Package sagbi/SB.SDA

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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.

SB.SDA

This function is an implementation of the Subalgebra Division Algorithm.

Syntax

SB.SDA(f: POLY, G: LIST of POLY): POLY

Description

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.

Example

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

See also

Package sagbi/SB.ReductionStep

Package sagbi/SB.Interreduced

Package sagbi/SB.IsInSubalgebra_SAGBI