Related papers: RationalMaps, a package for Macaulay2
Generating functions for a fixed genus map and hypermap enumeration become rational after a simple explicit change of variables. Their numerators are polynomials with integer coefficients that obey a differential recursion, and denominators…
In this paper a class of linear maps on the 2-torus and some planar piecewise isometries are discussed. For these discontinuous maps, by introducing codings underlying the map operations, symbolic descriptions of the dynamics and…
Finite group actions on free resolutions and modules arise naturally in many interesting examples. Understanding these actions amounts to describing the terms of a free resolution or the graded components of a module as group…
Let $\mathbb{Q}$ (resp. $\mathbb{R}$) be the field of rational (resp. real) numbers and $X = (X_1, \ldots, X_n)$ be variables. Deciding the non-negativity of polynomials in $\mathbb{Q}[X]$ over $\mathbb{R}^n$ or over semi-algebraic domains…
We classify rational solutions of a specific type of the set theoretical version of the pentagon equation. That is, we find all quadrirational maps $R:(x,y)\mapsto (u(x,y),v(x,y)),$ where $u, v$ are two rational functions on two arguments,…
The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
Requirements are formulated for a reaction kinetics package to be useful for an as wide as possible circle of users and illustrated with examples using ReactionKinetics, a Mathematica based package.
Sometimes we obtain attractive results when associating facts to simple elements. The goal of this work is to introduce a possible alternative in the study of the dynamics of rational maps.
Multimodal large language models (MLLMs) have demonstrated significant progress in semantic scene understanding and text-image alignment, with reasoning variants enhancing performance on more complex tasks involving mathematics and logic.…
L1Packv2 is a Mathematica package that contains a number of algorithms that can be used for the minimization of an $\ell_1$-penalized least squares functional. The algorithms can handle a mix of penalized and unpenalized variables. Several…
When attempting to understand the behavior of an executable, a binary analyst can make use of many different techniques. These include program slicing, dynamic instrumentation, binary-level rewriting, symbolic execution, and formal…
The MAP model was introduced in information system engineering in order to model processes on a flexible way. The intentional level of this model helps an engineer to execute a process with a strong relationship to the situation of the…
In this paper, we give an elementary new method for determining the rational points on algebraic curves using torsion packets. We also provide examples of curves for which all rational points can be completely determined by our method.
We investigate the birational geometry (in the sense of Mori's program) of the moduli space of rank 2 semistable parabolic vector bundles on a rational curve. We compute the effective cone of the moduli space and show that all birational…
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we…
In this paper, we give an explicit criterion when a rational holomorphic map between balls is equivalent to a polynomial holomorphic map. Making use of this criterion, we show that any proper rational holomorphic map from B^2 into B^N of…
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality…
The open-source Python package Gammapy, developed for the high-level analysis of gamma-ray data, requires gamma-like event lists combined with the corresponding instrument response functions. For a morphological analysis, these data have to…
This preprint contains a description of a package for Mathematica called EinS. This package allows one to perform various calculations with indexed objects.