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

LISI D'ALFONSO; GABRIELA JERONIMO; PABLO SOLERNÓ

JOURNAL OF COMPLEXITY

Elsevier

Año: 2006 vol. 22 p. 396 - 430

0885-064X

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.