I think QuotientRingElement is not meant to be instantiated directly like
that. The docstring of QuotientRing discourages that, and I suppose the
same applies to QuotientRingElement. Using S.from_sympy(x) works better.
Example:

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>>> S = FF(2).old_poly_ring(x, y)/[x**2, x*y, y**2]
>>> S
GF(2)[x,y]/<x**2,x*y,y**2>
>>> X = S.from_sympy(x)
>>> Y = S.from_sympy(y)
>>> print(X + X)
0 + <x**2,x*y,y**2>
>>> print(X + Y)
x + y + <x**2,x*y,y**2>
>>> print((X+Y)**2)
0 + <x**2,x*y,y**2>
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