Automate data entry into the Print

Question

There are a several variables a11, a12, a13,...,a21, a22, a23,... The standard output of these variables on the screen is as follows: Print[" a11= ", a11, " a12= ", a12, ...]

Is it possible to somehow automate (use a loop for example) the writing of all these variables to the Print function?

Answer 1

Create some variables

Table[Set[Evaluate[ToExpression["a" <> ToString[n] <> ToString[m]]], 
  RandomReal[]], {n, 1, 5}, {m, 1, 5}]

Now prints them all

vars = Flatten@Table["a" <> ToString[n] <> ToString[m], {n, 1, 5}, {m, 1, 5}];
Row[{#, "=", ToExpression[#]}] & /@ vars

Answer 2

You simply don't want to do this:

f[a[1,3]_,a[5,2]_]:=a[1,3] + a[5,2]

I don't mean because it's not syntactically correct, I mean that it doesn't make any sense as a function definition. When you define a function with formal arguments, you don't want to add overly specific semantics to your variables. For example, you'd never define a function that computes the area of a circle like this:

circleArea[radius16_] := Pi * radius16^2

The "16" bit just has nothing to do with the radius or circles or area or anything. It's a distraction.

So, in

f[a[1,3]_,a[5,2]_]:=a[1,3] + a[5,2]

the indices 1,3 in a[1,3] can't possibly mean anything. As they are used in the right hand side, a[1,3] + a[5,2], they are just formal arguments.

On the other hand, if what you're trying to do is really to index into something, then the indices do mean something. Let's say I have

a = {{1, 2}, {3, 4}}

and I want to define a function that adds the diagonal values. I could do this:

f[x_] := x[[1, 1]] + x[[2, 2]]
f[a]
(* 5 *)

Now those indices mean something, but the argument x is still just a formal argument that is expected to represent a 2x2 matrix. (You could enforce and check that it is a matrix, but I haven't shown that.)

And now you can send your individual values to the Print function like this:

Scan[Print, a, {2}]