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.

翻译：Pourchet于1971年证明：每个具有有理系数的非负单变量多项式可表示为不超过五个平方项之和。然而，目前尚无已知算法能够构造此类分解。本文的唯一目的是提出一系列算法，将给定的非负多项式分解为六个平方项之和（在某个未证猜想成立或允许加权的情况下可降为五个）。此外，我们证明二元复杂性可通过计算机代数与算法数论中的经典运算以多项式形式表达。