On the effective Pourchet's Theorem
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917080938315776 |
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| author | Benitez, Teresa Cortadellas D'Andrea, Carlos de Felipe, Ana Belen Moreno, Joel Hurtado Montoro, M. Eulalia |
| author_facet | Benitez, Teresa Cortadellas D'Andrea, Carlos de Felipe, Ana Belen Moreno, Joel Hurtado Montoro, M. Eulalia |
| contents | With the aid of Hensel Lemma, we refine the 2-adic Newton polygon algorithm proposed by Magron, Koprowski, and Vaccon at ISSAC 2023 to express computationally a given positive univariate polynomial with rational coefficients as a sum of five squares of rational polynomials -the effective Pourchet's Theorem- and extend it to cover almost all the possible inputs. We also provide examples which are covered with our methods but cannot be detected by previous conjectural algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the effective Pourchet's Theorem Benitez, Teresa Cortadellas D'Andrea, Carlos de Felipe, Ana Belen Moreno, Joel Hurtado Montoro, M. Eulalia Number Theory Commutative Algebra With the aid of Hensel Lemma, we refine the 2-adic Newton polygon algorithm proposed by Magron, Koprowski, and Vaccon at ISSAC 2023 to express computationally a given positive univariate polynomial with rational coefficients as a sum of five squares of rational polynomials -the effective Pourchet's Theorem- and extend it to cover almost all the possible inputs. We also provide examples which are covered with our methods but cannot be detected by previous conjectural algorithms. |
| title | On the effective Pourchet's Theorem |
| topic | Number Theory Commutative Algebra |
| url | https://arxiv.org/abs/2511.11783 |