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

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Lingling Fan
Lingling Fan 2019-5-14
评论： Lingling Fan 2019-5-14
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.
Screen Shot 2019-05-13 at 10.47.35 PM.png

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Walter Roberson
Walter Roberson 2019-5-14
(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.
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Walter Roberson
Walter Roberson 2019-5-14
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
Lingling Fan 2019-5-14
Thank you for your answer.
So what would be the symbolic command for commutator of multiplication? Thanks

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