### D.4.19 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 elements 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.4.19.1 separator |  | computes a list of separators of prime ideals
> D.4.19.2 PrimdecA |  | (not necessarily minimal) primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
> D.4.19.3 PrimdecB |  | (not necessarily minimal) primary decomposition for pseudo-primary ideals
> D.4.19.4 modDec |  | minimal primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
> D.4.19.5 zeroMod |  | minimal zero-dimensional primary decomposition via Gianni, Trager and Zacharias
> D.4.19.6 GTZmod |  | minimal primary decomposition via Gianni, Trager and Zacharias
> D.4.19.7 dec1var |  | primary decomposition for one variable
> D.4.19.8 annil |  | the annihilator of M/N in the basering
> D.4.19.9 splitting |  | splitting to simpler modules
> D.4.19.10 primTest |  | tests whether i is prime or homogeneous
> D.4.19.11 preComp |  | enhanced Version of splitting
> D.4.19.12 indSet |  | lists with varstrings of(in)dependent variables
> D.4.19.13 GTZopt |  | a faster version of GTZmod
> D.4.19.14 zeroOpt |  | a faster version of zeroMod

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