How can I force simplify function I want?

I have a problem about both simplify and subs functions.

1. Simplify function is not working in the following example.

syms mu B cc M M_bar E V_N sigma_1;
sigma_1 = sqrt((M+M_bar-4*E*V_N)^2+(2*mu*B)^2);
cantSimplified_Var = simplify(sqrt(4*B^2*mu^sym(2) + 16*E^sym(2)*V_N^2 - 8*E*M*V_N - 8*E*M_bar*V_N + M^2 + 2*M*M_bar + M_bar^2));

isequal(expand(sigma_1),cantSimplified_Var)
    ans =

  logical

   1

isequal(sigma_1,cantSimplified_Var)
    ans =

  logical

   0

2. I want to continue with my new defined function. For example,

syms A B C
A = B^2;
C = A + B^2

    C =
 
    2*B^2

Here, I want to see equation like "C = 2*A". Is it possible?

It is related to my first question, because if I can see the expression like "C = 2*A", I will continue my calculation whether MATLAB simplify it correctly or not.

Answer 1

[Star Strider]

Tell MATLAB to keep slimplfying until it cannot simplify it further (or reaches the iteration limit), then test equality with the isAlways function:

syms mu B cc M M_bar E V_N sigma_1;
sigma_1 = sqrt((M+M_bar-4*E*V_N)^2+(2*mu*B)^2);
cantSimplified_Var = simplify(sqrt(4*B^2*mu^sym(2) + 16*E^sym(2)*V_N^2 - 8*E*M*V_N - 8*E*M_bar*V_N + M^2 + 2*M*M_bar + M_bar^2), 'Steps',500);

Test = isAlways(sigma_1 == cantSimplified_Var)

producing:

Test =

  logical

   1

.

[Ismail Taygun Bulmus]

Thank you for your answer. As I understand your answer, MATLAB can not simplify "cantSimplified_Var" formula to "sqrt((M+M_bar-4*E*V_N)^2+(2*mu*B)^2)". I tried 2000 steps and it gives same results.

[Star Strider]

My pleasure!

It simplifies as much as it can. The point is that the isAlways function proved the two expressions are the same.

[Ismail Taygun Bulmus]

Okay, thank you again.

[Star Strider]

As always, my pleasure!