How do I get the coefficients of a 9th order symbolic polynom without root on them?

Question

Javier 2019-9-16

0
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https://ww2.mathworks.cn/matlabcentral/answers/480599-how-do-i-get-the-coefficients-of-a-9th-order-symbolic-polynom-without-root-on-them

编辑： Javier 2019-9-18

Hello,

I am using the symbolic toolbox to get the roots of a polynom order 9th. The symbolic solution that I am gettting from solve is the one below

(root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)*(- b3*a1^2*b1^2*b2^2*b5 + b4*a1^2*b1*b2^3*b5 + 2*b3*a1*a2*b1^3*b2*b5 - 2*b4*a1*a2*b1^2*b2^2*b5 - 2*a1*a2*b2^4*b5^2 - a4*b3*a1*b1^4*b2 + a4*b4*a1*b1^3*b2^2 + a4*a1*b1*b2^4*b5 - b3*a2^2*b1^4*b5 + b4*a2^2*b1^3*b2*b5 + a2^2*b1*b2^3*b5^2 + a4*b3*a2*b1^5 - a4*b4*a2*b1^4*b2 - a4*a2*b1^2*b2^3*b5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^3*(- a1^2*b1^3*b2*b3^2 + 2*a1^2*b1^2*b2^2*b3*b4 - a1^2*b1*b2^3*b4^2 + 2*b5*a1^2*b2^4*b3 + a1*a2*b1^4*b3^2 - 3*a1*a2*b1^3*b2*b3*b4 + 2*a1*a2*b1^2*b2^2*b4^2 - 3*b5*a1*a2*b1*b2^3*b3 + 4*b5*a1*a2*b2^4*b4 - 2*a5*b5*a1*b2^5 + a2^2*b1^4*b3*b4 - a2^2*b1^3*b2*b4^2 + b5*a2^2*b1^2*b2^2*b3 - 2*b5*a2^2*b1*b2^3*b4 - 2*b5*a2*a4*b2^5 + a3^2*b2^5*b3 + a4^2*b1*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^2*(- b3*a1^2*b1^3*b2*b4 + a1^2*b1^2*b2^2*b4^2 - b3*a1^2*b1*b2^3*b5 + 2*a1^2*b2^4*b4*b5 + b3*a1*a2*b1^4*b4 - a1*a2*b1^3*b2*b4^2 + 2*b3*a1*a2*b1^2*b2^2*b5 - 3*a1*a2*b1*b2^3*b4*b5 + a5*b3*a1*b1^4*b2 - a5*a1*b1^3*b2^2*b4 - a5*a1*b1*b2^4*b5 - 2*a4*a1*b2^5*b5 - b3*a2^2*b1^3*b2*b5 + a2^2*b1^2*b2^2*b4*b5 + a2^2*b2^4*b5^2 - a5*b3*a2*b1^5 + a5*a2*b1^4*b2*b4 + a5*a2*b1^2*b2^3*b5 + a3^2*b2^5*b4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (- b3*a1^2*b1^3*b2*b5 + b4*a1^2*b1^2*b2^2*b5 + a1^2*b2^4*b5^2 + a2*b3*a1*b1^4*b5 - a2*b4*a1*b1^3*b2*b5 - a2*a1*b1*b2^3*b5^2 + a3^2*b2^5*b5)/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (a2^2*b2^4*b3^2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^8)/(a2*a3*b1^5*b3 + a1*a3*b1^3*b2^2*b4 - a2*a3*b1^2*b2^3*b5 - a1*a3*b1^4*b2*b3 + a1*a3*b1*b2^4*b5 - a2*a3*b1^4*b2*b4) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^4*(a1^2*b1^2*b2^2*b3^2 - 2*a1^2*b1*b2^3*b3*b4 + a1^2*b2^4*b4^2 - 2*a1*a2*b1^3*b2*b3^2 + 4*a1*a2*b1^2*b2^2*b3*b4 - 2*a1*a2*b1*b2^3*b4^2 + 4*b5*a1*a2*b2^4*b3 - 2*a1*a4*b2^5*b4 + a2^2*b1^4*b3^2 - 2*a2^2*b1^3*b2*b3*b4 + a2^2*b1^2*b2^2*b4^2 - 2*b5*a2^2*b1*b2^3*b3 + 2*b5*a2^2*b2^4*b4 - 2*a5*b5*a2*b2^5 + a4^2*b2^6 + 2*a5*a4*b1*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (b2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^5*(- a1^2*b1*b2^2*b3^2 + 2*a1^2*b2^3*b3*b4 + 2*a1*a2*b1^2*b2*b3^2 - 4*a1*a2*b1*b2^2*b3*b4 + 2*a1*a2*b2^3*b4^2 - 2*a1*a5*b2^4*b4 - 2*a4*a1*b2^4*b3 - a2^2*b1^3*b3^2 + 2*a2^2*b1^2*b2*b3*b4 - a2^2*b1*b2^2*b4^2 + 2*b5*a2^2*b2^3*b3 - 2*a4*a2*b2^4*b4 + a5^2*b1*b2^4 + 2*a4*a5*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (b2^2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^6*(a1^2*b2^2*b3^2 - 2*a1*a2*b1*b2*b3^2 + 4*a1*a2*b2^2*b3*b4 - 2*a1*a5*b2^3*b3 + a2^2*b1^2*b3^2 - 2*a2^2*b1*b2*b3*b4 + a2^2*b2^2*b4^2 - 2*a2*a5*b2^3*b4 - 2*a4*a2*b2^3*b3 + a5^2*b2^4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) + (a2*b2^3*b3*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^7*(2*a5*b2^2 - 2*a1*b2*b3 + a2*b1*b3 - 2*a2*b2*b4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4))

