Commit fb338180 authored by Philippe Helluy's avatar Philippe Helluy

start patapon kernels

parent 3c3de2af
{VERSION 15 1 "Mac OS X" "15.1" }
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "restart:with(linalg
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20 "7>I,BinaryPlaceG6\"I-BinarySearchGF$I+CategorizeGF$I+DotProductGF$
I*EnumerateGF$I3FindMaximalElementGF$I3FindMinimalElementGF$I0FindRepe
titionsGF$I(FlattenGF$I,FlattenOnceGF$I&GroupGF$I+InterleaveGF$I%JoinG
F$I-JoinSequenceGF$I,LengthSplitGF$I+MakeUniqueGF$I,OccurrencesGF$I$Pa
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dk:=proc(i,j) if (i = j) the
n 1 else 0 fi:end;dk(2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"iG6
\"I\"jGF%F%F%F%@%/9$9%\"\"\"\"\"!F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH
20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "node:=matrix(2
0,3,[0,0,0,1,0,0,1,1,0,0,1,0,0,0,1," }{MPLTEXT 1 0 6 "1,0,1," }
{MPLTEXT 1 0 6 "1,1,1," }{MPLTEXT 1 0 129 "0,1,1,1/2,0,0,0,1/2,0,0,0,1
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,1,1]):node:=convert(node,list);" }}{PARA 11 "" 1 "" {XPPMATH 20 "767%
\"\"!F$F$7%\"\"\"F$F$7%F&F&F$7%F$F&F$7%F$F$F&7%F&F$F&7%F&F&F&7%F$F&F&7
%#F&\"\"#F$F$7%F$F.F$7%F$F$F.7%F&F.F$7%F&F$F.7%F.F&F$7%F&F&F.7%F$F&F.7
%F.F$F&7%F$F.F&7%F&F.F&7%F.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT
1 0 57 "node2:=matrix(20,3):for i to 20 do node2[i,1]:=node[i,2];" }
{MPLTEXT 1 0 22 "node2[i,2]:=node[i,3];" }{MPLTEXT 1 0 107 "node2[i,3]
:=node[i,1];od:node2:=convert(node2,list);permut:=[seq(Search(node2[j]
,node),j=1..20)];C(permut);" }}{PARA 11 "" 1 "" {XPPMATH 20 "767%\"\"!
F$F$7%F$F$\"\"\"7%F&F$F&7%F&F$F$7%F$F&F$7%F$F&F&7%F&F&F&7%F&F&F$7%F$F$
#F&\"\"#7%F.F$F$7%F$F.F$7%F.F$F&7%F$F.F&7%F&F$F.7%F&F.F&7%F&F.F$7%F$F&
F.7%F.F&F$7%F.F&F&7%F&F&F." }}{PARA 11 "" 1 "" {XPPMATH 20 "76\"\"\"\"
\"&\"\"'\"\"#\"\"%\"\")\"\"(\"\"$\"#6\"\"*\"#5\"#<\"#=\"#8\"#>\"#7\"#;
\"#9\"#?\"#:" }}{PARA 6 "" 1 "" {TEXT 213 10 "cg[0] = 1;" }{TEXT 213
11 "\ncg[1] = 5;" }{TEXT 213 11 "\ncg[2] = 6;" }{TEXT 213 11 "\ncg[3] \+
= 2;" }{TEXT 213 11 "\ncg[4] = 4;" }{TEXT 213 11 "\ncg[5] = 8;" }{TEXT
213 11 "\ncg[6] = 7;" }{TEXT 213 11 "\ncg[7] = 3;" }{TEXT 213 12 "\nc
g[8] = 11;" }{TEXT 213 11 "\ncg[9] = 9;" }{TEXT 213 13 "\ncg[10] = 10;
" }{TEXT 213 13 "\ncg[11] = 17;" }{TEXT 213 13 "\ncg[12] = 18;" }{TEXT
213 13 "\ncg[13] = 13;" }{TEXT 213 13 "\ncg[14] = 19;" }{TEXT 213 13
"\ncg[15] = 12;" }{TEXT 213 13 "\ncg[16] = 16;" }{TEXT 213 13 "\ncg[17
] = 14;" }{TEXT 213 13 "\ncg[18] = 20;" }{TEXT 213 13 "\ncg[19] = 15;"
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "P:=vector(20,[1,x,y,z,x
*y,x*z,y*z,x*x,y*y,z*z,x*y*z,x^2*y,x^2*z,y^2*x,y^2*z,z^2*x,z^2*y,x^2*y
*z,x*y^2*z,x*y*z^2]);phi:=vector(20);" }}{PARA 11 "" 1 "" {XPPMATH 20
"=6\"6#;\"\"\"\"#?E\\[l5F&F&\"\"#I\"xGF#\"\"$I\"yGF#\"\"%I\"zGF#\"\"&*
&F*F&F,F&\"\"'*&F*F&F.F&\"\"(*&F,F&F.F&\"\")*$F*F)\"\"**$F,F)\"#5*$F.F
)\"#6*(F*F&F,F&F.F&\"#7*&F*F)F,F&\"#8*&F*F)F.F&\"#9*&F,F)F*F&\"#:*&F,F
)F.F&\"#<*&F.F)F,F&\"#;*&F.F)F*F&\"#>*(F*F&F,F)F.F&\"#=*(F*F)F,F&F.F&F
'*(F*F&F,F&F.F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"#?E\\[
