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];
Eric
  • 11,392
  • 13
  • 57
  • 100

3 Answers3

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]}
dreeves
  • 26,430
  • 45
  • 154
  • 229
  • I had to run that a few ways before it made sense! But you're right, that does seem like the most natural interpretation. – Eric Jul 17 '09 at 13:06
12

@@@ is the short form for Apply at level 1.

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

is equivalent to

Apply[f, {{a, b, c}, {d, e}}, {1}]

Reference: http://reference.wolfram.com/mathematica/ref/Apply.html

You may need to expand the Scope and Level Specification sections.

tvanfosson
  • 524,688
  • 99
  • 697
  • 795
8

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

documents.wolfram.com

Tim Sylvester
  • 22,897
  • 2
  • 80
  • 94