Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts. The theory is illustrated by many examples using different software packages.

翻译：求解多项式方程是多项式优化的一个子任务。本文介绍此类方程组及其主要求解方法。我们讨论临界点方程、代数簇和解的计数问题。通过使用不同软件包的多个实例来阐释该理论。