       Re: When is Exp[z]==Exp[w]??

• To: mathgroup at smc.vnet.net
• Subject: [mg113657] Re: When is Exp[z]==Exp[w]??
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sat, 6 Nov 2010 05:00:39 -0500 (EST)

```OK, but it's still strange to have to add that.

And that also leaves the peculiar term Log[E^z], which is also totally
redundant (even though Log[E^z] need not equal z, but still it will
differe from z by an integer multiple of 2 Pi I).

On 11/5/2010 7:06 AM, Bob Hanlon wrote:
>
> You can "force" it by being just as redundant.
>
> Simplify[Reduce[Exp[z] == Exp[w], {z, w}], E^z != 0]
>
> Element[C, Integers]&&
>     w == 2*I*Pi*C + Log[E^z]
>
>
> Bob Hanlon
>
> ---- Murray Eisenberg<murray at math.umass.edu>  wrote:
>
> =============
> Mathematica 7.0.1 gives (as InputForm of the result):
>
>     Reduce[Exp[z]==Exp[w],{z,w}]
> Element[C, Integers]&&  E^z != 0&&  w == (2*I)*Pi*C + Log[E^z]
>
> How can Mathematica be forced to simplify this to what is the fact,
> namely, the following?
>
>     Element[C, Integers]&&  w == (2*I)*Pi*C + z
>
> (At the very least, certainly the expression E^z != 0 is redundant.)
>

--
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

```

• Prev by Date: Re: adding lists term by term
• Next by Date: Re: Embed extra info?
• Previous by thread: Re: When is Exp[z]==Exp[w]??
• Next by thread: Re: When is Exp[z]==Exp[w]??