Difference between revisions of "ApCoCoA1:CharP.GBasisF4"
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m (ApCoCoA:Char2.GBasisF4 moved to ApCoCoA:Charp.GBasisF4) 
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Revision as of 15:14, 6 December 2010
Char2.GBasisF4
Computing a Groebner Basis of a given ideal in F_4.
Syntax
Char2.GBasisF4(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_4 = (Z/(2))[x]/(x^2 + x +1).
@param Ideal An Ideal in a Ring over Z, where the elements 0,...,3 represent the elements of the field F_4. 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(xy^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  GBasisrelated computations could fail to terminate or be wrong  I:=Ideal(xy^2,x^2+xy,y^3); Char2.GBasisF4(I);  WARNING: Coeffs are not in a field  GBasisrelated computations could fail to terminate or be wrong  CoCoAServer: computing Cpu Time = 0  [y^2 + 2x, x^2, xy] 
See also
Introduction to Groebner Basis in CoCoA
Representation of finite fields