Re: Can I get ComplexExpand to really work?

*To*: mathgroup at smc.vnet.net*Subject*: [mg14553] Re: Can I get ComplexExpand to really work?*From*: Hans Staugaard Nielsen <hsn at imf.au.dk>*Date*: Fri, 30 Oct 1998 03:07:26 -0500*Organization*: University of Aarhus, Department of Computer Science (DAIMI)*References*: <719f5p$lc6@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Try this Integrate[E^(I a x^2),{x,-Infinity,Infinity},Assumptions->{Im[a]==0,a>0}] Hans Topher Cawlfield wrote: > 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