Package sagbi/SB.IsSAGBIOf

From ApCoCoAWiki
This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.IsSagbiOf.


This function checks whether a given list of polynomials is a SAGBI basis of a specific subalgebra.


SB.IsSAGBIOf(G: LIST of POLY, S: TAGGED("$apcocoa/sagbi.Subalgebra")): BOOL


  • @param G A list of polynomials all of the same ring R

  • @param S A subalgebra of R

  • @return true if G is a SAGBI basis of S and false if not.


Use R ::= QQ[x,y];
fs := [x^2*y,  x^2 -y^2,  x^2*y^2 -y^4,  x^2*y^4];
S := SB.Subalgebra(R,fs);
G := [x^2 -y^2,  x^2*y,  x^2*y^2 -y^4,  y^6,  x^2*y^4];
SB.IsSAGBIOf(fs,S); -- false
SB.IsSAGBIOf(G,S); -- true

See also

Package sagbi/SB.Subalgebra

Package sagbi/SB.SAGBI