{VERSION 6 0 "IBM INTEL LINUX" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 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 "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plo t" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 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 58 "#################### ######################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "# Details of the computations in section 4.2" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "# yields asymmetric configur ations of type 5,4,1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "# # #######################################################" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "Digits:=20;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'Dig itsG\"#?" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "N1:=5;N2:=4;N3: =1;c1:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#N1G\"\"&" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%#N2G\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#N3G\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c1G\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "# In the paper we first stud y the case c2=1. Then we perturb the value of c2." }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 39 "# You may change the value of c2 here :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "c2:=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c2G\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "# compute the value of c3 -- do not touch" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "c3:=(N1*(N1-1)*c1^2+N2*(N2-1)*c2^2-N1*N2*c1*c2)/ (N2*c2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#c3G\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "# compute the configuration -- nota tions as in section 4.2 of the paper" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "P1:=z^5+sum(a[i]*z^i,i=0..4);P2:=z^4+sum(b[i]*z^i,i=0 ..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#P1G,.*$)%\"zG\"\"&\"\"\"F* &%\"aG6#\"\"!F**&&F,6#F*F*F(F*F**&&F,6#\"\"#F*)F(F5F*F**&&F,6#\"\"$F*) F(F:F*F**&&F,6#\"\"%F*)F(F?F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%# P2G,**$)%\"zG\"\"%\"\"\"F*&%\"bG6#\"\"!F**&%\"xGF*)F(\"\"#F*F**&F2F*)F (\"\"$F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "x:='x';b[1]:= 0;b[2]:=x;b[3]:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xGF$" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"\"\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"#%\"xG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"bG6#\"\"$\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "P 1p:=diff(P1,z);P1pp:=diff(P1p,z);P2p:=diff(P2,z);P2pp:=diff(P2p,z);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$P1pG,,*&\"\"&\"\"\")%\"zG\"\"%F(F( &%\"aG6#F(F(*(\"\"#F(&F-6#F0F(F*F(F(*(\"\"$F(&F-6#F4F()F*F0F(F(*(F+F(& F-6#F+F()F*F4F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%P1ppG,**&\"#? \"\"\")%\"zG\"\"$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#>%$P2pG ,(*&\"\"%\"\"\")%\"zG\"\"$F(F(*(\"\"#F(%\"xGF(F*F(F(*&\"\"'F()F*F-F(F( " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%P2ppG,(*&\"#7\"\"\")%\"zG\"\"#F (F(*&F+F(%\"xGF(F(*&F'F(F*F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "# below is equation 2.5 of the paper" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "EQ:=collect(expand(c1^2*z*P1pp*P2+c2^2*z*P2pp*P1 -c1*c2*z*P1p*P2p-c2*c3*P1*P2p),z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6# >%#EQG,0*&,&\"\"%\"\"\"*&F(F)&%\"aG6#F(F)!\"\"F))%\"zG\"\"(F)F)*&,(*& \"\"'F)F+F)F.*&F5F)&F,6#\"\"$F)F.*&F5F)%\"xGF)F)F))F0F5F)F)*&,&*&F5F)& F,6#\"\"#F)F.*&\"#7F)F7F)F.F))F0\"\"&F)F)*&,**(F(F)F7F)F;F)F.*&\"#?F)& %\"bG6#\"\"!F)F)*&\"#9F)F@F)F.*&F(F)&F,6#F)F)F.F))F0F(F)F)*&,(*(F5F)F@ F)F;F)F.*&FDF)FSF)F.*(FDF)F+F)FLF)F)F))F0F9F)F)*&,(*&F5F)&F,FNF)F.*(F5 F)F;F)FSF)F.