Can I get ComplexExpand to really work?
- To: mathgroup at smc.vnet.net
- Subject: [mg14536] Can I get ComplexExpand to really work?
- From: Topher Cawlfield <cawlfiel at uiuc.edu>
- Date: Thu, 29 Oct 1998 04:33:31 -0500
- Organization: University of Illinois at Champaign-Urbana
- Sender: owner-wri-mathgroup at wolfram.com
Hi, I'm having lots of problems getting Mathematica to make simplifying assumptions. It always seems to want to produce horribly complex results because it assumes every variable is complex. I wish I had better control of that. In fact, it would also be nice if I could assure Mathematica that certain variables were positive as well. It sounds like the function ComplexExpand should do the trick, at least by assuming that variables are real unless otherwise specified. But it doesn't really seem to work for me. Here's an example: ComplexExpand[Integrate[E^(I a x^2), {x, -Infinity, Infinity}]] produces: If[Im[a] == 0, Sqrt[Pi/2] (1 + I Sign[a]) / (a^2)^(1/4), Integrate[E^(I a x^2), {x, -Infinity, Infinity}]] But if it really was assuming that 'a' was real, then it should know that Im[a] == 0! If I could also tell it that 'a' was positive, the answer would be: (1 + I) Sqrt[Pi/a] or better still, Sqrt[2 Pi I / a] This is much simpler, and is the answer I want. Of course, my real application of this problem is much more complicated, but ultimately comes down to doing that integral (several times over). The right answer should be just about that simple, but instead Mathematica gives me about 5 pages of output. Is there any hope of getting reasonable symbolic results here? - Topher Cawlfield