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In Mathematica, what does @@@ mean?

Asked 2009-07-17T02:03:11.330
16

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?

EDIT: 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];
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2 Answers

25

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

But I like to think of 

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

as shorthand for 

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

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]}
answered 2009-07-17T06:39:45.833
8

f @@@ expr is equivalent to Apply[f, expr, {1}].

documents.wolfram.com

answered 2009-07-17T02:34:15.090

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