What I'm doing wrong? 1st function works as expected but the 2nd one doesn't. What I want is to enter an algebraic expression and two numeric constants and get the same result as with the first function. Thanks in advance.
f[u_, v_] := Module[{g}, g[x_] := 3 x - 2; g[u] + g[v]]
f[2, 3]
(* 11 *)
h[m_, u_, v_] := Module[{g}, g[x_] := m; g[u] + g[v]]
h[3 x - 2, 2, 3]
(* -4 + 6 x *)
Updated to fix my first answer
(I had some lingering definitions that misled me to thinking my first answer worked. Here's an update that should work)
I think it would be better to include the independent variable explicitly in your function. For example:
h[m_, x_, u_, v_] := With[{g = Function[x, m]}, g[u]+g[v]]
(The above definition gets a benign syntax warning about repeated symbols in a nested scoping construct. If this bothers you, you can use the equivalent alternative):
h[m_, x_, u_, v_] := With[{g = Function @@ Hold[x, m]}, g[u] + g[v]]
Then:
h[3x - 2, x, 2, 3]
11
On the other hand, we can repair your method by using Activate and Inactive to get around the lexical renaming that happens with SetDelayed:
h[m_, u_, v_] := Module[{g},
Activate @ Inactive[SetDelayed][g[x_],m];
g[u]+g[v]
]
Then:
h[3x - 2, 2, 3]
11
ClearAll[h1]
h1[m_, u_, v_] := Module[{g},
g[y_] := Block[{x = y}, m];
g[u] + g[v]]
h1[3 x - 2, 2, 3]
11
Alternatively,
ClearAll[h2]
h2[m_, u_, v_] := Module[{g},
g[y_] := m /. First[Cases[m, _Symbol, Infinity]] -> y;
g[u] + g[v]]
h2[3 x - 2, 2, 3]
11
h2[3 foo - 2, 2, 3]
11
Change your approach: pass the function.
h2[g_, u_, v_] := g[u] + g[v]
h2[x \[Function] 3 x - 2, 2, 3]
If you are stuck with the expression, you can still do this:
xpr = 3 x - 2;
h2[x \[Function] Evaluate@xpr, 2, 3]
