4 papers
Rational Solutions of Parametric First-Order Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
In this paper, we give an algorithm for finding general rational solutions of a given first-order ODE with parametric coefficients that occur rationally. We present an analysis, co…
On real and observable rational realizations of input-output equations
Sebastian Falkensteiner, Dmitrii Pavlov, Rafael Sendra
Given a single (differential-algebraic) input-output equation, we present a method for finding different representations of the associated system in the form of rational realizatio…
Rationality and Parametrizations of Algebraic Curves under Specializations
Sebastian Falkensteiner, Rafael Sendra
Rational algebraic curves have been intensively studied in the last decades, both from the theoretical and applied point of view. In applications (e.g. level curves, linear homotop…
Transforming Radical Differential Equations to Algebraic Differential Equations
Sebastian Falkensteiner, Rafael Sendra
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 unknow…