## 7.5 PLURAL libraries

The content of libraries, created for PLURAL is described in the following subsections.

Use the `LIB` command for loading of single libraries.

Note: For any computation in PLURAL, the monomial ordering must be a global ordering.

See also jacobson_lib for the diagonalization of matrices over Ore Euclidean domains.

> 7.5.1 bimodules_lib |  | Tools for handling bimodules
> 7.5.2 bfun_lib |  | Algorithms for b-functions and Bernstein-Sato polynomial
> 7.5.3 central_lib |  | Computation of centralizer and center in GR-algebras
> 7.5.4 dmod_lib |  | Fundamental algorithms for algebraic D-modules
> 7.5.5 dmodapp_lib |  | Applications of algebraic D-modules such as integration
> 7.5.6 dmodideal_lib |  | Algorithms for Bernstein-Sato ideals of morphisms
> 7.5.14 dmodloc_lib |  | Localization of algebraic D-modules such as Weyl closure
> 7.5.7 dmodvar_lib |  | Algebraic D-modules and Bernstein-Sato polynomial for varieties
> 7.5.8 involut_lib |  | Computations and operations with involutive endomorphisms
> 7.5.9 gkdim_lib |  | Computation of the Gelfand-Kirillov dimension of modules
> 7.5.10 ncalg_lib |  | Definitions of important G- and GR-algebras
> 7.5.11 ncdecomp_lib |  | Algorithmic decomposition of a module with central characters
> 7.5.12 ncfactor_lib |  | Tools for factorization in some noncommutative algebras
> 7.5.15 ncfrac_lib |  | fractions in Ore localizations of a G-algebras
> 7.5.13 nchilbert_lib |  | Hilbert series for LetterPlace
> 7.5.16 nchomolog_lib |  | Noncommutative Homological Algebra
> 7.5.17 ncloc_lib |  | Ore-localization in G-Algebras
> 7.5.18 ncModslimgb_lib |  | modular slimgb for Groebner bases in G-algebras
> 7.5.19 ncpreim_lib |  | Non-commutative elimination and preimage computations
> 7.5.20 nctools_lib |  | General tools for noncommutative algebras
> 7.5.21 olga_lib |  | Ore-localization in G-Algebras
> 7.5.22 perron_lib |  | Method of Perron to compute algebraic dependence
> 7.5.23 purityfiltration_lib |  | Purity (equidimensional) filtration of a given module
> 7.5.24 qmatrix_lib |  | Quantum matrices, quantum minors and symmetric groups
> 7.5.25 ratgb_lib |  | Groebner bases in Ore localizations of noncommutative G-algebras

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