Function with number of arguments as parameter

Question

I would like to write a function that generates the expression $\sum_{i_1,\ldots,i_L} f(i_1,\ldots,i_L) \left(s_{i_1}\ldots s_{i_L}\right)$

where $i_j\in \left\{0,1,2,3\right\}$ and $s_{i_j}$ are string variables. The parameter to be passed to the function is the number of terms $L$. For example for L=2 one could generate it with

Sum[f[{j, k}] ("s" <> ToString@j <> " " <> "s" <> ToString@k), {j, 0, 3}, {k, 0, 3}]

However I would like to create a function

g[L_]:=...

That generalise the previous expression for arbitrary L. Maybe this could be done by creating a list

variables={j1,... ,jL}

which could be passed to a function of variable number of arguments as

g[variables__]:=... 

? Is it a better way to do it?

Answer 1

There are many ways to do this kind of thing, but the least work is probably to use Array. For example, if we define

sumindices[func_,numindices_Integer]:=Plus@@Flatten@Array[func,Table[2,{numindices}],0]

Given a generic function g, if we type

sumindices[g, 2]

we then get

g[0, 0] + g[0, 1] + g[1, 0] + g[1, 1]

To get the output you want, we then define a function to make the string

makestr[indices___]:= StringDrop[StringJoin@@("s"<>ToString[#]<>" "&/@{indices}),-1]

Then we can define

makef[indices___]:= f[{indices}][makestr[indices]]

And your desired output should be

sumindices[makef,2]

which gives

f[{0, 0}]["s0 s0"] + f[{0, 1}]["s0 s1"] + f[{1, 0}]["s1 s0"] + f[{1, 1}]["s1 s1"]