为什么取幂从右到左? [英] Why is exponentiation applied right to left?

问题描述

我正在阅读 Python 简介教科书并遇到了这一行:

I am reading an Intro to Python textbook and came across this line:

同一行上的运算符具有相同的优先级，并且从左到右应用，但取幂除外，它从右到左应用.

Operators on the same row have equal precedence and are applied left to right, except for exponentiation, which is applied right to left.

我了解其中的大部分内容，但我不明白为什么他们说取幂是从右到左应用的.他们也没有提供任何示例.另外，我可以问这样的一般性问题，还是只喜欢解决问题的问题?

I understand most of this, but I do not understand why they say exponentiation is applied right to left. They do not provide any examples either. Also, am I allowed to ask general questions like this, or are only problem solving questions preferred?

推荐答案

** 运算符遵循 正常的数学约定；它是右结合的:

The ** operator follows normal mathematical conventions; it is right-associative:

在通常的计算机科学术语中，数学中的取幂是右结合的，这意味着 x^yz 应该读作 x^(yz)，而不是 (x^y)^z.在对 BODMAS 规则的阐述中，对这个问题的处理非常谨慎，规则是首先评估最高指数.

In the usual computer science jargon, exponentiation in mathematics is right-associative, which means that x^yz should be read as x^(yz), not (x^y)^z. In expositions of the BODMAS rules that are careful enough to address this question, the rule is to evaluate the top exponent first.

来自维基百科关于操作顺序:

如果用堆叠符号表示求幂，通常的规则是从上到下工作，因为求幂在数学中是右结合的.

If exponentiation is indicated by stacked symbols, the usual rule is to work from the top down, because exponention is right-associative in mathematics.

所以 2 ** 3 ** 4 计算为 2 ** (3 ** 4) (== 2417851639229258349412352) 而不是 (2 **3) ** 4 (== 4096).

So 2 ** 3 ** 4 is calculated as 2 ** (3 ** 4) (== 2417851639229258349412352) not (2 ** 3) ** 4 (== 4096).

这在编程语言中非常普遍；它被称为右关联性，尽管有个例外，其中 Excel 和 MATLAB 是最值得注意的.

This is pretty universal across programming languages; it is called right-associativity, although there are exceptions, with Excel and MATLAB being the most notable.

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