l!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#?find" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "for i to 20 do;phi[i]:=sum(alpha[i,
k]*P[k],k=1..20);eq:=\{seq(subs(x=node[j,1],y=" }{MPLTEXT 1 0 9 "node[
j,2]" }{MPLTEXT 1 0 3 ",z=" }{MPLTEXT 1 0 9 "node[j,3]" }{MPLTEXT 1 0
58 ",phi[i])=dk(i,j),j=1..20)\};inc:=\{seq(alpha[i,l],l=1..20)\};" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "assign(solve(eq,inc));" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 41 "for i to 20 do phi[i]:=factor(phi[i]);od;" }}{PARA 11 "" 1 ""
{XPPMATH 20 "**,&!\"\"\"\"\"I\"zG6\"F%F%,&F$F%I\"yGF'F%F%,&F$F%I\"xGF'
F%F%,*F+\"\"#F)F-F&F-F$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "**I\"xG6
\"\"\"\",&!\"\"F%I\"zGF$F%F%,&F'F%I\"yGF$F%F%,*F*!\"#F(F,F#\"\"#F'F%F%
" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F&,&!\"\"F&
I\"zGF%F&F&,*F'\"\"#F*!\"#!\"$F&F$F,F&F)" }}{PARA 11 "" 1 "" {XPPMATH
20 ",$**I\"yG6\"\"\"\",&!\"\"F&I\"zGF%F&F&,&F(F&I\"xGF%F&F&,*F+\"\"#F)
F-F&F&F$!\"#F&F(" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"zG6\"\"\"\",&
!\"\"F&I\"yGF%F&F&,&F(F&I\"xGF%F&F&,*F+\"\"#F)F-F$!\"#F&F&F&F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"zGF%F&,&!\"\"F&I\"y
GF%F&F&,*F*!\"#F'\"\"#!\"$F&F$F-F&F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "
**I\"xG6\"\"\"\"I\"yGF$F%I\"zGF$F%,*F&\"\"#F'F)!\"&F%F#F)F%" }}{PARA
11 "" 1 "" {XPPMATH 20 "**I\"yG6\"\"\"\"I\"zGF$F%,&!\"\"F%I\"xGF$F%F%,
*F)\"\"#F&!\"#\"\"$F%F#F,F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG
6\"\"\"\",&!\"\"F&I\"zGF%F&F&,&F(F&I\"yGF%F&F&,&F(F&F$F&F&!\"%" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"yG6\"\"\"\",&!\"\"F&I\"zGF%F&F&,&
F(F&F$F&F&,&F(F&I\"xGF%F&F&!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I
\"zG6\"\"\"\",&!\"\"F&F$F&F&,&F(F&I\"yGF%F&F&,&F(F&I\"xGF%F&F&!\"%" }}
{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F&,&!\"\"F&I\"z
GF%F&F&,&F)F&F'F&F&\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"
\"\"\"I\"zGF%F&,&!\"\"F&F'F&F&,&F)F&I\"yGF%F&F&\"\"%" }}{PARA 11 "" 1
"" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F&,&!\"\"F&I\"zGF%F&F&,&F)F&F
$F&F&\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F
&I\"zGF%F&,&!\"\"F&F(F&F&!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"
yG6\"\"\"\"I\"zGF%F&,&!\"\"F&F'F&F&,&F)F&I\"xGF%F&F&\"\"%" }}{PARA 11
"" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"zGF%F&,&!\"\"F&I\"yGF%F&F&,&
F)F&F$F&F&\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"yG6\"\"\"\"I\"
zGF%F&,&!\"\"F&F$F&F&,&F)F&I\"xGF%F&F&\"\"%" }}{PARA 11 "" 1 ""
{XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F&I\"zGF%F&,&!\"\"F&F'F&F&!\"%"
}}{PARA 11 "" 1 "" {XPPMATH 20 ",$**I\"xG6\"\"\"\"I\"yGF%F&I\"zGF%F&,&
!\"\"F&F$F&F&!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "#Dd:=m
atrix(20,20,(i,j)->" }{MPLTEXT 1 0 19 "subs(x=node[j,1],y=" }{MPLTEXT
1 0 21 "node[j,2],z=node[j,3]" }{MPLTEXT 1 0 18 ",phi[i])-dk(i,j));" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(CodeGeneration):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "C(phi);" }}{PARA 6 "" 1 ""
{TEXT 213 70 "phi[0] = (-1 + z) * (-1 + y) * (-1 + x) * (2 * x + 2 * y
