arXiv Open Access 2023

Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares

Victor Magron Przemysław Koprowski Tristan Vaccon

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Abstrak

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.

Topik & Kata Kunci

cs.SC

Penulis (3)

Victor Magron

Przemysław Koprowski

Tristan Vaccon

Format Sitasi

APA MLA BibTeX

Magron, V., Koprowski, P., Vaccon, T. (2023). Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares. https://arxiv.org/abs/2302.02202

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