In the discussion [1] it was noticed out that sage cannot reduce elements 
in polynomial rings over arbitrary rings modulo non-principal ideals and 
(more importantly) how to react to this. There was a general tendency for 
raising an exception rather than returning bogus results. But in the 
current version the issue still persists.

The same is true of PowerSeriesRings (even over fields):

R.<t> = PowerSeriesRing(GF(2))
Q.<tbar> = QuotientRing(R,t)
tbar == tbar^2
False

The difference here is that sage should be able to reduce elements 
(otherwise power series rings are not very useful). So I have two questions:

1. Is there a particular reason, why this is not implemented?
2. Is there a general policy of returning wrong results rather than raising 
NotImplementedError?

[1] https://groups.google.com/d/msg/sage-devel/DAOo9nxpGNA/L9qMXvq5yK0J

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