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

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.

Answer 1

[Yuichi Tadokoro]

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