Two-slot pure function

Question

I come across this problem in many different forms when doing arithmetic in MMA and have until now just suffered along doing it the long way – having given up trying to figure it out myself – but now I have to admit that's getting a bit repetitive.

How does one get two slots working in a pure function? I'm trying to work out the % differences in the following list but it just returns can not be filled errors.

data={16,24,36,54,81};
(100*#2)/#1 &/@ Partition[data,2,1]

(100*#[[1]])/(#[[2]]) & /@ p where p=Partition[data,2,1] is one way — Nasser, Nov 30 '17 at 05:33
Okay that does work. :) Is there a way to use #1/#2 directly from data? Else the main big mystery remains. — BBirdsell, Nov 30 '17 at 05:38
Compare the output of f[#1, #2] & @@@ Partition[data, 2, 1] with that of f[#] & /@ Partition[data, 2, 1] (for undefined f). @@@ replaces the head, List, of each sublist with f, whereas /@ applies f to each sublist. — aardvark2012, Nov 30 '17 at 06:56
You need "apply at the first level", which is shorthanded @@@. — Αλέξανδρος Ζεγγ, Nov 30 '17 at 12:12

score 5 · Accepted Answer · answered Nov 30 '17 at 05:49

With p=Partition[data,2,1], you can do any of the following :

(100*#2)/#1 & @@@ p   (* parsed as Apply[ (100*#2)/#1 &, p, {1} ] *)
Apply[ (100*#2)/#1 & ] /@ p
(100*#[[2]])/(#[[1]]) & /@ p  (* Credit to Nasser in the comments *)

All evaluate to {150, 150, 150, 150}.

Your original try failed because Map (/@) passes only one argument to the function -- for example, #1 gets replaced by {16,24} for the first element of p. You need to take parts of #1 (which is equivalent to #), as in Nasser's example (the third example I included above), or you need to use Apply to pass 16 and 24 as the first and second arguments, as you seem to desire.

Two-slot pure function

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