Related papers: An algorithm for the normal bundle of rational mon…
Given two closed curves in a surface, we propose an algorithm to detect whether they are of the same type or not.
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
We present a certified algorithm based on subdivision for computing an isotopic approximation to any number of curves in the plane. Our algorithm is based on the certified curve approximation algorithm of Plantinga and Vegter. The main…
The divisor theory of the complete graph $K_n$ is in many ways similar to that of a plane curve of degree $n$. We compute the splitting types of all divisors on the complete graph $K_n$. We see that the possible splitting types of divisors…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We prove a formula for the motive of the stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with rational coefficients.
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…
Elimination theory has many applications, in particular, it describes explicitly an image of a complex line under rational transformation and determines the number of common zeroes of two polynomials in one variable. We generalize classical…
The Chow ring of the moduli space of marked rational curves is generated by Keel's divisor classes. The top graded part of this Chow ring is isomorphic to the integers, generated by the class of a single point. In this paper, we give an…
We study the normal map for plane projective curves, i.e., the map associating to every regular point of the curve the normal line at the point in the dual space. We first observe that the normal map is always birational and then we use…
Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling drawing each edge of a bundle separately as in metro-maps and call our method ordered bundles. To…
We define and study the motive of the moduli stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's category of motives. We prove that this motive can be written as a homotopy colimit of motives of…
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
We provide an algorithm to check whether two rational space curves are related by a similarity. The algorithm exploits the relationship between the curvatures and torsions of two similar curves, which is formulated in a computer algebra…
Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…
We compute the rational Chow ring of the moduli stack of planar nodal curves of fixed degree and express it in terms of tautological classes. Along the way, we extend Vial's results on Chow groups of Brauer-Severi varieties to…
An effective method of computing division polynomials in terms of Mumford coordinates is presented. As an example, division polynomials for $3$- and $4$-torsion divisors on a genus two curve are obtained explicitly in terms of Mumford…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…