User:LongLe

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

SB.SAGBI

Computes a finite SAGBI-basis of a subalgebra if existing.

Syntax

SB.SAGBI(G:LIST of POLY):LIST of POLY

Description

This function computes a finite SAGBI-basis of a subalgebra S generated by the polynomials of the list G, if a finite SAGBI-basis of S exists. Then a list of polynomials is returned which form a SAGBI-basis of S. Otherwise the computation runs until it is interrupted.

• @param G A list of polynomials which generates a subalgebra.

• @return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by G.

Example

Use QQ[x,y,z], DegRevLex;
S := SB.SAGBI([x^2 -z^2,  x*y +z^2,  y^2 -2*z^2]);
indent(S);
-- [
--   y^2 -2*z^2,
--   x*y +z^2,
--   x^2 -z^2,
--   x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
-- ]

See also

Package sagbi/SB.TruncSAGBI

Package sagbi/SB.SAGBITimeout

Package sagbi/SB.IsSAGBIOf

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI