Resolvent Representation for Regular Differential Ideals

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Abstract

 We show that the generic zeros of a differential ideal [A]:H A defined by a differential chain A are birationally equivalent to the general zeros of a single regular differential polynomial. This provides a generalization of both the cyclic vector construction for system of linear differential equations and the rational univariate representation of algebraic zero dimensional radical ideals. In order to achieve generality, we prove new results on differential dimension and relative orders which are of independent interest.

Received: June 13, 2001; revised version: May 2, 2002
Key words: Differential algebra, Differential primitive element, Cyclic vector, Computer algebra, Resolvent.