>> 2) Why should <an_integer> * sqrt(1/2) belong to SR? Why isn't it
>> turned into an algebraic number immediately? If it did, the problem,
>
> Nils answered 2 already and I agree with Nils.

I do not think that he did. The __repr__ function of algebraic numbers
is bad indeed, but if we can have this:

    sage: QQbar(sqrt(2))
    sqrt(2)

Then I believe that <an_integer>*sqrt(2) should be a member of QQbar,
and not rely on SymbolicRing.

I just created a thread about this __repr__ issue:
https://groups.google.com/forum/#!topic/sage-devel/dB-E7VjEFr4

Nathann

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