simplify function does not work properly

Hello,

I have an equation with 5 variables and a condition. Once I set the condition, when I simplify the equation, Matlab returns 0. However, this equation is the multiplication of some terms, but, when I try to simplify them separately, I do not get any 0.

Here is the code:

syms kd z mean_t mean_t2 p
assume(assumptions(),'clear');
eq = 8*kd^2*p^2*z*(mean_t - kd*mean_t2)^2*(- mean_t^2 + mean_t2)^2*(mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2);
assume( p~=0 & kd*mean_t2*(3*p*mean_t^2 - 2*kd*mean_t2*p*mean_t + z + mean_t2*p) == p*mean_t^3 + mean_t2*p*mean_t + kd*mean_t2*z );
simplify(eq)
simplify(children(eq).')

Here is this code with some analytical simplifications:

syms kd z mean_t mean_t2 p
assume(assumptions(),'clear');
assume( 3*kd*mean_t2*mean_t^2 - 2*kd^2*mean_t2^2*mean_t + kd*mean_t2^2 - mean_t^3 - mean_t2*mean_t == 0 )
eq = (mean_t - kd*mean_t2)^2 * (mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2);
simplify(eq)
simplify(children(eq).')

I'm running R2016b

Any help with this? Thank you very much!

Answer 1

[Paul]

Consider a simpler case

syms x y
term1 = x - 1;
term2 = y - 2;
eq = term1*term2

eq = 

assume(term1*term2 == 0)
simplify(eq)

ans = 

0

simplify(term1)

ans = 

simplify(term2)

ans = 

Because of the assumption, simplify() "knows" that the eq is zero, basically because that's what we've explicitly asserted via the assumption. Is that assumption sufficient to assert that x == 1? Or y == 2? Or both? To be sure, one or both must be true, but how should Matlab choose which of the three possibilities to enforce?

I'm guessing a similar behavior is in effect in for the code in the Question.

[Nieves Lopez]

This makes sense! Thank you for the explanation.

By the way, could you help me with this? https://es.mathworks.com/matlabcentral/answers/1699065-function-solve-cannot-find-explicit-solution-with-returnconditions-true-but-it-finds-when-it-is-fa

Answer 2

[Jan]

syms kd z mean_t mean_t2 p
assume(assumptions(),'clear');
eq = 8*kd^2*p^2*z*(mean_t - kd*mean_t2)^2 * ...
    (- mean_t^2 + mean_t2)^2*(mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2);
assume( p~=0 & ...
    kd*mean_t2*(3*p*mean_t^2 - 2*kd*mean_t2*p*mean_t + z + mean_t2*p) == ...
    p*mean_t^3 + mean_t2*p*mean_t + kd*mean_t2*z );
simplify(eq)

ans = 

0

% simplify(children(eq).')

syms kd z mean_t mean_t2 p
assume(assumptions(),'clear');
assume( 3*kd*mean_t2*mean_t^2 - 2*kd^2*mean_t2^2*mean_t + ...
    kd*mean_t2^2 - mean_t^3 - mean_t2*mean_t == 0 )
eq = (mean_t - kd*mean_t2)^2 * (mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2);
simplify(eq)

ans = 

0

% simplify(children(eq).')

Check for incorrect argument data type or missing argument in call to function 'simplify'.

What exactly do you observe or expect instead?

Answer 3

[Nieves Lopez]

syms kd z mean_t mean_t2 p
assume(assumptions(),'clear');
assume( 3*kd*mean_t2*mean_t^2 - 2*kd^2*mean_t2^2*mean_t + ...
    kd*mean_t2^2 - mean_t^3 - mean_t2*mean_t == 0 )
eq = (mean_t - kd*mean_t2)^2 * (mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2);
simplify(children(eq).')

ans =

(mean_t - kd*mean_t2)^2

mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2

(copied the result from the Matlab command window, since in R2016b the behaviour of simplify was slightly different)

Thank you for the answer. What I mean is that eq is the product of two terms, none of them are simplified to 0. However, the whole expression does get simplificated to 0. If a*b=0, then a=0 or b=0, but i this case neither a nor b are0.

[Jan]

Is this an answer or a comment?

[Nieves Lopez]

Sorry that I was not clear. I don't see how it is possible to have both simplify(mean_t - kd*mean_t2)~=0 and simplify(mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2)~=0, and the product simplify((mean_t - kd*mean_t2)*(mean_t^2 - 2*kd*mean_t2*mean_t + mean_t2))==0