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:

- J. E. Björk,
*Rings of Differential Operators*, North Holland, 1979, - 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:

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