# Difference between revisions of "ApCoCoA-1:CharP.GBasisF4"

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## Latest revision as of 09:55, 7 October 2020

This article is about a function from ApCoCoA-1. |

## CharP.GBasisF4

Computing a Groebner Basis of a given ideal in `F_4`.

### Syntax

CharP.GBasisF4(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 command computes a Groebner basis in the field `F_4 = (Z/(2))[x]/(x^2 + x +1)`.

@param

*Ideal*An Ideal in a Ring over`Z`, where the elements`0,...,3`represent the elements of the field`F_4`. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g.`11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0`. So the number`11`corresponds to the polynomial`x^3 + x + 1`.@return A 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.GBasisF4(I); -- WARNING: Coeffs are not in a field -- GBasis-related computations could fail to terminate or be wrong -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [y^2 + 2x, x^2, xy] -------------------------------

### See also

Introduction to Groebner Basis in CoCoA

Representation of finite fields