Generalized Reduction in Rings of Differential Polynomials

Authors:
A. I. Zobnin
Affiliations:
Department of Mechanics and Mathematics, Moscow State University, Vorob'evy gory, Moscow, 119992 Russia al_zobnin@shade.msu.ru
Venue:
Programming and Computing Software
Year:
2004

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Abstract

In this paper, concepts of algebraic reduction and pseudoreduction in rings of differential polynomials are generalized. Specific features of this generalization, such as the uniqueness of separants and termination of the generalized reduction process, are considered. A method for the construction of generalized almost triangular simplificators similar to that for the construction of medians by Gröbner bases is suggested. A particular case, the generalized reduction in an ordinary polynomial ring, is considered.