The
*Stafford*
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
coefficients):

- J. T. Stafford,
*Module structure of Weyl algebras,*J. London Math. Soc., 18 (1978), 429-442.

This version of the *Stafford* package computes:

- two generators of a finitely generated left ideal,
- bases of a finitely generated free left module,
- 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*( paper.pdf), 48 pages, INRIA Research Report n. 8225 ( paper.pdf ), 2013.

The Stafford package is built upon the
*OreModules*
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.