# ApCoCoA-1:CharP.GBasisModSquares

## Char2.GBasisModSquares

Computing a Groebner Basis of a given ideal intersected with x^2-x for all indeterminates x.

### Syntax

Char2.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-algorithm.

@param

*Ideal*An Ideal.@return The reduced Groebner Basis of the given ideal.

### See also

Introduction to Groebner Basis in CoCoA

Representation of finite fields