{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }{CSTYLE "2D Output" -1 20 "Times" 0 1 0 0 255 1 0 0 2 2 2 2 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Ou tput" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output " -1 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 3 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "Left Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }1 3 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }3 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 } {PSTYLE "_pstyle1" -1 201 1 {CSTYLE "" -1 -1 "Courier" 0 1 255 0 0 1 0 1 0 2 1 2 0 0 0 1 }0 0 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }{PSTYLE "_pstyle 3" -1 203 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 2 2 2 0 0 0 1 }1 3 0 -1 -1 -1 1 0 1 0 2 2 -1 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "#################### ######################################################" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 49 "# Compute balanced configurations of type 1, n, m" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 21 "# wor ks if m is small" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "####### ###################################################################" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%'DigitsG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "# choose the value of n and m" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 10 "n:=5;m:=4;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"nG\"\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"mG\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "# necksizes - do not touch" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 64 "c2:=1:c3:='c3';c1:=(n*( n-1)*c2^2+m*(m-1)*c3^2-n*m*c2*c3)/(n*c2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c3GF$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c1G,(\" \"%\"\"\"*&#\"#7\"\"&F'*$)%#c3G\"\"#F'F'F'*&F&F'F.F'!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "# compute logarithmic growths to ch eck embeddedness" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 43 "Q1:=- c1;Q2:=c1-n*c2;Q3:=n*c2-m*c3;Q4:=m*c3;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q1G,(\"\"%!\"\"*&#\"#7\"\"&\"\"\"*$)%#c3G\"\"#F,F,F'*&F&F,F/F ,F," }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q2G,(\"\"\"!\"\"*&#\"#7\"\"& F&*$)%#c3G\"\"#F&F&F&*&\"\"%F&F.F&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#Q3G,&\"\"&\"\"\"*&\"\"%F'%#c3GF'!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#Q4G,$*&\"\"%\"\"\"%#c3GF(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "# compute range of parameter c3 so that configur ation is embedded" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 43 "solv e(evalf(Q1-F'6#$\"5gm*=%3I)Q6 e\"F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "# chose value of p arameter c3, should be in the above interval for embedded surfaces" }} }{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 9 "c3:=3/2.;" }}{PARA 201 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c3G$\"5+++++++ ++:!#>" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 18 "evalf([c1,c2,c3 ]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%$\"5+++++++++M!#>$\"\"\"\"\"! $\"5+++++++++:F&" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 21 "evalf ([Q1,Q2,Q3,Q4]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$!5+++++++++M!#> $!5+++++++++;F&$!5+++++++++5F&$\"5+++++++++gF&" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "# compute all balanced configurations" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "# point at level 1 : 0" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "# points at level 2 : zeros \+ of P" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "# points at level 3 : zeros of Q" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "a[1]:=0;P: =z^n+sum(a[k]*z^k,k=0..n-1);Q:=z^m+z^(m-1)+sum(b[k]*z^k,k=0..m-2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"aG6#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG,,*$)%\"zG\"\"&\"\"\"F*&%\"aG6#\"\"!F**&&F,6# \"\"#F*)F(F2F*F**&&F,6#\"\"$F*)F(F7F*F**&&F,6#\"\"%F*)F(F%\"QG,,*$)%\"zG\"\"%\"\"\"F**$)F(\"\" $F*F*&%\"bG6#\"\"!F**&&F/6#F*F*F(F*F**&&F/6#\"\"#F*)F(F8F*F*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "Pp:=diff(P,z);Ppp:=diff(Pp,z );Qp:=diff(Q,z);Qpp:=diff(Qp,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% #PpG,**&\"\"&\"\"\")%\"zG\"\"%F(F(*(\"\"#F(&%\"aG6#F-F(F*F(F(*(\"\"$F( &F/6#F2F()F*F-F(F(*(F+F(&F/6#F+F()F*F2F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$PppG,**&\"#?\"\"\")%\"zG\"\"$F(F(*&\"\"#F(&%\"aG6#F- F(F(*(\"\"'F(&F/6#F+F(F*F(F(*(\"#7F(&F/6#\"\"%F()F*F-F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#QpG,**&\"\"%\"\"\")%\"zG\"\"$F(F(*&F+F()F*\" \"#F(F(&%\"bG6#F(F(*(F.F(&F06#F.F(F*F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$QppG,(*&\"#7\"\"\")%\"zG\"\"#F(F(*&\"\"'F(F*F(F(*&F+F(&%\"bG6 #F+F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "eq:=collect(expa nd(c2^2*Ppp*Q*z-c1*c2*Pp*Q-c2*c3*Pp*Qp*z+c3^2*Qpp*P*z),z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#eqG,0*&,&$\"4+++++++++'!#=!\"\"*&$\"4++++ ++++S\"F*\"\"\"&%\"aG6#\"\"%F/F/F/)%\"zG\"\"(F/F/*&,(*&$\"4++++++++5'F *F/F0F/F+*&$\"4++++++++![F*F/&F16#\"\"$F/F/*&$\"5+++++++++v!#>F/&%\"bG 6#\"\"#F/F+F/)F5\"\"'F/F/*&,**&$\"4++++++++?%F*F/F?F/F+*($\"5+++++++++ \"*FEF/F0F/FFF/F+*&$\"5+++++++++XFEF/&FG6#F/F/F+*&$\"5++++++++?5F*F/&F 1FHF/F/F/)F5\"\"&F/F/*&,**($\"5+++++++++wFEF/F0F/FWF/F+*&$\"4+++++++++ $FEF/FfnF/F+*($\"4++++++++q)F*F/F?F/FFF/F+*&$\"4+++++++++$F*F/&FG6#\" \"!F/F/F/)F5F3F/F/*&,**($\"5+++++++++jFEF/FfnF/FFF/F+*($\"4++++++++q)F *F/F?F/FWF/F+*&$\"5+++++++++FF*F/&F1FhoF/F/*($\"4++++++++g\"F*F/F0F/Fg oF/F+F/)F5FAF/F/*&,(*&$\"5++++++++]8F*F/FfpF/F/*($\"5+++++++++yFEF/Ffn F/FWF/F+*($\"4++++++++?%F*F/F?F/FgoF/F+F/)F5FIF/F/*&,&*($\"5+++++++++[ FEF/FfnF/FgoF/F+*($\"5+++++++++XFEF/FFF/FfpF/F/F/F5F/F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "eqalist:=\{\}:for i from 1 to n-1 \+ do eqalist:=\{op(eqalist),coeff(eq,z^i)\};od:alist:=\{a[0]\}:for i fro m 2 to n-1 do alist:=\{op(alist),a[i]\};od:eqlist;alist;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#%'eqlistG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<&& %\"aG6#\"\"!&F%6#\"\"#&F%6#\"\"$&F%6#\"\"%" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 27 "sola:=solve(eqalist,alist);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solaG<&/&%\"aG6#\"\"!,$*($\"5nmmmmmmm')H!#<\"\"\"&% \"bGF)\"\"%,,*($\"&oF\"F*F0)F1\"\"#F0&F26#F0F0F0**$\"%,VF*F0F:F0F1F0)& F26#F9F9F0!\"\"*($\"&CK\"F*F0)F:F9F0F1F0FB*($\"%jrF*F0)F:\"\"$F0F@F0F0 *($\"%7GF*F0F8F0F@F0F0FBF0/&F(6#F3,$**$\"5+++++++++v!#>F0F1F0,**($\"$Z \"F*F0F1F0F?F0FB*&$\"$s'F*F0F8F0F0*($\"$'pF*F0F1F0F:F0FB*($\"$x$F*F0FF F0F@F0F0F0F4FBF0/&F(6#FK,$**$\"#SF*F0F1F9,&*&$\"#CF*F0F1F0F0*($\"#8F*F 0F:F0F@F0FBF0F4FBF0/&F(FA,$**$\"$!GF*F0F1FKF@F0F4FBF0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 171 "eqblist:=\{\}:for i from n to n+m- 2 do eqblist:=\{op(eqblist),numer(normal(subs(sola,coeff(eq,z^i))))\}; od:eqblist;blist:=\{\}:for i from 0 to m-2 do blist:=\{op(blist),b[i] \};od:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#<%,2*&$\"%KS\"\"!