Computations in Differential and Difference Modules

E. V. Pankrat’ev
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E. V. Pankrat’ev: Moscow State University

A chapter in Symmetries of Partial Differential Equations, 1989, pp 381-403 from Springer

Abstract: Abstract Constructive methods based on the Gröbner bases theory have been used many times in commutative algebra over the past 20 years, in particular, they allow the computation of such important invariants of manifolds given by systems of algebraic equations as their Hilbert polynomials. In differential and difference algebra, the analogous roles play characteristic sets. In this paper, algorithms for computations in differential and difference modules, which allow for the computation of characteristic sets (Gröbner bases) in differential, difference, and polynomial modules and differential (difference) dimension polynomials, are described. The algorithms are implemented in the algorithmic language REFAL.

Keywords: Gröbner bases; characteristic sets; differential dimension polynomials; Hilbert polynomials. (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-1948-8_13

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DOI: 10.1007/978-94-009-1948-8_13

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