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[1], Integers]&& > w == 2*I*Pi*C[1] + 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[1], Integers]&& E^z != 0&& w == (2*I)*Pi*C[1] + Log[E^z] > > How can Mathematica be forced to simplify this to what is the fact, > namely, the following? > > Element[C[1], Integers]&& w == (2*I)*Pi*C[1] + 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