Transpose of a symbolic 'real' results in conj()

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Chris B
Chris B 2018-7-11
回答： Yuichi Tadokoro 2018-7-13
Hello,
I'm facing an issue where I define a symbol as real, assign an expression to it (trigonometric in this case) and transpose it. Unfortunately, the result includes conjugate elements.
Minimal example:
a = sym('a', 'real');
b = sym('b', 'real');
c = sym('c', [3,1], 'real');
c(1) = sin(a)*cos(b);
assume(c,'real')
result = c'
Result:
[ cos(conj(b))*sin(conj(a)), c2, c3]
The issue does not occur with assume(c, 'real') removed. The reason why it would make sense to have it is that overwriting c with a term might remove the assumption of the former definition.
If I run "assumptions", for the case without assume(c,'real') it shows:
[ in(a, 'real'), in(b, 'real'), in(c1, 'real'), in(c2, 'real'), in(c3, 'real')]
and with assume(c,'real'):
[ in(cos(b)*sin(a), 'real'), in(c1, 'real'), in(c2, 'real'), in(c3, 'real')]
The only difference is that it now assumes the whole term c(1) = cos(b)*sin(a) to be real.
Of course, I could use the element-wise transpose:
result = c.'
This works and does not result in conjugate elements. But the overall issue I'm facing is that I depend on all functions that are used on c, would need to do element-wise transpose. I, for instance, calculate the rank of a matrix based on elements similar to c and it seems that there is one more linear dependent row than compared to other mathematical tools.
Thanks in advance.

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采纳的回答

Yuichi Tadokoro
Yuichi Tadokoro 2018-7-13
You need to use
assumeAlso(c, 'real')
instead of 'assume' to keep the assumptions on a and b.
>> assumptions
ans =
[ in(cos(b)*sin(a), 'real'), in(a, 'real'), in(b, 'real'), in(c1, 'real'), in(c2, 'real'), in(c3, 'real')]
https://jp.mathworks.com/help/symbolic/assumptions-for-symbolic-objects.html?lang=en#brvhirb-1

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