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Question: differentiating and taking limit of complex vector valued function

Question:differentiating and taking limit of complex vector valued function

paul1981 5
May 06 2014
1

I would like to do the following with maple let

omega := z -> 2*<Re(z), Im(z), 1>/(1+abs(z)^2):

and

phi := -> z (l*z+a)/(1-l*conjugate(a)*z):

where a is complex and l is real. I consider Omega=omega(phi(z)) and i would like to evaluate diff(Omega,x) diff(Omega,y) but also compute some limit like

> expr := omega(phi(1/e));
> Omega := simplify(map(limit, expr, e = 0));
> expr2 := (omega(phi(1/(e^2*conjugate(z))))-Omega)/e^2; 
> H := limit(expr2, e = 0);

Unfortunately i have tried every thing (Vector Calculus , Complex...) and i have always a probleme either because i work with vector or because the variable is complex.

Does someone have any idea of the good way to code such a problem? Thx

 
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