\"\"\")&%\" bG6#F(\"\"$F)!\"\"**$\"&Kq$F(F)&F,6#F)F))F+\"\"#F)&F,6#F6F)F)*($\"5+++ +++]F.5!#:F)F5F))F7F.F)F)*($\"&3I%F(F)F*F)F7F)F/**$\"5+++++++vvj!#;F)) F3F6F)F+F))F7F6F)F/*($\"&cu&F(F)F5F)FEF)F/*($\"&3&fF(F))F3F.F)F+F)F)*( $\"5+++++++NBKF)F " 0 "" {MPLTEXT 1 0 41 "so lb:=evalf(solve(evalf(eqblist),blist));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%%solbG6+<%/&%\"bG6#\"\"\"$\"\"!F-/&F)6#F-F,/&F)6#\"\"#F2<%/F(F (F./F2F,<%/F/$\"5pL&=Rf`&)H\"o!#>/F2$!5*p]Z\"G;0C\">&F!4dar[!GF()>\"3>My!#?/F/$\"5X!>0Fi!z5q>FE\"4>B w=FG$!5LO&))*[cq_69FG/F/^$$\"51H++jo " 0 "" {MPLTEXT 1 0 13 "nops([solb]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\" *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "# select a solution a mongst list of all solutions. Choosing a complex value gives an asymme trical configuration." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "ch oice:=9;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'choiceG\"\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "sol:=subs([solb][choice],sol a) union [solb][choice];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$solG<)/ &%\"aG6#\"\"!^$$\"5IdA\"HB<4\\3#!#;$!5pyh*=O88'4DF./&%\"bG6#\"\"\"^$$! 5t7?`g0K`,E\"4>Bw=F9$\"5LO&))*[cq_69F9/&F(6#\"\"$^$$\"5 l@WD::_DwMF9$\"5#*)eWld-6b?#F9/&F(6#\"\"%^$$\"5wr&G9dG9dG%!#>$\"5\"oel %[Qw!f7\"!#O/&F(FF^$$\"50C6r$)z1bayF9$!5*>O9HAez%eOF9" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# check equations are solved" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(sol,eq);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#,0*&^$$\"#Y!#>$\"5`@=&yQpqid\"!#O\"\"\")%\"zG\" \"(F,F,*&^$$!\"\"!#<$\"#OF4F,)F.\"\"'F,F,*&^$$\"$_#F4$!$s\"F4F,)F.\"\" &F,F,*&^$$!#!)!#;$!$`(F4F,)F.\"\"%F,F,*&^$$\"#;FE$!#PFEF,)F.\"\"$F,F,* &^$$\"\"!FU$F,!#:F,)F.\"\"#F,F,*&^$FT$!\"&FWF,F.F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "# compute the zeros of P and Q" }}} {EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 33 "p:=[solve(evalf(subs(sol,P )),z)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"pG7'^$$!5))fVt\"z>'*o,& !#>$\"5?XH*y[yZoP#F)^$$!5OJv>+9vJ&e#F)$\"5TTz5B'*R)yd&F)^$$!5fI]&F)^$$\"5\"Rl #\\Tp/DSHF)$\"50b " 0 "" {MPLTEXT 1 0 33 "q:=[solve(evalf(subs(sol,Q)),z)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"qG7&^$$!5D$ya#yX@Pac!#>$\"5#zeG.;wfx0&F)^$$\"5^XpW \"=&pVbR!#@$!5I]dT)Q%QQ)y&F)^$$\"5oQ.$o!oA6)4&!#?$!5r'3:^AJQzD$F)^$$\" 5$*zsvX\\l+0TF)$\"53\\A?`%Ri&))RF)" }}}{EXCHG {PARA 203 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "# plot the config uration. level 1 -> green, level 2 -> red, level3 -> blue." }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords has been redefined\n" }}} {EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 78 "plotO:=complexplot(\{0\},a xes=none,style=point,color=green,scaling=constrained):" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 74 "plotP:=complexplot(p,axes=none,st yle=point,color=red,scaling=constrained):" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 75 "plotQ:=complexplot(q,axes=none,style=point,color=b lue,scaling=constrained):" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 27 "display(plotO,plotP,plotQ);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 400 400 {PLOTDATA 2 "6)-%'CURVESG6%7#7$$\"\"!F)F(-%'COLOURG6&%$RGBGF($\"*+ +++\"!