### D.4.33 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.4.33.1 sagbiSPoly |  | computes SAGBI S-polynomials of A
> D.4.33.2 sagbiReduce |  | performs subalgebra reduction of I by A
> D.4.33.3 sagbi |  | computes SAGBI basis for A
> D.4.33.4 sagbiPart |  | computes partial SAGBI basis for A
> D.4.33.5 algebraicDependence |  | performs iterations of SAGBI for algebraic dependencies of I

See also: algebra_lib.

User manual for Singular version 4.4.1, 2025, generated by texi2html.