Singular Manual: mprimdec_lib

> | ### 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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