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More strange behavior by ComplexExpand

• To: mathgroup at smc.vnet.net
• Subject: [mg60603] More strange behavior by ComplexExpand
• From: Raul Martinez <raulm231 at comcast.net>
• Date: Wed, 21 Sep 2005 03:20:48 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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.  
This is puzzling to say the least. Moreover, it renders a^(1/4) as  
(a^2)^(1/8), which seems bizarre.

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.

I welcome comments and suggestions.

Thanks in advance,

Raul Martinez

• Follow-Ups:
  • Re: More strange behavior by ComplexExpand
    • From: Pratik Desai <pdesai1@umbc.edu>
  • Re: More strange behavior by ComplexExpand
    • From: Andrzej Kozlowski <andrzej@yhc.att.ne.jp>