I do not understand this :
sage: t,u=(1.4,0.7)
sage: z=complex(t,u)
This works :
sage: QQ(t)
7/5
But :
sage: AA(t)
---------------------------------------------------------------------------
TypeError
# Redacted...
TypeError: Illegal initializer for algebraic number
Similarly :
sage: QQbar(t)
---------------------------------------------------------------------------
TypeError
## Redacted...
TypeError: Illegal initializer for algebraic number
However, this works :
sage: QQbar(QQ(t))
7/5
Similarly :
sage: QQbar(z)
---------------------------------------------------------------------------
TypeError
# Redacted...
TypeError: Illegal initializer for algebraic number
One has to do ! sage: QQbar(QQ(real_part(z))+IQQ(imag_part(z))) 7/10I + 7/5
The same happens when you try to use other numerical types (RDF, CDF, etc...)
There must be (good) reasons to have direct coercions from numerical real types to QQ but not to have a direct coercion from numerical complex types to algebraic types (AA and QQbar), but I do not know them.
Or does it happen to be an oversight ?
