sure, i think it is a bit weird as well.  It certainly has behaviour
that is unexpected.  I think this will cause a lot of confusion, so I
think openning a ticket is a good idea.

As for multiplying those two polynomials, it seems that what you have
said works.  I will give it a try.

Cheers

On 30 May, 13:16, simon.k...@uni-jena.de wrote:
> Hi!
>
> A little addendum:
>
> > For a similar reason, neither f nor g are elements of R.
>
> I would agree that it is a little confusing that something is equal to
> an element of a polynomial ring but is not an element of that ring, or
> in pure form:
>   sage: R = QQ['x','y']
>   sage: R1.<x>=QQ[]
>   sage: R2.<y>=QQ[]
>   sage: x in R
>   False
>   sage: x == R.gen(0)
>   True
>
> This is at least inconsistent, because for rational numbers that
> happen to be integers, the containment is answered in a different way:
>   sage: (1/1).parent()
>   Rational Field
>   sage: (1/1).parent() == ZZ
>   False
>   sage: 1/1 in ZZ
>   True
>
> So, although 1/1 is given as an element of the rationals, it is
> recognized as an element of the integers.
>
> But why is the generator x of a univariate polynomial ring not
> recognized as an element of a bivariate polynomial ring in x and y?
>
> Question to the developers: Is this perhaps due to the following (a
> bug in the coercion system?):
>   sage: R._has_coerce_map_from(R)
>
> ---------------------------------------------------------------------------
>   TypeError                                 Traceback (most recent
> call last)
>
>   /home/SimonKing/.sage/temp/sage.math.washington.edu  /5548/
> _home_SimonKing__sage_init_sage_0.py in <module>()
>
>   TypeError: 'dict' object is not callable
>
> This happens on sage.math with sage-3.4.2. Shall I open a ticket?
>
> Cheers,
>   Simon
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