Singular

D.7.3 rinvar_lib

Library:

rinvar.lib

Purpose:

Invariant Rings of Reductive Groups

Author:

Thomas Bayer, tbayer@in.tum.de
http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/ Current Address: Institut fuer Informatik, TU Muenchen

Overview:

Implementation based on Derksen's algorithm. Written in the scope of the diploma thesis (advisor: Prof. Gert-Martin Greuel) 'Computations of moduli spaces of semiquasihomogenous singularities and an implementation in Singular'

Procedures:

D.7.3.1 HilbertSeries		Hilbert series of the ideal I w.r.t. weight w
D.7.3.2 HilbertWeights		weighted degrees of the generators of I
D.7.3.3 ImageVariety		ideal of the image variety F(variety(I))
D.7.3.4 ImageGroup		ideal of G w.r.t. the induced representation
D.7.3.5 InvariantRing		generators of the invariant ring of G
D.7.3.6 InvariantQ		decide if f is invariant w.r.t. G
D.7.3.7 LinearizeAction		linearization of the action 'Gaction' of G
D.7.3.8 LinearActionQ		decide if action is linear in var(s..nvars)
D.7.3.9 LinearCombinationQ		decide if f is in the linear hull of 'base'
D.7.3.10 MinimalDecomposition		minimal decomposition of f (like coef)
D.7.3.11 NullCone		ideal of the nullcone of the action 'act' of G
D.7.3.12 ReynoldsImage		image of f under the Reynolds operator 'RO'
D.7.3.13 ReynoldsOperator		Reynolds operator of the group G
D.7.3.14 SimplifyIdeal		simplify the ideal I (try to reduce variables)