A perturbed differential resultant based implicitization algorithm for linear DPPEs

作者：Rueda Sonia L^*

来源：Journal of Symbolic Computation, 2011, 46(9): 977-996.

DOI：10.1016/j.jsc.2011.05.001

• Differential rational parametric equations
• Differential resultant
• Implicitization
• Perturbation

Let K be an ordinary differential field with derivation partial derivative. 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(phi) of P, so that the linear complete differential resultant partial derivative CRes(phi), associated to P(phi), is nonzero. A nonzero linear differential polynomial in ID is obtained, from the lowest degree term of partial derivative CRes(phi), and used to provide an implicitization for P.

• 出版日期2011-9