7.7 Non-commutative libraries

The content of libraries, created for non-commutative extensions of SINGULAR like PLURAL and LETTERPLACE 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.

7.7.1 bimodules_lib		Tools for handling bimodules
7.7.2 bfun_lib		Algorithms for b-functions and Bernstein-Sato polynomial
7.7.3 central_lib		Computation of centralizer and center in GR-algebras
7.7.4 dmod_lib		Fundamental algorithms for algebraic D-modules
7.7.5 dmodapp_lib		Applications of algebraic D-modules
7.7.6 dmodvar_lib		Algebraic D-modules and Bernstein-Sato polynomial for varieties
7.7.7 fpadim_lib		Algorithms for quotient algebras in the letterplace case
7.7.8 freegb_lib		Two-sided Groebner bases in free algebras via Letterplace
7.7.9 involut_lib		Computations and operations with involutions
7.7.10 gkdim_lib		Computation of the Gelfand-Kirillov dimension of modules
7.7.11 ncalg_lib		Definitions of important G- and GR-algebras
7.7.12 ncdecomp_lib		Algorithmic decomposition of a module with central characters
7.7.13 ncfactor_lib		Tools for factorization in some noncommutative algebras
7.7.14 ncpreim_lib		Non-commutative elimination and preimage computations
7.7.15 nctools_lib		General tools for noncommutative algebras
7.7.16 perron_lib		Method of Perron to compute algebraic dependence
7.7.17 qmatrix_lib		Quantum matrices, quantum minors and symmetric groups
7.7.18 purityfiltration_lib		purity filtration of a given module
7.7.19 nchomolog_lib		Noncommutative Homological Algebra
7.7.20 ratgb_lib		Groebner bases in Ore localizations of noncommutative G-algebras
7.7.21 dmodloc_lib		Localization of algebraic D-modules