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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(Groebner);" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#7B%&BasisG%%FGLMG%1HilbertDimensionG%2
HilbertPolynomialG%.HilbertSeriesG%+HomogenizeG%,InitialFormG%,InterRe
duceG%)IsProperG%2IsZeroDimensionalG%3LeadingCoefficientG%0LeadingMono
mialG%,LeadingTermG%,MatrixOrderG%6MaximalIndependentSetG%.MonomialOrd
erG%5MultiplicationMatrixG%9MultivariateCyclicVectorG%+NormalFormG%*No
rmalSetG%ARationalUnivariateRepresentationG%'ReduceG%.RememberBasisG%,
SPolynomialG%&SolveG%5SuggestVariableOrderG%*TestOrderG%0ToricIdealBas
isG%-TrailingTermG%5UnivariatePolynomialG%%WalkG%/WeightedDegreeG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "?Groebner" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 28 "F := \{x*y-x^2*y^2, y^3 - x\};" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%\"FG<$,&*$)%\"yG\"\"$\"\"\"F+%\"xG!\"\",&*&F,
F+F)F+F+*&)F,\"\"#F+)F)F2F+F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 35 "B:=Groebner['Basis'](F, tdeg(x,y));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"BG7%,&*$)%\"yG\"\"$\"\"\"F+%\"xG!\"\",&*$)F,F*F+F+*
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" 0 "" {MPLTEXT 1 0 26 "B1 := Basis(F, tdeg(y,x));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#B1G7&,&*&%\"xG\"\"\")%\"yG\"\"#F)F)*$)F(\"\"$F)!\"
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F0" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "?plex" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "B2 := Basis(F, plex(x,y));" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#B2G7$,&*$)%\"yG\"\"%\"\"\"!\"\"*$)F
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{MPLTEXT 1 0 26 "B3 := Basis(F, plex(y,x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#B3G7%,&*$)%\"xG\"\"#\"\"\"!\"\"*$)F)\"\"'F+F+,&*$)F)
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0 "" {MPLTEXT 1 0 38 "NormalForm(x^2*y^3+y^3, F, tdeg(x,y));" }}{PARA 
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{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "NormalForm(x^2*y^3+y^3, B, tdeg(x,y
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{XPPMATH 20 "6#,&%\"xG\"\"\"*&F$F%)%\"yG\"\"#F%F%" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 67 "NormalForm(expand(x^2*y^3+y^3 + x^5*F[1]+y^8
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\"*$)F$\"\"$F%F%*$)F$\"\"%F%F%*&)F$\"\"&F%%\"yGF%!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F[2];" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#,&*&%\"xG\"\"\"%\"yGF&F&*&)F%\"\"#F&)F'F*F&!\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "?basis" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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