Package sagbi/SB.TruncSAGBI

This article is about a function in ApCoCoA-2.0.

SB.TruncSAGBI

Computes a truncated SAGBI-basis of a standard-graded subalgebra.

Syntax

SB.SAGBI(G:LIST of POLY,d:RAT):LIST of POLY

Description

This function computes a d-truncated SAGBI-basis of the subalgebra S generated by the polynomials in the list G, i.e. a set of polynomials F such that any term appearing as the leading term of a polynomial in S of degree smaller than or equal to d is a product of terms appearing as leading term of a polynomial in F.

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

• @param d An integer specifying the truncation degree.

• @return A tuple [L,b] where L is a list of polynomials which form a d-truncated finite SAGBI-basis of the subalgebra generated by G. b is a boolean value which is true if L is already a complete SAGBI basis.

Example

Use QQ[x,y,z];
S := SB.TruncSAGBI([x^2 -z^2,  x*y +z^2,  y^2 -2*z^2],3);
indent(S);
-- [
--   [y^2 -2*z^2,  x*y +z^2,  x^2 -z^2],
--   false
-- ]

Example

Use QQ[x,y];
S := SB.TruncSAGBI([x +y,  x*y,  x*y^2],7); -- K[x+y,xy,xy^2] does not have a finite SAGBI basis
indent(S);
-- [
--   [x +y,  x*y,  x*y^2,  x*y^3,  x*y^4,  x*y^5,  x*y^6],
--   false
-- ]

See also

Package sagbi/SB.SAGBI

Package sagbi/SB.SAGBITimeout

Package sagbi/SB.IsSAGBIOf

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI