### 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

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