+ 2 * z - 1);" }}{PARA 6 "" 1 "" {TEXT 213 64 "phi[1] = x * (-1 + z) \+
* (-1 + y) * (-2 * y - 2 * z + 2 * x - 1);" }{TEXT 213 58 "\nphi[2] = \+
-x * y * (-1 + z) * (2 * y - 2 * z - 3 + 2 * x);" }{TEXT 213 65 "\nphi
[3] = -y * (-1 + z) * (-1 + x) * (2 * x + 2 * z + 1 - 2 * y);" }{TEXT
213 65 "\nphi[4] = -z * (-1 + y) * (-1 + x) * (2 * x + 2 * y - 2 * z +
1);" }{TEXT 213 59 "\nphi[5] = -x * z * (-1 + y) * (-2 * y + 2 * z - \+
3 + 2 * x);" }{TEXT 213 50 "\nphi[6] = x * y * z * (2 * y + 2 * z - 5 \+
+ 2 * x);" }{TEXT 213 57 "\nphi[7] = y * z * (-1 + x) * (2 * x - 2 * z
+ 3 - 2 * y);" }{TEXT 213 50 "\nphi[8] = -4 * x * (-1 + z) * (-1 + y)
* (-1 + x);" }{TEXT 213 50 "\nphi[9] = -4 * y * (-1 + z) * (-1 + y) *
(-1 + x);" }{TEXT 213 51 "\nphi[10] = -4 * z * (-1 + z) * (-1 + y) * \+
(-1 + x);" }{TEXT 213 43 "\nphi[11] = 4 * x * y * (-1 + z) * (-1 + y);
" }{TEXT 213 43 "\nphi[12] = 4 * x * z * (-1 + z) * (-1 + y);" }{TEXT
213 43 "\nphi[13] = 4 * x * y * (-1 + z) * (-1 + x);" }{TEXT 213 37 "
\nphi[14] = -4 * x * y * z * (-1 + z);" }{TEXT 213 43 "\nphi[15] = 4 *
y * z * (-1 + z) * (-1 + x);" }{TEXT 213 43 "\nphi[16] = 4 * x * z * \+
(-1 + y) * (-1 + x);" }{TEXT 213 43 "\nphi[17] = 4 * y * z * (-1 + y) \+
* (-1 + x);" }{TEXT 213 37 "\nphi[18] = -4 * x * y * z * (-1 + y);" }
{TEXT 213 37 "\nphi[19] = -4 * x * y * z * (-1 + x);" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 39 "tau:=vector(3,[0,0,0]);p:=array(1..60);"
}}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"$E\\[l$F&\"\"!\"\"#F)
F'F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"#gE\\[l!" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "#?submatrix" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "i:='i';for k to 3 do tau[k]:=sum(ph
i[i]*p[3*(i-1)+k],i=1..20);od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "I\"iG6
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!\"&F&F,F.F&&F06#\"#?F&F&*,F*F&F'F&F+F&,*F,F.F'F4\"\"$F&F*F4F&&F06#\"#
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$F&F+F&&F06#\"#UF&Fdo*,F,F&F*F&F'F&F$F&&F06#\"#XF&Fgn*,F*F&F'F&F$F&F+F
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3F&F1F&F-F&FipF&Fbp**F1F&F/F&F-F&F]qF&Fdo**F1F&F/F&F-F&FaqF&Fbp**F/F&F
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7F;F<F*F@F;FDF*FHF;FLF*FPF;**F0F&F2F&FUF&F4F&F&**F3F&F0F&FWF&F8F&F&**F
3F&F1F&FYF&F=F&F.**F1F&F2F&FfnF&FAF&F.**F0F&F2F&FhnF&FEF&F.**F3F&F0F&F
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F&Fdo**F1F&F0F&F2F&FfoF&Fdo**F-F&F0F&F2F&F[pF&Fdo**F/F&F0F&F2F&F[pF&Fd
o**F3F&F1F&F0F&F_pF&Fbp**F3F&F-F&F0F&FepF&Fbp**F3F&F/F&F0F&FepF&Fbp**F
3F&F1F&F2F&FipF&Fbp**F3F&F1F&F-F&F]qF&Fdo**F3F&F1F&F/F&F]qF&Fdo**F1F&F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "C(dtau);" }}{PARA 6 "" 1 "" {TEXT
213 256 "dtau[0][0] = 2 * (-1 + z) * (-1 + y) * (-1 + x) * p[0] + 2 * \+
x * (-1 + z) * (-1 + y) * p[3] - 2 * x * y * (-1 + z) * p[6] - 2 * y *
(-1 + z) * (-1 + x) * p[9] - 2 * z * (-1 + y) * (-1 + x) * p[12] - 2 \+
* x * z * (-1 + y) * p[15] + 2 * x * y * z * p[18] + 2 " }{TEXT 213
256 "* y * z * (-1 + x) * p[21] + (-1 + z) * (-1 + y) * (2 * x + 2 * y
+ 2 * z - 1) * p[0] + (-1 + z) * (-1 + y) * (-2 * y - 2 * z + 2 * x -
