Singular

D.4.27 sagbi_lib

Library:

sagbi.lib

Purpose:

Compute SAGBI basis (subalgebra bases analogous to Groebner bases for ideals) of a subalgebra

Authors:

Jan Hackfeld, [email protected]
Gerhard Pfister, [email protected]
Viktor Levandovskyy, [email protected]

Overview:

SAGBI stands for 'subalgebra bases analogous to Groebner bases for ideals'. SAGBI bases provide important tools for working with finitely presented subalgebras of a polynomial ring. Note, that in contrast to Groebner bases, SAGBI bases may be infinite.

References:

Ana Bravo: Some Facts About Canonical Subalgebra Bases, MSRI Publications 51, p. 247-254

Procedures:

D.4.27.1 sagbiSPoly		computes SAGBI S-polynomials of A
D.4.27.2 sagbiReduce		performs subalgebra reduction of I by A
D.4.27.3 sagbi		computes SAGBI basis for A
D.4.27.4 sagbiPart		computes partial SAGBI basis for A
D.4.27.5 algebraicDependence		performs iterations of SAGBI for algebraic dependencies of I