{VERSION 3 0 "DEC ALPHA UNIX" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
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0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 
-1 0 0 0 0 0 0 -1 0 }}
{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 30 "X:=array(1..2,1..1,[[x],[y]]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"XG-%'matrixG6#7$7#%\"xG7#%\"yG" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 98 "Phi:=7/8*x^2-3/8*x*y+sqrt(3)/8*x*z+23/32*y^2
+3*sqrt(3)/16*y*z+29/32*z^2-2*sqrt(3)*x+sqrt(3)*y-z+3;" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$PhiG,6*$)%\"xG\"\"#\"\"\"#\"\"(\"\")*&F(\"\"\"%
\"yGF/#!\"$F-*(-%%sqrtG6#\"\"$F*F(F*%\"zGF/#F/F-*$)F0F)F*#\"#B\"#K*(F4
F*F0F*F8F*#F7\"#;*$)F8F)F*#\"#HF>*&F4F*F(F*!\"#*&F4F*F0F*F/F8!\"\"F7F/
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "Dec:=dismantle(Phi,[x,y
,z]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$DecG6&-%'matrixG6#7%7%#\"
\"(\"\")#!\"$\"#;,$*$-%%sqrtG6#\"\"$\"\"\"#\"\"\"F07%F.#\"#B\"#K,$F2#F
6F=7%F1F>#\"#HF=-F'6#7%7#,$F2!\"#7#F27#!\"\"F67%%\"xG%\"yG%\"zG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "A:=Dec[1]:" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 10 "b:=Dec[2]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 10 "c:=Dec[3]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
20 "linalg[jordan](A,P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG
6#7%7%\"\"\"\"\"!F)7%F)#F(\"\"#F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 8 "eval(P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matri
xG6#7%7%,&*$-%%sqrtG6#\"\"$\"\"\"#\"\"\"\"\"##F-\"\"%F0#F0F3,$F)F/7%#!
\"$\"\")#F-F9\"\"!7%,&F0F0F)#F0F9,$F)#!\"\"F9F0" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 30 "tPP:=evalm(transpose(P) &* P);" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%$tPPG-%'matrixG6#7%7%,(*$),&*$-%%sqrtG6#\"\"$\"
\"\"#\"\"\"\"\"##F2\"\"%F5F6F3F5#\"\"*\"#kF5*$),&F5F5F.#F5\"\")F6F3F5,
(F.F?#F2F;F5*&F>F5F/F3#!\"\"F@,(*&F-F5F/F3F4F5F5F.F?7%FA#F5F8\"\"!7%FF
FJ#\"\"(F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "tPP:=map(radn
ormal,eval(tPP));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tPPG-%'matrixG
6#7%7%,&#\"\"&\"\"#\"\"\"*$-%%sqrtG6#\"\"$\"\"\"F.\"\"!,&#\"\"(\"\"%F.
F/#F.F-7%F5#F.F9F57%F6F5F7" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
57 "for j to 3 do \n  f(j):=linalg[submatrix](P,1..3,j..j)\nod:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "scalarproduct:=proc(v,w)\n  \+
local i;\n  add(v[i,1]*w[i,1],i=1..3)\nend:" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 77 "e(1):=map(radnormal,evalm(f(1)/sqrt(scalarproduct(
f(1),f(1)))),rationalized):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
246 "for j from 2 to 3 do\n  s:=evalm(scalarproduct(e(1),f(j))*e(1));
\n  for k from 2 to j-1 do\n    s:=evalm(s+scalarproduct(e(k),f(j))*e(
k))\n  od;\n  e(j):=evalm(f(j)-s);\n  e(j):=map(radnormal,evalm(e(j)/s
qrt(scalarproduct(e(j),e(j)))),rationalized)\nod:" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "P1:=linalg[augment](seq(e(j),j=1..3));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#P1G-%'matrixG6#7%7%,&*&-%%sqrtG6#,&
\"$g\"\"\"\"*$-F-6#\"\"$\"\"\"\"#kF6F3F6#F1\"#_*$F,F6#F5\"$3##F1\"\"#,
&F:#!#:F<F+#F5\"$/\"7%,&F:#FA\"$;%F+F;#F5\"\"%,&F:#\"#BFGF+#!\"\"FC7%,
&F:#\"#<F<F+#!#6FG,$F2#FNFI,&*$-F-6#,&#\"#XFCF1F2#!\"*F9F6F1*&FYF6F3F6
F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "map(radnormal,evalm(t
ranspose(P1) &* P1));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7
