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.
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