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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 2 "Bi" }{TEXT 256 0 "" }
{TEXT -1 45 "furcation problem from the Frisco test suite." }}{PARA 
257 "" 0 "" {TEXT -1 23 "B. Mourrain  3/02/1999." }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 149 "var := [z[1],z[2],z[3]];\n\nS := [5*z[1]^9-6
*z[1]^5*z[2]+z[1]*z[2]^4+2*z[1]*z[3],\n -2*z[1]^6*z[2]+2*z[1]^2*z[2]^3
+2*z[2]*z[3], z[1]^2+z[2]^2-0.265625];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%$varG7%&%\"zG6#\"\"\"&F'6#\"\"#&F'6#\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"SG7%,**$)&%\"zG6#\"\"\"\"\"*\"\"\"\"\"&*&)F)F/F.&F*
6#\"\"#F,!\"'*&F)F,)F2\"\"%F.F,*&F)F.&F*6#\"\"$F,F4,(*&)F)\"\"'F.F2F.!
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{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Using Bezoutian matrices." }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "read multires;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "mbezout(S,[z[2],z[3]]);" }}{PARA 6 
"" 1 "" {TEXT -1 31 "[1, z[2]^3, z[2], z[3], z[2]^2]" }}{PARA 6 "" 1 "
" {TEXT -1 37 "[1, xi[1], xi[1]^4, xi[1]^2, xi[1]^3]" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#-%'matrixG6#7'7',&*$)&%\"zG6#\"\"\"\"\"(\"\"\"$!(+D1
\"!\"'*$)F+\"\"*F0\"\"%,&F)!#7*$)F+\"\"&F0$\"(+v=$F3,&F+$!']7`F3*$)F+
\"\"$F0\"\"#,(F4!#5F:!\"%FB$\"(+D1\"F3\"\"!7'FKF?FKFK,$F+FE7'FK,*FBFIF
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B!\"#FK" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "T := map(u->conv
ert(u,rational),triang(%)):ffgausselim(%):\nf := lasts(%):factor(f);fs
olve(%);" }}{PARA 6 "" 1 "" {TEXT -1 1 "4" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,$*()&%\"zG6#\"\"\"\"\"&\"\"\",&*$)F&\"\"#F+\"#k!#<F)F)
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a^#\"&@N)F)F)#F)\");sx;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6-$!5tov?-K?)
Q:&!#?$!5v`P#yG5rd,&F%$!5I`0Az1kO>EF%\"\"!F*F*F*F*$\"5I`0Az1kO>EF%$\"5
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1 0 23 "mbezout(S,[z[1],z[2]]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "
T := map(u->convert(u,rational),triang(%)):shape(T);" }}{PARA 6 "" 1 "
" {TEXT -1 495 "[1, z[2]^2*z[1]^3, z[2]^3, z[2]^2*z[1]^2, z[1]*z[2]^4,
 z[1]^5*z[2], z[1]^6*z[2], z[1]^2*z[2]^3, z[1], z[2], z[1]^5, z[2]^4, \+
z[1]^6, z[1]^2, z[2]^2, z[1]^4, z[1]^4*z[2], z[1]^3, z[1]^5*z[2]^2, z[
1]^8, z[1]^7, z[2]^5, z[1]^3*z[2]^4, z[1]^5*z[2]^4, z[1]*z[2], z[1]^3*
z[2], z[1]^2*z[2], z[1]^4*z[2]^4, z[1]*z[2]^2, z[2]^4*z[1]^2, z[2]^2*z
[1]^6, z[2]^2*z[1]^8, z[2]^6*z[1], z[1]^8*z[2], z[1]*z[2]^3, z[2]^2*z[
1]^7, z[1]^4*z[2]^2, z[2]*z[1]^7, z[1]*z[2]^5, z[1]^3*z[2]^3, z[1]^5*z
[2]^3, z[1]^4*z[2]^3]" }}{PARA 6 "" 1 "" {TEXT -1 557 "[1, xi[1]^2*xi[
2]^2, xi[1]^6, xi[1]^8, xi[1]^14, xi[1]^10*xi[2]^2, xi[1]^5*xi[2], xi[
1]^9, xi[1]^7, xi[1]^3, xi[1]^3*xi[2]^2, xi[1]^7*xi[2]^2, xi[1]^11, xi