1) * p[3] - y * (-1 + z) * (2 * y - 2 * z - 3 + 2 * x) * p[6] - y * (
-1 + z) * (2 * x + 2 * z + 1 - 2 * y) * p[9] - z * " }{TEXT 213 256 "(
-1 + y) * (2 * x + 2 * y - 2 * z + 1) * p[12] - z * (-1 + y) * (-2 * y
+ 2 * z - 3 + 2 * x) * p[15] + y * z * (2 * y + 2 * z - 5 + 2 * x) * \+
p[18] + y * z * (2 * x - 2 * z + 3 - 2 * y) * p[21] - 4 * (-1 + z) * (
-1 + y) * (-1 + x) * p[24] - 4 * x * (-1 + z)" }{TEXT 213 256 " * (-1 \+
+ y) * p[24] - 4 * y * (-1 + z) * (-1 + y) * p[27] - 4 * z * (-1 + z) \+
* (-1 + y) * p[30] + 4 * y * (-1 + z) * (-1 + y) * p[33] + 4 * z * (-1
+ z) * (-1 + y) * p[36] + 4 * y * (-1 + z) * (-1 + x) * p[39] + 4 * x
* y * (-1 + z) * p[39] - 4 * y * z * (" }{TEXT 213 233 "-1 + z) * p[4
2] + 4 * y * z * (-1 + z) * p[45] + 4 * z * (-1 + y) * (-1 + x) * p[48
] + 4 * x * z * (-1 + y) * p[48] + 4 * y * z * (-1 + y) * p[51] - 4 * \+
y * z * (-1 + y) * p[54] - 4 * y * z * (-1 + x) * p[57] - 4 * x * y * \+
z * p[57];" }{TEXT 213 257 "\ndtau[0][1] = 2 * (-1 + z) * (-1 + y) * (
-1 + x) * p[0] - 2 * x * (-1 + z) * (-1 + y) * p[3] - 2 * x * y * (-1 \+
+ z) * p[6] + 2 * y * (-1 + z) * (-1 + x) * p[9] - 2 * z * (-1 + y) * \+
(-1 + x) * p[12] + 2 * x * z * (-1 + y) * p[15] + 2 * x * y * z * p[18
] - 2 " }{TEXT 213 256 "* y * z * (-1 + x) * p[21] + (-1 + z) * (-1 + \+
x) * (2 * x + 2 * y + 2 * z - 1) * p[0] + x * (-1 + z) * (-2 * y - 2 *
z + 2 * x - 1) * p[3] - x * (-1 + z) * (2 * y - 2 * z - 3 + 2 * x) * \+
p[6] - (-1 + z) * (-1 + x) * (2 * x + 2 * z + 1 - 2 * y) * p[9] - z *
" }{TEXT 213 256 "(-1 + x) * (2 * x + 2 * y - 2 * z + 1) * p[12] - x *
z * (-2 * y + 2 * z - 3 + 2 * x) * p[15] + x * z * (2 * y + 2 * z - 5
+ 2 * x) * p[18] + z * (-1 + x) * (2 * x - 2 * z + 3 - 2 * y) * p[21]
- 4 * x * (-1 + z) * (-1 + x) * p[24] - 4 * (-1 + z) * (-1 + y)" }
{TEXT 213 256 " * (-1 + x) * p[27] - 4 * y * (-1 + z) * (-1 + x) * p[2
7] - 4 * z * (-1 + z) * (-1 + x) * p[30] + 4 * x * (-1 + z) * (-1 + y)
* p[33] + 4 * x * y * (-1 + z) * p[33] + 4 * x * z * (-1 + z) * p[36]
+ 4 * x * (-1 + z) * (-1 + x) * p[39] - 4 * x * z * (-1 + z)" }{TEXT
213 233 " * p[42] + 4 * z * (-1 + z) * (-1 + x) * p[45] + 4 * x * z * \+
(-1 + x) * p[48] + 4 * z * (-1 + y) * (-1 + x) * p[51] + 4 * y * z * (
-1 + x) * p[51] - 4 * x * z * (-1 + y) * p[54] - 4 * x * y * z * p[54]
- 4 * x * z * (-1 + x) * p[57];" }{TEXT 213 257 "\ndtau[0][2] = 2 * (
-1 + z) * (-1 + y) * (-1 + x) * p[0] - 2 * x * (-1 + z) * (-1 + y) * p
[3] + 2 * x * y * (-1 + z) * p[6] - 2 * y * (-1 + z) * (-1 + x) * p[9]
+ 2 * z * (-1 + y) * (-1 + x) * p[12] - 2 * x * z * (-1 + y) * p[15] \+
+ 2 * x * y * z * p[18] - 2 " }{TEXT 213 256 "* y * z * (-1 + x) * p[2
1] + (-1 + y) * (-1 + x) * (2 * x + 2 * y + 2 * z - 1) * p[0] + x * (-
1 + y) * (-2 * y - 2 * z + 2 * x - 1) * p[3] - x * y * (2 * y - 2 * z \+
- 3 + 2 * x) * p[6] - y * (-1 + x) * (2 * x + 2 * z + 1 - 2 * y) * p[9
] - (-1 + y) * (-1 + x" }{TEXT 213 256 ") * (2 * x + 2 * y - 2 * z + 1
) * p[12] - x * (-1 + y) * (-2 * y + 2 * z - 3 + 2 * x) * p[15] + x * \+
y * (2 * y + 2 * z - 5 + 2 * x) * p[18] + y * (-1 + x) * (2 * x - 2 * \+
z + 3 - 2 * y) * p[21] - 4 * x * (-1 + y) * (-1 + x) * p[24] - 4 * y *
