In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which rationalizes the square roots. In this paper, we give an algorithm for rationalizing roots. The algorithm is applicable whenever the algebraic hypersurface associated with the root has a point of multiplicity $(d-1)$, where $d$ is the degree of the algebraic hypersurface. We show that one can use the algorithm iteratively to rationalize multiple roots simultaneously. Several examples from high energy physics are discussed.

中文翻译：

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合理化根源：一种算法方法

在计算费曼积分的过程中，人们经常会遇到平方根。为了用多个多对数表示费曼积分，人们寻求变量的变换，使平方根合理化。在这篇论文中，我们给出了一个合理化根的算法。当与根相关联的代数超曲面具有重数 $(d-1)$ 时，该算法适用，其中 $d$ 是代数超曲面的次数。我们表明可以迭代地使用该算法来同时对多个根进行合理化。讨论了来自高能物理学的几个例子。