17 citations · 44 across the 6 of their papers we have counts for
9 papers
Sufficient conditions for the surjectivity of radical curve parametrizations
Jorce Caravantes, J. Rafael Sendra, David Sevilla +1
In this paper, we introduce the notion of surjective radical parametrization and we prove sufficient conditions for a radical curve parametrization to be surjective.
A note about rational surfaces as unions of affine planes
Jorge Caravantes, J. Rafael Sendra, David Sevilla +1
We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.
Covering rational surfaces with rational parametrization images
Jorge Caravantes, J. Rafael Sendra, David Sevilla +1
Let be a rational projective surface given by means of a projective rational parametrization whose base locus satisfies a mild assumption. In this paper we present an algorithm…
Transforming ODEs and PDEs with radical coefficients into rational coefficients
Jorge Caravantes, J. Rafael Sendra, David Sevilla +1
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 var…
On the existence of birational surjective parametrizations of affine surfaces
Jorge Caravantes, J. Rafael Sendra, David Sevilla +1
In this paper we show that not all affine rational complex surfaces can be parametrized birationally and surjectively. For this purpose, we prove that, if S is an affine complex su…
Algebraic and algorithmic aspects of radical parametrizations
J. Rafael Sendra, David Sevilla, Carlos Villarino
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, varia…
Missing sets in rational parametrizations of surfaces of revolution
J. Rafael Sendra, David Sevilla, Carlos Villarino
Parametric representations do not cover, in general, the whole geometric object that they parametrize. This can be a problem in practical applications. In this paper we analyze the…
Computing the Singularities of Rational Surfaces
S. Perez-Diaz, J. R. Sendra, C. Villarino
Given a rational projective parametrization $\cP(\ttt,\sss,\vvv)$ of a rational projective surface $\cS$ we present an algorithm such that, with the exception of a finite set (mayb…
Generalizing circles over algebraic extensions
Tomas Recio, J. Rafael Sendra, Luis Felipe Tabera +1
This paper deals with a family of spatial rational curves that were introduced by Andradas, Recio and Sendra, under the name of hypercircles, as an algorithmic cornerstone tool in…