Difference between revisions of "ApCoCoA1:CharP.GBasisModSquares"
(No difference)

Revision as of 20:23, 16 September 2019
CharP.GBasisModSquares
Computing a Groebner Basis of a given ideal intersected with x^2x for all indeterminates x.
Syntax
CharP.GBasisModSquares(Ideal:IDEAL):LIST
Description
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^2x for all indeterminates. If x^2x 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.FGLMalgorithm.
@param Ideal An Ideal.
@return The reduced Groebner Basis of the given ideal.
Example
Use R::=QQ[x,y,z]; I:=Ideal(xy^2,x^2+xy,y^3); GBasis(I); [x^2 + xy, y^2 + x, xy]  Use Z::=ZZ[x,y,z];  WARNING: Coeffs are not in a field  GBasisrelated computations could fail to terminate or be wrong  I:=Ideal(xy^2,x^2+xy,y^3); CharP.GBasisModSquares(I);  WARNING: Coeffs are not in a field  GBasisrelated computations could fail to terminate or be wrong  CoCoAServer: computing Cpu Time = 0  [y, x] 
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields