I've noticed the following strange behavior (bug):

sage: A.<a> = PolynomialRing(QQ)
sage: 3 in A
True

sage: A2.<a,b> = PolynomialRing(QQ)
sage: 3 in A2
False

So apparently "in" for multivariate polynomial rings is slightly
broken, but I don't know where to look to fix it.  I did spend some
time looking for documentation or previous email threads, but "in"
makes for a tough search.  (This seems to be called "membership
testing" sometimes, but I haven't found documentation for that
either.)

thanks,
Niles

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