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Simplify a long symbolic expression

1 次查看（过去 30 天）
Lu Zhao
Lu Zhao 2021-3-8
The variable "U_j0" can be canceled by simplifying the equation by hand, but it doesn't work by using command "simplify()".
- My guess is the variable "U_j0" is in a natral log and somehow it's not fully simplified.
Here is the symbolic expression:
% Equation is:
clc
clear
syms u(r) alpha m omega Omega R0 R Uinf U_j0 alpha1 omega1 S U1 delta c1
syms dIm Im dKm Km
-(Km*U_j0^2*alpha1*((U_j0*((U_j0*(- S^2*delta^2*m^2 + 2*S^2*delta^2 + 2*S^2*delta + 2*S*alpha1*c1*delta*m - 2*S*alpha1*delta*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(R^2*delta*(alpha1 - alpha1*c1 + S*delta*m)) - (S*U_j0*m*(delta - 1)*((2*log(-(U_j0*(alpha1 - alpha1*c1 + S*delta*m))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2) - (log(R)*(m^2 - 2))/m^2 + (Im*alpha1^2*((R*dIm*delta*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(Im*alpha1) - (R^2*delta^2*((U_j0*alpha1*(c1 - 1))/(R^2*delta*(delta - 1)) + (S*U_j0*m*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(R^2*delta*(delta - 1))))/(U_j0*alpha1^2*(c1 - 1)))*(c1 - 1)*(delta - 1))/(delta*(Im*S*m - R*alpha1*dIm + R*alpha1*c1*dIm + R*alpha1*dIm*delta - R*alpha1*c1*dIm*delta)) + (2*S*alpha1*(c1 - 1)*(delta - 1)*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2*(alpha1 - alpha1*c1 + S*delta*m))))/(R^2*delta))*(alpha1 - alpha1*c1 + S*delta*m))/alpha1 + (2*S*U_j0^2*m*(alpha1 - alpha1*c1 + S*delta*m)*((2*log(-(U_j0*(alpha1 - alpha1*c1 + S*delta*m))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2) - (log(R)*(m^2 - 2))/m^2 + (Im*alpha1^2*((R*dIm*delta*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(Im*alpha1) - (R^2*delta^2*((U_j0*alpha1*(c1 - 1))/(R^2*delta*(delta - 1)) + (S*U_j0*m*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(R^2*delta*(delta - 1))))/(U_j0*alpha1^2*(c1 - 1)))*(c1 - 1)*(delta - 1))/(delta*(Im*S*m - R*alpha1*dIm + R*alpha1*c1*dIm + R*alpha1*dIm*delta - R*alpha1*c1*dIm*delta)) + (2*S*alpha1*(c1 - 1)*(delta - 1)*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2*(alpha1 - alpha1*c1 + S*delta*m))))/(R^2*alpha1))*(U1*alpha1 - alpha1*c1 + S*delta*m)^2)/delta^2 == (U_j0^4*dKm*(alpha1 - alpha1*c1 + S*delta*m)^2*((2*log(-(U_j0*(alpha1 - alpha1*c1 + S*delta*m))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2) - (log(R)*(m^2 - 2))/m^2 + (Im*alpha1^2*((R*dIm*delta*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(Im*alpha1) - (R^2*delta^2*((U_j0*alpha1*(c1 - 1))/(R^2*delta*(delta - 1)) + (S*U_j0*m*((2*S*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2) - (log(-R*(delta - 1))*(m^2 - 2))/m^2 + (2*log(-(U_j0*alpha1*(c1 - 1)*(delta - 1))/delta)*(S^2*m^2 + 2*S*alpha1*c1*m - 2*S*alpha1*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(m^2*(alpha1 + S*m - alpha1*c1)^2)))/(R^2*delta*(delta - 1))))/(U_j0*alpha1^2*(c1 - 1)))*(c1 - 1)*(delta - 1))/(delta*(Im*S*m - R*alpha1*dIm + R*alpha1*c1*dIm + R*alpha1*dIm*delta - R*alpha1*c1*dIm*delta)) + (2*S*alpha1*(c1 - 1)*(delta - 1)*(S*m - alpha1 + alpha1*c1))/(m*(alpha1 + S*m - alpha1*c1)^2*(alpha1 - alpha1*c1 + S*delta*m)))*(- S^2*delta^2*m^2 + 2*S^2*delta^2 + 2*S^2*delta + 2*S*alpha1*c1*delta*m - 2*S*alpha1*delta*m - alpha1^2*c1^2 + 2*alpha1^2*c1 - alpha1^2))/(R*delta^3) ;
% Please help to simplify the above equation : cancel out "U_j0"
Anyone would like to take the challenge to deal with this long equation and help me out? lol.

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