The Parameter Continuation Theorem is the theoretical foundation for polynomial homotopy continuation, which is one of the main tools in computational algebraic geometry. In this note, we give a short proof using Gr\"obner bases. Our approach gives a method for computing discriminants.

翻译：参数连续定理是多项式同伦连续法的理论基础，后者是计算代数几何的主要工具之一。本文利用Gröbner基给出了该定理的一个简短证明。我们的方法还提供了一种计算判别式的途径。