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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 852 "dismantle:=proc(Phi
,vars::\{set,list\})\n  local Psi,n,V,d,A,i,j,b;\n  if not type(Phi,po
lynom(anything,vars)) then\n    ERROR(`Phi is expected to be a polynom
 with respect to `,vars,` but dismantle received `,Phi, vars)\n  fi;\n
  Psi:=collect(Phi,vars);\n  if not degree(Psi,vars)<=2  then\n    ERR
OR(`Phi is expected to have degree at most 2, but dismantle received `
,Phi, vars)\n  fi;\n  n:=nops(vars);\n  if type(vars,set) then \n    V
:=[op(vars)]\n  else \n    V:=[op(\{op(vars)\})]\n  fi;\n  Psi:=collec
t(subs(seq(v=t*v,v=V),Psi),t);\n  for d from 0 to 2 do\n    Psi.d:=coe
ff(Psi,t,d)\n  od;\n  A:=array(1..n,1..n,symmetric);\n  for i to n do
\n    A[i,i]:=coeff(Psi2,V[i],2);\n    for j from i+1 to n do \n      \+
A[i,j]:=coeff(coeff(Psi2,V[i],1),V[j],1)/2\n    od\n  od;\n  b:=array(
1..n,1..1);\n  for i to n do\n    b[i,1]:=coeff(Psi1,V[i],1)\n  od;\n \+
 eval(A),eval(b),Psi0,V\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 47 "A:=array(1..2,1..2,[[7/8,-sqrt(3)/4],[0,5/8]]);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"AG-%'MATRIXG6#7$7$#\"\"(\"\"),$*$\"\"$#\"\"\"
\"\"##!\"\"\"\"%7$\"\"!#\"\"&F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 38 "b:=array(1..2,1..1,[[2],[2*sqrt(3)]]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"bG-%'MATRIXG6#7$7#\"\"#7#,$*$\"\"$#\"\"\"F*F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "c:=7;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"cG\"\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "X:=array(1..2,1..1,[[x],[y]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%\"XG-%'MATRIXG6#7$7#%\"xG7#%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 90 "Phi:=collect(evalm(transpose(X) &* A &* X + transpose
(b) &* X +c)[1,1],\{x,y\},distributed);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$PhiG,.*$%\"xG\"\"##\"\"(\"\")*(\"\"$#\"\"\"F(F'F/%\"yGF/#!\"
\"\"\"%*$F0F(#\"\"&F+F'F(*&F-F.F0F/F(F*F/" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "dismantle(Phi,[x,y]);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6&-%'MATRIXG6#7$7$#\"\"(\"\"),$*$\"\"$#\"\"\"\"\"##!\"\"F*7$F+#\"
\"&F*-F$6#7$7#F07#,$F,F0F)7$%\"xG%\"yG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "A1:=matrix([[7/8, -1/8*sqrt(3)], [-1/8*sqrt(3), 5/8]]
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A1G-%'MATRIXG6#7$7$#\"\"(\"\"
),$*$\"\"$#\"\"\"\"\"##!\"\"F,7$F-#\"\"&F," }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 26 "evalm((transpose(A)+A)/2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'MATRIXG6#7$7$#\"\"(\"\"),$*$\"\"$#\"\"\"\"\"##!\"\"F
*7$F+#\"\"&F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "linalg[jor
dan](A1,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7$7$\"\"\"
\"\"!7$F)#F(\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "eval(P)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7$7$#\"\"$\"\"%#\"\"
\"F*7$,$*$F)#F,\"\"##!\"\"F*,$F/F+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "tPP:=evalm(transpose(P) &* P);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$tPPG-%'MATRIXG6#7$7$#\"\"$\"\"%\"\"!7$F-#\"\"\"F," }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "Q:=array(1..2,1..2,diagona
l):\nQ[1,1]:=1/sqrt(tPP[1,1]):\nQ[2,2]:=1/sqrt(tPP[2,2]):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "P1:=evalm(P&*Q);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#P1G-%'MATRIXG6#7$7$,$*$\"\"$#\"\"\"\"\"#F-F-7$#!\"
\"F/F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalm(transpose(P
1) &* P1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7$7$\"\"\"\"
\"!7$F)F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "newX:=array(1.
.2,1..1,[[newx],[newy]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%newXG-
%'MATRIXG6#7$7#%%newxG7#%%newyG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 20 "XX:=evalm(P1&*newX);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#XXG
-%'MATRIXG6#7$7#,&*&\"\"$#\"\"\"\"\"#%%newxGF.F-%%newyGF-7#,&F0#!\"\"F
/*&F,F-F1F.F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "tosubs1:=
\{x=XX[1,1],y=XX[2,1]\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 
"newPhi:=collect(subs(tosubs1,Phi),\{newx,newy\},distributed);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'newPhiG,**$%%newxG\"\"#\"\"\"\"\"(F
)*$%%newyGF(#F)F(F,\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 
"\{diff(newPhi,newx),diff(newPhi,newy)\};" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$,$%%newxG\"\"#,&%%newyG\"\"\"\"\"%F)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "center:=solve(\{diff(Phi,x),diff(Ph
i,y)\},\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'centerG<$/%\"yG
,$*$\"\"$#\"\"\"\"\"#!\"#/%\"xGF." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 68 "newcenter:=solve(\{diff(newPhi,newx),diff(newPhi,newy
)\},\{newx,newy\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*newcenterG<$
/%%newxG\"\"!/%%newyG!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
24 "subs(newcenter,tosubs1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"
yG,$*$\"\"$#\"\"\"\"\"#!\"#/%\"xGF," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 84 "tosubs2:=subs(newxx=newx,newyy=newy,subs(newcenter,\{
newxx=xi+newx,newyy=eta+newy\}));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%(tosubs2G<$/%%newxG%#xiG/%%newyG,&%$etaG\"\"\"!\"%F-" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "newnewPhi:=collect(subs(tosubs2,new
Phi),\{xi,eta\},distributed);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*ne
wnewPhiG,(*$%$etaG\"\"##\"\"\"F(*$%#xiGF(F*!\"\"F*" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 30 "tosubs:=subs(tosubs2,tosubs1);" }}{PARA 11 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "arc:=subs(subs(xi=cos(t),eta=sqrt(2
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#F*,&F,#!\"\"F+*&F(F),&F0F*!\"%F*F*F)/F/;\"\"!,$%#PiGF+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(arc,scaling=constrained,labels
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