Hi,
in the definition of a QuotientRing there is the following assumption
ASSUMPTION:
``I`` has a method ``I.reduce(x)`` returning the normal form
of elements `x\in R`. In other words, it is required that
``I.reduce(x)==I.reduce(y)`` `\iff x-y \in I`, and
``x-I.reduce(x) in I``, for all `x,y\in R`.
On the other hand, the default definition of reduce in
sage/rings/ideal.py says
def reduce(self, f):
return f # default
Wouldn't it be better to raise a NotImplementedError?
These are the consequences:
sage: Z16x.<x> = Integers(16)[]
sage: GR.<y> = Z16x.quotient(x**2 + x+1 )
sage: I = GR.ideal(4)
sage: I.reduce(GR(6))
6 # should be reduced mod 4
another example is
sage: J = Z16x.ideal([x+1, x+1]) # just to avoid that the ideal is
identified as a principal ideal
sage: R.<z> = Z16x.quotient(J)
sage: R(x) # should be 15
Best,
Thomas
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