在 Mathematica 中，@@@ 是什么意思? [英] In Mathematica, what does @@@ mean?

问题描述

我一直在解决 Project Euler 上的问题，其他人发布的一些解决方案使用了三重符号，即@@@".在 v7 的帮助浏览器中，我找到了 @@ 的条目(表示它是Apply"的中缀版本)，但没有找到 @@@.什么意思?

I've been working through problems on Project Euler, and some of the solutions that other people have posted use a triple-at-sign, i.e. '@@@'. In the help browser for v7, I find an entry for @@ (which says it's the infix version of 'Apply') but none for @@@. What does it mean?

这是一个例子，我想我可以在不违反 Project Euler 精神的情况下发布它:

Here's an example, which I think I can post without violating the spirit of Project Euler:

bloc[n_, f_][t_] := {f @@@ #, #~Tr~f} & /@ Join @@ Partition[t, {n, n}, 1];

推荐答案

正如其他人所指出的，@@@ 在技术上是 Apply 的简写，带有可选的第三个参数，正如 Apply 文档.

As others have noted, @@@ is, technically, shorthand for Apply with an optional third argument, as is explained deep in the documentation for Apply.

但我喜欢想

f @@@ {{a,b}, {c,d}, {e,i}}

作为

f @@#& /@ {{a,b} {c,d}, {e,i}}

换句话说，采用一个纯函数(简写:...#...&)执行 Apply(简写:@@) 到参数列表，以及 Map(简写:/@)覆盖这些参数列表.结果是

In other words, take a pure function (shorthand: ...#...&) that does an Apply (shorthand: @@) to a list of arguments, and Map (shorthand: /@) that over a list of such lists of arguments. The result is

{f[a,b], f[c,d], f[e,i]}

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