Singular

D.4.25 sagbi_lib

Library:

sagbi.lib

Purpose:

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

Authors:

Jan Hackfeld, Jan.Hackfeld@rwth-aachen.de
Gerhard Pfister, pfister@mathematik.uni-kl.de
Viktor Levandovskyy, levandov@math.rwth-aachen.de

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.4.25.1 sagbiSPoly		computes SAGBI S-polynomials of A
D.4.25.2 sagbiReduce		performs subalgebra reduction of I by A
D.4.25.3 sagbi		computes SAGBI basis for A
D.4.25.4 sagbiPart		computes partial SAGBI basis for A
D.4.25.5 algebraicDependence		performs iterations of SAGBI for algebraic dependencies of I