# ApCoCoA-1:CharP.BBasisMutantStrategyF2

From ApCoCoAWiki

## 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 F2. 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.

@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)); [x[4] + 1, x[3], x[2] + 1, x[1]]

### See also

Introduction to Groebner Basis in CoCoA