\")F(-%&STYLEG6#%&POINTG-F$6%7'7$$!5))fVt\"z>'*o,&!#>$\"5?XH*y[y ZoP#F;7$$!5OJv>+9vJ&e#F;$\"5TTz5B'*R)yd&F;7$$!5fI]&F;7$$\"5\"Rl#\\Tp/DSHF;$\" 50b " 0 "" {MPLTEXT 1 0 57 "# check that configuration is bal anced and non-degenerate" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 10 "nn:=1+n+m;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nnG\"#5" }}} {EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 " " 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have b een redefined and unprotected\n" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 19 "QQ:=matrix(nn,4,0):" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 135 "QQ[1,1]:=-c1:QQ[1,2]:=c1:for i from 1 to n do QQ[1+i ,2]:=-c2;QQ[1+i,3]:=c2;od:for i from 1 to m do QQ[1+n+i,3]:=-c3;QQ[1+n +i,4]:=c3;od:" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 30 "pp:=vect or(nn);FF:=vector(nn);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ppG-%&arr ayG6$;\"\"\"\"#57\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#FFG-%&arrayG 6$;\"\"\"\"#57\"" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 144 "for \+ i from 1 to nn do FF[i]:=sum(sum(QQ[i,kk]*QQ[jj,kk]/(pp[i]-pp[jj]),jj= 1..i-1)+sum(QQ[i,kk]*QQ[jj,kk]/(pp[i]-pp[jj]),jj=i+1..nn),kk=1..4);od: " }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 140 "SUBS:=\{pp[1]=0.\}: \+ for i from 1 to n do SUBS:=\{op(SUBS),pp[1+i]=p[i]\};od:for i from 1 t o m do SUBS:=\{op(SUBS),pp[1+n+i]=q[i]\};od:print(SUBS);" }}{PARA 12 " " 1 "" {XPPMATH 20 "6#<,/&%#ppG6#\"\"\"$\"\"!F*/&F&6#\"\"%^$$!5fI]/&F&6#\"\"&^$$\"5Q'o\"G=Xae.\"*F2$!56GJu:tEi# >&F5/&F&6#\"\"$^$$!5OJv>+9vJ&e#F5$\"5TTz5B'*R)yd&F5/&F&6#\"\"'^$$\"5\" Rl#\\Tp/DSHF5$\"50b'*o,&F5$\"5?XH* y[yZoP#F5/&F&6#\"\"(^$$!5D$ya#yX@PacF5$\"5#zeG.;wfx0&F5/&F&6#\"\")^$$ \"5^XpW\"=&pVbR!#@$!5I]dT)Q%QQ)y&F5/&F&6#\"\"*^$$\"5oQ.$o!oA6)4&F2$!5r '3:^AJQzD$F5/&F&6#\"#5^$$\"5$*zsvX\\l+0TF5$\"53\\A?`%Ri&))RF5" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "# check that forces are zero " }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 49 "for i from 1 to nn do evalf(subs(SUBS,FF[i]));od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\" \"!F%$!\"\"!#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"#9!#?$!$H'!#@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"#;!#?$!$7#!#@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$!&')[\"!#@$!$=(!#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$!%rE!#@$\"%W;!#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$!\"#!# ?$!#8F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^$$!#A!#?$\"$[(!#@" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#^$$\"%U>!#?$!$()*F&" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#^$$!$1#!#?$\"#sF&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# ^$$\"\"'!#?$\"#6F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "# com pute Jacobian matrix A" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 37 "A:=evalf(subs(SUBS,jacobian(FF,pp))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "# configuration is non-degenerate if only two singula r values are zero (up to rounding errors)" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 16 "singularvals(A);" }}{PARA 12 "" 1 "" {XPPMATH 20 " 6#7,^$$\"5j$3$p=h5Z4R!#>$!5Ke`[SJl&p%=!#R^$$\"5byWM61&fxP\"F'$\"5CwyQu *)Ri7A!#S^$$\"5GV)Ga,hR=V)!#?$!5@:&fs0rW8)\\F*^$$\"5w&*oS?ns@=]F4$!5\" z$\\@za%48%QF0^$$\"5neOy$p3PYW$F4$!5)3WaB&HI*z]&F*^$$\"5UeI&Qm!=][6F4$ \"55(3TY3X/W@*F*^$$\"5%=Xo&G;G,c=F4$!5**\\vtu)4poy)F*^$$\"5kCoP)*fIir; F4$\"5c^l.