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D.4.4 mprimdec_lib
- Library:
mprimdec.lib
- Purpose:
procedures for primary decomposition of modules
- Authors:
Alexander Dreyer, dreyer@mathematik.uni-kl.de; adreyer@web.de
- Remark:
These procedures are implemented to be used in characteristic 0.
They also work in positive characteristic >> 0.
In small characteristic and for algebraic extensions, the procedures via Gianni, Trager, Zacharias may not terminate.
Procedures:
D.4.4.1 separator computes a list of separators of prime ideals D.4.4.2 PrimdecA (not necessarily minimal) primary decomposition via Shimoyama/Yokoyama (suggested by Graebe) D.4.4.3 PrimdecB (not necessarily minimal) primary decomposition for pseudo-primary ideals D.4.4.4 modDec minimal primary decomposition via Shimoyama/Yokoyama (suggested by Graebe) D.4.4.5 zeroMod minimal zero-dimensional primary decomposition via Gianni, Trager and Zacharias D.4.4.6 GTZmod minimal primary decomposition via Gianni, Trager and Zacharias D.4.4.7 dec1var primary decomposition for one variable D.4.4.8 annil the annihilator of M/N in the basering D.4.4.9 splitting splitting to simpler modules D.4.4.10 primTest tests whether i is prime or homogeneous D.4.4.11 preComp enhanced Version of splitting D.4.4.12 indSet lists with varstrings of(in)dependent variables D.4.4.13 GTZopt a faster version of GTZmod D.4.4.14 zeroOpt a faster version of zeroMod D.4.4.15 clrSBmod extracts an minimal SB from a SB D.4.4.16 minSatMod minimal saturation of N w.r.t. I D.4.4.17 specialModulesEqual checks for equality of standard bases of modules if N1 is contained in N2 or vice versa D.4.4.18 stdModulesEqual checks for equality of standard bases D.4.4.19 modulesEqual checks for equality of modules D.4.4.20 getData extracts oldData and computes the remaining data