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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 polyno
m with respect to \",vars,\" but dismantle received \",Phi, vars)\n  f
i;\n  Psi:=collect(Phi,vars);\n  if not degree(Psi,vars)<=2  then\n   \+
 ERROR(\"Phi is expected to have degree at most 2, but dismantle recei
ved \",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:
=collect(subs(seq(v=t*v,v=V),Psi),t);\n  for d from 0 to 2 do\n    Psi
.d:=coeff(Psi,t,d)\n  od;\n  A:=array(1..n,1..n,symmetric);\n  for i t
o 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$7$#\"\"(\"\"),$*$-
%%sqrtG6#\"\"$\"\"\"#!\"\"\"\"%7$\"\"!#\"\"&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$7#\"\"#7#,$*$-%%sq
rtG6#\"\"$\"\"\"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,.*$)%\"xG\"\"#\"\"\"#\"\"(\"\")F(F)*(-%
%sqrtG6#\"\"$F*%\"yG\"\"\"F(F4#!\"\"\"\"%*&F/F*F3F*F)*$)F3F)F*#\"\"&F-
F,F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dismantle(Phi,[x,y]
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&-%'matrixG6#7$7$#\"\"(\"\"),$*$-
%%sqrtG6#\"\"$\"\"\"#!\"\"F*7$F+#\"\"&F*-F$6#7$7#\"\"#7#,$F,F;F)7$%\"x
G%\"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$7$#\"\"(\"\"),$*$-%%sqrtG6#\"\"$\"\"\"#!\"\"
F,7$F-#\"\"&F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalm((tr
anspose(A)+A)/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7$7$#
\"\"(\"\"),$*$-%%sqrtG6#\"\"$\"\"\"#!\"\"F*7$F+#\"\"&F*" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "linalg[jordan](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$7$#\"\"$\"\"%#\"\"\"F*7$,$*$-%%sqrtG6#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,diagonal):\nQ[1,1]:=1/sqrt(tP
P[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$7$,$*$-%%sqrtG6#\"\"$\"\"\"#\"\"\"\"\"#F17$#!\"\"F3
F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "evalm(transpose(P1) &
* 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-%'ma
trixG6#7$7#%%newxG7#%%newyG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "XX:=evalm(P1&*newX);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#XXG-%'m
atrixG6#7$7#,&*&-%%sqrtG6#\"\"$\"\"\"%%newxG\"\"\"#F2\"\"#%%newyGF37#,
&F1#!\"\"F4*&F,F0F5F2F3" }}}{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\},distr
ibuted);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'newPhiG,**$)%%newxG\"\"
#\"\"\"\"\"\"\"\"(F+*$)%%newyGF)F*#F+F)F/\"\"%" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 38 "\{diff(newPhi,newx),diff(newPhi,newy)\};" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#<$,&%%newyG\"\"\"\"\"%F&,$%%newxG\"\"#
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "center:=solve(\{diff(Ph
i,x),diff(Phi,y)\},\{x,y\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'cen
terG<$/%\"xG!\"#/%\"yG,$*$-%%sqrtG6#\"\"$\"\"\"F(" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 68 "newcenter:=solve(\{diff(newPhi,newx),diff(ne
wPhi,newy)\},\{newx,newy\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*new
centerG<$/%%newyG!\"%/%%newxG\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "subs(newcenter,tosubs1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#<$/%\"xG!\"#/%\"yG,$*$-%%sqrtG6#\"\"$\"\"\"F&" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "tosubs2:=subs(newxx=newx,new
yy=newy,subs(newcenter,\{newxx=xi+newx,newyy=eta+newy\}));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(tosubs2G<$/%%newyG,&%$etaG\"\"\"!\"%F*/%%
newxG%#xiG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "newnewPhi:=co
llect(subs(tosubs2,newPhi),\{xi,eta\},distributed);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%*newnewPhiG,(*$)%$etaG\"\"#\"\"\"#\"\"\"F)*$)%#xiGF
)F*F,!\"\"F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "tosubs:=sub
s(tosubs2,tosubs1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'tosubsG<$/%
\"yG,&%#xiG#!\"\"\"\"#*&-%%sqrtG6#\"\"$\"\"\",&%$etaG\"\"\"!\"%F5F5#F5
F,/%\"xG,(*&F.F2F)F5F7F4F7!\"#F5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "arc:=subs(subs(xi=cos(t),eta=sqrt(2)*sin(t),tosubs),[
x,y,t=0..2*Pi]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$arcG7%,(*&-%%sq
rtG6#\"\"$\"\"\"-%$cosG6#%\"tG\"\"\"#F1\"\"#*&-F)6#F3F,-%$sinGF/F1F2!
\"#F1,&F-#!\"\"F3*&F(F,,&F4F1!\"%F1F1F2/F0;\"\"!,$%#PiGF3" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "plot(arc,scaling=constrained,labels
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