%7%\"\"\"\"\"!F)7%F)F(F)7%F)F)F(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 46 "newX:=array(1..3,1..1,[[newx],[newy],[newz]]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%newXG-%'matrixG6#7%7#%%newxG7#%%new
yG7#%%newzG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "XX:=evalm(P1
&*newX):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "tosubs1:=\{x=XX
[1,1],y=XX[2,1],z=XX[3,1]\}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 92 "newPhi:=map(radnormal,collect(subs(tosubs1,Phi),\{newx,newy,newz
\},distributed),rationalized);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'n
ewPhiG,.*$)%%newzG\"\"#\"\"\"\"\"\"\"\"$F+*(-%%sqrtG6#,&\"$g\"F+*$-F/6
#F,F*\"#kF*,&!\"'F+F3\"\"&F+F(F+#F+\"#E*$)%%newyGF)F*#F+F)*$)%%newxGF)
F*F+*(F.F*,&F3F+\"\"%F+F+FBF+#!\"\"F;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "center:=solve(\{diff(Phi,x),diff(Phi,y),diff(Phi,z)\}
,\{x,y,z\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'centerG<%/%\"yG,$*$
-%%sqrtG6#\"\"$\"\"\"#!\"\"\"\"#/%\"zG#\"\"\"F1/%\"xGF)" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "newcenter:=solve(\{diff(newPhi,newx
),diff(newPhi,newy),diff(newPhi,newz)\},\{newx,newy,newz\});" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#>%*newcenterG<%/%%newyG\"\"!/%%newxG,&*&-%%s
qrtG6#,&\"#5\"\"\"*$-F.6#\"\"$\"\"\"\"\"%F7F4F7#F2\"#8*$F-F7#F8F:/%%ne
wzG,&F;#\"\"'F:F,#!\"&F:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 
"map(radnormal,subs(newcenter,tosubs1));" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#<%/%\"yG,$*$-%%sqrtG6#\"\"$\"\"\"#!\"\"\"\"#/%\"zG#\"\"\"F//%\"x
GF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "tosubs2:=subs(newxx
=newx,newyy=newy,newzz=newz,subs(newcenter,\{newxx=xi+newx,newyy=eta+n
ewy,newzz=zeta+newz\}));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(tosubs2
G<%/%%newyG%$etaG/%%newzG,(%%zetaG\"\"\"*$-%%sqrtG6#,&\"#5F-*$-F06#\"
\"$\"\"\"\"\"%F8#\"\"'\"#8*&F/F8F5F8#!\"&F</%%newxG,(%#xiGF-F=#F-F<F.#
F9F<" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "newnewPhi:=map(radn
ormal,collect(subs(tosubs2,newPhi),\{xi,eta,zeta\},distributed));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%*newnewPhiG,**$)%#xiG\"\"#\"\"\"\"\"
\"!\"\"F+*$)%$etaGF)F*#F+F)*$)%%zetaGF)F*F+" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 45 "tosubs:=map(radnormal,subs(tosubs2,tosubs1));" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%'tosubsG<%/%\"zG,$*(-%%sqrtG6#,&\"#5
\"\"\"*$-F+6#\"\"$\"\"\"\"\"%F4,&!#MF/F0\"#6F/,0*$F*F4\"#;*&F*F4F1F4!
\"#%#xiG\"#h*&F*F4%$etaGF/F3*(F*F4F1F4FAF4!\")*&%%zetaGF/F1F4\"#=FE\"#
RF/#!\"\"\"%Wj/%\"yG,$*(F*F4,&!\"&F/F0\"\"#F/,,F<FQF>F3F@!\"$FE!\"(FDF
=F/#F/\"$/\"/%\"xG,$*(-F+6#,&\"$g\"F/F0\"#kF4,&F0F5F3F/F/,0*&FenF4F1F4
!\"'*$FenF4\"#7F>F_o*(FenF4F1F4FAF4FQ*&FenF4FAF4FSFD!#CFE\"#OF/#F/\"%'
\\#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "surface:=subs(subs(
xi=cos(phi)*sin(theta),eta=sqrt(2)*sin(phi)*sin(theta),zeta=cos(theta)
,tosubs),[x,y,z]);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(surfaceG7%,$*
(-%%sqrtG6#,&\"$g\"\"\"\"*$-F)6#\"\"$\"\"\"\"#kF2,&F.\"\"%F1F-F-,0*&F(
F2F/F2!\"'*$F(F2\"#7*&-%$cosG6#%$phiGF--%$sinG6#%&thetaGF-F:*,F(F2F/F2
-F)6#\"\"#F2-FAF>F-F@F2FG**F(F2FEF2FHF2F@F2!\"$*&-F=FBF-F/F2!#CFL\"#OF
-#F-\"%'\\#,$*(-F)6#,&\"#5F-F.F5F2,&!\"&F-F.FGF-,,*&FSF2F/F2FGF;F1**FS
F2FEF2FHF2F@F2FJFL!\"(FK!\"#F-#F-\"$/\",$*(FSF2,&!#MF-F.\"#6F-,0*$FSF2
\"#;FZFgnF;\"#hFenF1*,FSF2F/F2FEF2FHF2F@F2!\")FK\"#=FL\"#RF-#!\"\"\"%W
j" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "plot3d(surface,theta=0
..Pi,phi=-Pi..Pi,scaling=constrained,labels=[x,y,z],axes=boxed);" }}
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