Partial fraction decompositions on hyperplane arrangements
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914416022257664 |
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| author | de Korte, Claire Yu, Teresa |
| author_facet | de Korte, Claire Yu, Teresa |
| contents | We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained by examining the primary decomposition of ideals coming from hyperplane arrangements. We then present an algorithm for finding a PFD that satisfies properties desired for simplifying the calculation of scattering amplitudes. We demonstrate the effectiveness of this algorithm by computing practical examples coming from Feynman integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06531 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Partial fraction decompositions on hyperplane arrangements de Korte, Claire Yu, Teresa Commutative Algebra High Energy Physics - Theory Combinatorics 13C05, 13C70, 13P25, 05E40 We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained by examining the primary decomposition of ideals coming from hyperplane arrangements. We then present an algorithm for finding a PFD that satisfies properties desired for simplifying the calculation of scattering amplitudes. We demonstrate the effectiveness of this algorithm by computing practical examples coming from Feynman integrals. |
| title | Partial fraction decompositions on hyperplane arrangements |
| topic | Commutative Algebra High Energy Physics - Theory Combinatorics 13C05, 13C70, 13P25, 05E40 |
| url | https://arxiv.org/abs/2602.06531 |