Home Online Manual
Back: facGBIdeal
Forward: Ann
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.4.21 primdec_lib

Primary Decomposition and Radical of Ideals
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)

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.


D.4.21.1 Ann  annihilator of R^n/M, R=basering, M in R^n
D.4.21.2 primdecGTZ  complete primary decomposition via Gianni,Trager,Zacharias
D.4.21.3 primdecGTZE  complete primary decomposition via Gianni,Trager,Zacharias. Returns empty list for the unit ideal
D.4.21.4 primdecSY  complete primary decomposition via Shimoyama-Yokoyama
D.4.21.5 primdecSYE  complete primary decomposition via Shimoyama-Yokoyama. Returns empty list for the unit ideal
D.4.21.6 minAssGTZ  the minimal associated primes via Gianni,Trager,Zacharias (with modifications by Laplagne)
D.4.21.7 minAssGTZE  the minimal associated primes via Gianni,Trager,Zacharias. Returns empty list for unit ideal
D.4.21.8 minAssChar  the minimal associated primes using characteristic sets
D.4.21.9 minAssCharE  the minimal associated primes using characteristic sets. Returns empty list for unit ideal
D.4.21.10 testPrimary  tests the result of the primary decomposition
D.4.21.11 testPrimaryE  tests the result of the primary decomposition. Handles also empty list L.
D.4.21.12 radical  computes the radical of I via Krick/Logar (with modifications by Laplagne) and Kemper
D.4.21.13 radicalEHV  computes the radical of I via Eisenbud,Huneke,Vasconcelos
D.4.21.14 equiRadical  the radical of the equidimensional part of the ideal I
D.4.21.15 prepareAss  list of radicals of the equidimensional components of I
D.4.21.16 equidim  weak equidimensional decomposition of I
D.4.21.17 equidimMax  equidimensional locus of I
D.4.21.18 equidimMaxEHV  equidimensional locus of I via Eisenbud,Huneke,Vasconcelos
D.4.21.19 zerodec  zerodimensional decomposition via Monico
D.4.21.20 absPrimdecGTZ  the absolute prime components of I
D.4.21.21 absPrimdecGTZE  the absolute prime components of I. Assumes I is not unit ideal.
D.4.21.22 sep  the separabel part of f as polynomial in Fp(t1,...,tm)
See also: primdecint_lib.