Help with simplifying a complex symbolic expression

7 次查看（过去 30 天）
Lu Zhao
Lu Zhao 2021-3-26
评论： Lu Zhao 2021-3-29
There is a symbolic expression, and one of the variable "U_j0" can be cancled out.
But when I use "simplify()" command, "U_j0" is still in the expression. Can anyone help me out to further simplify the expression below?
syms dIm Im dKm Km alpha1 omega1 S U1 delta c1 m
syms omega Omega R0 R Uinf U_j0
% The following is the symbolic expression waiting to be simplified. ^ O ^
% Thank you!
term1=((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)));
I tried to combine "log()" terms by hand and simplified the above expression to get a new one shown below (cancel variable "U_j0") , but the expression I got is not correct. I wondered anyone could help me to use MATLAB program to simplify this expression and cancel variable "U_j0"?

请先登录，再回答此问题。

采纳的回答

Paul
Paul 2021-3-26
This code eliminates U_j0:
[num,den]=numden(term1);
newnum = combine(num,'log','IgnoreAnalyticConstraints',true);
newterm1 = newnum/den;
  4 个评论
显示 2更早的评论
Paul
Paul 2021-3-26
Im and dIm are left over in Y3 - Y1. Substitute values in for those too:
>> Y1 = subs(term1,[alpha1,c1,S,delta,m, R, Im, dIm, U_j0],[1,0.1,1,0.1,1,1,3,2,1]);
>> Y3 = subs(newterm1,[alpha1,c1,S,delta,m, R, Im , dIm],[1,0.1,1,0.1,1,1,3,2]);
>> simplify(Y1-Y3,500)
ans =
0
Here is the code I used to show that num and newnum are identical (ignoring the Analytic Constraints):
>> syms dIm Im dKm Km alpha1 omega1 S U1 delta c1 m
syms omega Omega R0 R Uinf U_j0
% The following is the symbolic expression waiting to be simplified. ^ O ^
% Thank you!
term1=((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)));
[num,den]=numden(term1);
newnum = combine(num,'log','IgnoreAnalyticConstraints',true);
>> simplify(combine(newnum-num,'log','IgnoreAnalyticConstraints',true),500)
ans =
0
It may be possible to get simpler expressions by putting appropriate assumptions (e.g., real, positive, etc.) on the variables if appropriate.
Lu Zhao
Lu Zhao 2021-3-29
That is great! I learned a lot from it. Than you. I really appreciate it. : D

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by