Computing Canonical Representatives of Regular Differential Ideals

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-Gröbner. It is a variant of lextriangular but does not need any Gröbner basis computation. The second one is theoretical: a characterization of the output of Rosenfeld-Gröbner and a clarification of the 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 Gröbner bases.
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Conference papers
International Symposium on Symbolic and Algebraic Computation, 2000, France. Association for Computing Machinery, pp.37-46, 2000, <10.1145/345542.345571>


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François Boulier, François Lemaire. Computing Canonical Representatives of Regular Differential Ideals. International Symposium on Symbolic and Algebraic Computation, 2000, France. Association for Computing Machinery, pp.37-46, 2000, <10.1145/345542.345571>. <hal-00139177>

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