Difference between revisions of "ApCoCoA-1:CharP.GBasisF32"

From ApCoCoAWiki
m (fixed links to namespace ApCoCoA)
m (insert version info)
 
Line 1: Line 1:
 +
{{Version|1}}
 
<command>
 
<command>
 
     <title>CharP.GBasisF32</title>
 
     <title>CharP.GBasisF32</title>

Latest revision as of 09:54, 7 October 2020

This article is about a function from ApCoCoA-1.

CharP.GBasisF32

Computing a Groebner Basis of a given ideal in F_32.

Syntax

CharP.GBasisF32(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_32 = (Z/(2))[x]/(x^5 + x^2 + 1).

  • @param Ideal An Ideal in a Ring over Z, where the elements 0,...,31 represent the elements of the field F_32. 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.

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];
-- WARNING: Coeffs are not in a field
-- GBasis-related computations could fail to terminate or be wrong

-------------------------------
I:=Ideal(x-y^2,x^2+xy,y^3);
CharP.GBasisF32(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 + 27x, x^2, xy]
-------------------------------


See also

GBasis

Introduction to CoCoAServer

Introduction to Groebner Basis in CoCoA

CharP.GBasisF2

CharP.GBasisF4

CharP.GBasisF8

CharP.GBasisF16

CharP.GBasisF64

CharP.GBasisF128

CharP.GBasisF256

CharP.GBasisF512

CharP.GBasisF1024

CharP.GBasisF2048

CharP.GBasisModSquares

Representation of finite fields