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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$
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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$9%\"\"\"\"\"!F%F%F%" }}{PARA 11 "" 1 "" {XPPMATH 
20 "\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "node:=matrix(8
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 1 0 6 "1,1,1," }{MPLTEXT 1 0 33 "0,1,1]):node:=convert(node,list);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "7*7%\"\"!F$F$7%\"\"\"F$F$7%F&F&F$7%F$F&
F$7%F$F$F&7%F&F$F&7%F&F&F&7%F$F&F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "node2:=matrix(8,3):for i to 8 do node2[i,1]:=node[i,2
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[i,3]:=node[i,1];od:node2:=convert(node2,list);permut:=[seq(Search(nod
e2[j],node),j=1..8)];C(permut);" }}{PARA 11 "" 1 "" {XPPMATH 20 "7*7%
\"\"!F$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
ctor(8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\")E\\[l)F&F&
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}}{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 
"" 1 "" {XPPMATH 20 ",$*(,&!\"\"\"\"\"I\"zG6\"F&F&,&F%F&I\"yGF(F&F&,&F
%F&I\"xGF(F&F&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "*(I\"xG6\"\"\"\",&!
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{XPPMATH 20 "*(I\"yG6\"\"\"\",&!\"\"F%I\"zGF$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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{MPLTEXT 1 0 23 "#Dd:=matrix(8,8,(i,j)->" }{MPLTEXT 1 0 19 "subs(x=nod
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,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) \+
* (-1 + x);" }{TEXT 214 28 "\nphi[5] = -x * z * (-1 + y);" }{TEXT 214 
20 "\nphi[6] = x * y * z;" }{TEXT 214 28 "\nphi[7] = -y * z * (-1 + x)
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "tau:=vector(3,[0,0,0])
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E\\[l$F&\"\"!\"\"#F)F'F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"
\"\"#CE\\[l!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "#?submatrix
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "i:='i';for k to 3 do ta
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F&F'F&&F.6#\"#>F&F&**F*F&F'F&F+F&&F.6#\"#AF&F%" }}{PARA 11 "" 1 "" 
{XPPMATH 20 ",2**,&!\"\"\"\"\"I\"zG6\"F&F&,&F%F&I\"yGF(F&F&,&F%F&I\"xG
F(F&F&&I\"pGF(6#\"\"#F&F%**F,F&F$F&F)F&&F.6#\"\"&F&F&**F,F&F*F&F$F&&F.
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&F'F&F)F&&F.6#\"#<F&F%**F,F&F*F&F'F&&F.6#\"#?F&F&**F*F&F'F&F+F&&F.6#\"
#BF&F%" }}{PARA 11 "" 1 "" {XPPMATH 20 ",2**,&!\"\"\"\"\"I\"zG6\"F&F&,
&F%F&I\"yGF(F&F&,&F%F&I\"xGF(F&F&&I\"pGF(6#\"\"$F&F%**F,F&F$F&F)F&&F.6
#\"\"'F&F&**F,F&F*F&F$F&&F.6#\"\"*F&F%**F*F&F$F&F+F&&F.6#\"#7F&F&**F'F
&F)F&F+F&&F.6#\"#:F&F&**F,F&F'F&F)F&&F.6#\"#=F&F%**F,F&F*F&F'F&&F.6#\"
