### 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)

See also: qhmoduli_lib; zeroset_lib.

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