simplify symbolic expression with complex, square, sqrt. & Assume commutation in Matlab

Hi team

I find some symbolic expression can't be simplified by the simplified by matlab function.

Like this, the long symbolic expression (A ^2)^{1/2} is actually A squared then sqrt. When sqrt operates on the outside, it should return A.

But it didn't simplify this part.

Is it because of A*B \=B*A? Should we assume commutation between symbols?

How could we assume the commutation? Any example would help a lot! Thanks in advance.

Answer 1

[Walter Roberson]

(A ^2)^{1/2} Should not return A.

For real values it could return abs(A)

For complex values, A^2 might be a different branch. For example -2i squared is -4 and square root of that is 2i.

[Lingling Fan]

so it doesn't result from the assume of simplification?

[Walter Roberson]

syms Areal real
syms Apositive positive
>> simplify(sqrt(Areal^2))
 
ans =
 
abs(Areal)
 
>> simplify(sqrt(Apositive^2))
 
ans =
 
Apositive
>> sqrt((-1-i)^2)

ans =

                          1 +                     1i

>> syms Areal Aimag positive
>> simplify(sqrt((Areal+1i*Aimag)^2))
 
ans =
 
Areal + Aimag*1i

simplify() does what it can taking into account assumptions. If you had an assumption that A was positive then it would have resolved the sqrt.

[Lingling Fan]

Thank you for your answer.

So what would be the symbolic command for commutator of multiplication? Thanks