Introduction to OreModules
OreModules is a Maple implementation of algorithms which
compute parametrizations, extension modules (ext), resolutions and
other algebraic objects for linear systems of differential equations,
time-delay systems, etc.
The package OreModules, based on an original program by
F. Chyzak and
A. Quadrat, is maintained and further developed by
A. Quadrat and D. Robertz.
The algebraic framework for OreModules are Ore algebras. In order to deal
with modules over Ore algebras computationally, this package is based on
the Maple library Mgfun
(e.g. Ore algebras and non-commutative Gröbner bases are
developed in Mgfun).
Within this unified framework, OreModules handles
- ordinary differential equations,
- partial differential equations,
- multidimensional discrete systems,
- differential time-delay systems,
- repetitive systems,
- multidimensional convolutional codes, etc.
These systems may be time-invariant or time-varying with polynomial or rational coefficients.
In the context of linear control systems, the main features of OreModules are
the following:
- Decide controllability and parametrizability.
- Construct (minimal) parametrizations.
- Compute Bezout identities (left/right/generalized inverses).
- Decide flatness (also π-freeness).
The latest version of OreModules is available for download.