Let $\mathcal {T} $ be a set of $ n $ flat (planar) semi-algebraic regions in $\mathbb {R}^ 3$
of constant complexity (eg, triangles, disks), which we call plates. We wish to preprocess …

In this paper, we consider the class of first-order algebraic ordinary differential equations
(AODEs), and study their rational general solutions. A rational general solution contains an …

We introduce the notion of radical parametrization of a surface, and we provide algorithms to
compute such type of parametrizations for families of surfaces, like: Fermat surfaces …

Feynman integral computations in theoretical high energy particle physics frequently involve
square roots in the kinematic variables. Physicists often want to solve Feynman integrals in …

In this article algebraic constructions are introduced in order to study the variety defined by a
radical parametrization (a tuple of functions involving complex numbers, n variables, the four …

In this paper we study a differential equation which arises from the theory of Zolotarev
polynomials. By extending a symbolic algorithm for finding rational solutions of algebraic …

We present an algorithm that, given a non-rational irreducible real space curve, satisfying
certain conditions, computes a rational parametrization of a space curve near the input one …

For finding global approximate solutions to an algebraic equation in n unknowns, the
Hadamard open polygon for the case n= 1 and Hadamard polyhedron for the case n= 2 are …

In this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples
of real rational expressions involving circular and hyperbolic trigonometric functions as well …

Algebraic ordinary differential equations are described by polynomial relations between the
unknown function and its derivatives. There are no general solution methods available for …