exact reals do not know when they might be algebraic

[saraedum]

Currently, containment in number fields does not always work correctly:

sage: ExactReals().one() in QQ
True
sage: ExactReals().one() in AA
False :(

The underlying issue is that ExactReals().one() and AA(ExactReals().one()) cannot be coerced into a common parent.

[saraedum]

I looked into overriding __richcmp__. However, this only works for the comparison ExactReals().one() == AA(1) and not for AA(1) == ExactReals().one().

Setting the Parent_richcmp_element_without_coercion flag also won't help since it disable all coercion. Even when comparing ExactReals().one() == QQ(1).

[saraedum]

The proper solution would be to support ExactReals(AA) so there is a common parent we can coerce into. However, the elements of this ring would then not be contained in a single exactreal::Module.