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Re: Complex Analysis using Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg52632] Re: [mg52621] Complex Analysis using Mathematica
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 5 Dec 2004 02:08:09 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <200412040908.EAA13455@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

Why not just the following?

      u[x_, y_] := ComplexExpand[Re[Sinh[x + I y]]]
      v[x_, y_] := ComplexExpand[Im[Sinh[x + I y]]]
      {u[x, y], v[x, y]}
   {Cos[y] Sinh[x], Cosh[x] Sin[y]}

For related matters, you might want to take a look at notebook 
CartesianPolarForms.nb on the Files page at:

   http://www.math.umass.edu/Courses/Math_421

That includes examples of using the neat utility functions ReImExpand 
and ToCoordinates and ToComplex from David Park's Cardano2 application.


Pratik Desai wrote:
> 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
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

• References:
  • Complex Analysis using Mathematica
    • From: "Pratik Desai" <pdesai1@umbc.edu>