Question: Equalise multivariate polynomials coefficients

Hello,

I'm writing to ask how to equalize the coefficients of two multivariate polynomials. In particluar, I have two polynomials whose arguments are ln(E),ln(K),ln(L) (their levels, squared levels and interaction terms). The first one is:

(1/2*(p*a*b+(g-p)*b-g))*b*v*a*ln(E)^2-(-1+b)*v*(g-p+a*p)*b*a*ln(E)*ln(K)-b*p*(a-1)*v*a*ln(E)*ln(L)+v*a*b*ln(E)+(1/2*(p*(-1+b)*a+(g-p)*b+p))*(-1+b)*v*a*ln(K)^2+(-1+b)*v*p*(a-1)*a*ln(K)*ln(L)-v*a*(-1+b)*ln(K)+(1/2)*a*p*v*(a-1)*ln(L)^2-v*(a-1)*ln(L)

the second one is:

x_1*ln(E)+x_11*ln(E)^2+x_12*ln(E)*ln(K)+x_13*ln(E)*ln(L)+x_2*ln(K)+x_22*ln(K)^2+x_23*ln(K)*ln(L)+x_3*ln(L)`+x_33*ln(L)^2

I would like to know if it is possible to equalize the coefficients of the two polynomials and find the following system:

v*a*b = x_1, -v*(a-1) x_3, -v*a*(-1+b) = x_2, a*b*v*(b*rho*a-b*rho+g*(-1+b)) = x_11, v*rho*a*(a-1) = x_33, v*a*(rho*(-1+b)*a-rho*(-1+b)+b*g)*(-1+b) = x_22, -a*v*rho*(a-1)*b = x_13, -a*v*(a*rho-rho*u+g)*b*(-1+b) = x_12, a*v*u*rho*(a-1)*(-1+b) = x_23

I tried using "coeffs" and creating a sequence of values for x but then I don't know how to equalize them.

Thank you very much in advance for your time,

Elena