2 research outputs found
A perturbed differential resultant based implicitization algorithm for linear DPPEs
Let \bbK be an ordinary differential field with derivation . Let
\cP be a system of linear differential polynomial parametric equations in
differential parameters with implicit ideal \id. Given a nonzero linear
differential polynomial in \id we give necessary and sufficient
conditions on for \cP to be dimensional. We prove the existence of
a linear perturbation \cP_{\phi} of \cP so that the linear complete
differential resultant \dcres_{\phi} associated to \cP_{\phi} is nonzero. A
nonzero linear differential polynomial in \id is obtained from the lowest
degree term of \dcres_{\phi} and used to provide an implicitization algorithm
for \cP