ApCoCoA-1:CharP.XLSolve
CharP.GBasisF2
Computing the unique F_2-rational zero of a given polynomial system over F_2.
Syntax
CharP.XLSolve(F:LIST):LIST
Description
This function computes the unique zero in F_2^n of a polynomial system over F_2 . It uses XL-Algorithm to find the unique zero. The XL-Algorithm is impelemented only to find a unique solution. If the given polynomial system has more than one zeros in F_2^n then this function does not find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.
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.
@param F A system of polynomial over F_2 having a unique zero in F_2^n.
@return The unique solution of the given system in F_2^n.
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.GBasisF2(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 + x, x^2, xy] -------------------------------
See also
Introduction to Groebner Basis in CoCoA