(-1 + y) * (-1 " }{TEXT 213 256 "+ x) * p[27] - 4 * (-1 + z) * (-1 + \+
y) * (-1 + x) * p[30] - 4 * z * (-1 + y) * (-1 + x) * p[30] + 4 * x * \+
y * (-1 + y) * p[33] + 4 * x * (-1 + z) * (-1 + y) * p[36] + 4 * x * z
* (-1 + y) * p[36] + 4 * x * y * (-1 + x) * p[39] - 4 * x * y * (-1 +
z) * p[42" }{TEXT 213 233 "] - 4 * x * y * z * p[42] + 4 * y * (-1 + \+
z) * (-1 + x) * p[45] + 4 * y * z * (-1 + x) * p[45] + 4 * x * (-1 + y
) * (-1 + x) * p[48] + 4 * y * (-1 + y) * (-1 + x) * p[51] - 4 * x * y
* (-1 + y) * p[54] - 4 * x * y * (-1 + x) * p[57];" }{TEXT 213 257 "
\ndtau[1][0] = 2 * (-1 + z) * (-1 + y) * (-1 + x) * p[1] + 2 * x * (-1 + z) * (-1 + y) * p[4] - 2 * x * y * (-1 + z) * p[7] - 2 * y * (-1 + z) * (-1 + x) * p[10] - 2 * z * (-1 + y) * (-1 + x) * p[13] - 2 * x * z * (-1 + y) * p[16] + 2 * x * y * z * p[19] + 2
" }{TEXT 213 256 " * y * z * (-1 + x) * p[22] + (-1 + z) * (-1 + y) * \+
(2 * x + 2 * y + 2 * z - 1) * p[1] + (-1 + z) * (-1 + y) * (-2 * y - 2
* z + 2 * x - 1) * p[4] - y * (-1 + z) * (2 * y - 2 * z - 3 + 2 * x) \+
* p[7] - y * (-1 + z) * (2 * x + 2 * z + 1 - 2 * y) * p[10] - z " }
{TEXT 213 256 "* (-1 + y) * (2 * x + 2 * y - 2 * z + 1) * p[13] - z * \+
(-1 + y) * (-2 * y + 2 * z - 3 + 2 * x) * p[16] + y * z * (2 * y + 2 *
z - 5 + 2 * x) * p[19] + y * z * (2 * x - 2 * z + 3 - 2 * y) * p[22] \+
- 4 * (-1 + z) * (-1 + y) * (-1 + x) * p[25] - 4 * x * (-1 + " }{TEXT
213 256 "z) * (-1 + y) * p[25] - 4 * y * (-1 + z) * (-1 + y) * p[28] -
4 * z * (-1 + z) * (-1 + y) * p[31] + 4 * y * (-1 + z) * (-1 + y) * p
[34] + 4 * z * (-1 + z) * (-1 + y) * p[37] + 4 * y * (-1 + z) * (-1 + \+
x) * p[40] + 4 * x * y * (-1 + z) * p[40] - 4 * y * z *" }{TEXT 213
235 " (-1 + z) * p[43] + 4 * y * z * (-1 + z) * p[46] + 4 * z * (-1 + \+
y) * (-1 + x) * p[49] + 4 * x * z * (-1 + y) * p[49] + 4 * y * z * (-1
+ y) * p[52] - 4 * y * z * (-1 + y) * p[55] - 4 * y * z * (-1 + x) * \+
p[58] - 4 * x * y * z * p[58];" }{TEXT 213 257 "\ndtau[1][1] = 2 * (-1
+ z) * (-1 + y) * (-1 + x) * p[1] - 2 * x * (-1 + z) * (-1 + y) * p[4
] - 2 * x * y * (-1 + z) * p[7] + 2 * y * (-1 + z) * (-1 + x) * p[10] \+
- 2 * z * (-1 + y) * (-1 + x) * p[13] + 2 * x * z * (-1 + y) * p[16] +
2 * x * y * z * p[19] - 2" }{TEXT 213 256 " * y * z * (-1 + x) * p[22
] + (-1 + z) * (-1 + x) * (2 * x + 2 * y + 2 * z - 1) * p[1] + x * (-1
+ z) * (-2 * y - 2 * z + 2 * x - 1) * p[4] - x * (-1 + z) * (2 * y - \+
2 * z - 3 + 2 * x) * p[7] - (-1 + z) * (-1 + x) * (2 * x + 2 * z + 1 -
2 * y) * p[10] - z " }{TEXT 213 256 "* (-1 + x) * (2 * x + 2 * y - 2 \+
* z + 1) * p[13] - x * z * (-2 * y + 2 * z - 3 + 2 * x) * p[16] + x * \+
z * (2 * y + 2 * z - 5 + 2 * x) * p[19] + z * (-1 + x) * (2 * x - 2 * \+
z + 3 - 2 * y) * p[22] - 4 * x * (-1 + z) * (-1 + x) * p[25] - 4 * (-1
+ z) * (-1 + " }{TEXT 213 256 "y) * (-1 + x) * p[28] - 4 * y * (-1 + \+
z) * (-1 + x) * p[28] - 4 * z * (-1 + z) * (-1 + x) * p[31] + 4 * x * \+
(-1 + z) * (-1 + y) * p[34] + 4 * x * y * (-1 + z) * p[34] + 4 * x * z
* (-1 + z) * p[37] + 4 * x * (-1 + z) * (-1 + x) * p[40] - 4 * x * z \+
* (-1 + " }{TEXT 213 235 "z) * p[43] + 4 * z * (-1 + z) * (-1 + x) * p
[46] + 4 * x * z * (-1 + x) * p[49] + 4 * z * (-1 + y) * (-1 + x) * p[
