|This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.NFS.|
This function is an implementation of the Subalgebra Division Algorithm.
SB.SDA(f: POLY, G: LIST of POLY): POLY
The function takes a polynomial f and a list of polynomials G all of the same ring RingOf(f) and performs the Subalgebra Division Algoritm on f and G. Note that this algorithm is different from the Subduction algorithm written by Robbiano and Sweedler, for more informations see Package sagbi.
@param f A polynomial
@param G A list of polynomials
@return A polynomial g such that f Subalgebra reduces (with respect to G) to g and g is irreducible with respect to the rewrite relation defined by G.
Use QQ[x,y], DegRevLex; f := x^4*y^2 + x^2*y^4+1; G := [x^2-1, y^2-1]; SB.SDA(f,G); -- 0