[1]^3*xi[2], xi[1]^5*xi[2]^2, xi[1]*xi[2], xi[1]^2*xi[2]^3, xi[1]^6*xi
[2], xi[1]^2*xi[2], xi[1]^10*xi[2], xi[1]^6*xi[2]^2, xi[1]^6*xi[2]^3, \+
xi[1]^4, xi[1]^4*xi[2], xi[1]^8*xi[2]^2, xi[1]^10, xi[1]^12, xi[1]^4*x
i[2]^2, xi[1], xi[1]^5, xi[1]*xi[2]^2, xi[1]*xi[2]^3, xi[1]^7*xi[2], x
i[1]^3*xi[2]^3, xi[1]^8*xi[2], xi[1]^4*xi[2]^3, xi[1]^9*xi[2]^2, xi[1]
^13, xi[2], xi[1]^2, xi[1]^9*xi[2], xi[1]^5*xi[2]^3]" }}{PARA 12 "" 1 
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7LF=F=F?F=F=F=F=F=F=F=F=F=F=F=F=F=F=F/F=F=F=F=FFFCF=F=F=F?F=F=F=F=F=F=
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{PARA 6 "" 1 "" {TEXT -1 7 "42   42" }}{PARA 6 "" 1 "" {TEXT -1 46 "[x
x                      x  x    xx x x x  ] 1" }}{PARA 6 "" 1 "" {TEXT 
-1 46 "[xx    xx             x             x      ] 2" }}{PARA 6 "" 1 
"" {TEXT -1 46 "[xx            x      x     x       x      ] 3" }}
{PARA 6 "" 1 "" {TEXT -1 46 "[  xx      xx             x            x \+
  ] 4" }}{PARA 6 "" 1 "" {TEXT -1 46 "[  xx                  x        \+
x      x x ] 5" }}{PARA 6 "" 1 "" {TEXT -1 46 "[  xx                  \+
xx x   xxx    x   x ] 6" }}{PARA 6 "" 1 "" {TEXT -1 46 "[    xx   x   \+
   x               xxx  x x x] 7" }}{PARA 6 "" 1 "" {TEXT -1 46 "[    \+
xx          xxx         x   x  x     x] 8" }}{PARA 6 "" 1 "" {TEXT -1 
46 "[    xx            x         x   x    x    ] 9" }}{PARA 6 "" 1 "" 
{TEXT -1 47 "[      xx                x       x  x     x] 10" }}{PARA 
6 "" 1 "" {TEXT -1 47 "[      xx             x  x   x   xxx  x   x] 11
" }}{PARA 6 "" 1 "" {TEXT -1 47 "[        x                    xx     \+
x x x ] 12" }}{PARA 6 "" 1 "" {TEXT -1 47 "[        x   xx x          \+
x  xxx    x   x ] 13" }}{PARA 6 "" 1 "" {TEXT -1 47 "[        x      x
    x  x x    x     x x   ] 14" }}{PARA 6 "" 1 "" {TEXT -1 47 "[      \+
   x    x x x        xx    xx  x x  ] 15" }}{PARA 6 "" 1 "" {TEXT -1 
47 "[         x                       xxx x   x] 16" }}{PARA 6 "" 1 "
" {TEXT -1 47 "[          xx       x  x       xx    x x x ] 17" }}
{PARA 6 "" 1 "" {TEXT -1 47 "[          xx             xx  x          \+
  ] 18" }}{PARA 6 "" 1 "" {TEXT -1 47 "[            xx      x  x      \+
 x    x     ] 19" }}{PARA 6 "" 1 "" {TEXT -1 47 "[            xx x    \+
x         xx    x x x ] 20" }}{PARA 6 "" 1 "" {TEXT -1 47 "[          \+
    x      x     x      xx   x  ] 21" }}{PARA 6 "" 1 "" {TEXT -1 47 "[
              x         x       x    x x  ] 22" }}{PARA 6 "" 1 "" 
{TEXT -1 47 "[               x       x      x     x     ] 23" }}{PARA 
6 "" 1 "" {TEXT -1 47 "[                x           x    x   x    ] 24
" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                 x   x  x  xx   xxxx
   x  ] 25" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                 x        \+
  x    x   x    ] 26" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                \+
