        return map(y->y[],x);\n    end proc:\n\n    # 对成立条件进行排序\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    # 选择最简成立条件\n    selectCon:=proc(r::RepSol,sid)\n        r:-sid:=sid;\n        return;\n    end proc:\n\n    # 删除某个成立条件的一部分\n    rmCon:=proc(r::RepSol,id::posint,con::set)\n        r:-acon[id]:=r:-acon[id] minus con;\n    end proc:\n\n    # 简要显示代表元和所有可能的成立条件\n    printRep:=proc(r::RepSol)\n        print(r:-rep);\n        print~(getCon(r));\n        return ;\n    end proc:\n\n    # 显示代表元和完整的成立条件以及对应的不变量方程和变换方程的解\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    # 删去重复条件\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    # 简要显示代表元\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": "`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": "`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": "# 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}}