### D.4.27 primdec_lib

Library:
  primdec.lib
Purpose:
  Primary Decomposition and Radical of Ideals
Authors:
  Gerhard Pfister, pfister@mathematik.uni-kl.de (GTZ)
  Wolfram Decker, decker@math.uni-sb.de (SY)
  Hans Schoenemann, hannes@mathematik.uni-kl.de (SY)
  Santiago Laplagne, slaplagn@dm.uba.ar (GTZ)

Overview:
  Algorithms for primary decomposition based on the ideas of Gianni, Trager and Zacharias (implementation by Gerhard Pfister), respectively based on the ideas of Shimoyama and Yokoyama (implementation by Wolfram Decker and Hans Schoenemann).
  The procedures are implemented to be used in characteristic 0.
  They also work in positive characteristic >> 0.
  In small characteristic and for algebraic extensions, primdecGTZ may not terminate.
  Algorithms for the computation of the radical based on the ideas of Krick, Logar, Laplagne and Kemper (implementation by Gerhard Pfister and Santiago Laplagne). They work in any characteristic.
  Baserings must have a global ordering and no quotient ideal. Exceptions: primdecGTZ, absPrimdecGTZ, minAssGTZ, primdecSY, minAssChar, radical accept non-global ordering.

Procedures:

> D.4.27.1 Ann |  | annihilator of R^n/M, R=basering, M in R^n
> D.4.27.2 primdecGTZ |  | complete primary decomposition via Gianni,Trager,Zacharias
> D.4.27.3 primdecGTZE |  | complete primary decomposition via Gianni,Trager,Zacharias. Returns empty list for the unit ideal
> D.4.27.4 primdecSY |  | complete primary decomposition via Shimoyama-Yokoyama
> D.4.27.5 primdecSYE |  | complete primary decomposition via Shimoyama-Yokoyama. Returns empty list for the unit ideal
> D.4.27.6 primdec |  | wrapper for primdecGTZ and primdecSY
> D.4.27.7 minAssGTZ |  | the minimal associated primes via Gianni,Trager,Zacharias (with modifications by Laplagne)
> D.4.27.8 minAssGTZE |  | the minimal associated primes via Gianni,Trager,Zacharias. Returns empty list for unit ideal
> D.4.27.9 minAssChar |  | the minimal associated primes using characteristic sets
> D.4.27.10 minAssCharE |  | the minimal associated primes using characteristic sets. Returns empty list for unit ideal
> D.4.27.11 minAss |  | wrapper for minAssGTZ and minAssChar
> D.4.27.12 testPrimary |  | tests the result of the primary decomposition
> D.4.27.13 testPrimaryE |  | tests the result of the primary decomposition. Handles also empty list L.
> D.4.27.14 radical |  | computes the radical of I via Krick/Logar (with modifications by Laplagne) and Kemper
> D.4.27.15 radicalEHV |  | computes the radical of I via Eisenbud,Huneke,Vasconcelos
> D.4.27.16 equiRadical |  | the radical of the equidimensional part of the ideal I
> D.4.27.17 prepareAss |  | list of radicals of the equidimensional components of I
> D.4.27.18 equidim |  | weak equidimensional decomposition of I
> D.4.27.19 equidimMax |  | equidimensional locus of I
> D.4.27.20 equidimMaxEHV |  | equidimensional locus of I via Eisenbud,Huneke,Vasconcelos
> D.4.27.21 zerodec |  | zerodimensional decomposition via Monico
> D.4.27.22 absPrimdecGTZ |  | the absolute prime components of I
> D.4.27.23 absPrimdecGTZE |  | the absolute prime components of I. Assumes I is not unit ideal.
> D.4.27.24 sep |  | the separabel part of f as polynomial in Fp(t1,...,tm)
> D.4.27.25 primaryTest |  |
> D.4.27.26 zeroRad |  | radical of I (I zero dimensional)
> D.4.27.27 idealsEqual |  | equality of I and J
> D.4.27.28 gcdTest |  |
> D.4.27.29 zero_decomp |  | list of primary ideals and their radicals (I zero dimensional)

See also: modprimdec_lib; primdecint_lib.

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