Abstract:Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive process when developing related code. Currently, some existing GA software packages rely on manually written scripts for code generation and visualization, but their high learning curve hinders widespread adoption. Meanwhile, methods based on Large Language Models (LLMs) often produce logical errors when generating specific GA scripts, such as GAALOPScript, resulting in generally low accuracy. To address these issues, this study proposes GA-VisAgent -- a multi-agent interactive learning application for GA code generation and visualization -- building upon a Geometric algebra large language model (GAGPT). Integrating task planning mechanisms with ReAct reasoning strategies, GA-VisAgent can decompose complex operations into five standardized subtasks, including core operations like geometric products, rotations, and reflections. It supports natural language and mathematical formulas as input to automatically generate executable code, accompanied by interactive visualizations to aid user comprehension. Experimental results show that GA-VisAgent achieved a 90% code generation success rate across 40 typical Conformal GA tasks, representing a 70% improvement over GPT-4o. This application introduces an extensible new paradigm for teaching GA and developing visualization tools for related mathematical concepts. The online service for this project will be available at this http URL.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.01299 [cs.LG] |
| (or arXiv:2605.01299v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.01299 arXiv-issued DOI via DataCite (pending registration) |
From: Jian Wang [view email]
[v1]
Sat, 2 May 2026 07:15:31 UTC (2,156 KB)
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