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Re: Complex Analysis using Mathematica
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52645] Re: [mg52621] Complex Analysis using Mathematica
*From*: DrBob <drbob at bigfoot.com>
*Date*: Sun, 5 Dec 2004 02:08:49 -0500 (EST)
*References*: <200412040908.EAA13455@smc.vnet.net>
*Reply-to*: drbob at bigfoot.com
*Sender*: owner-wri-mathgroup at wolfram.com
You haven't told us what you're trying to accomplish with all this, but here's a go anyway.
ComplexExpand assumes all the parameters are real, by DEFAULT.
lamda = a + I*b;
z = lamda*p;
toXY = Simplify[ComplexExpand[{Re[#1], Im[#1]}]] & ;
toXY[z]
{a*p, b*p}
{u, v} = toXY@TrigToExp@Sinh@z
{((1/2)*(-1 + E^(2*a*p))*
Cos[b*p])/E^(a*p),
((1/2)*(1 + E^(2*a*p))*
Sin[b*p])/E^(a*p)}
Not sure why you want u[x,y] and v[x,y], since a, b, and p are the variables.
Bobby
On Sat, 4 Dec 2004 04:08:00 -0500 (EST), Pratik Desai <pdesai1 at umbc.edu> 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
>
>
>
>
>
--
DrBob at bigfoot.com
www.eclecticdreams.net
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