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D.15.11 ncfactor_lib

Library:
ncfactor.lib
Purpose:
Tools for factorization in some noncommutative algebras
Authors:
Albert Heinle, albert.heinle@rwth-aachen.de
Viktor Levandovskyy, levandov@math.rwth-aachen.de

Overview:
In this library, new methods for factorization on polynomials are implemented for two algebras, both generated by two generators (Weyl and shift algebras) over a field K. Recall, that the first Weyl algebra over K is generated by x,d obeying the relation d*x=x*d+1.
The first shift algebra over K is generated by x,s obeying the relation s*x=x*s+s.
More detailled description of the algorithms can be found at @url{http://www.math.rwth-aachen.de/~Albert.Heinle}.

Guide: We are interested in computing a tree of factorizations, that is at the moment a list of all found factorizations is returned. It may contain factorizations, which are further reducible.

Procedures:

D.15.11.1 facFirstWeyl  factorization in the first Weyl algebra
D.15.11.2 testNCfac  tests factorizations from a given list for correctness
D.15.11.3 facSubWeyl  factorization in the first Weyl algebra as a subalgebra
D.15.11.4 facFirstShift  factorization in the first shift algebra


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