Singular

D.4.15 mprimdec_lib

Library:

mprimdec.lib

Purpose:

procedures for primary decomposition of modules

Authors:

Alexander Dreyer, dreyer@mathematik.uni-kl.de; adreyer@web.de

Overview:

Algorithms for primary decomposition for modules based on the algorithms of Gianni, Trager and Zacharias and
Shimoyama and Yokoyama (generalization of the latter suggested by Hans-Gert Graebe, Leipzig )
using elments of primdec.lib

Remark:

These procedures are implemented to be used in characteristic 0.
They also work in positive characteristic >> 0.
In small characteristic and for algebraic extensions, the procedures via Gianni, Trager, Zacharias may not terminate.

Procedures:

D.4.15.1 separator		computes a list of separators of prime ideals
D.4.15.2 PrimdecA		(not necessarily minimal) primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
D.4.15.3 PrimdecB		(not necessarily minimal) primary decomposition for pseudo-primary ideals
D.4.15.4 modDec		minimal primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
D.4.15.5 zeroMod		minimal zero-dimensional primary decomposition via Gianni, Trager and Zacharias
D.4.15.6 GTZmod		minimal primary decomposition via Gianni, Trager and Zacharias
D.4.15.7 dec1var		primary decomposition for one variable
D.4.15.8 annil		the annihilator of M/N in the basering
D.4.15.9 splitting		splitting to simpler modules
D.4.15.10 primTest		tests whether i is prime or homogeneous
D.4.15.11 preComp		enhanced Version of splitting
D.4.15.12 indSet		lists with varstrings of(in)dependend variables
D.4.15.13 GTZopt		a faster version of GTZmod
D.4.15.14 zeroOpt		a faster version of zeroMod