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How to hunt wild constants
arXiv - CS - Symbolic Computation Pub Date : 2021-03-30 , DOI: arxiv-2103.16720
David R. Stoutemyer

There are now several comprehensive web applications, stand-alone computer programs and computer algebra functions that, given a floating point number such as 6.518670730718491, can return concise nonfloat constants such as \,3\arctan2+\ln9+1\, that closely approximate the float. Examples include AskConstants, Inverse Symbolic Calculator, the Maple identify function, MESearch, OEIS, RIES, and WolframAlpha. Usefully often such a result is the exact limit as the float is computed with increasing precision. Therefore these program results are candidates for proving an exact result that you could not otherwise compute or conjecture without the program. Moreover, candidates that are not the exact limit can be provable bounds, or convey qualitative insight, or suggest series that they truncate, or provide sufficiently close efficient approximations for subsequent computation. This article describes some of these programs, how they work, and how best to use each of them. Almost everyone who uses or should use mathematical software can benefit from acquaintance with several such programs, because these programs differ in the sets of constants that they can return.

中文翻译:

如何寻找野生常数

现在有几种综合的Web应用程序,独立的计算机程序和计算机代数函数,给定一个浮点数(例如6.518670730718491),它们可以返回简洁的非浮点常量,例如\,3 \ arctan2 + \ ln9 + 1 \,这些近似常数近似于漂浮。示例包括AskConstants,逆符号计算器,Maple识别函数,MESearch,OEIS,RIES和WolframAlpha。通常有用的结果是精确的极限,因为浮点数的计算精度越来越高。因此,这些程序结果可用于证明确切的结果,而如果没有该程序,您将无法计算或猜想出正确的结果。此外,并非确切限制的候选者可以是可证明的界限,可以传达定性见解,也可以建议他们截断的序列,或为后续计算提供足够接近的有效近似值。本文介绍了其中一些程序,它们如何工作以及如何最好地使用它们。几乎每个使用或应使用数学软件的人都可以从熟悉几个这样的程序中受益,因为这些程序在可以返回的常量集方面有所不同。
更新日期:2021-04-01
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