On the complexity of the resolvent representation of some prime differential ideals |
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Institution: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina |
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Abstract: | We prove upper bounds on the order and degree of the polynomials involved in a resolvent representation of the prime differential ideal associated with a polynomial differential system for a particular class of ordinary first order algebraic-differential equations arising in control theory. We also exhibit a probabilistic algorithm which computes this resolvent representation within time polynomial in the natural syntactic parameters and the degree of a certain algebraic variety related to the input system. In addition, we give a probabilistic polynomial-time algorithm for the computation of the differential Hilbert function of the ideal. |
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