*(F5F)F7F)FLF)F)F))F0FBF)F)*&,&*(FBF)F@F)FLF)F)*(F(F)F;F)F inF)F.F)F0F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "for j fro m 1 to 7 do eq[j]:=coeff(EQ,z,j):od:print(eq);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#K%&TABLEG6#7)/\"\" \",&*(\"\"#F(&%\"aG6#F+F(&%\"bG6#\"\"!F(F(*(\"\"%F(%\"xGF(&F-F1F(!\"\" /F+,(*&\"\"'F(F6F(F7*(F;F(F5F(&F-6#F(F(F7*(F;F(&F-6#\"\"$F(F/F(F(/FB,( *(F;F(F,F(F5F(F7*&\"#7F(F=F(F7*(FGF(&F-6#F4F(F/F(F(/F4,**(F4F(F@F(F5F( F7*&\"#?F(F/F(F(*&\"#9F(F,F(F7*&F4F(F=F(F7/\"\"&,&*&F;F(F,F(F7*&FGF(F@ F(F7/F;,(*&F;F(FIF(F7*&F;F(F@F(F7*&F;F(F5F(F(/\"\"(,&F4F(*&F4F(FIF(F7Q (pprint26\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "sol:=solve( \{eq[7],eq[6],eq[5],eq[4],eq[3],eq[2]\},\{a[0],a[1],a[2],a[3],a[4],b[0 ]\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$solG<(/&%\"aG6#\"\"%\"\"\" /&F(6#\"\"$,&F+!\"\"%\"xGF+/&F(6#\"\"#,&F6F+*&F6F+F2F+F1/&F(6#\"\"!,*# \"\"(F*F1*&#F+F6F+*$)F2F6F+F+F+*$)F2F/F+F1*&#\"\"*F*F+F2F+F+/&%\"bGF;, (*&#FHF*F+F2F+F1*&FAF+FBF+F+#F?F*F+/&F(6#F+,(*&#\"#8F*F+F2F+F1*&#F/F6F +FBF+F+FPF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "P:=expand(su bs(sol,eq[1]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG,,*&\"\"*\"\" \"%\"xGF(!\"\"*&\"\"#F()F)F,F(F(\"\"(F(*&\"\"%F()F)\"\"$F(F**&F0F()F)F 0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "x:=[solve(evalf(P) ,x)][2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG^$$!5)eZhSVC6sL&!#?$ !5\"\\!orA$)>'Q;\"!#>" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "# \+ compute points of the configuration" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "p1:=[solve(subs(sol,P1),z)];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#p1G7'^$$!5*3d*\\\"*)o@)4$!5d4P:!fk`9.$!#?^$$!5u& [3#p)o@)4 " 0 "" {MPLTEXT 1 0 28 "p2:=[solve(subs(sol,P2),z)]; " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#p2G7&^$$!5zaDV%))o@)4$!5>\" pEj^k`9.$!#?^$$!5%=]vi()o@)4'Q;\"F)^$$\"5R!4>I<`A#f))F,$!5))z'o*>SDrvbF," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "p3:=[0];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#p3G7#\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "# plot the configuration" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "# note that several points are equal when c2=1. To see all 10 \+ points, perturb the value of c2." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7Z%(a nimateG%*animate3dG%-animatecurveG%&arrowG%-changecoordsG%,complexplot G%.complexplot3dG%*conformalG%,conformal3dG%,contourplotG%.contourplot 3dG%*coordplotG%,coordplot3dG%-cylinderplotG%,densityplotG%(displayG%* display3dG%*fieldplotG%,fieldplot3dG%)gradplotG%+gradplot3dG%,graphplo t3dG%-implicitplotG%/implicitplot3dG%(inequalG%,interactiveG%-listcont plotG%/listcontplot3dG%0listdensityplotG%)listplotG%+listplot3dG%+logl ogplotG%(logplotG%+matrixplotG%(odeplotG%'paretoG%,plotcompareG%*point plotG%,pointplot3dG%*polarplotG%,polygonplotG%.polygonplot3dG%4polyhed ra_supportedG%.polyhedraplotG%'replotG%*rootlocusG%,semilogplotG%+seto ptionsG%-setoptions3dG%+spacecurveG%1sparsematrixplotG%+sphereplotG%)s urfdataG%)textplotG%+textplot3dG%)tubeplotG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "plot1:=complexplot(p1,axes=none,style=point,color= blue,scaling=constrained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "plot2:=complexplot(p2,axes=none,style=point,color=red,scaling=cons trained):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "plot3:=complex plot(p3,axes=none,style=point,color=green,scaling=constrained):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "display(plot1,plot2,plot3); " }}{PARA 13 "" 1 "" {GLPLOT2D 529 529 529 {PLOTDATA 2 "6)-%'CURVESG6% 7'7$$!5*3d*\\\"*)o@)4$!5d4P:!fk`9.$!#?7$$!5u&[3#p)o@)4\"pEj ^k`9.$F-7$$!5%=]vi()o@)4'Q;\"F*7$$\"5R!4>I<`A#f))F-$!5))z'o*>SDrvbF--FC6&FEFHFFFFFK-F$6 %7#7$FFFF-FC6&FEFFFHFFFK-%+AXESLABELSG6%Q!6\"F[p-%%FONTG6#%(DEFAULTG-% (SCALINGG6#%,CONSTRAINEDG-%*AXESSTYLEG6#%%NONEG-%%VIEWG6$F`pF`p" 1 2 0 1 10 0 2 9 1 1 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2 " "Curve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK " 33 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }