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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 254 "sys:=[x[a],x[d],y[a
],y[h],y[c],x[b]-x[c],x[h]-x[e],(x[b]-x[a])*(y[e]-y[a])-(y[b]-y[a])*(x
[e]-x[a]),(x[c]-x[d])*(y[e]-y[d])-(y[c]-y[d])*(x[e]-x[d]),(x[b]-x[a])^
2+(y[b]-y[a])^2-4,(x[d]-x[c])^2+(y[d]-y[c])^2-9,y[e]-1,1-t*x[b],(x[a]-
x[c])^2+(y[a]-y[c])^2-u]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
71 "var:=[t,u,x[a],x[d],y[a],y[c],y[h],y[e],x[b],y[b],y[d],x[h],x[e],x
[c]];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG70%\"tG%\"uG&%\"xG6#%
\"aG&F)6#%\"dG&%\"yGF*&F06#%\"cG&F06#%\"hG&F06#%\"eG&F)6#%\"bG&F0F;&F0
F-&F)F5&F)F8&F)F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "gb:=gr
obner[gbasis](sys,var,plex);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#gbG
70,,&%\"xG6#%\"cG!$a%*$F'\"\"$\"$j\"*$F'\"\"&!#A*$F'\"\"(\"\"\"%\"tG\"
$&Q,&%\"uGF4*$F'\"\"#!\"\"&F(6#%\"aG&F(6#%\"dG&%\"yGF=&FCF)&FC6#%\"hG,
&&FC6#%\"eGF4F;F4,&&F(6#%\"bGF4F'F;,,&FCFN\"#5*$F'\"\"'F;F9!#T*$F'\"\"
%\"#8\"#?F4,,&FCF@FRFSF4F9\"#'*FV!#=!$N\"F4,*&F(FFFRF/F4F'F0F,!\"*,*&F
(FJFRF/F4F'F0F,F[o,,F6F4F9F+FVF.FSF1*$F'\"\")F4" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 42 "G:=array(1..nops(gb),1..nops(var),sparse):" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "for i to nops(gb) do\n  for
 j to nops(var) do\n    if has(gb[i],var[j]) then G[i,j]:=1 fi\n  od\n
od:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "print(G);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%'MATRIXG6#7070\"\"\"\"\"!F)F)F)F)F)F)F)F)F
)F)F)F(70F)F(F)F)F)F)F)F)F)F)F)F)F)F(70F)F)F(F)F)F)F)F)F)F)F)F)F)F)70F
)F)F)F(F)F)F)F)F)F)F)F)F)F)70F)F)F)F)F(F)F)F)F)F)F)F)F)F)70F)F)F)F)F)F
(F)F)F)F)F)F)F)F)70F)F)F)F)F)F)F(F)F)F)F)F)F)F)70F)F)F)F)F)F)F)F(F)F)F
)F)F)F)70F)F)F)F)F)F)F)F)F(F)F)F)F)F(70F)F)F)F)F)F)F)F)F)F(F)F)F)F(70F
)F)F)F)F)F)F)F)F)F)F(F)F)F(70F)F)F)F)F)F)F)F)F)F)F)F(F)F(70F)F)F)F)F)F
)F)F)F)F)F)F)F(F(70F)F)F)F)F)F)F)F)F)F)F)F)F)F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 150 "S:=array(1..nops(gb),1..nops(var),sparse):\nf
or i to nops(gb) do\n  for j to nops(var) do\n    if has(sys[i],var[j]
) then S[i,j]:=1 fi\n  od\nod:\nprint(S);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%'MATRIXG6#7070\"\"!F(\"\"\"F(F(F(F(F(F(F(F(F(F(F(70F(
F(F(F)F(F(F(F(F(F(F(F(F(F(70F(F(F(F(F)F(F(F(F(F(F(F(F(F(70F(F(F(F(F(F(
F)F(F(F(F(F(F(F(70F(F(F(F(F(F)F(F(F(F(F(F(F(F(70F(F(F(F(F(F(F(F(F)F(F(
F(F(F)70F(F(F(F(F(F(F(F(F(F(F(F)F)F(70F(F(F)F(F)F(F(F)F)F)F(F(F)F(70F(
F(F(F)F(F)F(F)F(F(F)F(F)F)70F(F(F)F(F)F(F(F(F)F)F(F(F(F(70F(F(F(F)F(F)
F(F(F(F(F)F(F(F)70F(F(F(F(F(F(F(F)F(F(F(F(F(F(70F)F(F(F(F(F(F(F(F)F(F(
F(F(F(70F(F)F)F(F)F)F(F(F(F(F(F(F(F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "equ1:=subs(x[c]=z,gb[nops(gb)]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%equ1G,,\"$&Q\"\"\"*$%\"zG\"\"#!$a%*$F)\"\"%\"$j\"*$F
)\"\"'!#A*$F)\"\")F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "fso
lve(equ1,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&$!+aN;t=!\"*$!+Cd=J7F%
$\"+Cd=J7F%$\"+aN;t=F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "r
eadlib(sturm);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#:6$%#ssG%#xxG60%#a1G
%#a2G%#c1G%#c2G%#s1G%#s2G%\"tG%\"iG%#n1G%#n2G%\"xG%\"aG%\"bG%\"sG6#%ao
Copyright~(c)~1991~by~the~University~of~Waterloo.~All~rights~reserved.
G6\"C1@'3/9#\"\"#-%%typeG6$9%/%%nameG%&rangeGC%>8.-%#opG6$\"\"\"FB>8/-
FJ6$7$F>FLFB>80-FJ6$7$F>F>FB/F=\"\"%C%>FHFB>FN&9\"6#\"\"$>FS&Fgn6#FX-%
&ERRORG6#%>incorrect~number~of~argumentsG>819$@$-F@6$Fbo-%(polynomG6$%
(numericGFH>Fbo-%)sturmseqG6$FboFH@$4-F@6$Fbo-%%listG6#Fgo-F^o6#%Zfirs
t~argument~should~be~a~Sturm~sequence~or~a~polynomialG@%/FN,$%)infinit
yG!\"\">8$-%$mapG6%:6$%\"pGF2F86$%)operatorG%&arrowGF8*&-%'lcoeffG6$Fc
oFBFL)F]q-%'degreeGF\\rFLF8F8FboFH>F_q-%%subsG6$/FHFNFbo@%/FSF\\q>8%-F
aq6%F[rFboFH>Fhr-Fbr6$/FHFSFbo>F_q-Fbr6$/\"\"!%%NULLGF_q>Fhr-Fbr6$FbsF
hr>8&Fcs>8,-%%nopsG6#F_q@$2FcsF[tC$>8(&F_q6#FL?(8+F>FLF[t%%trueGC%>8*&
F_q6#Fgt@$0-%%signG6#Fct-Fau6#F[u>Fis,&FisFLFLFL>FctF[u>8'Fcs>8--F]t6#
Fhr@$2FcsF[vC$>8)&FhrFet?(FgtF>FLF[vFhtC%>F[u&FhrF]u@$0-Fau6#FbvFcu>Fi
u,&FiuFLFLFL>FbvF[u,&FisFLFiuF]qF8F8" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "sturmseq(equ1,z);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#
7+,,\"$&Q\"\"\"*$%\"zG\"\"#!$a%*$F(\"\"%\"$j\"*$F(\"\"'!#A*$F(\"\")F&,
*F(#!$F#F)*$F(\"\"$#F-F)*$F(\"\"&#!#LF)*$F(\"\"(F&,*!#qF&F'#\"$\"o\"#6
F+#!$j\"FCF.F&,(F(#\"$d*\"#PF6#!$J%FIF9F&,(#\"%\\G\"$H\"F&F'#!$*[\"#VF
+F&,&F(#!#TF7F6F&,&#!#xF2F&F'!\"\"F(F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "sturm(sturmseq(equ1,z),z,0,infinity);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
38 "sturm(sturmseq(equ1,z),z,12/10,13/10);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "so
lve(equ1,z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'RootOfG6#,&-F$6#,,
\"$&Q\"\"\"%#_ZG!$a%*$F,\"\"#\"$j\"*$F,\"\"$!#A*$F,\"\"%F+!\"\"F.F+" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "equ2:=subs(z=w^(1/2),equ1)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%equ2G,,\"$&Q\"\"\"%\"wG!$a%*$F
(\"\"#\"$j\"*$F(\"\"$!#A*$F(\"\"%F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "solve(equ2,w);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'
RootOfG6#,,\"$&Q\"\"\"%#_ZG!$a%*$F)\"\"#\"$j\"*$F)\"\"$!#A*$F)\"\"%F(
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "allvalues(\");" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6&,(#\"#6\"\"#\"\"\"*&\"\"$#F'F&*&,(*$,&
\"&DN%F'*$\"#RF*\"%+7#F'F)\"#P*$F.#F&F)F'\"%D7F'F'F.#!\"\"F)F*#F'\"\"'
*&%\"IGF'*(,**&F.F3F+F*!$A#*&F+F*F.F6F)*$F+F*\"%vO*&F)F*F.F3\"$W\"F'F.
F8F+#F9F&F*F:,(F$F'F(F:F<#F9F;,(F$F'F(FI*$*(,*F@\"$A#FB!\"$FC!%vOFEFFF
'F.F8F+FGF*F:,(F$F'F(FIFKFI" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}}{MARK "17 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }