Strange behaviour of simplify

Hello, when solving a math Problem today i noticed a strange behaviour of simplify and I cannot explain myself what I did wrong. Basically I do have two terms and want to compare if they are equal, but Matlab returns false, altough they actually are. Is there a syntax thing I did false?

syms a b c t
f1 = sqrt((a^2+b^2+c^2)/3) / t;
f2 = sqrt(((a/t)^2+(b/t)^2+(c/t)^2)/3);
pretty(simplify(f1==f2))

Here you can see, that both expressions are equal, but Matlab returns false:

logical(simplify(f1==f2))

Answer 1

[Star Strider]

use the isAlways function to compare symbolic expressions:

syms a b c t
f1 = sqrt((a^2+b^2+c^2)/3) / t;
f2 = sqrt(((a/t)^2+(b/t)^2+(c/t)^2)/3);
pretty(simplify(f1==f2, 'Steps',500))

equalityTest = isAlways(f1 == f2)

here:

equalityTest =

  logical

   0

and:

Warning: Unable to prove '(a^2/3 + b^2/3 + c^2/3)^(1/2)/t == (a^2/(3*t^2) + b^2/(3*t^2) +
c^2/(3*t^2))^(1/2)'. 

.

[Maximilian Schönau]

Thank you so much, I needed that function!

As for the assumed equality it is totally my fault that i did not notice the difference, in my function I use only Values bigger than zero...

[Star Strider]

As always, my pleasure!

You can set conditions in the syms call, for example:

syms a b c t positive real 
f1 = sqrt((a^2+b^2+c^2)/3) / t;
f2 = sqrt(((a/t)^2+(b/t)^2+(c/t)^2)/3);
pretty(simplify(f1==f2, 'Steps',500))

equalityTest = isAlways(f1 == f2)

however that does not change the ‘equalityTest’ result.

Answer 2

[Walter Roberson]

they are not the same. think about negative t