Re: More strange behavior by ComplexExpand

*To*: mathgroup at smc.vnet.net*Subject*: [mg60621] Re: More strange behavior by ComplexExpand*From*: Peter Pein <petsie at dordos.net>*Date*: Thu, 22 Sep 2005 02:08:14 -0400 (EDT)*References*: <dgr3c0$8g2$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Raul Martinez schrieb: > To Mathgroup, > > I use Mathematica 5.2 with Mac OS X (Tiger). > > Add the following to a recent thread on the sometimes strange > behavior of ComplexExpand. > > I used ComplexExpand with an argument in which all the variables in > the argument of the function are real. Since ComplexExpand is > supposed to assume that all variables are real by default, one would > expect ComplexExpand to return the expression without change, but it > doesn't. Instead, here is what it does: > > In[1]:= > > ComplexExpand[ (a / Pi)^(1/4) Exp[ -(a t^2)/2 ] ] > > Out[2]:= > > (Exp[-a t^2] Sqrt[Exp[a t^2]] (a^2)^(1/8) Cos[Arg[a] / 4]) / Pi^ > (1/4) + i (Exp[-a t^2] Sqrt[Exp[a t^2]] (a^2)^(1/8) Sin[Arg[a] / > 4]) / Pi^(1/4). > > I have inserted parentheses in a few places to improve the legibility > of the expressions. > > ComplexExpand treats the variable "a" as complex, but "t" as real. No, ComplexExpand treats your expression as complex. Have a look at (a/Pi)^(1/4)*Exp[-(a*t^2)/2] /. a->-1 (0.5311259660135985 + 0.5311259660135984*I)*E^(0.5*t^2) > This is puzzling to say the least. Moreover, it renders a^(1/4) as > (a^2)^(1/8), which seems bizarre. ((-1)^2)^(1/8) is easyer to handle than (-1)^(1/4). ComplexExpand _treats_ a as real and gets rid of the negative case. > > My interest is not in obtaining the correct result, which is easy to > do. Rather, I bring this up as yet another example of the > unreliability of ComplexExpand. In case anyone is wondering why I > would use ComplexExpand on an expression I know to be real, the > reason is that the expression in question is a factor in a larger > expression that contains complex variables. Applied to the larger > expression, ComplexExpand returned an obviously incorrect expansion > that I traced to the treatment of the example shown above. > Well, I guess you are thinking of FullSimplify[ComplexExpand[(a/Pi)^(1/4)*Exp[-(a*t^2)/2]], a > 0] a^(1/4)/(Sqrt[E^(a*t^2)]*Pi^(1/4)) > I welcome comments and suggestions. > > Thanks in advance, > > Raul Martinez > > > > > > -- Peter Pein, Berlin GnuPG Key ID: 0xA34C5A82 http://people.freenet.de/Peter_Berlin/