# ApCoCoA-1:CharP.GBasisF4

## Char2.GBasisF4

computing a gbasis of a given ideal in <formula>\mathbb{F}_{4}</formula>

### Syntax

$char2.GBasisF4(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 <formula> \mathbb{F}_{4} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^2 + x +1)}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class RingF4.

The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 3 represent the field's elements. Details on this representation can be found here. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g.

<formula> 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0</formula>

So the number <formula>11</formula> corresponds to the polynomial <formula>x^3 + x + 1</formula>.

### See also