ApCoCoA:CharP.GBasisF1024

From CoCoAWiki

CharP.GBasisF1024

Computing a Groebner basis of a given ideal in F_1024.

Syntax

CharP.GBasisF1024(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 F_1024 = (Z/(2))[x]/(x^10 + x^3 + x^2 + x + 1).

  • @param Ideal An Ideal in a Ring over Z, where the elements 0,...,1023 represent the elements of the finite field. For short, the binary representation of the number represents the coefficient vector of 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.

Example


Use R::=QQ[x,y,z];
I:=Ideal(x-y^2,x^2+xy,y^3);
GBasis(I);
[x^2 + xy, -y^2 + x, -xy]
-------------------------------
Use Z::=ZZ[x,y,z];
I:=Ideal(x-y^2,x^2+xy,y^3);
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
CharP.GBasisF1024(I);
-------------------------------
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[y^2 + 218x, x^2, xy]
-------------------------------


See also

ApCoCoA:GBasis

ApCoCoA:Introduction to Groebner Basis in CoCoA

ApCoCoA:Introduction to CoCoAServer

ApCoCoA:CharP.GBasisF2

ApCoCoA:CharP.GBasisF4

ApCoCoA:CharP.GBasisF8

ApCoCoA:CharP.GBasisF16

ApCoCoA:CharP.GBasisF32

ApCoCoA:CharP.GBasisF64

ApCoCoA:CharP.GBasisF128

ApCoCoA:CharP.GBasisF256

ApCoCoA:CharP.GBasisF512

ApCoCoA:CharP.GBasisF2048

ApCoCoA:CharP.GBasisModSquares

ApCoCoA:Representation of finite fields