Maple package Stafford

This is a preliminary version of the Stafford package which uses OreModules. It implements constructive versions of all theorems of J. T. Stafford developed in Stafford (1978).

Literature:

A. Quadrat, D. Robertz, Computation of bases of free modules over the Weyl algebras, Journal of Symbolic Computation, 42:11-12 (2007), pp. 1113-1141, cf. also Quadrat, Robertz (2007).
A. Quadrat, D. Robertz, A constructive study of the module structure of rings of partial differential operators, Acta Applicandae Mathematicae, 133:1 (2014), pp. 187-234, cf. also Quadrat, Robertz (2014).

Download Maple package Stafford

Stafford is available here for Maple 8 and newer versions.

library: Stafford.ind, Stafford.lib

If you need Stafford for earlier versions of Maple, then please contact one of the authors.

Please copy the above files into the same directory as the OreModules library files.

If you have problems concerning the installation of OreModules or Stafford please contact us.

Example worksheets

Examples for Quadrat, Robertz (2007):

Description	Maple Worksheet	Text version	References
Projective dimensions & Minimal free resolutions	Example1.mws	Example1.pdf	Quadrat, Robertz (2007), Pommaret (2001), Janet (1929)
Bases & injective parametrizations of ordinary differential systems	Example2.mws	Example2.pdf	Quadrat, Robertz (2007), Chyzak et al. (2005), Malrait (2001), Quadrat, Robertz (2005)
Bases & injective parametrizations of partial differential equations	Example3.mws	Example3.pdf	Quadrat, Robertz (2007), Pommaret (2001)
Computation of two generators (Theorem of Stafford)	Example4.mws	Example4.pdf	Quadrat, Robertz (2007), Pommaret (2001), Leykin (2004)

Examples for Quadrat, Robertz (2014):

Description	Maple Worksheet	Text version	References
Strong generation	StrongGeneration.mws	StrongGeneration.pdf	Quadrat, Robertz (2014)
Unimodular elements, and Serre's splitting-off theorem	UnimodularElement1.mws	UnimodularElement1.pdf	Quadrat, Robertz (2014), Pommaret (2001)
Unimodular elements, and Serre's splitting-off theorem	UnimodularElement2.mws	UnimodularElement2.pdf	Quadrat, Robertz (2014)
Unimodular elements, and Serre's splitting-off theorem	UnimodularElementInSubmodule.mws	UnimodularElementInSubmodule.pdf	Quadrat, Robertz (2014)
Stafford's reduction	StaffordReduction1.mws	StaffordReduction1.pdf	Quadrat, Robertz (2014)
Stafford's reduction	2D-IsentropicFlow.mws	2D-IsentropicFlow.pdf	Quadrat, Robertz (2014), Courant, Hilbert (1962)
Stafford's reduction	Contact.mws	Contact.pdf	Quadrat, Robertz (2014)
Stafford's reduction	ConstCoeffs.mws	ConstCoeffs.pdf	Quadrat, Robertz (2014), Manitius (1984)
Stafford's reduction	ConstCoeffs3.mws	ConstCoeffs3.pdf	Quadrat, Robertz (2014), Mounier et al. (1998)
Computation of bases of finitely generated free modules	Basis.mws	Basis.pdf	Quadrat, Robertz (2014)
Computation of bases of finitely generated free modules	Basis2.mws	Basis2.pdf	Quadrat, Robertz (2014)
Computation of bases of finitely generated free modules	FreeModule.mws	FreeModule.pdf	Quadrat, Robertz (2014)
Cancellation theorem	ReductionUnimodularElement.mws	ReductionUnimodularElement.pdf	Quadrat, Robertz (2014)
Cancellation theorem	Cancellation1.mws	Cancellation1.pdf	Quadrat, Robertz (2014)
Cancellation theorem	Cancellation2.mws	Cancellation2.pdf	Quadrat, Robertz (2014)