Related papers: A FAIR File Format for Mathematical Software
This paper extends the FAIR (Findable, Accessible, Interoperable, Reusable) guidelines to provide criteria for assessing if software conforms to best practices in open source. By adding 'USE' (User-Centered, Sustainable, Equitable),…
Background: With the ever increasing use of computational models in the biosciences, the need to share models and reproduce the results of published studies efficiently and easily is becoming more important. To this end, various standards…
Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and…
This demo presents the implementation and usage details of GASSERT, the first tool to automatically improve assertion oracles. Assertion oracles are executable boolean expressions placed inside the program that should pass (return true) for…
Optical Character Recognition (OCR) for mathematical formula is essential for the intelligent analysis of scientific literature. However, both task-specific and general vision-language models often struggle to handle the structural…
Cadabra is an open access program ideally suited to complex tensor commutations in General Relativity. Tensor expressions are written in LaTeX while an enhanced version of Python is used to control the computations. This tutorial assumes no…
We propose a sufficient condition of the convergence of a power-log series that formally satisfies an algebraic ordinary differential equation (ODE) of arbitrary order. A general form and properties of the functional coefficients of such a…
CSV is a widely used format for data representing systems control, information exchange and processing, logging, etc. Nevertheless, the format is riddled with tricky corner cases and inconsistencies, which can make input data unreliable,…
We present a free open source package for high performance simulation and numerical investigation of boson samplers and, more generally, multi-photon interferometry. Our package is written in Julia, allowing C-like performance with easy…
Computer algebra is widely used in various fields of mathematics, physics and other sciences. The simplification of tensor expressions is an important special case of computer algebra. In this paper, we consider the reduction of tensor…
Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…
Simplification of expressions in computer algebra systems often involves a step known as "canonicalisation", which reduces equivalent expressions to the same form. However, such forms may not be natural from the perspective of a…
We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well as an arbitrary number of simple compact Lie groups. While…
Gaussian processes are a class of flexible nonparametric Bayesian tools that are widely used across the sciences, and in industry, to model complex data sources. Key to applying Gaussian process models is the availability of well-developed…
We describe a framework for solving a broad class of infinite-dimensional linear equations, consisting of almost banded operators, which can be used to resepresent linear ordinary differential equations with general boundary conditions. The…
This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
We present SeqSee, a software system that addresses spectral sequence visualization through a schema-based approach. By introducing a standardized JSON schema as an intermediate representation, SeqSee decouples the mathematical computations…
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…
The Pierre Auger Observatory is designed to unveil the nature and the origins of the highest energy cosmic rays. The large and geographically dispersed collaboration of physicists and the wide-ranging collection of simulation and…