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arXiv · 2511.11783

On the effective Pourchet's Theorem

Teresa Cortadellas Benitez·Carlos D'Andrea·Ana Belen de Felipe·Joel Hurtado Moreno·M. Eulalia Montoro
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Abstract

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.

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Teresa Cortadellas Benitez, Carlos D'Andrea, Ana Belen de Felipe, Joel Hurtado Moreno, M. Eulalia Montoro. 2025-11-14. On the effective Pourchet's Theorem. https://arxiv.org/abs/2511.11783

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