*)QXEX$*F*^$$\"5'yw&>i%Qd&e)*!#I$\"5BZQ4$!#H$\"5p]1E-WE\"4c'FS" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "# export the configuration as a list of points" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 25 "lprint([0.,op(p),op(q)]);" }}{PARA 6 " " 1 "" {TEXT -1 434 "[0., -5.0168961979173435988+2.3768477848789294520 *I, -2.5853175140019753136+5.5778839962310794141*I, -.5341095877281750 3059-4.9328020936764951467*I, .91035854451828168638-5.1926226731574312 811*I, 2.9402504694149265391+2.1706929857239175505*I, -5.6543721457825 478325+5.0577597616032858792*I, .39554369518144694551e-1-5.78838384388 41575030*I, .50981122680683033868-3.2579383122511508671*I, 4.105006549 4575727993+3.9885623945320224908*I]" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 19 "lprint([c1,c2,c3]);" }}{PARA 6 "" 1 "" {TEXT -1 49 "[ 3.4000000000000000000, 1, 1.5000000000000000000]" }}}{EXCHG {PARA 201 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "# e xport the configuration in latex picture format (the result needs to b e edited somewhat...)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 327 "x min:=1000:ymin:=1000:xmax:=-1000:ymax:=-1000:for i from 1 to n do xmin :=min(xmin,Re(p[i])):xmax:=max(xmax,Re(p[i])):ymin:=min(ymin,Im(p[i])) :ymax:=max(ymax,Im(p[i])):od:for i from 1 to m do xmin:=min(xmin,Re(q[ i])):xmax:=max(xmax,Re(q[i])):ymin:=min(ymin,Im(q[i])):ymax:=max(ymax, Im(q[i])):od:height:=max(xmax-xmin,ymax-ymin):" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 0 323 "lprint(begin(picture)(100*(xmax-xmin),100*he ight)(100*xmin,100*(ymin+ymax-height)/2));lprint(setlength(unitlength) (0.5/(xmax-xmin)));lprint(put(0,0));lprint(\{bullet\});for i from 1 to n do lprint(put(100*Re(p[i]),100*Im(p[i])));lprint(\{circ\});od;for i from 1 to m do lprint(put(100*Re(q[i]),100*Im(q[i])));lprint(\{star\} );od;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 6 "" 1 "" {TEXT -1 106 "begin(picture)(975.93786952401206318,1136.6267840115236917)(-5 65.43721457825478325,-578.83838438841575030)" }}{PARA 6 "" 1 "" {TEXT -1 47 "setlength(unitlength)(.51232769586435026130e-1)" }}{PARA 6 "" 1 "" {TEXT -1 8 "put(0,0)" }}{PARA 6 "" 1 "" {TEXT -1 8 "\{bullet\}" } }{PARA 6 "" 1 "" {TEXT -1 49 "put(-501.68961979173435988,237.684778487 89294520)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{circ\}" }}{PARA 6 "" 1 "" {TEXT -1 49 "put(-258.53175140019753136,557.78839962310794141)" }} {PARA 6 "" 1 "" {TEXT -1 6 "\{circ\}" }}{PARA 6 "" 1 "" {TEXT -1 50 "p ut(-53.410958772817503059,-493.28020936764951467)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{circ\}" }}{PARA 6 "" 1 "" {TEXT -1 49 "put(91.0358544518 28168638,-519.26226731574312811)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{circ \}" }}{PARA 6 "" 1 "" {TEXT -1 48 "put(294.02504694149265391,217.06929 857239175505)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{circ\}" }}{PARA 6 "" 1 "" {TEXT -1 49 "put(-565.43721457825478325,505.77597616032858792)" }} {PARA 6 "" 1 "" {TEXT -1 6 "\{star\}" }}{PARA 6 "" 1 "" {TEXT -1 49 "p ut(3.9554369518144694551,-578.83838438841575030)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{star\}" }}{PARA 6 "" 1 "" {TEXT -1 49 "put(50.9811226806 83033868,-325.79383122511508671)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{star \}" }}{PARA 6 "" 1 "" {TEXT -1 48 "put(410.50065494575727993,398.85623 945320224908)" }}{PARA 6 "" 1 "" {TEXT -1 6 "\{star\}" }}}}{MARK "53 0 0" 49 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }