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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