# ApCoCoA-1:CharP.MXLSolve

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## 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]
-------------------------------
```