MathGroup Archive 1997

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Mapping onto a held expression

One way to make my Mathematica functions easier to read by non-programmers
is to use Subscript notation. For example, the set of elastic moduli
{Subscript[e,11],Subscript[e,22],Subscript[e,12],..} is easier to read (in
the front end, not here!) than {e11,e22,e12,..}. So I've written a function
toSubcript[var_Symbol,root_] which converts from flat to subscripted
notation. This function examines the variable name to see if it begins with
root. If so, then it makes the rest of the name a subscript. If not, or if
the "variable" is not a symbol, then it returns var. For example,

toSubscript[e11,e] yields Subscript[e,11]
toSubscript[g12,e] yields g12
toSubscript[123,1] yields 123

Now I want to map this function onto all the leaves of an
expression--typically a module definition. For example,

myfunct[disp_List]/; Length[disp]==2 := 
     Module[{e11=3,e22=4}, {e11,e22}.disp],

is supposed to yield

myfunct[disp_List]/; Length[disp]==2 := 

My problem is that I have been unable to find a way to apply my function to
the leaves of the expression without letting Mathematica attempt to
evaluate the expression. If I wrap my function in Unevaluated[], then this
wrapper comes off part-way through the mapping process and I get a mess. If
I wrap my function in Hold[], then the toSubscript function is mapped, but
remains unevaluated:

       (toSubscript[#1, e] & )[
       Blank[(toSubscript[#1, e] & )[
         List]]]] /; 
     Length[(toSubscript[#1, e] & )[
        disp]] == 
      (toSubscript[#1, e] & )[2] := 
    Module[{(toSubscript[#1, e] & )[
        e11] = 
       (toSubscript[#1, e] & )[3], 
      (toSubscript[#1, e] & )[e22] = 
       (toSubscript[#1, e] & )[4]}, 
     {(toSubscript[#1, e] & )[e11], 
       (toSubscript[#1, e] & )[e22]} . 
      (toSubscript[#1, e] & )[disp]]

This state of affairs leads me to two questions:

(1) Given an expression like the held one above, is there a way to let the
functions toSubscript evaluate within this expression without letting the
expression itself evaluate?

(2) Should I be doing this another way?

I think this concept is useful, perhaps to other people. Any suggestions
would be appreciated. Thanks.

Tom Burton

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