Abstract
This paper deals with the computation of the formally integrable systems underlying a given quasi-linear polynomial DAE. We use as stopping condition the criterium of differential stability, which happens to be equivalent to the formal integrability in dimension 1. A symbolic method is developed to compute effectively a finite collection of so-called triangular stable DAEs, whose solutions are precisely all the solutions of the initial system. Besides, this algorithm enables to determine the generic points of a triangular DAE, by checking the non-nullity of a single polynomial.
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Macutan, Y., Thomas, G. Theory of formal integrability and DAEs: effective computations. Numerical Algorithms 19, 147–157 (1998). https://doi.org/10.1023/A:1019162624913
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DOI: https://doi.org/10.1023/A:1019162624913