Related papers: Arithmetic in big number fields: the '+Ideals' pac…
Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…
We estimate the number of principal ideals $ I $ of norm $ \mathrm{N}(I) \leq x $ in the family of the simplest cubic fields. The advantage of our result is that it provides the correct order of magnitude for arbitrary $ x \geq 1 $, even…
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
In many applications (hupergeometric-type) special functions like orthogonal polynomials are needed. For example in more than 50% of the published solutions for the (application-oriented) questions in the "Problems Section" of SIAM Review…
We engineer a new probabilistic Monte-Carlo algorithm for isomorphism testing. Most notably, as opposed to all other solvers, it implicitly exploits the presence of symmetries without explicitly computing them. We provide extensive…
This paper extends the article of the Bruns and Conca on SAGBI bases and their computation (J. Symb. Comput. 120 (2024)) in two directions. (i) We describe the extension of the Singular library sagbiNormaliz.sing to the computation of…
This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…
Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…
We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of the quantum partition function in its…
Several relations and bounds for the dimension of principal ideals in group algebras are determined by analyzing minimal polynomials of regular representations. These results are used in the two last sections. First, in the context of…
This paper explores the application of automated planning to automated theorem proving, which is a branch of automated reasoning concerned with the development of algorithms and computer programs to construct mathematical proofs. In…
Many computer vision applications require robust estimation of the underlying geometry, in terms of camera motion and 3D structure of the scene. These robust methods often rely on running minimal solvers in a RANSAC framework. In this paper…
We present a first-principles computer code package (ABACUS) that is based on density functional theory and numerical atomic basis sets. Theoretical foundations and numerical techniques used in the code are described, with focus on the…
I describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given…
The numerical simulation of the physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large scale simulations are…
An algorithm is presented that formalizes different steps in a classical Supersymmetric (SUSY) calculation. Based on the algorithm Dill, a symbolic software package, that can perform the calculations, is developed in the Mathematica…
Although Buchberger's algorithm, in theory, allows us to compute Gr\"obner bases over any field, in practice, however, the computational efficiency depends on the arithmetic of the ground field. Consider a field $K = \mathbb{Q}(\alpha)$, a…
In this paper, we describe an algorithm that efficiently collect relations in class groups of number fields defined by a small defining polynomial. This conditional improvement consists in testing directly the smoothness of principal ideals…
We introduce and study monomial ideals with regular quotients, which can be seen as an extension of monomial ideals with linear quotients. Based on these investigations, we are able to calculate the Betti numbers of toric ideals belonging…