I was wondering how I can just get the coefficients of this polynom without the word root, meaning a solution such as

[ 1, (2*(a1*b3 + a2*b4 - a5*b2))/(a2*b3), (a1^2*b3^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 + a2^2*b4^2 - 2*a2*a5*b2*b4 - 2*b1*a2*a5*b3 - 2*a4*a2*b2*b3 + a5^2*b2^2)/(a2^2*b3^2),...]

I have been using coeffs, but I have to remove manually the word root for each solution of my polynom and I would like to automatize this. Any hint of how I can get these coefficients?

Thanks in advance

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Answer 1

Walter Roberson 2019-9-16

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https://ww2.mathworks.cn/matlabcentral/answers/480599-how-do-i-get-the-coefficients-of-a-9th-order-symbolic-polynom-without-root-on-them#answer_392108

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Walter Roberson 2019-9-17

在 MATLAB Online 中打开

That expression is not a polynomial of order 9. That expression involves a polynomial-like expression up to the 8th power, multiplied by various expressions (that are not polynomial as there are variables in the denominator). The expression is the set of roots of a polynomial of order 9.

If you let TTT be the roots of the polynomial of degree 9, then the expression becomes (collected on TTT):

-a2^2*b3^2*b2^4/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)*TTT^8+(2*a2*
a5*b3*b2^5+(-2*a1*a2*b3^2-2*a2^2*b3*b4)*b2^4+a2^2*b3^2*b1*b2^3)/a3/b1/(-b1^3*b3
+b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)*TTT^7+(-a5^2*b2^6+((2*a4*b3+2*a5*b4)*a2+2*a1
*a5*b3)*b2^5+(-a1^2*b3^2-4*a1*a2*b3*b4-a2^2*b4^2)*b2^4+(2*a1*a2*b3^2+2*a2^2*b3*
b4)*b1*b2^3-a2^2*b3^2*b1^2*b2^2)/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*
b1)*TTT^6+(-2*a4*a5*b2^6+(-a5^2*b1+2*a2*a4*b4+2*a1*(a4*b3+a5*b4))*b2^5+(-2*a1^2
*b3*b4-2*a1*a2*b4^2-2*a2^2*b3*b5)*b2^4+(a1^2*b3^2+4*a1*a2*b3*b4+a2^2*b4^2)*b1*
b2^3-(2*a1*a2*b3^2+2*a2^2*b3*b4)*b1^2*b2^2+a2^2*b3^2*b1^3*b2)/a3/b1/(-b1^3*b3+
b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)*TTT^5+(-a4^2*b2^6+(2*a1*a4*b4+2*a2*a5*b5-2*a4
*a5*b1)*b2^5+(-a1^2*b4^2-4*a1*a2*b3*b5-2*a2^2*b4*b5)*b2^4+(2*a1^2*b3*b4+2*a1*a2
*b4^2+2*a2^2*b3*b5)*b1*b2^3-(a1^2*b3^2+4*a1*a2*b3*b4+a2^2*b4^2)*b1^2*b2^2+(2*a1
*a2*b3^2+2*a2^2*b3*b4)*b1^3*b2-a2^2*b3^2*b1^4)/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^3*
b5)/(a1*b2-a2*b1)*TTT^4+((2*a1*a5*b5+2*a2*a4*b5-a3^2*b3-a4^2*b1)*b2^5-2*a1*b5*(
a1*b3+2*a2*b4)*b2^4+(a1^2*b4^2+3*a1*a2*b3*b5+2*a2^2*b4*b5)*b1*b2^3-(2*a1^2*b3*
b4+2*a1*a2*b4^2+a2^2*b3*b5)*b1^2*b2^2+(a1^2*b3^2+3*a1*a2*b3*b4+a2^2*b4^2)*b1^3*
b2-b3*(a1*b3+a2*b4)*a2*b1^4)/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)*
TTT^3+((2*a1*a4*b5-a3^2*b4)*b2^5+(-2*a1^2*b4*b5+a1*a5*b1*b5-a2^2*b5^2)*b2^4+b5*
(a1^2*b3+3*a1*a2*b4-a2*a5*b1)*b1*b2^3-(a1^2*b4^2+2*a1*a2*b3*b5-a1*a5*b1*b4+a2^2
*b4*b5)*b1^2*b2^2+(-a5*(a1*b3+a2*b4)*b1+a1^2*b3*b4+a1*b4^2*a2+b5*b3*a2^2)*b1^3*
b2-b3*(a1*b4-a5*b1)*a2*b1^4)/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)*
TTT^2+((-2*a1*a2*b5^2+a1*a4*b1*b5)*b2^4+b5*(a1^2*b4+a2^2*b5-a2*a4*b1)*b1*b2^3-
a1*(-a4*b4*b1+b5*(a1*b3+2*a2*b4))*b1^2*b2^2+(-a4*(a1*b3+a2*b4)*b1+2*b5*a2*(a1*
b3+1/2*b4*a2))*b1^3*b2-b3*(a2*b5-a4*b1)*a2*b1^4)/a3/b1/(-b1^3*b3+b1^2*b2*b4+b2^
3*b5)/(a1*b2-a2*b1)*TTT+(-b5*a3^2*b2^5-a1^2*b5^2*b2^4+a1*b5^2*a2*b1*b2^3-a1^2*
b5*b4*b1^2*b2^2+a1*b5*(a1*b3+a2*b4)*b1^3*b2-a1*a2*b3*b5*b1^4)/a3/b1/(-b1^3*b3+
b1^2*b2*b4+b2^3*b5)/(a1*b2-a2*b1)

You could coeffs() on that, but it is not a polynomial at all and is not of degree 9.

