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：解决多项式方程是多项式优化的一个子任务。本文介绍了这类方程组以及解决它们的主要方法。我们讨论了关键点方程、代数曲面和解决方案数量。理论通过使用不同的软件包进行许多示例进行了说明。