Related papers: Computing basepoints of linear series in the plane
Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…
The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the index of a base point. In this paper we generalize Whitney's formula to curves on an oriented punctured surface. To…
Tipping points occur in many real-world systems, at which the system shifts suddenly from one state to another. The ability to predict the occurrence of tipping points from time series data remains an outstanding challenge and a major…
We propose an algorithm based on Newton's method and subdivision for finding all zeros of a polynomial system in a bounded region of the plane. This algorithm can be used to find the intersections between a line and a surface, which has…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
The `linear orbit' of a plane curve of degree $d$ is its orbit in $\P^{d(d+3)/2}$ under the natural action of $\PGL(3)$. In this paper we obtain an algorithm computing the degree of the closure of the linear orbit of an arbitrary plane…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We introduce an estimator for the curvature of curves and surfaces by using finite sample points drawn from sampling a probability distribution that has support on the curve or surface. First we give an algorithm for estimation of the…
In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the…
We apply an old method for constructing points-and-lines configurations in the plane to study some recent questions in incidence geometry.
Given a real algebraic curve, embedded in projective space, we study the computational problem of deciding whether there exists a hyperplane meeting the curve in real points only. More generally, given any divisor on such a curve, we may…
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…
We describe a method that allows, under some hypotheses, to compute all the rational points of some genus 5 curves defined over a number field. This method is used to solve some arithmetic problems that remained open.
A point on a plane curve is said to be Galois (for the curve) if the projection from the point as a map from the curve to a line induces a Galois extension of function fields. It is known that the number of Galois points is finite except…
A new algorithm for computing a point on a polynomial or rational curve in B\'{e}zier form is proposed. The method has a geometric interpretation and uses only convex combinations of control points. The new algorithm's computational…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
We present a matrix-based algorithm for deciding if the parametrization of a curve or a surface is invertible or not, and for computing the inverse of the parametrization if it exists.