Here is a simple example:
sage: var('a,b,y')
(a, b, y)
sage: assume(a,'real')
sage: real_part(a)
real_part(a)
sage: assume(b,'real')
sage: real_part(b)
real_part(b)
sage: real_part(a+b*I)
real_part(a) - imag_part(b)
It seems that the 'real' assumption is completely ignored.
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