We study the problem of recovering a collection of $n$ numbers from the evaluation of $m$ power sums. This yields a system of polynomial equations, which can be underconstrained ($m < n$), square ($m = n$), or overconstrained ($m > n$). Fibers and images of power sum maps are explored in all three regimes, and in settings that range from complex and projective to real and positive. This involves surprising deviations from the B\'ezout bound, and the recovery of vectors from length measurements by $p$-norms.

翻译：我们研究了从对美元电量的评价中收回一美元数字的问题,这产生了一个多面方程式系统,其控制不足(mm < n美元)、方形(mm=n美元)或过度控制(mm > n美元),在所有三种制度中,以及在从复杂和投影到真实和正面的环境中,都探索了电量图的纤维和图像,这涉及出乎意料地偏离B\'ez outbound,以及从长度测量中回收矢量($-n美元)。