How to simplify a common factor in a symbolic equation

My code is as follows

syms I_1   phi_1_d2   R_1   f_g   mu_1   I_2   phi_2_d2   R_2   mu_2


eq_1= mu_1== I_1 * phi_1_d2 + R_1 * f_g;
eq_2= mu_2== I_2 * phi_2_d2 - R_2 * f_g;

eq_1= expand(eq_1 * (I_2 * R_1));

eq_2= expand(eq_2 * (I_1 * R_2));

eq_3= eq_1 - eq_2;

eq_3= collect(eq_3, [I_1, I_2]);
eq_3= collect(eq_3, f_g);

eq_4= eq_3 / ((I_2 * (R_1 ^2)) + (I_1 * (R_2 ^2)));

eq_4= collect(eq_4, f_g)

With the output being

eq_4 =
 
(R_1*mu_1*I_2 + (-R_2*mu_2)*I_1)/(I_2*R_1^2 + I_1*R_2^2) == ((I_2*R_1^2 + I_1*R_2^2)/(I_2*R_1^2 + I_1*R_2^2))*f_g + (I_1*I_2*(R_1*phi_1_d2 - R_2*phi_2_d2))/(I_2*R_1^2 + I_1*R_2^2)

This is correct as far as I can tell, however I'm unsure how to make matlab recognise that the coefficient for the f_g term is 1

Any help would be appreciated, I am new to MATLAB and unfamiliar with the symbolic toolkit

[John D'Errico]

The coef of the f_g term, meaning this expression from eq_4?

((I_2*R_1^2 + I_1*R_2^2)/(I_2*R_1^2 + I_1*R_2^2))

So now you wish to (programmatically) extract that coefficient, and set it to 1 as a new equation? I'll admit to being a bit lazy. I'd probably just use cut and paste, a far faster alternative to reading the help for the function coeffs. ;-)

Ok, I think you are saying that you see this expression is just the ratio of two numbers, which happen to be the same, and you are asking how to force MATLAB to recognize that X/X is just 1? Sometimes getting a computer to recognize what you see as obvious is harder than just using pencil and paper. But is that your question?

[Kieran Corrigan]

Your edit is correct I’m trying to get matlab to recognise the coefficients of the f_g term are alike and cancel to 1.

Answer 1

[John D'Errico]

Its still easier to just use cut and paste. ;-) Damn these computers. I want my slide rule back!

As I said, sometimes it gets complicated to tell the computer what seems obvious. What happens if I try this:

simplify(expand(eq_4))
ans =
I_2*R_1^2 + I_1*R_2^2 ~= 0 & I_2*(R_1*mu_1 + I_1*R_2*phi_2_d2) == I_2*f_g*R_1^2 + I_1*I_2*phi_1_d2*R_1 + I_1*f_g*R_2^2 + I_1*mu_2*R_2

Now we see an anded expression, thus:

I_2*R_1^2 + I_1*R_2^2 ~= 0

AND

I_2*(R_1*mu_1 + I_1*R_2*phi_2_d2) == I_2*f_g*R_1^2 + I_1*I_2*phi_1_d2*R_1 + I_1*f_g*R_2^2 + I_1*mu_2*R_2

The problem is X/X is not ALWAYS 1. When X == 0, we have a problem, and then MATLAB gets obstinate, worrying about the singular case where X == 0. It could happen.

But I think this is what you need:

combine(eq_4)
ans =
(I_2*R_1*mu_1 - I_1*R_2*mu_2)/(I_2*R_1^2 + I_1*R_2^2) == f_g + (I_1*I_2*(R_1*phi_1_d2 - R_2*phi_2_d2))/(I_2*R_1^2 + I_1*R_2^2)

[Kieran Corrigan]

Yeah that seems to have resolved it, I did forget about the 0/0 case