 xx                  x    ] 27" }}{PARA 6 "" 1 "" {TEXT -1 47 "[      \+
            x        xx    x     x x] 28" }}{PARA 6 "" 1 "" {TEXT -1 
47 "[                   x      x             x ] 29" }}{PARA 6 "" 1 "
" {TEXT -1 47 "[                   x      x             x ] 30" }}
{PARA 6 "" 1 "" {TEXT -1 47 "[                   x  x  xx  x x    x x \+
  ] 31" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                   x  x  xx  x
 x    x x   ] 32" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                    \+
x  x      x           ] 33" }}{PARA 6 "" 1 "" {TEXT -1 47 "[          \+
          x  x      x           ] 34" }}{PARA 6 "" 1 "" {TEXT -1 47 "[
                     x  x       x x    x x] 35" }}{PARA 6 "" 1 "" 
{TEXT -1 47 "[                      x  xx  x x        x ] 36" }}{PARA 
6 "" 1 "" {TEXT -1 47 "[                           x           x x] 37
" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                           x        \+
   x x] 38" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                          \+
   x        x x ] 39" }}{PARA 6 "" 1 "" {TEXT -1 47 "[                \+
             x        x x ] 40" }}{PARA 6 "" 1 "" {TEXT -1 47 "[      \+
                            xx     x] 41" }}{PARA 6 "" 1 "" {TEXT -1 
47 "[                                  xx     x] 42" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 55 "ffgausselim(%):f := lasts(%): factor(%);f
solve(%,z[3]);" }}{PARA 6 "" 1 "" {TEXT -1 2 "35" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,$*()&%\"zG6#\"\"$\"\"#\"\"\"),&F&\")KWbL\"'0wT\"\"\"F*
F+),4*$)F&\"\")F+\":+++/zQF%=go6Y*$)F&\"\"(F+\";+?N[,\"yM4bP/m\"*$)F&
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+_6gJYeDMD!3.$G>q>'Q\"3$F0F*F+#!+DJqqu\"O'\\')4`X0)zzxQ9LU_RQ#3x!**3d
" }}{PARA 12 "" 1 "" {XPPMATH 20 "6.$!5D)GYbY4K%>8!#@F#$!5x4]82%))fXC
\"F%F&\"\"!F($\"5?8\"frQJ^*Q7F%F)$\"5`m?>iji'G,$!#?F+$\"5(e*4xI^dU_KF-
F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "mbezout(S,[z[1],z[2]]
):\nT := map(u->convert(u,rational),triang(%)):" }}{PARA 6 "" 1 "" 
{TEXT -1 495 "[1, z[2]^2*z[1]^3, z[2]^3, z[2]^2*z[1]^2, z[1]*z[2]^4, z
[1]^5*z[2], z[1]^6*z[2], z[1]^2*z[2]^3, z[1], z[2], z[1]^5, z[2]^4, z[
1]^6, z[1]^2, z[2]^2, z[1]^4, z[1]^4*z[2], z[1]^3, z[1]^5*z[2]^2, z[1]
^8, z[1]^7, z[2]^5, z[1]^3*z[2]^4, z[1]^5*z[2]^4, z[1]*z[2], z[1]^3*z[
2], z[1]^2*z[2], z[1]^4*z[2]^4, z[1]*z[2]^2, z[2]^4*z[1]^2, z[2]^2*z[1
]^6, z[2]^2*z[1]^8, z[2]^6*z[1], z[1]^8*z[2], z[1]*z[2]^3, z[2]^2*z[1]
^7, z[1]^4*z[2]^2, z[2]*z[1]^7, z[1]*z[2]^5, z[1]^3*z[2]^3, z[1]^5*z[2
]^3, z[1]^4*z[2]^3]" }}{PARA 6 "" 1 "" {TEXT -1 557 "[1, xi[1]^2*xi[2]
^2, xi[1]^6, xi[1]^8, xi[1]^14, xi[1]^10*xi[2]^2, xi[1]^7, xi[1]^3*xi[
2]^2, xi[1]^9, xi[1]^5*xi[2], xi[1]^3, xi[1]^7*xi[2]^2, xi[1]^11, xi[1
]*xi[2], xi[1]^3*xi[2], xi[1]^5*xi[2]^2, xi[1]^2*xi[2]^3, xi[1]^6*xi[2
