A perturbed differential resultant based implicitization algorithm for linear DPPEs

Authors:
Sonia L. Rueda
Affiliations:
-
Venue:
Journal of Symbolic Computation
Year:
2011

Citing 4
Cited 1

Generalised characteristic polynomials

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Solving degenerate sparse polynomial systems faster

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Linear complete differential resultants and the implicitization of linear DPPEs

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Linear differential implicitization and differential resultants

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Abstract

Let K be an ordinary differential field with derivation @?. Let P be a system of n linear differential polynomial parametric equations in n-1 differential parameters, with implicit ideal ID. Given a nonzero linear differential polynomial A in ID, we give necessary and sufficient conditions on A for P to be n-1 dimensional. We prove the existence of a linear perturbation P"@f of P, so that the linear complete differential resultant @?CRes"@f associated to P"@f is nonzero. A nonzero linear differential polynomial in ID is obtained, from the lowest degree term of @?CRes"@f, and used to provide an implicitization for P.