@c -*-texinfo-*-

@c --------------------------------------------------------------------
@node Non-commutative libraries, , LETTERPLACE, Non-commutative subsystem
@section Non-commutative libraries
@cindex  Non-commutative libraries
@cindex  Non-commutative LIBs
@cindex  PLURAL LIBs

@c @sc{Plural} comes with a set of standard libraries. 
@c Their content is described in the following subsections.

The content of libraries, created for non-commutative extensions of
@sc{Singular} like @sc{Plural} and @sc{Letterplace} is described in the following subsections.

Use the @code{LIB} command for loading of single libraries.

@strong{Note:} For any computation in @sc{Plural}, the monomial ordering must be a global ordering.

See also @ref{jacobson_lib} for the diagonalization of matrices over Ore Euclidean domains.

@menu
* bfun_lib::  Algorithms for b-functions and Bernstein-Sato polynomial
* central_lib:: Computation of centralizer and center in GR-algebras
* dmod_lib:: Fundamental algorithms for algebraic D-modules
* dmodapp_lib::  Applications of algebraic D-modules
* dmodvar_lib:: Algebraic D-modules and Bernstein-Sato polynomial for varieties
* fpadim_lib::  Algorithms for quotient algebras in the letterplace case
* freegb_lib::  Two-sided Groebner bases in free algebras via Letterplace
* involut_lib::  Computations and operations with involutions
* gkdim_lib::  Computation of the Gelfand-Kirillov dimension of modules
* ncalg_lib::  Definitions of important G- and GR-algebras
* ncdecomp_lib::  Algorithmic decomposition of a module with central characters
* ncfactor_lib::  Tools for factorization in some noncommutative algebras
* nctools_lib::  General tools for noncommutative algebras
* perron_lib::  Method of Perron to compute algebraic dependence
* qmatrix_lib::  Quantum matrices, quantum minors and symmetric groups
@end menu

@c as @c lib generates parts of sections, but we need subsections:
@lowersections

@c ----------------------------------------------------------
@node bfun_lib, central_lib, , Non-commutative libraries
@section bfun_lib
@c lib bfun.lib
@c ----------------------------------------------------------
@node central_lib, dmod_lib, bfun_lib, Non-commutative libraries
@section central_lib
@c lib central.lib
@c ----------------------------------------------------------
@node dmod_lib, dmodapp_lib, central_lib, Non-commutative libraries
@section dmod_lib
@c lib dmod.lib
@c ----------------------------------------------------------
@node dmodapp_lib, dmodvar_lib, dmod_lib, Non-commutative libraries
@section dmodapp_lib
@c lib dmodapp.lib
@c ----------------------------------------------------------
@node dmodvar_lib, fpadim_lib, dmodapp_lib, Non-commutative libraries
@section dmodvar_lib
@c lib dmodvar.lib
@c ----------------------------------------------------------
@node fpadim_lib, freegb_lib, dmodvar_lib, Non-commutative libraries
@section fpadim_lib
@c lib fpadim.lib
@c ----------------------------------------------------------
@node freegb_lib, involut_lib, fpadim_lib, Non-commutative libraries
@section freegb_lib
@c lib freegb.lib
@c ----------------------------------------------------------
@node involut_lib,  gkdim_lib, freegb_lib, Non-commutative libraries
@section involut_lib
@c lib involut.lib
@c ----------------------------------------------------------
@node gkdim_lib, ncalg_lib, involut_lib, Non-commutative libraries
@section gkdim_lib
@c lib gkdim.lib
@c ----------------------------------------------------------
@node ncalg_lib, ncdecomp_lib, gkdim_lib, Non-commutative libraries
@section ncalg_lib
@c lib ncalg.lib
@c ----------------------------------------------------------
@node ncdecomp_lib, ncfactor_lib, ncalg_lib, Non-commutative libraries
@section ncdecomp_lib
@c lib ncdecomp.lib
@c ----------------------------------------------------------
@node ncfactor_lib, nctools_lib, ncdecomp_lib, Non-commutative libraries
@section ncfactor_lib
@c lib ncfactor.lib
@c ----------------------------------------------------------
@node nctools_lib, perron_lib, ncfactor_lib, Non-commutative libraries
@section nctools_lib
@c lib nctools.lib
@c ----------------------------------------------------------
@node perron_lib, qmatrix_lib, nctools_lib, Non-commutative libraries
@section perron_lib
@c lib perron.lib
@c ---------------------------------------------------------
@node qmatrix_lib,  , perron_lib, Non-commutative libraries
@section qmatrix_lib
@c lib qmatrix.lib
@c ----------------------------------------------------------
@raisesections