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programming - When should I use Apply (or Function) and when @@ (or &)?


This is a rather general question, which I fail to answer myself. I guess it is mainly due to my insufficient knowledge of the precise terms.


If I understand correctly, the following are equivalent:


f = Function[u, 3 + u]
f = Function[3 + #]
f = (3+#) &
f[x_]:=3+x


In all cases f[a] would yield 3+a. Similarly, f[a] is equivalent to f@@{a}.


I have mainly two questions:



  1. What is the right term to call the shorter version, i.e. the version where one uses @@, #, & etc.?

  2. When should I prefer the one method and not the other? It seems like many answers given around MA.SE uses the "shorter version". What are the advantages and disadvantages...


Bonus question: Note my first question. I hope I could get more fishing rods and less fish. In other words, what is the official term for these two notions? Where are can I find documentation of these differences? The examples I presented in the this questions are merely examples, and I try to understand where can I rigorously study these notions and similar ones.




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