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# Resolvent Representation for Regular Differential Ideals

1 CAFE - Computer algebra and functional equations
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : We show that the generic zeros of a differential ideal $\dreg[A]$ defined by a differential chain $A$ are birationally equivalent to the general zeros of a single regular differential polynomial. This equivalence will be constructed explicitly. This provides a generalisation of both the cyclic vector construction for system of linear differential equations and the rational univariate representation of algebraic zero dimensional radical ideals.
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Cited literature [1 references]

https://hal.inria.fr/inria-00072422
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Submitted on : Wednesday, May 24, 2006 - 9:55:10 AM
Last modification on : Friday, February 4, 2022 - 3:14:54 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:46:05 PM

### Identifiers

• HAL Id : inria-00072422, version 1

### Citation

Thomas Cluzeau, Evelyne Hubert. Resolvent Representation for Regular Differential Ideals. RR-4200, INRIA. 2001. ⟨inria-00072422⟩

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