Walter Roberson 2019-9-18

在 MATLAB Online 中打开

syms a1 a2 a3 a4 a5 b1 b2 b3 b4 b5 z
expr = (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)*(- b3*a1^2*b1^2*b2^2*b5 + b4*a1^2*b1*b2^3*b5 + 2*b3*a1*a2*b1^3*b2*b5 - 2*b4*a1*a2*b1^2*b2^2*b5 - 2*a1*a2*b2^4*b5^2 - a4*b3*a1*b1^4*b2 + a4*b4*a1*b1^3*b2^2 + a4*a1*b1*b2^4*b5 - b3*a2^2*b1^4*b5 + b4*a2^2*b1^3*b2*b5 + a2^2*b1*b2^3*b5^2 + a4*b3*a2*b1^5 - a4*b4*a2*b1^4*b2 - a4*a2*b1^2*b2^3*b5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^3*(- a1^2*b1^3*b2*b3^2 + 2*a1^2*b1^2*b2^2*b3*b4 - a1^2*b1*b2^3*b4^2 + 2*b5*a1^2*b2^4*b3 + a1*a2*b1^4*b3^2 - 3*a1*a2*b1^3*b2*b3*b4 + 2*a1*a2*b1^2*b2^2*b4^2 - 3*b5*a1*a2*b1*b2^3*b3 + 4*b5*a1*a2*b2^4*b4 - 2*a5*b5*a1*b2^5 + a2^2*b1^4*b3*b4 - a2^2*b1^3*b2*b4^2 + b5*a2^2*b1^2*b2^2*b3 - 2*b5*a2^2*b1*b2^3*b4 - 2*b5*a2*a4*b2^5 + a3^2*b2^5*b3 + a4^2*b1*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^2*(- b3*a1^2*b1^3*b2*b4 + a1^2*b1^2*b2^2*b4^2 - b3*a1^2*b1*b2^3*b5 + 2*a1^2*b2^4*b4*b5 + b3*a1*a2*b1^4*b4 - a1*a2*b1^3*b2*b4^2 + 2*b3*a1*a2*b1^2*b2^2*b5 - 3*a1*a2*b1*b2^3*b4*b5 + a5*b3*a1*b1^4*b2 - a5*a1*b1^3*b2^2*b4 - a5*a1*b1*b2^4*b5 - 2*a4*a1*b2^5*b5 - b3*a2^2*b1^3*b2*b5 + a2^2*b1^2*b2^2*b4*b5 + a2^2*b2^4*b5^2 - a5*b3*a2*b1^5 + a5*a2*b1^4*b2*b4 + a5*a2*b1^2*b2^3*b5 + a3^2*b2^5*b4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (- b3*a1^2*b1^3*b2*b5 + b4*a1^2*b1^2*b2^2*b5 + a1^2*b2^4*b5^2 + a2*b3*a1*b1^4*b5 - a2*b4*a1*b1^3*b2*b5 - a2*a1*b1*b2^3*b5^2 + a3^2*b2^5*b5)/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (a2^2*b2^4*b3^2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^8)/(a2*a3*b1^5*b3 + a1*a3*b1^3*b2^2*b4 - a2*a3*b1^2*b2^3*b5 - a1*a3*b1^4*b2*b3 + a1*a3*b1*b2^4*b5 - a2*a3*b1^4*b2*b4) - (root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^4*(a1^2*b1^2*b2^2*b3^2 - 2*a1^2*b1*b2^3*b3*b4 + a1^2*b2^4*b4^2 - 2*a1*a2*b1^3*b2*b3^2 + 4*a1*a2*b1^2*b2^2*b3*b4 - 2*a1*a2*b1*b2^3*b4^2 + 4*b5*a1*a2*b2^4*b3 - 2*a1*a4*b2^5*b4 + a2^2*b1^4*b3^2 - 2*a2^2*b1^3*b2*b3*b4 + a2^2*b1^2*b2^2*b4^2 - 2*b5*a2^2*b1*b2^3*b3 + 2*b5*a2^2*b2^4*b4 - 2*a5*b5*a2*b2^5 + a4^2*b2^6 + 2*a5*a4*b1*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (b2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^5*(- a1^2*b1*b2^2*b3^2 + 2*a1^2*b2^3*b3*b4 + 2*a1*a2*b1^2*b2*b3^2 - 4*a1*a2*b1*b2^2*b3*b4 + 2*a1*a2*b2^3*b4^2 - 2*a1*a5*b2^4*b4 - 2*a4*a1*b2^4*b3 - a2^2*b1^3*b3^2 + 2*a2^2*b1^2*b2*b3*b4 - a2^2*b1*b2^2*b4^2 + 2*b5*a2^2*b2^3*b3 - 2*a4*a2*b2^4*b4 + a5^2*b1*b2^4 + 2*a4*a5*b2^5))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) - (b2^2*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^6*(a1^2*b2^2*b3^2 - 2*a1*a2*b1*b2*b3^2 + 4*a1*a2*b2^2*b3*b4 - 2*a1*a5*b2^3*b3 + a2^2*b1^2*b3^2 - 2*a2^2*b1*b2*b3*b4 + a2^2*b2^2*b4^2 - 2*a2*a5*b2^3*b4 - 2*a4*a2*b2^3*b3 + a5^2*b2^4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4)) + (a2*b2^3*b3*root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 2)^7*(2*a5*b2^2 - 2*a1*b2*b3 + a2*b1*b3 - 2*a2*b2*b4))/(a3*b1*(a2*b1^4*b3 + a1*b2^4*b5 - a1*b1^3*b2*b3 - a2*b1^3*b2*b4 - a2*b1*b2^3*b5 + a1*b1^2*b2^2*b4));
ch = children(expr);
ch2 = children(ch(2));
ch23 = children(ch2(3));
root_expr = ch23(1);
syms R9
newexpr = subs(expr, root_expr, R9);
[R9coeffs, R9vars] = coeffs(newexpr, R9, 'all');
R9coeffs = simplify(R9coeffs);  %does not make a big difference

Javier 2019-9-18

编辑：Javier 2019-9-18

在 MATLAB Online 中打开

HI Walter, thanks again for investing your time in this issue.

