A perturbed differential resultant based implicitization algorithm for linear DPPEs

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...

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Vydáno v:Journal of symbolic computation Ročník 46; číslo 9; s. 977 - 996
Hlavní autor: Rueda, Sonia L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.09.2011
Témata:
Differential rational parametric equations
Differential resultant
Implicitization
Perturbation
Implicitization
Differential rational parametric equations
Perturbation
Differential resultant
ISSN:0747-7171, 1095-855X
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Shrnutí: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 Pϕ of P, so that the linear complete differential resultant ∂CResϕ associated to Pϕ is nonzero. A nonzero linear differential polynomial in ID is obtained, from the lowest degree term of ∂CResϕ, and used to provide an implicitization for P.
ISSN:0747-7171
1095-855X
DOI:10.1016/j.jsc.2011.05.001