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):

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

This version of the Stafford package computes:

  1. two generators of a finitely generated left ideal,

  2. bases of a finitely generated free left module,

  3. injective parametrizations,

  4. unimodular elements,

  5. decomposition of modules (Serre's splitting-off theorem),

  6. Stafford's reductions,

  7. Swan's lemma, Bass' cancellation theorem...

The Stafford package can be used to:

  1. compute flat outputs of linear control systems,

  2. Stafford's reductions of linear PD systems (i.e., high generalization of the cyclic vector theorem for linear PD systems),

  3. compute reductions and decompositions of linear functional systems using the OreMorphisms package,

  4. compute Serre's reduction of linear functional systems using the forthcoming Serre package...

For more details, see:

  1. A. Quadrat, D. Robertz, Computation of bases of free modules over the Weyl algebras, Journal of Symbolic Computation, 42 (2007), 1113-1141.

  2. 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.

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