In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial relations among them by means of a rational change of variables. The solutions of the given equation and its transformation correspond one-to-one. This work can be seen as a generalization of previous work on reparametrization of ODEs and PDEs with radical… Expand

This tutorial discusses aspects of this correspondence between radical differential ideals and their analytic solution sets in differential algebra involving symbolic computation, and an introduction to the Thomas decomposition method is given.Expand

We present an algorithm that transforms, if possible, a given ODE or PDE with radical function coefficients into one with rational coefficients by means of a rational change of variables so that… Expand

We prove that a first order ordinary differential equation (ODE) with a dicritical singularity at the origin has a one-parameter family of convergent fractional power series solutions. The notion of… Expand

This paper presents a reality test algorithm for plane curves, several algorithms to decide the reality and rationality of curves in the complex plane, and three different types of real parametrization algorithms that are called direct, algebraically optimal, and hybrid.Expand