PySymmetry: A Sage/Python Framework for the Symmetry Reduction of Linear G-Equivariant Systems

📝 Original Info

• Title: PySymmetry: A Sage/Python Framework for the Symmetry Reduction of Linear G-Equivariant Systems
• ArXiv ID: 2509.19479
• Date: 2025-09-23
• Authors: ** 논문에 명시된 저자 정보가 제공되지 않았습니다. (가능하면 원문에서 확인 필요) **

📝 Abstract

Despite the prevalence of symmetry in scientific linear systems, these structural properties are often underutilized by standard computational software. This paper introduces PySymmetry, an open-source Sage/Python framework that implements classical representation theory to simplify G-equivariant linear systems. PySymmetry uses projection operators to generate symmetry-adapted bases, transforming equivariant operators into a more efficient block-diagonal form. Its functionalities include defining and reducing representations, calculating multiplicities, and obtaining the explicit block structure. We demonstrate PySymmetry's versatility through three case studies: a chemistry application, a numerical benchmark on the non-Hermitian Schrödinger equation that achieved a performance increase of over 17x compared to standard methods, and a symbolic investigation that enabled the first complete analytical classification of a challenging problem in celestial mechanics. Designed for seamless integration with libraries like NumPy and SciPy, PySymmetry offers a powerful, user-friendly tool for exploring symmetries in theoretical and applied contexts. ```

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