Related papers: Using GXWeb for Theorem Proving and Mathematical M…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
We introduce QuiverTools, a new software package, available in both a SageMath and Julia version, to study quivers and their moduli spaces of representations. Its key features are the computation of general subdimension vectors, leading to…
This work discusses an approach to teach to mathematicians the importance and effectiveness of the application of Interactive Theorem Proving tools in their specific fields of interest. The approach aims to motivate the use of such tools…
Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…
The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in…
The article provides a brief description of the MathPartner service. This freely available cloud-based Mathematics is a universal system for symbolic-numeric calculations. Its Mathpar language is a subset of the LaTeX language, but allows…
This article focuses on the application of model development and opening the source code available and implemented by the Free Software and Open Source FLOSS to the instructional and teaching has both mathematics and computer by the…
Current paper reports the advantages of the application of GitHub and LaTeX for the MSc thesis writing. The existing code-based program implemented in GitHub portal provides a great tool for scientists and students for data sharing and…
A web application prototype is described, aimed at the generation of synthetic seismograms for user-defined earthquake models. The web application graphical user interface hides the complexity of the underlying computational engine, which…
The OpenMX Viewer (Open source package for Material eXplorer Viewer) is a web-based graphical user interface (GUI) program for visualization and analysis of crystalline and molecular structures and 3D grid data in the Gaussian cube format…
We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars.…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
This comprehensive survey examines Lean 4, a state-of-the-art interactive theorem prover and functional programming language. We analyze its architectural design, type system, metaprogramming capabilities, and practical applications in…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Explainable Artificial Intelligence (XAI) plays an important role in improving the transparency and reliability of complex machine learning models, especially in critical domains such as cybersecurity. Despite the prevalence of heuristic…
Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…
In the past decade, the modeling community has produced many feature-rich modeling editors and tool prototypes not only for modeling standards but particularly also for many domain-specific languages. More recently, however, web-based…
Transformers have revolutionized machine learning, yet their inner workings remain opaque to many. We present Transformer Explainer, an interactive visualization tool designed for non-experts to learn about Transformers through the GPT-2…