Singular

7.5.12 ncfactor_lib

Library:

ncfactor.lib

Purpose:

Tools for factorization in some noncommutative algebras

Authors:

Albert Heinle, aheinle at uwaterloo.ca
Viktor Levandovskyy, levandov at math.rwth-aachen.de

Overview:

In this library, new methods for factorization on polynomials
are implemented for several types of algebras, namely
- finitely presented (and also free) associative algebras (Letterplace subsystem)
- G-algebras (Plural subsystem), including (q)-Weyl and (q)-shift algebras in 2n variables
The determination of the best algorithm available for users input is done
automatically in the procedure ncfactor().

More detailed description of the algorithms and related publications can be found at @url{https://cs.uwaterloo.ca/~aheinle/}.

Procedures:

7.5.12.0. ncfactor		Factorization in any finitely presented algebra (incl. G-algebra)
7.5.12.0. facWeyl		Factorization in the n'th Weyl algebra
7.5.12.0. facFirstWeyl		Factorization in the first Weyl algebra
7.5.12.0. testNCfac		Tests factorizations from a given list for correctness
7.5.12.0. facSubWeyl		Factorization in the first Weyl algebra as a subalgebra
7.5.12.0. facShift		Factorization in the n'th shift algebra
7.5.12.0. facFirstShift		Factorization in the first shift algebra
7.5.12.0. homogfacNthWeyl		Homogeneous factorization in the n'th Weyl algebra
7.5.12.0. homogfacNthQWeyl		Homogeneous factorization in the n'th Q-Weyl algebra
7.5.12.0. homogfacFirstQWeyl		Homogeneous factorization in the first Q-Weyl algebra
7.5.12.0. homogfacNthQWeyl_all		Homogeneous factorization (complete) in the n'th Q-Weyl algebra
7.5.12.0. homogfacFirstQWeyl_all		Homogeneous factorization (complete) in the first Q-Weyl algebra
7.5.12.0. tst_ncfactor		Runs the examples of all contained not static functions. Test thing.