The
`OreMorphisms (click here)`

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.