When to use indexed variables

Question

Still learning the fundamentals of the language I would like to ask you what advantages there might be in writing something like:

a[1] = 2;
a[2] = 4;
a[3] = "x";

It seems to me that it is always better to write

a = {2, 4, "x"};

Do you know about any practical constructs where indexed variables would offer an advantage?

Indexed variables can be used as dictionary table. So anywhere you might need a dictionary table, they are useful. http://en.wikipedia.org/wiki/Associative_array — Nasser, May 26 '14 at 19:27
see http://library.wolfram.com/conferences/devconf99/lichtblau/ — Nasser, May 26 '14 at 19:30
Indexed variables can be used symbolically. You can Solve[a[1]^2==2, a[1]] but you can't Solve[a[[1]]^2==2, a[[1]] ]. This is what we typically use when we don't know the number of symbolic variables we need beforehand. I would sometimes define a 3 by 3 matrix with explicit symbolic elements as Array[a, {3,3}]. — Szabolcs, May 26 '14 at 19:55
@Szabolcs - Thanks, that was an easy to understand example. Since I regularly read your answers on all topics, I would like to ask you a favour: A couple of days ago another newbie asked an interesting question: link. However, he never got an answer from you experts. Would you please have a short look on this question? — eldo, May 26 '14 at 21:25
@Szabolcs please consider expanding on your comment as an answer, even if CW. — Verbeia, Jun 03 '14 at 10:26
@Verbeia You're right, I should be better about this ... done. — Szabolcs, Jun 03 '14 at 14:38

score 10 · Accepted Answer · answered Jun 03 '14 at 14:35

Indexed variables can be used in symbolic calculations. They're useful when the number of variables used needs to be changed programmatically.

Here's an example:

vars = Array[a, 3]
(* {a[1], a[2], a[3]} *)

Minimize[vars.vars, vars]
(* {0, {a[1] -> 0, a[2] -> 0, a[3] -> 0}} *)

They can also be used to emulate sparse arrays, as described here.

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