How to inject segments of code into functions defined by SetDelayed

Question

I need to define a set of functions that are written in terms of common but lengthy expressions. To effect this, I want to inject abbreviations for such expressions into the RHS of SetDelayed of multiple functions. Something like this:

Clear[f, g];
Module[{abbrev = Sum[int[i], {i, 1, n}]},
  f[n_] := abbrev + y;
  g[n_] := abbrev^2;
  (*and so on*)
]

But it doesn't work. First, the n_ in the LHS is failing to match the n in the RHS. Second, the kernel first evaluates the RHS of abbrev before injecting it into the RHSs of f and g. In my program, that consumes time that could otherwise be saved.

What can I do to solve these problems?

With isn't working on my computer (Mathematica 10.2 on Mac OS X). What version are you using? — QuantumDot, Dec 21 '15 at 21:28
int[i] is a recursively defined symbolic function (the result is usually a polynomial plus some logarithms), y is a similar object (polynomial+logs) but known explicitly (no recursive code). — QuantumDot, Dec 21 '15 at 21:35
Ok, here is one way: (f[n_] := # + y; g[n_] := #^2;) &[ Sum[int[i], {i, 1, n}] ] there should be a duplicate somewhere. — Kuba, Dec 21 '15 at 21:36
Not the one I've thought about but I think it's good enough: 20766 — Kuba, Dec 21 '15 at 21:39
Above you say With isn;t working on your computer. This would normally be done using With. Can you show us what you get? — Mike Honeychurch, Dec 21 '15 at 22:07
@MikeHoneychurch Input f[3] gives Sum[int[i],{i,1,n}]+y. The n didn't get replaced by 3. — QuantumDot, Dec 21 '15 at 22:13

Mike Honeychurch · Accepted Answer · 2015-12-22T07:28:27.830

I'm not sure how robust this is. It is quick and dirty so to speak.

With[{abbrev := Sum[int[i], {i, 1, n$}]},
 f[n_] := abbrev + y;
 g[n_] := abbrev^2
 (*and so on*)]

...but I think @kuba's link provides better alternatives.

Edit

Such an alternative includes:

Clear[f, g];
Module[{abbrev := Sum[int[i], {i, 1, n}]},
 SetDelayed @@ {f[n_], abbrev + y};
 g[n_] := abbrev^2]

Where you do not have to modify the n with dollar signs. The explanation for why this works is given in the post by Mr Wizard and Leonid.

How to inject segments of code into functions defined by SetDelayed

1 Answers1