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Computing a Groebner Basis of a given ideal intersected with
x^2-x for all indeterminates
x.
CharP.GBasisModSquares(Ideal:IDEAL):LIST
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Please note: The function(s) explained on this page is/are using the
ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
This function returns the reduced Groebner basis for the given ideal intersected with the ideal generated by
x^2-x for all indeterminates. If
x^2-x for all indeterminates is in the ideal (e.g. the set of zeros is a subset of
{0,1}^n) this method should produce the Groebner Basis much faster!
Please be aware, that this is much more efficient if the term ordering is
Lex,
DegLex or
DegRevLex. Otherwise, first a DegRevLex Groebner Basis is computed and then transformed with the
FGLM.FGLM-algorithm.
- @param Ideal An Ideal.
- @return The reduced Groebner Basis of the given ideal.
Use R::=QQ[x,y,z];
I:=Ideal(x-y^2,x^2+xy,y^3);
GBasis(I);
[x^2 + xy, -y^2 + x, -xy]
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Use Z::=ZZ[x,y,z];
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
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I:=Ideal(x-y^2,x^2+xy,y^3);
CharP.GBasisModSquares(I);
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
-- CoCoAServer: computing Cpu Time = 0
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[y, x]
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