# ApCoCoA-1:CharP.MXLSolve

## CharP.GBasisF2

Computing the unique `F_2-`rational zero of a given polynomial system over `F_2`.

### Syntax

CharP.XLSolve(F:LIST):LIST

### Description

This function computes the unique zero in `F_2^n` of a polynomial system over `F_2 `. It uses XL-Algorithm to find the unique zero. The XL-Algorithm is impelemented only to find a unique solution. If the given polynomial system has more than one zeros in `F_2^n ` then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.

*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.

@param

*F*A system of polynomial over`F_2`having a unique zero in`F_2^n`.@return The unique solution of the given system in

`F_2^n`.

#### 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.GBasisF2(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 + x, x^2, xy] -------------------------------

### See also

Introduction to Groebner Basis in CoCoA