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MathGroup Archive 1993

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the problem

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: the problem
  • From: ECORTES at indyvax.iupui.edu
  • Date: Wed, 29 Sep 1993 14:36:17 -0500

I have two algebraic coupled equations for two complex parameters a and b.
In the first equation I have the integral over x (real) from 0 to 1 of the 
function: x/(a^2+b^2) and we have this integral equal to a given complex 
constant u; in the second equation I have the integral over x (real) from 0 
to 1 of the function x Exp[-b/x]/(ax+b) and we have this integral equal to 
another given complex constant v. (We need the restriction Re[b]>0.)
Now I have two difficulties in handling this kind of problem with 
Mathematica, and of course I have to deal with some more complicated 
expressions, but this example gives the idea:
1) The first difficulty is that if I use the command ComplexExpand to 
rationalize each integrand and separate the real and imaginary parts for 
each integration, it gives me in the denominator the expression:
	Abs[ of a complex quatity] 
without evaluating it explicitly, and this is because the argument is not 
numerical. I would need the complete algebraic separation in order to do 
each integration.
2) The other problem is the next step, which is how to solve the system of  
4 coupled equations for the real parameters:
Re[a], Im[a], Re[b] and Im[b].
If we define the first integration as Y1 and the second as Y2, is it 
possible to use the command
FindRoot[{Re[Y1]==Re[u], Im[Y1]==Im[u], Re[Y2]==Re[v], Im[Y2]==Im[v],
{Re[a], a10}, {Im[a], a20}, {Re[b],b10}, {Im[b],b20}]?

If this idea is not clear enough, I could send a letter with the equations 
and other comments to the Math Group.
Thank you for your kindness
Emilio Cortes




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