Package sagbi/SB.ReductionStep

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This article is about a function from ApCoCoA-2.


This function computes a polynomial to which the given polynomial reduces in one step.


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


This function takes a polynomial f and a list of polynomials G and computes a polynomial g such that f reduces to g in one step with respect to the Subalgebra rewrite relation defined by G, see Package sagbi. If there is no such polynomial g, then f is returned.

  • @param f A polynomial

  • @param G A list of polynomials

  • @return see description above


Use QQ[x,y], DegRevLex;
f := x^4*y^2 + x^2*y^4;
G := [x^2-1, y^2-1];
-- x^4*y^3 +2*x^2*y^2 +y^4 -x^2 -2*y^2 +1


Use QQ[x,y], DegRevLex;
f := x^4*y^3 + x^2*y^3;
G := [x^2-1, y^2-1];
-- x^4*y^3 +x^2*y^3

See also

Package sagbi/SB.SDA

Package sagbi/SB.Interreduced

Package sagbi/SB.FindLTRepr

Package sagbi/SB.FindLTRepr_glpk