package is dedicated to
the implementation of Stafford's theorems on the Weyl algebras (i.e., rings
of partial differential operators with either polynomial or rational
- J. T. Stafford, Module structure of Weyl algebras,
J. London Math. Soc., 18 (1978), 429-442.
This version of the Stafford package computes:
generators of a finitely generated left ideal,
- bases of a finitely generated free left
- injective parametrizations,
- unimodular elements,
- decomposition of modules (Serre's splitting-off theorem),
- Stafford's reductions,
- Swan's lemma, Bass' cancellation theorem...
The Stafford package can be used to:
- compute flat outputs of linear control systems,
- Stafford's reductions of linear PD systems (i.e., high generalization
of the cyclic vector theorem for linear PD systems),
- compute reductions and decompositions of linear functional systems
using the OreMorphisms package,
- compute Serre's reduction of linear functional systems using
the forthcoming Serre package...
For more details, see:
- A. Quadrat, D. Robertz, Computation of bases of free
modules over the Weyl algebras, Journal of Symbolic Computation, 42 (2007), 1113-1141.
- A. Quadrat, D. Robertz, A constructive study of the module
structure of rings of partial differential operators,
to appear in
Acta Applicandæ Mathematicæ (
48 pages, INRIA
Research Report n. 8225
The Stafford package is built upon the
package. Thus, the OreModules package has to be
installed to run the Stafford package.
The Stafford package is developed by D. Robertz and A. Quadrat.
More results will be developed in a future version.
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