52] + 4 * y * z * (-1 + x) * p[52] - 4 * x * z * (-1 + y) * p[55] - 4 \+
* x * y * z * p[55] - 4 * x * z * (-1 + x) * p[58];" }{TEXT 213 257 "
\ndtau[1][2] = 2 * (-1 + z) * (-1 + y) * (-1 + x) * p[1] - 2 * x * (-1 + z) * (-1 + y) * p[4] + 2 * x * y * (-1 + z) * p[7] - 2 * y * (-1 + z) * (-1 + x) * p[10] + 2 * z * (-1 + y) * (-1 + x) * p[13] - 2 * x * z * (-1 + y) * p[16] + 2 * x * y * z * p[19] - 2
" }{TEXT 213 256 " * y * z * (-1 + x) * p[22] + (-1 + y) * (-1 + x) * \+
(2 * x + 2 * y + 2 * z - 1) * p[1] + x * (-1 + y) * (-2 * y - 2 * z + \+
2 * x - 1) * p[4] - x * y * (2 * y - 2 * z - 3 + 2 * x) * p[7] - y * (
-1 + x) * (2 * x + 2 * z + 1 - 2 * y) * p[10] - (-1 + y) * (-1 +" }
{TEXT 213 256 " x) * (2 * x + 2 * y - 2 * z + 1) * p[13] - x * (-1 + y
) * (-2 * y + 2 * z - 3 + 2 * x) * p[16] + x * y * (2 * y + 2 * z - 5 \+
+ 2 * x) * p[19] + y * (-1 + x) * (2 * x - 2 * z + 3 - 2 * y) * p[22] \+
- 4 * x * (-1 + y) * (-1 + x) * p[25] - 4 * y * (-1 + y) * (-" }{TEXT
213 256 "1 + x) * p[28] - 4 * (-1 + z) * (-1 + y) * (-1 + x) * p[31] -
4 * z * (-1 + y) * (-1 + x) * p[31] + 4 * x * y * (-1 + y) * p[34] + \+
4 * x * (-1 + z) * (-1 + y) * p[37] + 4 * x * z * (-1 + y) * p[37] + 4
* x * y * (-1 + x) * p[40] - 4 * x * y * (-1 + z) * p[" }{TEXT 213
235 "43] - 4 * x * y * z * p[43] + 4 * y * (-1 + z) * (-1 + x) * p[46]
+ 4 * y * z * (-1 + x) * p[46] + 4 * x * (-1 + y) * (-1 + x) * p[49] \+
+ 4 * y * (-1 + y) * (-1 + x) * p[52] - 4 * x * y * (-1 + y) * p[55] -
4 * x * y * (-1 + x) * p[58];" }{TEXT 213 257 "\ndtau[2][0] = 2 * (-1
+ z) * (-1 + y) * (-1 + x) * p[2] + 2 * x * (-1 + z) * (-1 + y) * p[5
] - 2 * x * y * (-1 + z) * p[8] - 2 * y * (-1 + z) * (-1 + x) * p[11] \+
- 4 * y * (-1 + z) * (-1 + y) * p[29] + (-1 + z) * (-1 + y) * (2 * x +
2 * y + 2 * z - 1) * p[2]" }{TEXT 213 256 " + (-1 + z) * (-1 + y) * (
-2 * y - 2 * z + 2 * x - 1) * p[5] - y * (-1 + z) * (2 * y - 2 * z - 3
+ 2 * x) * p[8] - y * (-1 + z) * (2 * x + 2 * z + 1 - 2 * y) * p[11] \+
- z * (-1 + y) * (2 * x + 2 * y - 2 * z + 1) * p[14] - z * (-1 + y) * \+
(-2 * y + 2 * z - 3 " }{TEXT 213 256 "+ 2 * x) * p[17] + y * z * (2 * \+
y + 2 * z - 5 + 2 * x) * p[20] + y * z * (2 * x - 2 * z + 3 - 2 * y) *
p[23] - 4 * (-1 + z) * (-1 + y) * (-1 + x) * p[26] - 4 * x * (-1 + z)
* (-1 + y) * p[26] - 2 * z * (-1 + y) * (-1 + x) * p[14] - 2 * x * z \+
* (-1 + y) * p" }{TEXT 213 256 "[17] + 2 * x * y * z * p[20] + 2 * y *
z * (-1 + x) * p[23] - 4 * z * (-1 + z) * (-1 + y) * p[32] + 4 * y * \+
(-1 + z) * (-1 + y) * p[35] + 4 * z * (-1 + z) * (-1 + y) * p[38] + 4 \+
* y * (-1 + z) * (-1 + x) * p[41] + 4 * x * y * (-1 + z) * p[41] - 4 *
y * z *" }{TEXT 213 235 " (-1 + z) * p[44] + 4 * y * z * (-1 + z) * p
[47] + 4 * z * (-1 + y) * (-1 + x) * p[50] + 4 * x * z * (-1 + y) * p[
50] + 4 * y * z * (-1 + y) * p[53] - 4 * y * z * (-1 + y) * p[56] - 4 \+
* y * z * (-1 + x) * p[59] - 4 * x * y * z * p[59];" }{TEXT 213 257 "
\ndtau[2][1] = 2 * (-1 + z) * (-1 + y) * (-1 + x) * p[2] - 2 * x * (-1 + z) * (-1 + y) * p[5] - 2 * x * y * (-1 + z) * p[8] + 2 * y * (-1 + z) * (-1 + x) * p[11] - 2 * z * (-1 + y) * (-1 + x) * p[14] + 2 * x * z * (-1 + y) * p[17] + 2 * x * y * z * p[20] - 2
