Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
| Autor: | Magron, Victor, Koprowski, Przemysław, Vaccon, Tristan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for constructing such a decomposition. The sole purpose of the present paper is to present a set of algorithms that decompose a given nonnegative polynomial into a sum of six (five under some unproven conjecture or when allowing weights) squares of polynomials. Moreover, we prove that the binary complexity can be expressed polynomially in terms of classical operations of computer algebra and algorithmic number theory. Comment: 10 pages, 9 algorithms, submitted at the ISSAC 2023 conference |
| Databáze: | arXiv |
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