Hi Keshav,
> Incidentally, `ZZ in Fields` works just fine::
>
> sage: 5/1 in ZZ
> True
> sage: 5/1 in ZZ()
>
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
>
> /home/fs/src/workflow/<ipython console> in <module>()
>
> TypeError: argument of type 'sage.rings.integer.Integer' is not iterable
> sage: ZZ in Fields
> False
> sage: ZZ in Fields()
> False
> sage: QQ in Fields
> True
> sage: QQ in Fields()
> True
>
> I don't pretend to understand why this is the case :) But maybe it's
> better if we tell new users to use `ZZ in Fields` instead of `ZZ in
> Fields()`, to minimize confusion...? Or maybe doing so would be
> misleading in ways I haven't realized?
It works because Nicolas did the work (Ticket #9469 Category membership,
without arguments, Merged in: sage-5.0.beta6). I think you are right
saying that we should teach "QQ in Fields" to beginner rather than
"QQ in Fields()", except that if I remember correctly, there is a performance
issue for the short notation. Also they don't have the exact same meaning. The
difference is apparent in
sage: QQ^2 in VectorSpaces(QQ)
True
sage: QQ^2 in VectorSpaces
True
sage: QQ^2 in VectorSpaces(CC)
False
Note that they are still some mathematically surprising answers:
sage: QQ in VectorSpaces(QQ) # bootstrap problem
False
sage: QQbar in VectorSpaces(QQ)
False
So the answer is: thinks are going better in each new Sage release.
Cheers,
Florent
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