Equidimensional triangularization of multidimensional linear systems

Alban Quadrat 1, 2
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : Based on the results obtained in [12] on the purity filtration of a finitely presented module associated with a multidimensional linear system, this paper aims at obtaining an equivalent block-triangular representation of the multidimensional linear system defined by equidimensional diagonal blocks. The multidimensional linear system can then be integrated in cascade by solving equidimensional homogeneous linear systems. Many multidimensional linear systems defined by under/overdetermined linear systems of partial differential equations can be explicitly solved by means of the PURITYFILTRATION and AbelianSystems packages, but cannot be computed by classical computer algebra systems such as Maple. The results developed in this paper generalize those obtained in the literature on Monge parametrizations and on the classification of autonomous elements by their codimensions.
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Alban Quadrat. Equidimensional triangularization of multidimensional linear systems. 7th International Workshop on Multidimensional (nD) systems (nDS'11), Sep 2011, Poitiers, France. pp.1-8. ⟨hal-00760101⟩

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