Re: Re: Complex Analysis using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg52706] Re: [mg52656] Re: Complex Analysis using Mathematica
- From: "Pratik Desai" <pdesai1 at umbc.edu>
- Date: Thu, 9 Dec 2004 20:23:49 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
David,
Thank you for your response
Basically, what I am trying to accomplish is to prove orthogonal conditions
of complex eigenfunctions
I have a matrix A
A=I-Identity matrix
And i have the state space eigenvectors
phi_real={Re[v]-Im[v],lamda*Re[v]-Im[v]}
phi_imag={Re[v]+Im[v],lamda*Re[v]+Im[v]}
phi=phi_real+i*phi_imag
Where v is the eigenfunction say Sinh[lamda*x]
<A*phi,phi>=2*I =
--><w1,w2>=Integrate[Transpose[w1]*Conjugate[w2]],{x,0,1}]-->(I
don't know whether this is the correct way to go about it)
lamda is some imaginary eigenvalue, lamda=a+I*b
Hope this helps
Thanks again,
Best Regards,
Pratik Desai
----- Original Message -----
From: "David Bailey" <dave at Remove_Thisdbailey.co.uk>
To: mathgroup at smc.vnet.net
Subject: [mg52706] [mg52656] Re: Complex Analysis using Mathematica
> 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
>>
>>
> Pratik,
>
> I think the most useful way to procede would be if you gave an explicit,
> simple example of the kind of input you would like to give Mathematica
> and the kind of output you would like it to produce. I am fairly certain
> that if you do this you will get a whole bunch of replies telling you
> how to achieve it and they will look a lot neater than what you have at
> present!
>
> Regards,
>
> David Bailey
>