" }{TEXT 213 256 " * y * z * (-1 + x) * p[23] + (-1 + z) * (-1 + x) * \+
(2 * x + 2 * y + 2 * z - 1) * p[2] + x * (-1 + z) * (-2 * y - 2 * z + \+
2 * x - 1) * p[5] - x * (-1 + z) * (2 * y - 2 * z - 3 + 2 * x) * p[8] \+
- (-1 + z) * (-1 + x) * (2 * x + 2 * z + 1 - 2 * y) * p[11] - z " }
{TEXT 213 256 "* (-1 + x) * (2 * x + 2 * y - 2 * z + 1) * p[14] - x * \+
z * (-2 * y + 2 * z - 3 + 2 * x) * p[17] + x * z * (2 * y + 2 * z - 5 \+
+ 2 * x) * p[20] + z * (-1 + x) * (2 * x - 2 * z + 3 - 2 * y) * p[23] \+
- 4 * x * (-1 + z) * (-1 + x) * p[26] - 4 * (-1 + z) * (-1 + " }{TEXT
213 256 "y) * (-1 + x) * p[29] - 4 * y * (-1 + z) * (-1 + x) * p[29] -
4 * z * (-1 + z) * (-1 + x) * p[32] + 4 * x * (-1 + z) * (-1 + y) * p
[35] + 4 * x * y * (-1 + z) * p[35] + 4 * x * z * (-1 + z) * p[38] + 4
* x * (-1 + z) * (-1 + x) * p[41] - 4 * x * z * (-1 + " }{TEXT 213
235 "z) * p[44] + 4 * z * (-1 + z) * (-1 + x) * p[47] + 4 * x * z * (-
1 + x) * p[50] + 4 * z * (-1 + y) * (-1 + x) * p[53] + 4 * y * z * (-1
+ x) * p[53] - 4 * x * z * (-1 + y) * p[56] - 4 * x * y * z * p[56] -
4 * x * z * (-1 + x) * p[59];" }{TEXT 213 257 "\ndtau[2][2] = 2 * (-1
+ z) * (-1 + y) * (-1 + x) * p[2] - 2 * x * (-1 + z) * (-1 + y) * p[5
] + 2 * x * y * (-1 + z) * p[8] - 2 * y * (-1 + z) * (-1 + x) * p[11] \+
+ 2 * z * (-1 + y) * (-1 + x) * p[14] - 2 * x * z * (-1 + y) * p[17] +
2 * x * y * z * p[20] - 2" }{TEXT 213 256 " * y * z * (-1 + x) * p[23
] + (-1 + y) * (-1 + x) * (2 * x + 2 * y + 2 * z - 1) * p[2] + x * (-1
+ y) * (-2 * y - 2 * z + 2 * x - 1) * p[5] - x * y * (2 * y - 2 * z -
3 + 2 * x) * p[8] - y * (-1 + x) * (2 * x + 2 * z + 1 - 2 * y) * p[11
] - (-1 + y) * (-1 +" }{TEXT 213 256 " x) * (2 * x + 2 * y - 2 * z + 1
) * p[14] - x * (-1 + y) * (-2 * y + 2 * z - 3 + 2 * x) * p[17] + x * \+
y * (2 * y + 2 * z - 5 + 2 * x) * p[20] + y * (-1 + x) * (2 * x - 2 * \+
z + 3 - 2 * y) * p[23] - 4 * x * (-1 + y) * (-1 + x) * p[26] - 4 * y *
(-1 + y) * (-" }{TEXT 213 256 "1 + x) * p[29] - 4 * (-1 + z) * (-1 + \+
y) * (-1 + x) * p[32] - 4 * z * (-1 + y) * (-1 + x) * p[32] + 4 * x * \+
y * (-1 + y) * p[35] + 4 * x * (-1 + z) * (-1 + y) * p[38] + 4 * x * z
* (-1 + y) * p[38] + 4 * x * y * (-1 + x) * p[41] - 4 * x * y * (-1 +
z) * p[" }{TEXT 213 235 "44] - 4 * x * y * z * p[44] + 4 * y * (-1 + \+
z) * (-1 + x) * p[47] + 4 * y * z * (-1 + x) * p[47] + 4 * x * (-1 + y
) * (-1 + x) * p[50] + 4 * y * (-1 + y) * (-1 + x) * p[53] - 4 * x * y
* (-1 + y) * p[56] - 4 * x * y * (-1 + x) * p[59];" }}}{EXCHG {PARA 0
"> " 0 "" {MPLTEXT 1 0 2 "?C" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1
0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 125 100 1803 1 1 1 1 }{PAGENUMBERS 0
1 2 33 1 1 }
\ No newline at end of file
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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "restart:with(linalg
):with(ListTools);with(CodeGeneration):" }}{PARA 11 "" 1 "" {XPPMATH
20 "7>I,BinaryPlaceG6\"I-BinarySearchGF$I+CategorizeGF$I+DotProductGF$
I*EnumerateGF$I3FindMaximalElementGF$I3FindMinimalElementGF$I0FindRepe
titionsGF$I(FlattenGF$I,FlattenOnceGF$I&GroupGF$I+InterleaveGF$I%JoinG
