The
OreMorphisms package is dedicated to the study of homomorphisms of finitely generated left modules over an Ore
algebra (available in the Ore_algebra package), and its
applications to mathematical systems theory and mathematical physics.
In particular, OreMorphisms package can be used to:
- compute homomorphisms between two finitely generated left modules,
- compute internal symmetries of linear functional
systems,
- compute quadratic conservation laws,
- compute the kernel, coimage, image and cokernel of homomorphisms,
- Fitting's theorem on isomorphisms and equivalences,
- compute idempotent endomorphisms,
- factorize linear functional systems,
- reduction linear functional systems,
- decompose linear functional systems...
For more details, see:
- T. Cluzeau, A. Quadrat, Factoring and decomposing a class of
linear functional systems, Linear Algebra and Its Applications,
428 (2008), 324-381.
- T. Cluzeau, A. Quadrat, OreMorphisms: A homological
algebraic package for factoring, reducing and decomposing linear
functional systems, in Topics in Time-Delay Systems: Analysis,
Algorithms and Control, J.-J. Loiseau, W. Michiels,
S.-I. Niculescu, R. Sipahi (Eds.), Lecture Notes in Control and
Information Sciences 388, Springer, 2009, 179-196.
- T. Cluzeau, A. Quadrat, A constructive version of
Fitting's theorem on isomorphisms and equivalences of linear
systems, Proceedings of nDS'11, Poitiers (France)
(05-07/09/11).
The OreMorphisms package is built
upon the
OreModules
package. Thus, the OreModules package has to be
installed to run the OreMorphisms package.
This package is developed by
T. Cluzeau and A. Quadrat.
A Mathematica version of the OreMorphisms package will be
soon available. It is developed by
Maris Tõnso,
T. Cluzeau and A. Quadrat
within the PHC
Parrot project CASCAC. The Mathematica version of the OreMorphisms package is based on the
implementation of Gröbner bases over Ore algebras available in the
Mathematica HolonomicFunctions package developed by Christoph Koutschan.
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