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An explicit C++ library is provided which deals with Zernike Functions over the unit circle as the main subject. The implementation includes basic means to evaluate the functions at points inside the unit circle and to convert the radial…

Cartogram drawing is a technique for showing geography-related statistical information, such as demographic and epidemiological data. The idea is to distort a map by resizing its regions according to a statistical parameter by keeping the…

We describe glsim, a C++ library designed to provide routines to perform basic housekeeping tasks common to a very wide range of simulation programs, such as reading simulation parameters or reading and writing self-describing binary files…

Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier…

This paper introduces PolyDiM, an open-source C++ library tailored for the development and implementation of polytopal discretization methods for partial differential equations. The library provides robust and modular tools to support…

The Virtual Element Method (VEM) is an extension of the Finite Element Method (FEM) used for handling polytopal meshes. This paper provides a brief introduction to the VEM for a two-dimensional Laplacian problem. Additionally, it highlights…

We construct a natural framed weight system on chord diagrams from the curvature tensor of any pseudo-Riemannian symmetric space. These weight systems are of Lie algebra type and realized by the action of the holonomy Lie algebra on a…

We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…

The introduced package MoebInv contains two CPP libraries for symbolic, numeric and graphical manipulations in non-Euclidean geometry. The first library cycle implements basic geometric operations on cycles, which are the zero sets of…

The article presents and documents the Mathematica package SymBuild. This package implements the computation and manipulation of integrable symbols appearing in various calculations in high-energy scattering amplitudes. By using Gr\"obner…

We present a novel technique for encoding and decoding constant weight binary codes that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight…

RGIsearch is a C++ program that searches for invariants of a user-defined set of renormalization group equations. Based on the general shape of the $\beta$-functions of quantum field theories, RGIsearch searches for several types of…

Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…

We propose to consider ensembles of cycles (quadrics), which are interconnected through conformal-invariant geometric relations (e.g. "to be orthogonal", "to be tangent", etc.), as new objects in an extended Moebius--Lie geometry. It was…

In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from…

Revisionist integral deferred correction (RIDC) methods are a family of parallel--in--time methods to solve systems of initial values problems. The approach is able to bootstrap lower order time integrators to provide high order…

This paper summarizes the development of Veamy, an object-oriented C++ library for the virtual element method (VEM) on general polygonal meshes, whose modular design is focused on its extensibility. The linear elastostatic and Poisson…

NUISANCE is an open source C++ framework which facilitates detailed studies of neutrino interaction cross-section models implemented in Monte Carlo neutrino event generators. It provides a host of automated methods to perform comparisons of…

Kernel quadratures and other kernel-based approximation methods typically suffer from prohibitive cubic time and quadratic space complexity in the number of function evaluations. The problem arises because a system of linear equations needs…

We review the dimensional check problem of the high-level programming languages, discuss the existing solutions, and come up with a new solution suited for scientific and engineering computations. Then, we introduce Univec, our C++ library…