# Difference between revisions of "ApCoCoA-1:CharP.GBasisF256"

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<see>Char2.GBasisF4096</see> | <see>Char2.GBasisF4096</see> | ||

<see>Char2.GBasisModSquares</see> | <see>Char2.GBasisModSquares</see> | ||

+ | <see>Representation of finite fields</see> | ||

</seealso> | </seealso> | ||

## Revision as of 14:17, 23 April 2009

## Char2.GBasisF256

Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{256}</formula>.

### Syntax

Char2.GBasisF256(Ideal: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}_{256} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1 )}</formula>.

@param

*Ideal*An Ideal in a Ring over Z, where the elements 0,...,255 represent the field's elements. For short, the binary representation of the number represents the coefficient vector if the polynomial in the field, e.g. 11 = 8 + 2 + 1 = 2^3 + 2^1 + 2^0. So the number 11 corresponds to the polynomial x^3 + x + 1.@return A Groebner Basis of the given ideal.

### See also

Representation of finite fields