Related papers: Using GXWeb for Theorem Proving and Mathematical M…
Diffusion models have been central to the development of recent image, video, and even text generation systems. They posses striking geometric properties that can be faithfully portrayed in low-dimensional settings. However, existing…
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…
Often user interfaces of theorem proving systems focus on assisting particularly trained and skilled users, i.e., proof experts. As a result, the systems are difficult to use for non-expert users. This paper describes a paper and pencil HCI…
As modeling becomes a crucial activity in software development the question may be asked whether currently used graphical representations are the best option to model systems efficiently. This position paper discusses the advantages of…
The output of an automated theorem prover is usually presented by using a text format, they are often too heavy to be understood. In model checking setting, it would be helpful if one can observe the structure of models and the verification…
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…
GeoGebra is an interactive geometry, algebra, statistics, and calculus application designed for teaching and learn-ing math, science, and engineering. Its dynamic interface allows its users to accurately and interactively visualize their…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
In this paper we present our experience in using visualization in mathematics education. The experience with our university courses: "Computer tools in matematics" and "Symbolic algebra" provides the basis for mathematics teacher education…
We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Groebner bases method), their implementation and integration in educational tools. The project includes formal…
An enhancement of the dynamic geometry system GeoGebra for the automatic symbolic computation of algebraic loci and envelopes is presented. Given a GeoGebra construction, the prototype, after rewriting the construction as a polynomial…
OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation,…
The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, GRworkbench has been significantly extended to facilitate numerical experimentation in…
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…
Many statistical models are algebraic in that they are defined by polynomial constraints or by parameterizations that are polynomial or rational maps. This opens the door for tools from computational algebraic geometry. These tools can be…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
We present an autoformalisation framework for the Lean theorem prover, called GFLean. GFLean uses a high-level grammar writing tool called Grammatical Framework (GF) for parsing and linearisation. GFLean is implemented in Haskell. We…
OSMnx is a Python package for downloading, modeling, analyzing, and visualizing urban networks and any other geospatial features from OpenStreetMap data. A large and growing body of literature uses it to conduct scientific studies across…
A step-by-step presentation of the code for a small theorem prover introduces theorem-proving techniques. The programming language used is Standard ML. The prover operates on a sequent calculus formulation of first-order logic, which is…
We introduce geoplotlib, an open-source python toolbox for visualizing geographical data. geoplotlib supports the development of hardware-accelerated interactive visualizations in pure python, and provides implementations of dot maps,…