Isabelle/HOL中无穷级数的无理性与超越准则

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2021-01-08 DOI:10.1080/10586458.2021.1980465

Angeliki Koutsoukou-Argyraki, Wenda Li, Lawrence Charles Paulson

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引用次数: 2

摘要

摘要:本文从Erdős和Straus, han l, han l和Rucki这三篇不同的研究论文中，概述了我们在无限级数的某些无理性和超越准则的证明助手Isabelle/HOL中的形式化。我们在Isabelle/HOL中的形式化可以在正式证明档案中找到。在这里，我们描述了形式化的选定方面，并讨论了这揭示了伊莎贝尔/霍尔在形式化现代数学研究中的使用和潜力，特别是在数论和分析的这些部分。

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Irrationality and Transcendence Criteria for Infinite Series in Isabelle/HOL

ABSTRACT We give an overview of our formalizations in the proof assistant Isabelle/HOL of certain irrationality and transcendence criteria for infinite series from three different research papers: by Erdős and Straus, Hančl, and Hančl and Rucki. Our formalizations in Isabelle/HOL can be found on the Archive of Formal Proofs. Here we describe selected aspects of the formalization and discuss what this reveals about the use and potential of Isabelle/HOL in formalizing modern mathematical research, particularly in these parts of number theory and analysis.

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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.