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D.4.26 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.4.26.1 sagbiSPoly  computes SAGBI S-polynomials of A
D.4.26.2 sagbiReduce  performs subalgebra reduction of I by A
D.4.26.3 sagbi  computes SAGBI basis for A
D.4.26.4 sagbiPart  computes partial SAGBI basis for A
D.4.26.5 algebraicDependence  performs iterations of SAGBI for algebraic dependencies of I
See also: algebra_lib.


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