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Linear differential implicitization and differential resultants

Published: 28 January 2011 Publication History

Abstract

Given a system P of n linear ordinary differential polynomial parametric equations (linear DPPEs) in n-1 differential parameters, we proved in [2] that if nonzero a differential resultant gives the implicit equation of P. Differential resultants often vanish under specialization, which prevented us from giving an implicitization algorithm in [2]. Motivated by Canny's method and its generalizations we consider now a linear perturbation of P and use it to give an algorithm to decide if the dimension of the implicit ideal of P is n-1 and in the affirmative case obtain the implicit equation of P. This poster presentation will contain this development together with examples illustrating the results. An extended version of this work can be found in [1].

References

[1]
S.L. Rueda, A perturbed differential resultant based implicitization algorithm for linear DPPEs. (2010) arXiv:1003.4375v1.
[2]
S.L. Rueda and J.R. Sendra. Linear complete differential resultants and the implicitization of linear DPPEs. J. Symbolic Comput., 45 (2010), 324--341.

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Published In

cover image ACM Communications in Computer Algebra
ACM Communications in Computer Algebra  Volume 44, Issue 3/4
September/December 2010
145 pages
ISSN:1932-2232
EISSN:1932-2240
DOI:10.1145/1940475
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 January 2011
Published in SIGSAM-CCA Volume 44, Issue 3/4

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