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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 65 "The first example in our \+
paper. Transform the root to the origin." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 
"interface(rtablesize = 30);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "with(LinearAlgebra):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "read`../polysolver.mpl`:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "lsys:=[x^2+2*x+y,x+1/8*y^2+
1/2*y];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%lsysG7$,(*$)%\"xG\"\"#\"
\"\"F+*&F*F+F)F+F+%\"yGF+,(F)F+*&#F+\"\")F+*$)F-F*F+F+F+*&#F+F*F+F-F+F
+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 40 "Same perturbation for the tw
o variables." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "lsysnew:=ex
pand(subs(\{x=x+a,y=y+a\},lsys));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%(lsysnewG7$,.*$)%\"xG\"\"#\"\"\"F+*(F*F+F)F+%\"aGF+F+*$)F-F*F+F+*&F*F
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{PARA 11 "" 1 "" {XPPMATH 20 "6$\"#7\"#5" }}}{EXCHG {PARA 0 "> " 0 "" 
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0 "> " 0 "" {MPLTEXT 1 0 54 "V:=SubMatrix(Matrix([NV[1],NV[2],NV[3]]),
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{MPLTEXT 1 0 47 "My:=SubMatrix(V,[2,3,5],1..3).MatrixInverse(B);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#MyG-%'RTABLEG6%\"*O$*3`\"-%'MATRIXG
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G\"\"%\"\"!!\"\"\"\"\"#\"\"$F%\"\"##!\"$\"\")F*-%\"OG6#F(F%" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "taylor((4*a^3-8*a^2+128)/(32
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"" {MPLTEXT 1 0 53 "taylor((3*a^4+40*a^3+128*a^2+384*a)/(32*a+64),a=0,
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0 "" {MPLTEXT 1 0 45 "lsysnewnew:=expand(subs(\{x=x+a,y=y+b\},lsys));
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%'MATRIXG6#7(7,\"\"!F.F.F.\"\"\"F.F.,&*&\"\"#F/%\"aGF/F/F2F/F/,(*&F2F/
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