> | ### D.4.18 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.4.18.1 separator |  | computes a list of separators of prime ideals
> D.4.18.2 PrimdecA |  | (not necessarily minimal) primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
> D.4.18.3 PrimdecB |  | (not necessarily minimal) primary decomposition for pseudo-primary ideals
> D.4.18.4 modDec |  | minimal primary decomposition via Shimoyama/Yokoyama (suggested by Graebe)
> D.4.18.5 zeroMod |  | minimal zero-dimensional primary decomposition via Gianni, Trager and Zacharias
> D.4.18.6 GTZmod |  | minimal primary decomposition via Gianni, Trager and Zacharias
> D.4.18.7 dec1var |  | primary decomposition for one variable
> D.4.18.8 annil |  | the annihilator of M/N in the basering
> D.4.18.9 splitting |  | splitting to simpler modules
> D.4.18.10 primTest |  | tests whether i is prime or homogeneous
> D.4.18.11 preComp |  | enhanced Version of splitting
> D.4.18.12 indSet |  | lists with varstrings of(in)dependent variables
> D.4.18.13 GTZopt |  | a faster version of GTZmod
> D.4.18.14 zeroOpt |  | a faster version of zeroMod

User manual for Singular version 4.4.0, 2024, generated by texi2html.