### 7.5.3 central_lib

Library:
  central.lib
Purpose:
  Computation of central elements of GR-algebras

Author:
  Oleksandr Motsak, U@D, where U={motsak}, D={mathematik.uni-kl.de}

Overview:
  A library for computing elements of the center and centralizers of sets of elements in GR-algebras.

Procedures:

> 7.5.3.0. centralizeSet |  | v.s. basis of the centralizer of F within V
> 7.5.3.0. centralizerVS |  | v.s. basis of the centralizer of F
> 7.5.3.0. centralizerRed |  | reduced basis of the centralizer of F
> 7.5.3.0. centerVS |  | v.s. basis of the center
> 7.5.3.0. centerRed |  | reduced basis of the center
> 7.5.3.0. center |  | reduced basis of the center
> 7.5.3.0. centralizer |  | reduced bais of the centralizer of F
> 7.5.3.0. sa_reduce |  | 's.a. reduction' of pairwise commuting elements
> 7.5.3.0. sa_poly_reduce |  | 's.a. reduction' of p by pairwise commuting elements
> 7.5.3.0. inCenter |  | checks the centrality of list/ideal/poly T
> 7.5.3.0. inCentralizer |  | checks whether list/ideal/poly T commute with S
> 7.5.3.0. isCartan |  | checks whether polynomial p is a Cartan element
> 7.5.3.0. applyAdF |  | images of elements under the k-linear map Ad_f
> 7.5.3.0. linearMapKernel |  | kernel of a linear map given by images
> 7.5.3.0. linearCombinations |  | k-linear combinations of elements
> 7.5.3.0. variablesStandard |  | set of algebra generators in their natural order
> 7.5.3.0. variablesSorted |  | heuristically sorted set of algebra generators
> 7.5.3.0. PBW_eqDeg |  | PBW monomials of given degree
> 7.5.3.0. PBW_maxDeg |  | PBW monomials up to given degree
> 7.5.3.0. PBW_maxMonom |  | PBW monomials up to given maximal monomial

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