Use the Euler relation to split a function into complex and imaginary parts

조회 수: 10 (최근 30일)
Hi, I found a thread considering to split a function into Re and Im, and used it's command:
if true
% code
end
y = C*exp(-(x*(g*i + (- 2*g^2 + E)^(1/2)))/h) + exp((g*i - (- 2*g^2 + E)^(1/2))/h)*exp(-(x*(g*1i - (- 2*g^2 + E)^(1/2)))/h)*(pi - C*exp(-(g*1i + (- 2*g^2 + E)^(1/2))/h))
y = rewrite(y, 'sincos')
Ref = simplify(collect(real(y))) % Real part
Imf = simplify(collect(imag(y))) % Imaginary part
however, the result does not split Im and Re parts:
Ref =
real((cos((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199) + sin((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199)* 1i)*(cos((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199) - sin((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199)* 1i)*(pi - C*cos((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199) + C*sin((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199)*1i)) + real(C*(cos((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199) - sin((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199)*1i))
Imf =
imag((cos((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199) + sin((524288*x*(67108864*15769878386734594^(1/2) - 5959077882784213))/616503364953199)*1i)*(cos((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199) - sin((35184372088832*15769878386734594^(1/2))/616503364953199 - 3124273025009169465344/616503364953199)*1i)*(pi - C*cos((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199) + C*sin((35184372088832*15769878386734594^(1/2))/616503364953199 + 3124273025009169465344/616503364953199)*1i)) + imag(C*(cos((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199) - sin((524288*x*(67108864*15769878386734594^(1/2) + 5959077882784213))/616503364953199)*1i))
Is this a technicallyimpossible case?
Thanks

채택된 답변

John D'Errico
John D'Errico 2018년 1월 2일
편집: John D'Errico 2018년 1월 2일
You CANNOT use real and imag as you have done. At least, it will be a waste of time.
A quick glance shows that at least C and x are still symbolic variables. What values do they take on? Who knows? So segregating a long expression that includes those variables into real and imaginary parts is impossible.
Depending on the values of C and x (and maybe some other variables that I missed) all it can say is that the real part is real(*stuff*) and the imaginary part is imag(*stuff*). That is exactly what the symbolic toolbox returned.
Addendum: you can use vpa to simplify the expression, resolving some of the nasty looking numbers. But until explicit numeric values for C and x are supplied, you cannot reduce the result into real and imaginary parts.

추가 답변 (1개)

Walter Roberson
Walter Roberson 2018년 1월 2일
If you add assumptions to the symbolic variables then MATLAB can potentially do the appropriate separation. In particular you can use
syms x real
to add an assumption of real value to x

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