Passive Complete Orthonomic Systems of PDEs and Involutive Bases of Polynomial Modules View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2003

AUTHORS

Joachim Apel

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. More... »

PAGES

88-107

References to SciGraph publications

  • 1894-01. Sur les invariants différentiels des groupes continus de transformations in ACTA MATHEMATICA
  • 1987-02. A criterion for detectingm-regularity in INVENTIONES MATHEMATICAE
  • 1982-06. Linear diophantine equations and local cohomology in INVENTIONES MATHEMATICAE
  • 1998-07. On the Relation Between Gröbner and Pommaret Bases in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • Book

    TITLE

    Symbolic and Numerical Scientific Computation

    ISBN

    978-3-540-40554-2
    978-3-540-45084-9

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/3-540-45084-x_3

    DOI

    http://dx.doi.org/10.1007/3-540-45084-x_3

    DIMENSIONS

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