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

Asked by Javier
on 16 Sep 2019
Latest activity Edited by Javier
on 18 Sep 2019 at 10:26
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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1 Answer

Answer by Walter Roberson
on 16 Sep 2019

children()

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Thanks Walter,
Could you show me an example of how to use subs in my case?
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
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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