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

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 specialization 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 input and output of the algorithms. This is the case of the algorithm presented. New algorithms are presented to compute a subsequent characteristic decomposition from the output of the triangulation decomposition algorithm where the initials need not appear.

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