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D.4.21 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.4.21.1 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)