# ApCoCoA-1:CharP.BBasisMutantStrategyF2

## CharP.BBasisMutantStrategyF2

Computes a Border Basis of a given ideal over F_2.

### Syntax

```CharP.BBasisMutantStrategyF2(I:IDEAL):LIST of POLY
```

### 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.

Let I be a zero-dimensional ideal over a polynomial ring with coefficient ring F_2. This function computes a border basis of the zero-dimensional radical ideal generated by I and the field polynomials. Furthermore, it uses the Mutant Strategy for stable span computations.

Please note that this function is a completely ApCoCoALib driven version of the function CharP.MBBasisF2.

• @param I A zero-dimensional ideal.

• @return A border basis of the zero-dimensional radical ideal generated by the Ideal I and the field polynomials.

#### Example

```Use Z/(2)[x[1..4]];
F:=[
x[1]x[2] + x[2]x[3] + x[2]x[4] + x[3]x[4] + x[1] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[1]x[4] + x[3]x[4] + x[2] + x[3] + 1,
x[1]x[2] + x[1]x[3] + x[2]x[3] + x[3]x[4] + x[1] + x[4] + 1,
x[1]x[3] + x[2]x[3] + x[1]x[4] + x[2]x[4] + 1
];

-- Then we compute a border basis with
CharP.BBasisMutantStrategyF2(Ideal(F));

-- Result is
[x[4] + 1, x[3], x[2] + 1, x[1]]
```