Pourchet定理的作用：将一元非负多项式分解为五个平方和
Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
摘要：
Pourchet证明在1971年，每一个非负的一元多项式的合理系数是一个总和的五个或更少的平方。然而，没有已知的算法来构建这样的分解。本论文的唯一目的是提出一套算法，将一个给定的非负多项式分解成6个（5个根据一些未经证明的猜想或允许权重）多项式的平方和。此外，我们证明了二进制复杂性可以表示多项式的经典运算的计算机代数和算法数论。
英文摘要：
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.
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