Related papers: Computing Weierstrass semigroups and the Feng-Rao …

We seek discrete approximations to solutions $u:\Omega \to R$ of semilinear elliptic partial differential equations of the form $\Delta u + f_s(u) = 0$, where $f_s$ is a one-parameter family of nonlinear functions and $\Omega$ is a domain…

We present a procedure to enumerate the whole set of numerical semigroups with a given Frobenius number F, S(F). The methodology is based on the construction of a partition of S(F) by a congruence relation. We identify exactly one…

We present a constructive procedure, based on the notion of Ap\'ery set, to obtain the value semigroup of a plane curve singularity from the value semigroup of its blow-up and viceversa. In particular we give a blow-down process that allows…

We present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to the construction of Fast…

We consider the structure of rational points on elliptic curves in Weierstrass form. Let x(P)=A_P/B_P^2 denote the $x$-coordinate of the rational point P then we consider when B_P can be a prime power. Using Faltings' Theorem we show that…

The Fisher-Rao distance is the geodesic distance between probability distributions in a statistical manifold equipped with the Fisher metric, which is a natural choice of Riemannian metric on such manifolds. It has recently been applied to…

We consider a pointed curve $(X,P)$ which is given by the Weierstrass normal form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\cdots + A_{r-1}(x) y + A_{r}(x)$ where $x$ is an affine coordinate on $\mathbb{P}^1$, the point $\infty$ on $X$…

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…

In this paper we investigate two-point algebraic-geometry codes (AG codes) coming from the Beelen-Montanucci (BM) maximal curve. We study properties of certain two-point Weierstrass semigroups of the curve and use them for determining a…

In this paper, we study an iteration in defined by a diffeomorphism polynomial bounded. Semi invariant curves tend to curves with parametric Weierstrass-Mandelbrot's functions. So, self-similarity and fractal dimension are justified. We…

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…

We study elliptic surfaces over $\mathbb{Q}(T)$ with coefficients of a Weierstrass model being polynomials in $\mathbb{Q}[T]$ with degree at most 2. We derive an explicit expression for their rank over $\mathbb{Q}(T)$ depending on the…

This paper presents algorithmic approaches to study superspecial hyperelliptic curves. The algorithms proposed in this paper are: an algorithm to enumerate superspecial hyperelliptic curves of genus $g$ over finite fields $\mathbb{F}_q$,…

A consistent notation for the Weierstrass elliptic function $\wp(z;g_{2},g_{3})$, for $g_{2} > 0$ and arbitrary values of $g_{3}$ and $\Delta \equiv g_{2}^{3} - 27 g_{3}^{2}$, is introduced based on the parametric solution for the motion of…

Let $\Lambda_s$ denote the inhomogeneous Lipschitz space of order $s\in(0,\infty)$ on $\mathbb{R}^n$. This article characterizes the distance $d(f, V)_{\Lambda_s}: = \inf_{g\in V} \|f-g\|_{\Lambda_s}$ from a function $f\in \Lambda_s$ to a…

We prove new sharp asymptotic for counting the semistable elliptic curves with two marked Weierstrass points at $\infty$ and $0$ and also the cases where $0$ is a 2-torsion or a 3-torsion marked Weierstrass point over $\mathbb{F}_q(t)$ by…

We introduce a principled way of computing the Wasserstein distance between two distributions in a federated manner. Namely, we show how to estimate the Wasserstein distance between two samples stored and kept on different devices/clients…

The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…

Effective reconstruction formulas of a curve from its theta hyperplanes are known classically in genus 2 (where the theta hyperplanes are Weierstrass points), and 3 (where, for a generic curve, the theta hyperplanes are bitangents to a…

We present algorithms to compute the topology of 2D and 3D hyperelliptic curves. The algorithms are based on the fact that 2D and 3D hyperelliptic curves can be seen as the image of a planar curve (the Weierstrass form of the curve), whose…