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 --Boundary (ID pzvat0CSAlpCGSqTarvSfg)--