MatLAB do not simplify (a^2)^(1/2) in symbolic ToolBox?

>> simplify((cos(phymi)^2)^(1/2), 3000)
ans =
(cos(phymi)^2)^(1/2)
>> rewrite (((cos(phymi))^2)^(1/2), 'exp')
ans =
((exp(-phymi*1i)/2 + exp(phymi*1i)/2)^2)^(1/2)
>> simplify((phymi^2)^(1/2), 5000)
ans =
(phymi^2)^(1/2)

Answer 1

[Walter Roberson]

MATLAB assumes that symbols might have complex values unless you tell it they are not complex. For complex values, sqrt(x^2) is not the same as x. For that matter, sqrt(x^2) is not the same as x even just for negative real values.

If you know for sure that your values are nonnegative, then add an assumption about that, such as

syms phymi
assume(phymi >= 0)

[Nathan Hardenberg]

You can also assume directly:

syms a 
syms b real
syms c positive
syms d real positive

A = simplify( sqrt(a^2) )

A = 

B = simplify( sqrt(b^2) )

B = 

C = simplify( sqrt(c^2) )

C = 

c

D = simplify( sqrt(d^2) )

D = 

d

Answer 2

[Star Strider]

It does:

syms phymi 
a = simplify((cos(phymi)^2)^(1/2), 'Steps',3000, 'IgnoreAnalyticConstraints',1)

a =
cos(phymi)