ApCoCoA-1:CharP.GBasisF2048

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Char2.GBasisF2048

Computing a Groebner Basis of a given ideal in <formula>\mathbb{F}_{2048}</formula>.

Syntax

Char2.GBasisF2048(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}_{2048} = (\mathbb{Z}_{\setminus(2)} [x])_{\setminus(x^{11} +x^3 + x^5 +x + 1)}</formula>.

  • @param Ideal An Ideal in a Ring over Z, where the elements 0,...,2047 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

GBasis

Introduction to Groebner Basis in CoCoA

Char2.GBasisF2

Char2.GBasisF4

Char2.GBasisF8

Char2.GBasisF16

Char2.GBasisF32

Char2.GBasisF64

Char2.GBasisF128

Char2.GBasisF256

Char2.GBasisF512

Char2.GBasisF1024

Char2.GBasisF4096

Char2.GBasisModSquares

Representation of finite fields