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Improvements to a triangulation-decomposition algorithm for ordinary differential systems in higher degree cases.

E. Hubert


We introduce new ideas to improve the efficiency and rationality of a triangulation decomposition algorithm. On the one hand we identify and isolate the polynomial remainder sequences in the triangulation-decomposition algorithm. Subresultant polynomial remainder sequences are then used to compute them and their specialisation properties are applied for the splittings. The gain is two fold: control of expression swell and reduction of the number of splittings. On the other hand, we remove the role that initials had in previous triangulation-decomposition algorithms. They are not needed in theoretical results and it was expected that they need not appear in the algorithms. This is the case of the algorithm presented.

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