On the complexity of the resolvent representation of some prime differential ideals

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.

• Type: Journal
• Year: 2006
• Where: JC
• Authors: Lisi D'Alfonso, Gabriela Jeronimo, Pablo Solernó
• Keywords: JC 2006, Polynomial, Probabilistic Polynomial-time Algorithm, Resolvent Representation