], xi[1]^2*xi[2], xi[1]^6*xi[2]^2, xi[1]^6*xi[2]^3, xi[1]^10*xi[2], xi
[1]^4, xi[1]^4*xi[2], xi[1]^8*xi[2]^2, xi[1]^12, xi[1]^10, xi[1]^4*xi[
2]^2, xi[1], xi[1]^5, xi[1]*xi[2]^2, xi[1]*xi[2]^3, xi[1]^3*xi[2]^3, x
i[1]^7*xi[2], xi[1]^8*xi[2], xi[1]^4*xi[2]^3, xi[1]^13, xi[1]^9*xi[2]^
2, xi[2], xi[1]^2, xi[1]^5*xi[2]^3, xi[1]^9*xi[2]]" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 50 "ffgausselim(%):f := lasts(%):\nfactor(f);fs
olve(%);" }}{PARA 6 "" 1 "" {TEXT -1 2 "35" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#,$*()&%\"zG6#\"\"$\"\"#\"\"\"),&F&\")KWbL\"'0wT\"\"\"F*
F+),4*$)F&\"\")F+\":+++/zQF%=go6Y*$)F&\"\"(F+\";+?N[,\"yM4bP/m\"*$)F&
\"\"'F+\";%)**3]GXS1O$y**>$*$)F&\"\"&F+!;)o!\\0gJy)GosvO#*$)F&\"\"%F+
\":Wx%[V'4#RPc4aJ*$)F&F)F+\"93UD3X['z#))R2<*$F%F+\"7kW(4z[AZJw\\\"F&!5
+_6gJYeDMD!3.$G>q>'Q\"3$F0F*F+#\"*D\"G))H\"O'\\')4`X0)zzxQ9LU_RQ#3x!**
3d" }}{PARA 12 "" 1 "" {XPPMATH 20 "6.$!5D)GYbY4K%>8!#@F#$!5x4]82%))fX
C\"F%F&\"\"!F($\"5?8\"frQJ^*Q7F%F)$\"5`m?>iji'G,$!#?F+$\"5(e*4xI^dU_KF
-F." }}}}{PARA 12 "" 1 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" 
{TEXT -1 12 "With gsolve." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 
"with(grobner):g1 := gsolve(convert(S,rational));" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%#g1G7%7%7%,&*$)&%\"zG6#\"\"\"\"\"#\"\"\"\"#k!#<F.&F,6
#F/,&&F,6#\"\"$\")KWbL\"'0wTF.-%%plexG6%F6F3F+<#F+7%7%,2*$)F3\"\")F0\"
)!3')Q)*$)F3\"\"'F0!*#R$oA\"*$)F3\"\"&F0!*'Hj15*$)F3\"\"%F0\"*cEe7\"*$
)F3F8F0\")wtZ`*$)F3F/F0!)+SIAF3!(kC5(\"(pk/\"F.,(F)F1FUF1F2F.,,FF\"'W@
EFN!'S5ZFU\"'?^7F6Ffn!%8\\F.-F<6%F6F+F3<$F+F37%7%,&FUF1F2F.F6F+-F<6%F+
F6F3<#F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "\{fsolve(g1[1][
1][1])\},fsolve(g1[1][1][2]),fsolve(g1[1][1][3]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6%<$$!5tov?-K?)Q:&!#?$\"5tov?-K?)Q:&F&\"\"!$!5x4]82%))fXC
\"!#@" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 181 "Digits := 20;\ns2
 := \{fsolve(g1[2][1][1])\}:\nfor z2 in s2 do\ns1 :=\{fsolve(subs(z[2]
=z2,g1[2][1][2]))\};\nfor z1 in s1 do print(z1,z2,\{fsolve(subs(z[1]=z
1,z[2]=z2,g1[2][1][3]))\});od;\nod:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%'DigitsG\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$!5w`P#yG5rd,&!#?$
\"5ID.Ro1I8&=\"F%<#$\"5?8\"frQJ^*Q7!#@" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6%$\"5w`P#yG5rd,&!#?$\"5ID.Ro1I8&=\"F%<#$\"5?8\"frQJ^*Q7!#@" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6%$!5I`0Az1kO>E!#?$\"5z3$fGW7G'QWF%<#$!5
E)GYbY4K%>8!#@" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%$\"5I`0Az1kO>E!#?$\"
5z3$fGW7G'QWF%<#$!5E)GYbY4K%>8!#@" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "fsolve(g1[3][1][3]),\{fsolve(g1[3][1][1])\}, fsolve(g
1[3][1][2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"!<$$!5tov?-K?)Q:&!
#?$\"5tov?-K?)Q:&F'F#" }}}}{PARA 12 "" 1 "" {TEXT -1 0 "" }}}{MARK "0 \+
0 2" 9 }{VIEWOPTS 1 1 0 1 1 1803 }