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Re: Complex Analysis using Mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52639] Re: [mg52621] Complex Analysis using Mathematica
*From*: "Pratik Desai" <pdesai1 at umbc.edu>
*Date*: Sun, 5 Dec 2004 02:08:26 -0500 (EST)
*References*: <NDBBJGNHKLMPLILOIPPOCEIPEEAA.djmp@earthlink.net>
*Sender*: owner-wri-mathgroup at wolfram.com
I am sorry I should have mentioned that I am trying to do the analysis
symbolically.As per Dr.Eisenberg's suggestion I have downloaded your add-on
package Cartano and it is quite helpful.
Yet whenever I have to use a new variable I have to make sure that
Mathematica understands that it is real. Things are especially tricky when
one is trying to define conjugates and complex inner products of matrix
populated by functions defined on Hilbert space.Do you have a package for
the latter :)
Thanks again for your help
Pratik Desai
----- Original Message -----
From: "David Park" <djmp at earthlink.net>
To: mathgroup at smc.vnet.net
Subject: [mg52639] Re: [mg52621] Complex Analysis using Mathematica
> 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
>
>
>
>
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