Ideal membership for univariate polynomial

[hivert]

sage: R.<x> = PolynomialRing(ZZ)
sage: p, q = 4 + 3*x + x^2, 1 + x^2
sage: I = R.ideal([p, q])
sage: S = R.quotient_ring(I)
sage: S(p) == S(0)
False

This is plain wrong !

sage: p in I
---------------------------------------------------------------------------
NotImplementedError                       Traceback (most recent call last)

/tmp/<ipython console> in <module>()

/home/data/Sage-Install/sage-5.6.rc1/local/lib/python2.7/site-packages/sage/rings/ideal.pyc in __contains__(self, x)
    316     def __contains__(self, x):
    317         try:
--> 318             return self._contains_(self.__ring(x))
    319         except TypeError:
    320             return False

/home/data/Sage-Install/sage-5.6.rc1/local/lib/python2.7/site-packages/sage/rings/ideal.pyc in _contains_(self, x)
    322     def _contains_(self, x):
    323         # check if x, which is assumed to be in the ambient ring, is actually in this ideal.
--> 324         raise NotImplementedError
    325 
    326     def __nonzero__(self):

NotImplementedError: 

Florent

[hivert]

I left a todo in #12510 deactivating some generic tests (TestSuite) in

sage/rings/quotient_ring.py

Those generic test should be reinstated when this ticket is fixed.

Florent

[slelievre]

See also #23621.