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- W2024532992 abstract "In this paper, we give three theoretical and practical contributions for solving polynomial ODE or PDE systems. The first one is practical: an algorithm which improves the purely algebraic part of Rosenfeld—Grobner (the polynomial ODE or PDE systems simplifier which is the core of the Maple 5.5 diffalg package). It is a variant of lextriangular but does not need any Grobner basis computation. The second one is theoretical: a characterization of the output of Rosenfeld—Grobner and a clarification of the existing relationship between algebraic and differential characteristic sets. The third one is theoretical as well as practical: an algorithm to compute canonical representatives of differential polynomials modulo regular differential ideals without any use of Grobner bases. This algorithm simplifies the theory (somehow a “pedagogic” contribution) but permits us also to perform easily linear algebra over the base field in the factor differential ring defined by a regular differential ideal." @default.
- W2024532992 created "2016-06-24" @default.
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- W2024532992 date "2000-07-01" @default.
- W2024532992 modified "2023-09-24" @default.
- W2024532992 title "Computing canonical representatives of regular differential ideals" @default.
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- W2024532992 doi "https://doi.org/10.1145/345542.345571" @default.
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