Resolvent Representation for Regular Differential Ideals

Notes on Triangular Sets and Triangulation-Decomposition Algorithms II: Differential Systems

“…Another way of solving regular differential systems is to use the results of [26]. It is shown there that any regular differential system is equivalent to a single differential equation.…”

Probabilistic algorithms for computing resolvent representations of regular differential ideals

“…Effective algorithms in differential algebra have brought to attention a wider class of differential ideals, namely regular differential ideals [7,8] and characterisable differential ideals [29]. In [14], we generalized the proof of existence of a resolvent representation to regular differential ideals (and thereby to characterisable ideals). The present follow up paper is devoted to effective methods for computing resolvent representations for regular differential ideals 1 .…”

“…After the publication of [14], this line of complexity analysis was pursued in [17] on a kind of prime differential ideals of interest in control theory. Though we handle here more general differential ideals, our work does not cover their case of interest.…”

“…The probabilistic aspect comes from the choice of a tuple of elements in the base field: the algorithms succeed in producing a resolvent representation when this tuple 1 As requested by a referee we splitted out the computational method proposed in the initial submission [13] to complete it with its probability analysis here. 2 We follow here the terminology of [19,Section 6.5].…”

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AbstractIn a previous article [14], we proved the existence of resolvent representations for regular differential ideals. The present paper provides practical algorithms for computing such representations.

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