I am afraid that I am getting totally confused with how the results of the sybolic solution are being given. I will briefly explain what I am tying to achieve.

I have the follwing equation system that I know the solver can solve

F1 = y^2*x*a1 + y^2*x^2*a2 + x^2*a5  + x*a4 - y*a3 ==0;
F2 =  y^2*x*b1 + y^2*x^2*b2 + x^3*b3 + x^2*b4+b5 ==0;
eqns = [F1, F2]
solution = solve(eqns,[y x])

whose coefficients can be taken (for now) as

a1 =   1.8777e-07
a2 =   5.8977e-12
a3 =   1.0067e-04
a4 =   2.6364e-07
a5 =   8.2805e-12
b1 =  -7.8209e-08
b2 =   9.4971e-10
b3 =   2.6668e-09
b4 =  -1.0981e-07
b5 =   1.1928e-04

From the symbolic solution I get solutions to the system equations like

solution.x(1)
 root(z^9 + (2*z^8*(a1*b3 + a2*b4 - a5*b2))/(a2*b3) + (z^7*(a1^2*b3^2 + a2^2*b4^2 + a5^2*b2^2 + 4*a1*a2*b3*b4 - 2*a1*a5*b2*b3 - 2*a2*a4*b2*b3 - 2*a2*a5*b1*b3 - 2*a2*a5*b2*b4))/(a2^2*b3^2) - (2*z^6*(- a1*a2*b4^2 - a4*a5*b2^2 - a1^2*b3*b4 - a5^2*b1*b2 - a2^2*b3*b5 + a1*a4*b2*b3 + a1*a5*b1*b3 + a2*a4*b1*b3 + a1*a5*b2*b4 + a2*a4*b2*b4 + a2*a5*b1*b4))/(a2^2*b3^2) + (z^5*(a1^2*b4^2 + a4^2*b2^2 + a5^2*b1^2 + 2*a2^2*b4*b5 - 2*a1*a4*b1*b3 + 4*a1*a2*b3*b5 - 2*a1*a4*b2*b4 - 2*a1*a5*b1*b4 - 2*a2*a4*b1*b4 + 4*a4*a5*b1*b2 - 2*a2*a5*b2*b5))/(a2^2*b3^2) + (z^4*(2*a4*a5*b1^2 + 2*a4^2*b1*b2 + a3^2*b2*b3 + 2*a1^2*b3*b5 - 2*a1*a4*b1*b4 + 4*a1*a2*b4*b5 - 2*a1*a5*b2*b5 - 2*a2*a4*b2*b5 - 2*a2*a5*b1*b5))/(a2^2*b3^2) + (z^3*(a4^2*b1^2 + a2^2*b5^2 + a3^2*b1*b3 + a3^2*b2*b4 + 2*a1^2*b4*b5 - 2*a1*a4*b2*b5 - 2*a1*a5*b1*b5 - 2*a2*a4*b1*b5))/(a2^2*b3^2) + (z^2*(2*a1*a2*b5^2 + a3^2*b1*b4 - 2*a1*a4*b1*b5))/(a2^2*b3^2) + (z*(a1^2*b5^2 + a3^2*b2*b5))/(a2^2*b3^2) + (a3^2*b1*b5)/(a2^2*b3^2), z, 1)

Since in my problem the coefficies ai and bi are likely to change, I was looking a way to have the solutions for x and y as function of those coefficients. Therefore, I thought I could get from the solutions (like solution.x(1)) the coefficients of them to create a "polynom", where I could apply roots and then get the real solutions for x and y to be processed later on.

Can I still apply the technique you have described above? Or is my whole procedure mistaken?

Thanks

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How do I get the coefficients of a 9th order symbolic polynom without root on them?

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How do I get the coefficients of a 9th order symbolic polynom without root on them?

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