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D.4.17 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.
Some of the algorithms in this library require a global ordering.
qrings are not possible as baserings in this library.
For local or mixed orderings, most procedures handle the appropriate
ring changes internally; otherwise an error message will be printed.
Procedures:
D.4.17.1 Ann | | annihilator of R^n/M, R=basering, M in R^n |
D.4.17.2 primdecGTZ | | complete primary decomposition via Gianni,Trager,Zacharias |
D.4.17.3 primdecSY | | complete primary decomposition via Shimoyama-Yokoyama |
D.4.17.4 minAssGTZ | | the minimal associated primes via Gianni,Trager,Zacharias (with modifications by Laplagne) |
D.4.17.5 minAssChar | | the minimal associated primes using characteristic sets |
D.4.17.6 testPrimary | | tests the result of the primary decomposition |
D.4.17.7 radical | | computes the radical of I via Krick/Logar (with modifications by Laplagne) and Kemper |
D.4.17.8 radicalEHV | | computes the radical of I via Eisenbud,Huneke,Vasconcelos |
D.4.17.9 equiRadical | | the radical of the equidimensional part of the ideal I |
D.4.17.10 prepareAss | | list of radicals of the equidimensional components of I |
D.4.17.11 equidim | | weak equidimensional decomposition of I |
D.4.17.12 equidimMax | | equidimensional locus of I |
D.4.17.13 equidimMaxEHV | | equidimensional locus of I via Eisenbud,Huneke,Vasconcelos |
D.4.17.14 zerodec | | zerodimensional decomposition via Monico |
D.4.17.15 absPrimdecGTZ | | the absolute prime components of I |
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