Reconstructing Laurent expansion of rational functions using p-adic numbers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917066275028992 |
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| author | Xia, Tianya Yang, Li Lin |
| author_facet | Xia, Tianya Yang, Li Lin |
| contents | We propose a novel method for reconstructing Laurent expansion of rational functions using $p$-adic numbers. By evaluating the rational functions in $p$-adic fields rather than finite fields, it is possible to probe the expansion coefficients simultaneously, enabling their reconstruction from a single set of evaluations. Compared with the reconstruction of the full expression, constructing the Laurent expansion to the first few orders significantly reduces the required computational resources. Our method can handle expansions with respect to more than one variables simultaneously. Among possible applications, we anticipate that our method can be used to simplify the integration-by-parts reduction of Feynman integrals in cutting-edge calculations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08452 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reconstructing Laurent expansion of rational functions using p-adic numbers Xia, Tianya Yang, Li Lin High Energy Physics - Theory High Energy Physics - Phenomenology We propose a novel method for reconstructing Laurent expansion of rational functions using $p$-adic numbers. By evaluating the rational functions in $p$-adic fields rather than finite fields, it is possible to probe the expansion coefficients simultaneously, enabling their reconstruction from a single set of evaluations. Compared with the reconstruction of the full expression, constructing the Laurent expansion to the first few orders significantly reduces the required computational resources. Our method can handle expansions with respect to more than one variables simultaneously. Among possible applications, we anticipate that our method can be used to simplify the integration-by-parts reduction of Feynman integrals in cutting-edge calculations. |
| title | Reconstructing Laurent expansion of rational functions using p-adic numbers |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2506.08452 |