The PurityFiltration package will be soon available.

For more details, see the Appendix of the paper A. Quadrat, Grade filtration of linear functional systems , INRIA Reasearch Report n. 7769 ( paper.pdf ), pages 52-83 of the document.

The PurityFiltration package computes the purity (codimension/bidualizing) filtration of a finitely presented left module over an Ore algebras (available in the Maple package Ore_algebra).

The purity filtration computation is based on a new efficient algorithm which does not compute time-consuming spectral sequences as explained in classical textbooks on algebraic D-modules such as:

1. J. E. Björk, Rings of Differential Operators, North Holland, 1979,

2. J. E. Björk, Analytic D-modules and Applications, Kluwer, 1993.

The PurityFiltration package also computes an equidimensional block-triangular presentation of the module, and thus an equidimensional block-triangular representation of the corresponding linear functional system, which is better suitable for its symbolic integration (e.g., Monge parametrization) or for the fine study of its structural properties.

The PurityFiltration package highly improves the pdsolve command of Maple for the integration of overdetermined and underdetermined linear systems of partial differential equations (very few of such systems can be directly integrated by Maple).

For more details, see:

1. A. Quadrat, Grade filtration of linear functional systems , INRIA Reasearch Report n. 7769 ( paper.pdf ), Acta Applicandæ Mathematicæ, 127 (2013), pp. 27-86.
2. A. Quadrat, Purity filtration of multidimensional linear systems, Proceedings of nDS'11, Poitiers (France) (05-07/09/11).
3. A. Quadrat, Equidimensional triangularization of multidimensional linear systems, Proceedings of nDS'11, Poitiers (France) (05-07/09/11).

The PurityFiltration package is built upon the OreModules package. Thus, the OreModules package has to be installed to run the PurityFiltration package.

This package is developed by A. Quadrat.

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