Defining variables in mathematica

[Qubix]

I need to define some "general" variables in Mathematica 8, and I wonder if this can be done the following way.

Say ta[n] and tb[m] are my variables, in turn depending on n and m.

I want to define a function, for example

E[ta[n]_ , tb[m]_ ] := Cos[ ta[n] ] + Sin [tb[m] ] (just a simple example).

Then I want to be able to use the above expression in yet another function

S := E[ta[1],tb[2]] + E[ta[3],tb[1]] + etc...

First of all, does this work in Mathematica ?

Second, is S also a function, for example, if the line would stop before etc, should i write it as

S[ta[1]_ , tb[2]_, ta[3]_, tb[1]_ ]?

Remember, ta[1] , ta[2] etc are different variables.

I am asking all this because it would save me a serious amount of time in writing everything down explicitly.

 

[Bill Simpson]

First, E is defined to be Euler's constant. Trying to use that name for something else is a path to grief.
Second, trying to use function names, like ta[1]_ as a name of a parameter in a function definition is going to be another path to grief. But just writing x_ and y_ should work for you.
This works

In[1]:= e[x_, y_] := Cos[x] + Sin[y] ;
e[ta[1], tb[2]] + e[ta[3], tb[1]]

Out[2]= Cos[ta[1]] + Cos[ta[3]] + Sin[tb[1]] + Sin[tb[2]]

If you could clearly explain what your real problem is then there might be a simpler way for you to get there.