The
`Stafford (click here)`

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., 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*, Acta Applicandæ Mathematicæ, 133 (2014), pp. 187-234 ( paper.pdf ).

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.