Related papers: The GF Mathematics Library
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
The Graph Automata have been the paradigm in the expression of utilizing Graphs as a language. Matrix Graph grammars \cite{Pedro} are an algebratization of graph rewriting systems. Here we present the dual of this formalizm which some…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.
A high-quality content analysis is essential for retrieval functionalities but the manual extraction of key phrases and classification is expensive. Natural language processing provides a framework to automatize the process. Here, a…
The integration of retrieval-augmented techniques with LLMs has shown promise in improving performance across various domains. However, their utility in tasks requiring advanced reasoning, such as generating and evaluating mathematical…
IGraph/M is an efficient general purpose graph theory and network analysis package for Mathematica. IGraph/M serves as the Wolfram Language interfaces to the igraph C library, and also provides several unique pieces of functionality not yet…
Mean-field games (MFGs) are limiting models to approximate $N$-player games, with a number of applications. Despite the ever-growing numerical literature on computation of MFGs, there is no library that allows researchers and practitioners…
This is a tract on the art and practice of mathematical writing. Not only does the book cover basic principles of grammar, syntax, and usage, but it takes into account developments of the last twenty years that have been inspired by the…
Informal mathematical text underpins real-world quantitative reasoning and communication. Developing sophisticated methods of retrieval and abstraction from this dual modality is crucial in the pursuit of the vision of automating discovery…
We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…
We introduce a novel task consisting in assigning a proof to a given mathematical statement. The task is designed to improve the processing of research-level mathematical texts. Applying Natural Language Processing (NLP) tools to research…
This continuously extended technical report collects and compares commonly used formulae from the literature and provides them in a machine readable way.
We present a new package for Mathematica system, called Libra. Its purpose is to provide convenient tools for the transformation of the first-order differential systems $\partial_i \boldsymbol j = M_i \boldsymbol j$ for one or several…
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…
We present GURLS, a least squares, modular, easy-to-extend software library for efficient supervised learning. GURLS is targeted to machine learning practitioners, as well as non-specialists. It offers a number state-of-the-art training…
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…
The technique of guessing can be very fruitful when dealing with sequences which arise in practice. This holds true especially when guessing is performed algorithmically and efficiently. One highly useful tool for this purpose is the…
Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in…