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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "p1:=a*x^3+3*b*x^2+3*
c*x+d;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p1G,**&%\"aG\"\"\"%\"xG\"
\"$F(*&%\"bGF(F)\"\"#F**&%\"cGF(F)F(F*%\"dGF(" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "p2:=collect(simplify(subs(x=(z-b)/a,p1)),z);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p2G,(*&%\"aG!\"#%\"zG\"\"$\"\"\"*(,
&*&%\"cGF+F'F+F**$%\"bG\"\"#!\"$F+F'F(F)F+F+*&,(*(F/F+F'F+F1F+F3*&%\"d
GF+F'F2F+*$F1F*F2F+F'F(F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
32 "p3:=collect(simplify(a^2*p2),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#p3G,,*$%\"zG\"\"$\"\"\"*&,&*&%\"cGF)%\"aGF)F(*$%\"bG\"\"#!\"$F)F'
F)F)*(F-F)F.F)F0F)F2*&%\"dGF)F.F1F)*$F0F(F1" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 16 "p4:=z^3+3*G*z+H;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%#p4G,(*$%\"zG\"\"$\"\"\"*&%\"GGF)F'F)F(%\"HGF)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 31 "p5:=simplify(subs(z=w-G/w,p4));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#p5G*&,(*$%\"wG\"\"'\"\"\"*$%\"GG\"\"$!\"
\"*&%\"HGF*F(F-F*F*F(!\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
21 "p6:=simplify(p5*w^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p6G,(*
$%\"wG\"\"'\"\"\"*$%\"GG\"\"$!\"\"*&%\"HGF)F'F,F)" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "p7:=subs(w^3=mu,w^6=mu^2,p6);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#p7G,(*$%#muG\"\"#\"\"\"*$%\"GG\"\"$!\"\"*&%\"
HGF)F'F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "qs:=solve(p7,
mu);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#qsG6$,&%\"HG#!\"\"\"\"#*$,&
*$F'F*\"\"\"*$%\"GG\"\"$\"\"%#F.F*F3,&F'F(F+F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 " with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 32 
"Warning, new definition for norm" }}{PARA 7 "" 1 "" {TEXT -1 33 "Warn
ing, new definition for trace" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 44 "A:=matrix(3,3,[a1,a2,a3,a4,a5,a6,a7,a8,a9]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7%7%%#a1G%#a2G%#a3G7%%#a4G%#a5G%#a6
G7%%#a7G%#a8G%#a9G" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "detA:
=det(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%detAG,.*(%#a1G\"\"\"%#a
5GF(%#a9GF(F(*(F'F(%#a6GF(%#a8GF(!\"\"*(%#a4GF(%#a2GF(F*F(F.*(F0F(%#a3
GF(F-F(F(*(%#a7GF(F1F(F,F(F(*(F5F(F3F(F)F(F." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "trA:=trace(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%$trAG,(%#a1G\"\"\"%#a5GF'%#a9GF'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "cp:=collect(charpoly(A,lambda),lambda);" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%#cpG,4*$%'lambdaG\"\"$\"\"\"*&,(%#a1G!\"\"%#a9
GF-%#a5GF-F)F'\"\"#F)*&,.*&%#a7GF)%#a3GF)F-*&F,F)F.F)F)*&F/F)F.F)F)*&%
#a4GF)%#a2GF)F-*&F,F)F/F)F)*&%#a6GF)%#a8GF)F-F)F'F)F)*(F4F)F:F)F=F)F-*
(F,F)F=F)F>F)F)*(F4F)F5F)F/F)F)*(F9F)F:F)F.F)F)*(F,F)F/F)F.F)F-*(F9F)F
5F)F>F)F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "prA:=coeff(cp,
lambda);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$prAG,.*&%#a7G\"\"\"%#a3
GF(!\"\"*&%#a1GF(%#a9GF(F(*&%#a5GF(F-F(F(*&%#a4GF(%#a2GF(F**&F,F(F/F(F
(*&%#a6GF(%#a8GF(F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "cp1:
=lambda^3-trA*lambda^2+prA*lambda-detA;" }}{PARA 12 "" 1 "" {XPPMATH 
20 "6#>%$cp1G,4*$%'lambdaG\"\"$\"\"\"*&,(%#a1GF)%#a5GF)%#a9GF)F)F'\"\"
#!\"\"*&,.*&%#a7GF)%#a3GF)F0*&F,F)F.F)F)*&F-F)F.F)F)*&%#a4GF)%#a2GF)F0
*&F,F)F-F)F)*&%#a6GF)%#a8GF)F0F)F'F)F)*(F,F)F-F)F.F)F0*(F,F)F=F)F>F)F)
*(F9F)F:F)F.F)F)*(F9F)F5F)F>F)F0*(F4F)F:F)F=F)F0*(F4F)F5F)F-F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "is(cp1=cp);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%%trueG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "p:=lambda^3-T*lambda^2+P*lambda-D;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"pG,**$%'lambdaG\"\"$\"\"\"*&%\"TGF)F'\"\"#!\"\"*&%\"PGF)F'F)
F)%\"DGF-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "p1:=collect(si
mplify(subs(lambda=z+T/3,p)),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
#p1G,,*$%\"zG\"\"$\"\"\"*&,&%\"PGF)*$%\"TG\"\"##!\"\"F(F)F'F)F)*&F,F)F
.F)#F)F(%\"DGF1*$F.F(#!\"#\"#F" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 15 "G:=(P-T^2/3)/3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG,&%\"
PG#\"\"\"\"\"$*$%\"TG\"\"##!\"\"\"\"*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "H:=1/3*P*T-D-2/27*T^3;" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%\"HG,(*&%\"PG\"\"\"%\"TGF(#F(\"\"$%\"DG!\"\"*$F)F+#!\"#\"#F" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "disc:=simplify(H^2+4*G^3);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%discG,,*&%\"PG\"\"#%\"TGF(#!\"
\"\"#F*(F'\"\"\"F)F.%\"DGF.#!\"#\"\"$*$F/F(F.*&F/F.F)F2#\"\"%F,*$F'F2F
5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "21 0 0" 0 
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