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MathGroup Archive 2004

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Re: transforming exponential of sums into product of exponentials

  • To: mathgroup at smc.vnet.net
  • Subject: [mg48692] Re: transforming exponential of sums into product of exponentials
  • From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
  • Date: Thu, 10 Jun 2004 02:44:30 -0400 (EDT)
  • References: <ca6igm$j2s$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

The reason for this behaviour is that your rules do indeed get applied to
give the result Exp[a]Exp[b], but then Mathematica "helpfully" simplifies
this back to Exp[x+y] to give the result you see displayed.

I generally find the easiest way around this sort of problem is to "fool"
Mathematica so that it doesn't recognise the expression that you want to be
output as one that it can "helpfully" simplify for you.

You might try something like

Exp[x + y] /. Exp[a_ + b_] -> exp[a]exp[b]

which gives the output

exp[x] exp[y]

because Mathematica doesn't recognise the function exp[x] as one that it
knows anything about, and indeed it is an entirely new function that you
have decided to use. To make Mathematica do anything with exp you would need
to define what is allowed.

For instance making the following definition

exp /: exp[x_]exp[y_] := exp[x + y]

causes Mathematica to give the following output when evaluating Exp[x + y]
/. Exp[a_ + b_] -> exp[a]exp[b]

exp[x + y]

Steve Luttrell

"Karim Mehadhebi" <Karim.Mehadhebi at wanadoo.fr> wrote in message
news:ca6igm$j2s$1 at smc.vnet.net...
> Dear All,
>
> I can not understand why Mathmatica refuses to apply rules which transform
> exponenials of sums into product of exponentails.
>
> For instance,
> f[x+y] /. f[a_ + b_]-> f[a] f[b] returns f[x] f[y],
> whereas
> Exp[x+y] /. Exp[a_+b_]->Exp[a]Exp[b] still returns Exp[x+y]
>
> Any help greatly appreciated
>
>
>
>
>


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