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We describe algorithms to represent and compute groups of Hecke characters. We make use of an id{\`e}lic point of view and obtain the whole family of such characters, including transcendental ones. We also show how to isolate the algebraic…
We evaluate AI-assisted generative capabilities on fundamental numerical kernels in high-performance computing (HPC), including AXPY, GEMV, GEMM, SpMV, Jacobi Stencil, and CG. We test the generated kernel codes for a variety of…
Presented is a Julia meta-program that discovers compact theories from data if they exist. It writes candidate theories in Julia and then validates: tossing the bad theories and keeping the good theories. Compactness is measured by a…
A research programme is set out for developing the use of high-level methods for quantum computation and information, based on the categorical formulation of quantum mechanics introduced by the author and Bob Coecke.
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
This note provides a lightweight tutorial on using Eigen, a C++ template library for linear algebra, to implement statistical and machine learning algorithms. The emphasis is practical rather than methodological: we show how common matrix…
We present FrankWolfe.jl, an open-source implementation of several popular Frank-Wolfe and Conditional Gradients variants for first-order constrained optimization. The package is designed with flexibility and high-performance in mind,…
We implement two algorithms in MATHEMATICA for classifying automorphisms of lower-dimensional non-commutative Lie algebras. The first algorithm is a brute-force approach whereas the second is an evolutionary strategy. These algorithms are…
Quantum computing, with its vast potential, is fundamentally shaped by the intricacies of quantum mechanics, which both empower and constrain its capabilities. The development of a universal, robust quantum programming language has emerged…
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…
Computational notebooks, such as Jupyter notebooks, are interactive computing environments that are ubiquitous among data scientists to perform data wrangling and analytic tasks. To measure the performance of AI pair programmers that…
Large Language Models (LLMs) have driven substantial progress in artificial intelligence in recent years, exhibiting impressive capabilities across a wide range of tasks, including mathematical problem-solving. Inspired by the success of…
TURTLE is a C library providing utilities allowing to navigate through a topography described by a Digital Elevation Model (DEM). The library has been primarily designed for the Monte Carlo transport of particles scattering over medium to…
We have developed a new programming framework, called Sieve, to support parallel numerical PDE algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic…
This report presents a brief review of matrix algebra and its implementation in Julia for power and energy applications. First, we present basic examples of data visualization, followed by conventional operations with matrices and vectors.…
This article introduces 'cpp11armadillo', a new R package that integrates the powerful Armadillo C++ library for linear algebra into the R programming environment. Targeted primarily at social scientists and other non-programmers, this…
It is now clear that the use of resilient encoding schemes will be required for any quantum computing device to be realised. However, quantum programmers of the future will not wish to be tied up in the particulars of such encoding schemes.…
HepLib is a C++ Library for computations in High Energy Physics, it works on top of GiNaC, a well-established C++ library used to perform symbolic computations. HepLib combines serval well-known packages to get high efficiency, including…
We introduce the Bandicoot C++ library for linear algebra and scientific computing on GPUs, overviewing its user interface and performance characteristics, as well as the technical details of its internal design. Bandicoot is the…
In paper describes the new logic programming language Delta, which have a many good properties. Delta-programs is p-computable, verifiable and can translation on other languages. Also we describe the Delta-methodology for constructing…