MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: More strange behavior by ComplexExpand

  • To: mathgroup at
  • Subject: [mg60615] Re: More strange behavior by ComplexExpand
  • From: "dennis" <dwangsness at>
  • Date: Thu, 22 Sep 2005 02:08:09 -0400 (EDT)
  • References: <dgr3c0$8g2$>
  • Sender: owner-wri-mathgroup at

Raul Martinez wrote:
> 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


The problem is that a could be negative and still real, in which case
raising it to a fractional power results in a complex number.  I don't
think there is an error, you are just assuming a is positive.


  • Prev by Date: Re: Mathemaica 5.2 are the 64 Bit an illusion !!!....?
  • Next by Date: Re: Bugs in Mathematica 5+
  • Previous by thread: Re: More strange behavior by ComplexExpand
  • Next by thread: Re: More strange behavior by ComplexExpand