### 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

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