### 7.5.13 nchilbert_lib

Library:
  nchilbert.lib
Purpose:
  Hilbert series, polynomial and multiplicity for G-Algebras (Plural)

Authors:
  Andre Ranft, andre.ranft at rwth-aachen.de
  Viktor Levandovskyy, levandov at rwth-aachen.de

Overview:
  The theory is found in the book by Bueso, Gomez-Torrecillas, and Verschoren Algorithmic Methods in Non-Commutative Algebra. Applications to Quantum Groups. and in the bachelor thesis by
  Andre Ranft, Hilbert polynomials of modules over noncommutative G-algebras, RWTH Aachen, 2014.

Procedures:

> 7.5.13.0. ncHilb |  | computes first resp. second Hilbert series of a module as bigintvec
> 7.5.13.0. ncHilbertSeries |  | computes first resp. second Hilbert series of a module as a poly
> 7.5.13.0. ncHilbertPolynomial |  | computes the Hilbert polynomial of coker(M)
> 7.5.13.0. ncHilbertMultiplicity |  | computes the (Hilbert) multiplicity of coker(M)
> 7.5.13.0. GKExp |  | computes the Gelfand-Kirillov dimension of coker(M)
> 7.5.13.0. mondim |  | computes the dimension of the monoid ideal B

See also: hilb; multigrading_lib; rinvar_lib.

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