#@F&F&**F*F&F'F&F+F&&F.6#\"#CF&F%" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 28 "dtau:=jacobian(tau,[x,y,z]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "=6\"6$;\"\"\"\"\"$F%E\\[l*6$F'F',2*(,&!\"\"F&I\"yGF#F&F&,
&F-F&I\"xGF#F&F&&I\"pGF#6#F'F&F-*(F0F&F,F&&F26#\"\"'F&F&*(F0F&F.F&&F26
#\"\"*F&F-*(F.F&F/F&&F26#\"#7F&F&*(F,F&F/F&&F26#\"#:F&F&*(F0F&F,F&&F26
#\"#=F&F-*(F0F&F.F&&F26#\"#@F&F&*(F.F&F/F&&F26#\"#CF&F-6$F'F&,2*(,&F-F
&I\"zGF#F&F&F,F&F1F&F-*(FSF&F,F&F5F&F&*(F.F&FSF&F9F&F-*(F.F&FSF&F=F&F&
*(FTF&F,F&FAF&F&*(FTF&F,F&FEF&F-*(F.F&FTF&FIF&F&*(F.F&FTF&FMF&F-6$F&F&
,2*(FSF&F,F&&F26#F&F&F-*(FSF&F,F&&F26#\"\"%F&F&*(F.F&FSF&&F26#\"\"(F&F
-*(F.F&FSF&&F26#\"#5F&F&*(FTF&F,F&&F26#\"#8F&F&*(FTF&F,F&&F26#\"#;F&F-
*(F.F&FTF&&F26#\"#>F&F&*(F.F&FTF&&F26#\"#AF&F-6$\"\"#Fhp,2*(FSF&F/F&&F
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "C(dtau,optimize);" }}{PARA 6 "" 1 "
" {TEXT 214 12 "t1 = -1 + z;" }}{PARA 6 "" 1 "" {TEXT 214 12 "t2 = -1 \+
+ y;" }{TEXT 214 14 "\nt3 = t1 * t2;" }{TEXT 214 13 "\nt6 = y * t1;" }
{TEXT 214 13 "\nt9 = z * t2;" }{TEXT 214 13 "\nt12 = y * z;" }{TEXT 
214 14 "\nt16 = -1 + x;" }{TEXT 214 16 "\nt17 = t1 * t16;" }{TEXT 214 
14 "\nt19 = x * t1;" }{TEXT 214 15 "\nt23 = z * t16;" }{TEXT 214 13 "
\nt25 = x * z;" }{TEXT 214 16 "\nt30 = t2 * t16;" }{TEXT 214 14 "\nt32
 = x * t2;" }{TEXT 214 13 "\nt34 = x * y;" }{TEXT 214 15 "\nt36 = y * \+
t16;" }{TEXT 214 115 "\ndtau[0][0] = -t3 * p[0] + t3 * p[3] - t6 * p[6
] + t6 * p[9] + t9 * p[12] - t9 * p[15] + t12 * p[18] - t12 * p[21];" 
}{TEXT 214 121 "\ndtau[0][1] = -t17 * p[0] + t19 * p[3] - t19 * p[6] +
 t17 * p[9] + t23 * p[12] - t25 * p[15] + t25 * p[18] - t23 * p[21];" 
}{TEXT 214 121 "\ndtau[0][2] = -t30 * p[0] + t32 * p[3] - t34 * p[6] +
 t36 * p[9] + t30 * p[12] - t32 * p[15] + t34 * p[18] - t36 * p[21];" 
}{TEXT 214 116 "\ndtau[1][0] = -t3 * p[1] + t3 * p[4] - t6 * p[7] + t6
 * p[10] + t9 * p[13] - t9 * p[16] + t12 * p[19] - t12 * p[22];" }
{TEXT 214 122 "\ndtau[1][1] = -t17 * p[1] + t19 * p[4] - t19 * p[7] + \+
t17 * p[10] + t23 * p[13] - t25 * p[16] + t25 * p[19] - t23 * p[22];" 
}{TEXT 214 122 "\ndtau[1][2] = -t30 * p[1] + t32 * p[4] - t34 * p[7] +
 t36 * p[10] + t30 * p[13] - t32 * p[16] + t34 * p[19] - t36 * p[22];"
 }{TEXT 214 116 "\ndtau[2][0] = -t3 * p[2] + t3 * p[5] - t6 * p[8] + t
6 * p[11] + t9 * p[14] - t9 * p[17] + t12 * p[20] - t12 * p[23];" }
{TEXT 214 122 "\ndtau[2][1] = -t17 * p[2] + t19 * p[5] - t19 * p[8] + \+
t17 * p[11] + t23 * p[14] - t25 * p[17] + t25 * p[20] - t23 * p[23];" 
}{TEXT 214 122 "\ndtau[2][2] = -t30 * p[2] + t32 * p[5] - t34 * p[8] +
 t36 * p[11] + t30 * p[14] - t32 * p[17] + t34 * p[20] - t36 * p[23];"
 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "?C" }}}{EXCHG {PARA 0 "> 
" 0 "" {MPLTEXT 1 0 0 "" }}}}
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