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Mma10 mystery: Failure of pure function substitution with Interpretation?

Posted 10 years ago

I had code to display with subscripts from http://mathematica.stackexchange.com/questions/30884/ which is now breaking an innocuous pure function substitution as in http://mathematica.stackexchange.com/questions/51103 The substitution itself has nothing to do with any actual display of subscripts.

I am having a little trouble creating a minimal example, but here goes. First, in Mathematica 10 try the pre-side effect code:

 ODE = F'[z] == g F[z]
Fguess = {F-> (Exp[a #]&)}
ODE /. Fguess //FullSimplify

(* => e^(a z)(a - g)== 0, the proper output *)

Now, add in the following code, stripped down from that previous example. This isn't intended to actually have anything to do with the substitution, but is causing side effects.

NotScriptedVarQ[z_] := ! MemberQ[$scriptedfunctionsvars, z, Infinity];
makeDef[pat_, body_] := (MakeBoxes[a : pat, fmt_] := 
ToBoxes[Interpretation[body, a], fmt] /; 
 MemberQ[Union[$scriptedconstants, $scriptedfunctions], 
  Unevaluated@h]; )
makeDef[h_Symbol[argssub__?NotScriptedVarQ], h[argssub]];
$scriptedconstants = {};
$scriptedfunctions = {};
$scriptedfunctionsvars = {};

Now, try the substitution and a few permutations:

 (*The ODE and guess are*)
ODE = F'[z] == g F[z]
Fguess = {F -> (Exp[a #] &)}
(*Substituting NOW DOESN'T work*)
ODE /. Fguess // FullSimplify
(*But if the guess is NOT displayed before the substitution(i.e., no ;) WORKS!*)
Fguess = {F -> (Exp[a #] &)};
ODE /. Fguess // FullSimplify
(*And if the guess is substituted directly, IT WORKS!*)
F'[z] == g F[z] /. {F -> (Exp[a #] &)} // FullSimplify

As this used to work fine in Mathematica 9, I imagine this is a bug. If so, any idea of a workaround? One last thing I learned: If you change the definition so that NotScriptedVarQ[z_] := True, or change it to always be False, the bug is no longer there!

POSTED BY: Jesse Perla
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