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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