Please help me to make sense of the ways to use the simplify function. In this particular case Maple does some computation and gives me some huge output which I paste below. When I try to simplify the huge output Maple just hangs. But if I use varied commands of simplify detailed below such as simplify(huge_output,symbolic)  or  simplify(huge_output,size)  Maple gives me an output but none of the output are equal to each other and I also noticed that in one instance...

 Okay so I can see how to get the poles. But I have some further questions.

1) For beta AND Q both GREATER THAN 0 WHICH poles have positive imaginary part and is there a PROGRAMMATIC way of selecting these ones?

2) How do I calculate the residue at these poles? The approach given by Alec above seems useful and is much...

> I would like to integrate the following expression that I call s2

 > s2 := (1/2/Pi+2*Q*u/(1+u^2))^2/((1+beta^2*(1/2/Pi+2*Q*u/(1+u^2))^2)*(1+u^2));

 using the residue theorem. To do this I first want to find the roots (poles) of the expression. I do this by solving for the denominator equal to zero as below.

> s3:=(1+beta^2*(1/2/Pi+2*Q*u/(1+u^2))^2)*(1+u^2);

Hello All,

From the list

t1 := [((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2), -((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2+8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2), ((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2))^(1/2), -((-4*Pi^2-beta^2+4*beta^2*Q^2*Pi^2-8*I*Pi^2*beta*Q)/(4*Pi^2+beta^2-4*beta^2*Q*Pi+4*beta^2*Q^2*Pi^2...

I have the following variable

s1:=(1/2/Pi+Q*cos(k*phi))^3*cos(k*phi)/(1+beta^2*(1/2/Pi+Q*cos(k*phi))^2)^2;

and then I make a substitution as follows

s2:= subs(cos(k*phi)=((1-u^2) / (1+u^2)),sin(k*phi)=((2*u) / (1+u^2)), s1)*1/(1 + u^2);  -----(1)

Now if I set up a function f that maps u to the right hand side of (1) above as follows

f:=u->(1/2/Pi+Q*(1-u^2)/(1+u^2...