# ApCoCoA-1:CharP.GBasisModSquares

## CharP.GBasisModSquares

Computing a Groebner Basis of a given ideal intersected with `x^2-x` 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^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.

#### Example

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] ------------------------------- Use Z::=ZZ[x,y,z]; -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong ------------------------------- 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 ------------------------------- [y, x] -------------------------------

### See also

Introduction to Groebner Basis in CoCoA

Representation of finite fields