数学极简主义

数学极简主义
Mathematical minimalism

原始链接: https://www.johndcook.com/blog/2026/04/13/the-smallest-math-library/

安杰伊·奥德日沃莱克最近在arXiv上发表了一篇文章，表明仅使用函数和常数1，就可以获得所有基本函数。以下方程摘自论文的补充材料，展示了如何从elm函数引导出加法、减法、乘法和除法。有关如何获得常数π以及平方、平方根等函数，以及标准的三角和双曲函数，请参阅论文和补充材料。

对不起。

Andrzej Odrzywolek recently posted an article on arXiv showing that you can obtain all the elementary functions from just the function

$\operatorname{eml}(x,y) = \exp(x) - \log(y)$

and the constant 1. The following equations, taken from the paper’s supplement, show how to bootstrap addition, subtraction, multiplication, and division from the elm function.

$\begin{align*} \exp(z) &\mapsto \operatorname{eml}(z,1) \\ \log(z) &\mapsto \operatorname{eml}(1,\exp(\operatorname{eml}(1,z))) \\ x - y &\mapsto \operatorname{eml}(\log(x),\exp(y)) \\ -z &\mapsto (\log 1) - z \\ x + y &\mapsto x - (-y) \\ 1/z &\mapsto \exp(-\log z) \\ x \cdot y &\mapsto \exp(\log x + \log y) \end{align*}$

See the paper and supplement for how to obtain constants like π and functions like square and square root, as well as the standard circular and hyperbolic functions.

数学极简主义 Mathematical minimalism

数学极简主义
Mathematical minimalism