Alternative to coeffs, giving incorrect answers, symbolic function coeffs

Hello, I have an expression in symbolic that looks like the following, as well as the following commands:

expr =

delta*lambda*g(2) + (delta*k*exp(-Ti*sigma*2i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (delta*k*exp(Ti*sigma*2i)*exp((To*wbar*1i)/2)*g(2))/2 + (delta*lambda*exp(-Ti*sigma*4i)*exp(-To*wbar*1i)*g(2))/2 + (delta*lambda*exp(Ti*sigma*4i)*exp(To*wbar*1i)*g(2))/2 + (A*delta*exp(-Ti*sigma*2i)*exp(To*wbar*1i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (A*delta*exp(Ti*sigma*2i)*exp(To*wbar*1i)*exp((To*wbar*1i)/2)*g(2))/2 + (Abar*delta*exp(-Ti*sigma*2i)*exp(-To*wbar*1i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (Abar*delta*exp(Ti*sigma*2i)*exp(-To*wbar*1i)*exp((To*wbar*1i)/2)*g(2))/2

[a,b]=coeffs(  expr      ,exp(i*wbar*To)  );
number=find(b==exp(i*wbar*To));
Terms=a(number)

Problem is Terms is giving me the following result:

(delta*lambda*exp(Ti*sigma*4i)*g(2))/2 + (A*delta*exp(-Ti*sigma*2i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (A*delta*exp(Ti*sigma*2i)*exp((To*wbar*1i)/2)*g(2))/2

Which is wrong, as I dont want the bolded terms, as they are not exactly what I specified in the coeffs, I only want the underlined, italic, bolded part.

Is there anyway to fix this so it gives me the values with exactly exp(i*wbar*To) , or alternative methods that might work better ?

Answer 1

[Walter Roberson]

delta*lambda*g(2) + (delta*k*exp(-Ti*sigma*2i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (delta*k*exp(Ti*sigma*2i)*exp((To*wbar*1i)/2)*g(2))/2 + (delta*lambda*exp(-Ti*sigma*4i)*exp(-To*wbar*1i)*g(2))/2 + (delta*lambda*exp(Ti*sigma*4i)*exp(To*wbar*1i)*g(2))/2 + (A*delta*exp(-Ti*sigma*2i)*exp(To*wbar*1i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (A*delta*exp(Ti*sigma*2i)*exp(To*wbar*1i)*exp((To*wbar*1i)/2)*g(2))/2 + (Abar*delta*exp(-Ti*sigma*2i)*exp(-To*wbar*1i)*exp(-(To*wbar*1i)/2)*g(2))/2 + (Abar*delta*exp(Ti*sigma*2i)*exp(-To*wbar*1i)*exp((To*wbar*1i)/2)*g(2))/2
                                                                                                                                                                                                                                ^^^^^^^^^^^^^^                                      ^^^^^^^^^^^^^^^                                                          ^^^^^^^^^^^^^^^
                                                                                                                                                                                                                                

Three exact copies of the same subexpression exp(To*wbar*1i) . No matter whether you say that that is the same as exp(i*wbar*To) (different order of multiplication which does not matter because communtivity), you have to agree that all three need to be treated the same way. If you match even one of them then you have to match all three. You therefore should not expect that only one term should come out of coeffs.

[Julio Beatriz]

Thank you very much, I see what you are saying. I was hoping matlab would combine the exponents, like exp(To*wbar*1i)*exp((To*wbar*1i)/2) into one and treat it differently .

This is since mathematica seems to be able to do something similar to this just fine, so I assumed matlab would, but now I see this is not the case. I think i'll continue trying to think of a solution to this.

[Walter Roberson]

expand() the expression. Or simplify(). Or rewrite() 'sincos' and then simplify() and possibly rewrite back to 'exp' and possibly simplify() again.

[Julio Beatriz]

Thank you very much, I have tried expand and simplify, but they dont work. As for converting the exp's that might work. Thank you for help, i really appreciate it.