Re: Complex Analysis using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg52628] Re: [mg52621] Complex Analysis using Mathematica
- From: "David Park" <djmp at earthlink.net>
- Date: Sun, 5 Dec 2004 02:08:04 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Pratik, I may not understand your question, but why not just use ComplexExpand. I don't think you need all those definitions. ComplexExpand assumes that symbols are Real, unless you tell it otherwise. Sinh[p(a + b I)] ComplexExpand[%] Sinh[(a + I*b)*p] I*Cosh[a*p]*Sin[b*p] + Cos[b*p]*Sinh[a*p] Or if you want to define real and imaginary part functions u[p_][x_, y_] = ComplexExpand[Re[Sinh[p(a + b I)]]] Cos[b p] Sinh[a p] v[p_][x_, y_] = ComplexExpand[Im[Sinh[p(a + b I)]]] Cosh[a p] Sin[b p] ComplexExpand is the real workhorse in doing complex analysis with Mathematica. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Pratik Desai [mailto:pdesai1 at umbc.edu] To: mathgroup at smc.vnet.net Here we go again, I have to define a complex function So I go through this procedure to define that the variables are really "real" TagSet[p, Im[p], 0]; TagSet[a, Im[a], 0]; TagSet[b, Im[b], 0]; TagSet[p, Re[p], p]; TagSet[a, Re[a], a]; TagSet[b, Re[b], b]; lamda = a + I*b z = ComplexExpand[lamda*p] x=Re[z] y=Im[z] TagSet[u, Im[u[x, y]], 0]; TagSet[v, Im[v[x, y]], 0]; TagSet[x, Re[x], x]; TagSet[y, Re[y], y]; TagSet[u, Re[u[x, y]], u[x, y]]; TagSet[v, Re[v[x, y]], v[x, y]]; Then I define my actual function u1 = TrigToExp[Sinh[z]] (*By this time I have realized that Mathematica or for that matter most of the CAS work better with exponentials when it comes to complex analysis*) u[x, y] = Re[u1] v[x, y] = Im[u1] The problem I face is that the software is not able to identify x and y as I have defined above. May be I am making a trivial mistake. Please advise Thanks in advance Pratik Desai