Related papers: Exchange of Geometric Information Between Applicat…
The Web Geometry Laboratory, (WGL), is a blended-learning, collaborative and adaptive, Web environment for geometry. It integrates a well known dynamic geometry system. In a collaborative session, exchange of geometrical and textual…
The "Web Geometry Laboratory" (WGL) project's goal is to build an adaptive and collaborative blended-learning Web-environment for geometry. In its current version (1.0) the WGL is already a collaborative blended-learning Web-environment…
The area of geometry with its very strong and appealing visual contents and its also strong and appealing connection between the visual content and its formal specification, is an area where computational tools can enhance, in a significant…
Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future…
The geometry automated theorem proving area distinguishes itself by a large number of specific methods and implementations, different approaches (synthetic, algebraic, semi-synthetic) and different goals and applications (from research in…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
Electronic Geometry Textbook is a knowledge management system that manages geometric textbook knowledge to enable users to construct and share dynamic geometry textbooks interactively and efficiently. Based on a knowledge base organizing…
With a large number of software tools dedicated to the visualisation and/or demonstration of properties of geometric constructions and also with the emerging of repositories of geometric constructions, there is a strong need of linking…
Well-designed open-source software drives progress in Machine Learning (ML) research. While static graph ML enjoys mature frameworks like PyTorch Geometric and DGL, ML for temporal graphs (TG), networks that evolve over time, lacks…
Geometry theorem proving forms a major and challenging component in the K-12 mathematics curriculum. A particular difficult task is to add auxiliary constructions (i.e, additional lines or points) to aid proof discovery. Although there…
The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This…
We report about significant enhancements of the complex algebraic geometry theorem proving subsystem in GeoGebra for automated proofs in Euclidean geometry, concerning the extension of numerous GeoGebra tools with proof capabilities. As a…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Knowledge Graphs (KG) provide us with a structured, flexible, transparent, cross-system, and collaborative way of organizing our knowledge and data across various domains in society and industrial as well as scientific disciplines. KGs…
Geometry problem solving presents a formidable challenge within the NLP community. Existing approaches often rely on models designed for solving math word problems, neglecting the unique characteristics of geometry math problems.…
Formal methods for verification of programs are extended to testing of programs. Their combination is intended to lead to benefits in reliable program development, testing, and evolution. Our geometric theory of testing is intended to serve…
This paper proposes MapGPT which is a novel approach that integrates the capabilities of language models, specifically large language models (LLMs), with spatial data processing techniques. This paper introduces MapGPT, which aims to bridge…
Deep graph learning has achieved remarkable progresses in both business and scientific areas ranging from finance and e-commerce, to drug and advanced material discovery. Despite these progresses, how to ensure various deep graph learning…
Torch Geometric Pool (tgp) is a pooling library built on top of PyTorch Geometric. Graph pooling methods differ in how they assign nodes to supernodes, how they handle batches, what they return after pooling, and whether they expose…
Geometric ability is a significant challenge for large language models (LLMs) due to the need for advanced spatial comprehension and abstract thinking. Existing datasets primarily evaluate LLMs on their final answers, but they cannot truly…