论文标题
代数的基本定理和平行多项式估计算法的可视化，建设性证明
A Visualizable, Constructive Proof of the Fundamental Theorem of Algebra, and a Parallel Polynomial Root Estimation Algorithm
论文作者
论文摘要
本文提供了代数基本定理的替代证明，该定理具有几个不同的优势。证明是基于涉及连续性和差异化的简单想法。视觉软件演示可用于传达证明的要旨。可以仅使用单变量的演算和复数的基本属性来开发严格的证明版本，但技术细节有些涉及。为了促进读者对证明的直观掌握，我们首先介绍了参数的要点，可以通过计算机实验来说明这一点。接下来，我们使用单变量的计算填写一些细节。最后，我们通过并联求解2N微分方程来找到一个数值程序，以查找N'th级多项式的所有根。
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to convey the gist of the proof. A rigorous version of the proof can be developed using only single-variable calculus and basic properties of complex numbers, but the technical details are somewhat involved. In order to facilitate the reader's intuitive grasp of the proof, we first present the main points of the argument, which can be illustrated by computer experiments. Next we fill in some of the details, using single-variable calculus. Finally, we give a numerical procedure for finding all roots of an n'th degree polynomial by solving 2n differential equations in parallel.
