Dear sage community,

I am new to sage, so please forgive me if I am reporting well-known
behaviour here.
When generating multivariate polynomial rings, some (seemingly) odd
things can happen:

1. Sage seems to guess the meaning of 'x' in some cases:

sage: QX=MPolynomialRing(QQ,2,'xy'); QX
Multivariate Polynomial Ring in x, y over Rational Field
sage: x in QX     # no variables assinged to indeterminates yet...
False
sage: indets=QX.objgens()[1];indets
(x, y)
sage: x in indets
True

But x and indets[0] have different types.

2. indeterminates are sometimes shared between rings:
sage: R.<x,y>=QQ[];R
Multivariate Polynomial Ring in x, y over Rational Field
sage: R2=MPolynomialRing(QQ,2,'xy')
sage: R==R2
True
sage: R2=MPolynomialRing(QQ,1,'x')
sage: x in R2
False

This looks inconsistent. Shouldn't R2 have it's own set of
indeterminates? If the user wants to have the same display names for
indeterminates of different rings that shouldn't be sage's problem.

Thanks very much,
marc

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