Formalizing Galois Theory

IF 0.7 4区数学 Q2 MATHEMATICS Experimental Mathematics Pub Date : 2021-07-23 DOI:10.1080/10586458.2021.1986176

Thomas Browning, P. Lutz

引用次数: 3

Abstract

ABSTRACT We describe a project to formalize Galois theory using the Lean theorem prover, which is part of a larger effort to formalize all of the standard undergraduate mathematics curriculum in Lean. We discuss some of the challenges we faced and the decisions we made in the course of this project. The main theorems we formalized are the primitive element theorem, the fundamental theorem of Galois theory, and the equivalence of several characterizations of finite degree Galois extensions.

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伽罗瓦理论的形式化

摘要：我们描述了一个使用Lean定理证明器形式化Galois理论的项目，该项目是在Lean中形式化所有标准本科数学课程的更大努力的一部分。我们讨论了我们在这个项目过程中面临的一些挑战和做出的决定。我们形式化的主要定理是原元定理，伽罗瓦理论的基本定理，以及有限度伽罗瓦扩展的几个特征的等价性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.

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