
7.5.13 ncpreim_lib
 Library:
 ncpreim.lib
 Purpose:
 Noncommutative elimination and preimage computations
 Author:
 Daniel Andres, daniel.andres@math.rwthaachen.de
Support: DFG Graduiertenkolleg 1632 `Experimentelle und konstruktive Algebra'
 Overview:
 In Galgebras, elimination of variables is more involved than in the
commutative case.
One, not every subset of variables generates an algebra, which is again a
Galgebra.
Two, even if the subset of variables in question generates an admissible
subalgebra, there might be no admissible elimination ordering, i.e. an
elimination ordering which also satisfies the ordering condition for
Galgebras.
The difference between the procedure eliminateNC provided in this
library and the procedure eliminate (plural) from the kernel is that
eliminateNC will always find an admissible elimination if such one exists.
Moreover, the use of slimgb for performing Groebner basis computations
is possible.
As an application of the theory of elimination, the procedure preimageNC
is provided, which computes the preimage of an ideal under a homomorphism
f: A > B between Galgebras A and B. In contrast to the kernel procedure
preimage (plural) , the assumption that A is commutative is not required.
 References:
 (BGL) J.L. Bueso, J. GomezTorrecillas, F.J. Lobillo:
`Refiltering and exactness of the GelfandKirillov dimension',
Bull. Sci. math. 125, 8, 689715, 2001.
(GML) J.I. Garcia Garcia, J. Garcia Miranda, F.J. Lobillo:
`Elimination orderings and localization in PBW algebras',
Linear Algebra and its Applications 430(89), 21332148, 2009.
(Lev) V. Levandovskyy: `Intersection of ideals with noncommutative
subalgebras', ISSAC'06, 212219, ACM, 2006.
Procedures:
See also:
elim_lib;
preimage (plural).
