Trouble using recursive function on list with Mathematica

Question

I am trying to write a recursive function in Mathematica whose argument is a list. If the list is of length 1, it returns a value. If not, the function breaks it down into several smaller lists according to some rules and the function is then evaluated on those lists. Here is my code :

f[u_] :=
 (Print["u : ", u];
  If[Length[u] == 1, 
   Subscript[T, u[[1]]] - Subscript[\[Lambda], 1]^u[[1]],
   v = SetPartitions[Length[u]];
   aux[v_] := Sum[u[[v[[i]]]], {i, 1, Length[v]}];
   res = Map[aux, v, {2}];
   res = Drop[res, -1];
   Print[res];
   Product[Subscript[T, u[[i]]], {i, 1, Length[u]}] - 
    Sum[f[res[[i]]], {i, 1, Length[res]}]]
  )

It works fine for

f[{1, 2}]

or

f[{3}]

but it does not work anymore when the list is of length 3 or more, like for example

f[{1,1,2}].

Here is the error message I get :

f[{1, 1, 2}]

u : {1,1,2}
{{4},{1,3},{2,2},{3,1}}
u : {4}
u : {1,3}
{{4}}
u : {4}

Part::partw: Part 3 of {{4}} does not exist. >>

u : {{4}}[[3]]
{{{{7}}}}
u : {{{7}}}

Part::partw: Part 4 of {{{{7}}}} does not exist. >>

u : {{{{7}}}}[[4]]
{{{{{{11}}}}}}
u : {{{{{11}}}}}

Does anyone have an idea what to do ? I guess it has something to do with the variables res being overwritten, but I don't know how to get round the problem....

Thank you !

Chris Degnen Chris Degnen · Accepted Answer · 2015-07-05T13:38:40

You are correct, res is being overwritten. The solution is to localise res to each call of function f using a module like so:

f[u_] := Module[{res},
  Print["u : ", u];
  If[Length[u] == 1, 
   Subscript[T, u[[1]]] - Subscript[\[Lambda], 1]^u[[1]], 
   v = SetPartitions[Length[u]];
   aux[v_] := Sum[u[[v[[i]]]], {i, 1, Length[v]}];
   res = Map[aux, v, {2}];
   res = Drop[res, -1];
   Print[res];
   Product[Subscript[T, u[[i]]], {i, 1, Length[u]}] - 
    Sum[f[res[[i]]], {i, 1, Length[res]}]]]

Trouble using recursive function on list with Mathematica

1 Answers