The Waring Problem over polynomial rings asks how to decompose a homogeneous polynomial p of degree d as a linear combination of d-th powers of linear forms. In this work we give an algorithm to obtain a real Waring decomposition of any given real binary form p of length at most its degree. In fact, we construct a semialgebraic family of Waring decompositions for p. We illustrate our results with some examples.

中文翻译：

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半代数集和实二元形式分解

多项式环上的Waring问题询问如何将次数为d的齐次多项式p分解为线性形式的d次幂的线性组合。在这项工作中，我们给出了一种算法，可以在最大程度上获得任何给定的真实二进制形式p的真实Waring分解。实际上，我们构造了p的Waring分解的半代数族。我们用一些例子来说明我们的结果。