Surprising comparisons with complex numbers

[fredrik-johansson]

julia> AcbField(64)(1) == 1+0im
false

julia> fmpq(1) == 1+0im
false

[wbhart]

Probably more off by 0.7 bugs.

[fredrik-johansson]

Note that

julia> QQ(1) == 1+0im
true

works in AbstractAlgebra, so this appears to be a Nemo-exclusive feature.

[wbhart]

The reason this happens is that complex numbers are just not supported outside Arb in Nemo or AbstractAlgebra.

It just happens to work in AbstractAlgebra because QQ(1) returns a Julia Rational{BigInt} and Julia has defined an appropriate comparison.

In Nemo, the equality test falls back to the default Julia one which just tests if they are the same object.

This is a rather massive thing to fix as it means defining ad hoc comparison, binary operations and divisions for every type in AbstractAlgebra and Nemo with complex numbers.

You can tell we aren't numerical people can't you. :-)

[fredrik-johansson]

It also needs to be fixed for qqbar and ca.