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International Conference on Symbolic and Numerical Scientific Computation

SNSC 2001: Symbolic and Numerical Scientific Computation pp 88–107Cite as

Passive Complete Orthonomic Systems of PDEs and Involutive Bases of Polynomial Modules

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2630))

Abstract

The objective of this article is to enlighten the relationship between the two classical theories of passive complete orthonomic systems of PDEs on the one hand and Gröbner bases of finitely generated modules over polynomial rings on the other hand. The link between both types of canonical forms are the involutive bases which are both, a particular type of Gröbner bases which carry some additional structure and a natural translation of the notion of passive complete orthonomic systems of linear PDEs with constant coefficients into the language of polynomial modules.

We will point out some desirable applications which a “good” notion of involutive bases could provide. Unfortunately, these desires turn out to collide and we will discuss the problem of finding a reasonable compromise.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, Augustusplatz 10-11, 04109, Leipzig, Germany

    Joachim Apel

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  1. Joachim Apel
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Editor information

Editors and Affiliations

  1. RISC-Linz, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Franz Winkler

  2. Institute of Computational Mathematics, Johannes Kepler University Linz, Altenberger Str. 69, 4040, Linz, Austria

    Ulrich Langer

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Apel, J. (2003). Passive Complete Orthonomic Systems of PDEs and Involutive Bases of Polynomial Modules. In: Winkler, F., Langer, U. (eds) Symbolic and Numerical Scientific Computation. SNSC 2001. Lecture Notes in Computer Science, vol 2630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45084-X_3

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  • DOI: https://doi.org/10.1007/3-540-45084-X_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40554-2

  • Online ISBN: 978-3-540-45084-9

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