Recursive ReplaceRepeated fails

Questions
1

Hi !

I’ve developed a little function to split an exponential in 2 if its argument is a sum :

replace[e_] := e //. Exp[x_ + y_] :> HoldForm[E^x E^y];

Here is the Failing case :

xx = ReleaseHold[
   E^(-(((1 + r) (t - t1))/(2 Q tau)) - t/tau1 - t1/tau1)];
xx = replace[xx]; xx = replace[xx]

Here is the reult :

1351func.png
1351func.png364×118 1.35 KB

May I ask you why the function does not operate recursively despite the use of //. (ReplaceRepeated[ ]) ?
Cheers!

2

If you look closely at the output of replace, you see that there is nothing that matches the form:

Exp[x_ + y_]

Instead, you only see “E” to the power of “some product”. Yes this might be a product of sums, but Mathematica will not expand out the products unless it is told to do so.

You may consider using Expand first:

exponent = Expand[(-(((1 + r) (t - t1))/(2 Q tau)) - t/tau1 - t1/tau1)]

You can then run:

replace[Exp[exponent]]

Or you may consider building Expand into your definition of replace.

3

Many thanks Sean !
Absent-mindedness affair !
Regards

4

Dear Sean,

I 'am trapped in a new pitfall.. here my new code :

replace[e_] := Module[
   {z},
   z = e /. Exp[x_] :> Exp[Expand[x]];
   z = z //. Exp[u_ + v_] :> HoldForm[E^u E^v]
   ];

Here is the result :

1024func.png
1024func.png1148×104 1.89 KB

May I ask you how to remove this Expand[] from the result ?

Regards

Sylvain

5

You could do

output /. Expand -> Identity

…
It should do it automatically though…

6

Thanks Sanders !