PySymmetry: A Sage/Python Framework for the Symmetry Reduction of Linear G-Equivariant Systems
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911173024153600 |
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| author | da Silva, Leon D. Santos, Marcelo P. |
| author_facet | da Silva, Leon D. Santos, Marcelo P. |
| contents | 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. ``` |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19479 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PySymmetry: A Sage/Python Framework for the Symmetry Reduction of Linear G-Equivariant Systems da Silva, Leon D. Santos, Marcelo P. Group Theory Numerical Analysis Symbolic Computation Mathematical Physics Representation Theory 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. ``` |
| title | PySymmetry: A Sage/Python Framework for the Symmetry Reduction of Linear G-Equivariant Systems |
| topic | Group Theory Numerical Analysis Symbolic Computation Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2509.19479 |