# Difference between revisions of "ApCoCoA:CharP.GBasisF8"

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− | This command computes a Groebner basis in the field <formula> \mathbb{F}_{8} = ( | + | This command computes a Groebner basis in the field <formula> \mathbb{F}_{8} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^3 + x +1)}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class [[ApCoCoALib:RingF8|RingF8]]. |

The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 7 represent the field's elements. Details on this representation can be found [[ApCoCoA:Representation_of_finite_fields|here]]. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g. | The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 7 represent the field's elements. Details on this representation can be found [[ApCoCoA:Representation_of_finite_fields|here]]. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g. |

## Revision as of 21:59, 30 March 2008

## Char2.GBasisF8

computing a gbasis of a given ideal in <formula>\mathbb{F}_{8}</formula>

### Syntax

$char2.GBasisF8(Ideal):List

### Description

This command computes a Groebner basis in the field <formula> \mathbb{F}_{8} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^3 + x +1)}</formula>. It uses the ApCoCoA Server and the ApCoCoALib's class RingF8.

The command's input is a an Ideal in a Ring over Z, where the elements 0,..., 7 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

ApCoCoA:char2.GBasisModSquares