Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was decisively linked to modern developments in algebraic geometry by the polyhedral homotopy algorithm of Huber and Sturmfels, which exploited the combinatorial structure of the equations and led to efficient software for solving polynomial equations. Subsequent growth of numerical nonlinear algebra continues to be informed by algebraic geometry and its applications. These include new approaches to solving, algorithms for studying positive-dimensional varieties, certification, and a range of applications both within mathematics and from other disciplines. With new implementations, numerical nonlinear algebra is now a fundamental computational tool for algebraic geometry and its applications.

翻译：数字非线性代数是一种计算模式,它使用数字分析来研究多元分子方程式。它的起源是基于B\'ezout的古典理论解决多元分子方程式系统的方法。这与Huber和Sturmfels的多元同质同质算法在代数几何学方面的现代发展决定性地联系在一起,后者利用了方程式的组合结构,并导致高效的软件解决多元分子方程式。数字非线性代数的随后增长继续以代数几何学及其应用为基础。其中包括新的解析方法、研究正维数品种的算法、认证以及数学和其他学科中的一系列应用。有了新的实施,数字非线性代数数数数法现在成为代数几何地理测量及其应用的基本计算工具。