This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. The special case of rational functions sharing the same denominator, a.k.a.Simultaneous Rational Function Reconstruction (SRFR), has many applications from linear system solving to coding theory, provided that SRFR has a unique solution. The number of unknowns in SRFR is smaller than for a general vector of rational function. This allows to reduce the number of evaluation points needed to guarantee the existence of a solution, but we may lose its uniqueness. In this work, we prove that uniqueness is guaranteed for a generic instance.

中文翻译：

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论同时有理函数重构的唯一性

这篇论文的重点是在给定一些评估的情况下重建有理函数向量的问题，或者更一般地说，给定它们的余数以不同的多项式为模。共享相同分母的有理函数的特殊情况，又名同步有理函数重构 (SRFR)，在从线性系统求解到编码理论的许多应用中，只要 SRFR 具有唯一的解决方案。SRFR 中未知数的数量小于一般有理函数向量。这允许减少保证解决方案存在所需的评估点的数量，但我们可能会失去它的唯一性。在这项工作中，我们证明了通用实例的唯一性。