F$I-JoinSequenceGF$I,LengthSplitGF$I+MakeUniqueGF$I,OccurrencesGF$I$Pa
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "dk:=proc(i,j) if (i = j) the
n 1 else 0 fi:end;dk(2,1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "f*6$I\"iG6
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1 0 6 "1,1,1," }{MPLTEXT 1 0 33 "0,1,1]):node:=convert(node,list);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "7*7%\"\"!F$F$7%\"\"\"F$F$7%F&F&F$7%F$F&
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{MPLTEXT 1 0 55 "node2:=matrix(8,3):for i to 8 do node2[i,1]:=node[i,2
];" }{MPLTEXT 1 0 22 "node2[i,2]:=node[i,3];" }{MPLTEXT 1 0 106 "node2
[i,3]:=node[i,1];od:node2:=convert(node2,list);permut:=[seq(Search(nod
e2[j],node),j=1..8)];C(permut);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*7%
\"\"!F$F$7%F$F$\"\"\"7%F&F$F&7%F&F$F$7%F$F&F$7%F$F&F&7%F&F&F&7%F&F&F$"
}}{PARA 11 "" 1 "" {XPPMATH 20 "7*\"\"\"\"\"&\"\"'\"\"#\"\"%\"\")\"\"
(\"\"$" }}{PARA 6 "" 1 "" {TEXT 214 10 "cg[0] = 1;" }{TEXT 214 11 "\nc
g[1] = 5;" }{TEXT 214 11 "\ncg[2] = 6;" }{TEXT 214 11 "\ncg[3] = 2;" }
{TEXT 214 11 "\ncg[4] = 4;" }{TEXT 214 11 "\ncg[5] = 8;" }{TEXT 214
11 "\ncg[6] = 7;" }{TEXT 214 11 "\ncg[7] = 3;" }}}{EXCHG {PARA 0 "> "
0 "" {MPLTEXT 1 0 56 "P:=vector(8,[1,x,y,z,x*y,x*z,y*z,x*y*z]);phi:=ve
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\"\"#I\"xGF#\"\"$I\"yGF#\"\"%I\"zGF#\"\"&*&F*F&F,F&\"\"'*&F*F&F.F&\"\"
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\"\"\"\")E\\[l!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "#?find" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "for i to 8 do;phi[i]:=sum(
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9 "node[j,2]" }{MPLTEXT 1 0 3 ",z=" }{MPLTEXT 1 0 9 "node[j,3]" }
{MPLTEXT 1 0 56 ",phi[i])=dk(i,j),j=1..8)\};inc:=\{seq(alpha[i,l],l=1.
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}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od:" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 40 "for i to 8 do phi[i]:=factor(phi[i]);od;" }}{PARA 11
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%F&I\"xGF(F&F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"xG6\"\"\"\",&!
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{XPPMATH 20 "*(I\"yG6\"\"\"\",&!\"\"F%I\"zGF$F%F%,&F'F%I\"xGF$F%F%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"zG6\"\"\"\",&!\"\"F%I\"yGF$F%F%,&F'
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\"\"\"I\"yGF$F%I\"zGF$F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I\"yG6\"
\"\"\"I\"zGF%F&,&!\"\"F&I\"xGF%F&F&F)" }}}{EXCHG {PARA 0 "> " 0 ""
{MPLTEXT 1 0 23 "#Dd:=matrix(8,8,(i,j)->" }{MPLTEXT 1 0 19 "subs(x=nod
e[j,1],y=" }{MPLTEXT 1 0 21 "node[j,2],z=node[j,3]" }{MPLTEXT 1 0 18 "
,phi[i])-dk(i,j));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "with(
CodeGeneration):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "C(phi);"
}}{PARA 6 "" 1 "" {TEXT 214 41 "phi[0] = -(-1 + z) * (-1 + y) * (-1 +
x);" }}{PARA 6 "" 1 "" {TEXT 214 33 "phi[1] = x * (-1 + z) * (-1 + y)
;" }{TEXT 214 28 "\nphi[2] = -x * y * (-1 + z);" }{TEXT 214 34 "\nphi[
3] = y * (-1 + z) * (-1 + x);" }{TEXT 214 34 "\nphi[4] = z * (-1 + y) \+