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How to divide a polynomial into two polynomials, one with the odd coefficients of w and the other with the even coefficients of w?

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Alex Muniz
Alex Muniz 2022-10-24
编辑： Torsten 2022-10-24
I have the polynomial p(w) described below and I need to split it into two polynomials one with odd coefficients of w and the other with even coefficients of w, how can I do that?
P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*(ki - 25*kd + 41/5)
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Alex Muniz
Alex Muniz 2022-10-24
kp is a constant. The polynomial is a function of w.
I would like two polynomials as follows:
P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*( ki - 25*kd + 41/5)
P(w) = P_odd(w) + P_even(w)
P_odd(w) = w^3*(kp + 33/5)*1i + w*(25*kp - 1)*1i
P_even(w) = -w^4*(kd + 1) + w^2*( ki - 25*kd + 41/5) + 25*ki

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Torsten
Torsten 2022-10-24
编辑：Torsten 2022-10-24
Ran in:
Odd part:
(P(w) - P(-w))/2
Even part:
(P(w) + P(-w))/2
syms w kd ki kp
P(w) = 25*ki - w^4*(kd + 1) + w*(25*kp - 1)*1i + w^3*(kp + 33/5)*1i + w^2*( ki - 25*kd + 41/5);
P_odd(w) = (P(w)-P(-w))/2
P_odd(w) = 
P_even(w) = (P(w) + P(-w))/2
P_even(w) = 
P_odd(w) + P_even(w) - P(w)
ans = 
0

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