Singular

D.4.20 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.4.20.1 Ann		annihilator of R^n/M, R=basering, M in R^n
D.4.20.2 primdecGTZ		complete primary decomposition via Gianni,Trager,Zacharias
D.4.20.3 primdecGTZE		complete primary decomposition via Gianni,Trager,Zacharias. Returns empty list for the unit ideal
D.4.20.4 primdecSY		complete primary decomposition via Shimoyama-Yokoyama
D.4.20.5 primdecSYE		complete primary decomposition via Shimoyama-Yokoyama. Returns empty list for the unit ideal
D.4.20.6 minAssGTZ		the minimal associated primes via Gianni,Trager,Zacharias (with modifications by Laplagne)
D.4.20.7 minAssGTZE		the minimal associated primes via Gianni,Trager,Zacharias. Returns empty list for unit ideal
D.4.20.8 minAssChar		the minimal associated primes using characteristic sets
D.4.20.9 minAssCharE		the minimal associated primes using characteristic sets. Returns empty list for unit ideal
D.4.20.10 testPrimary		tests the result of the primary decomposition
D.4.20.11 testPrimaryE		tests the result of the primary decomposition. Handles also empty list L.
D.4.20.12 radical		computes the radical of I via Krick/Logar (with modifications by Laplagne) and Kemper
D.4.20.13 radicalEHV		computes the radical of I via Eisenbud,Huneke,Vasconcelos
D.4.20.14 equiRadical		the radical of the equidimensional part of the ideal I
D.4.20.15 prepareAss		list of radicals of the equidimensional components of I
D.4.20.16 equidim		weak equidimensional decomposition of I
D.4.20.17 equidimMax		equidimensional locus of I
D.4.20.18 equidimMaxEHV		equidimensional locus of I via Eisenbud,Huneke,Vasconcelos
D.4.20.19 zerodec		zerodimensional decomposition via Monico
D.4.20.20 absPrimdecGTZ		the absolute prime components of I
D.4.20.21 absPrimdecGTZE		the absolute prime components of I. Assumes I is not unit ideal.
D.4.20.22 sep		the separabel part of f as polynomial in Fp(t1,...,tm)