Dear all,
obviously Sage does not distinguish between precisions of power series:
sage: R.<t> = PowerSeriesRing(ZZ)
sage: O(t).is_zero()
True
sage: O(t) == O(t**2)
True
Similarly for p-adics:
sage: O(3).is_zero()
True
sage: O(3) == O(3^2)
True
sage:
This seems to be explicitly intended:
def __nonzero__(self):
"""
Return True if this power series is not equal to 0.
EXAMPLES::
sage: R.<q> = ZZ[[ ]]; R
Power Series Ring in q over Integer Ring
sage: f = 1 + 3*q + O(q^10)
sage: f.is_zero()
False
sage: (0 + O(q^2)).is_zero()
True
sage: R(0).is_zero()
True
sage: (0 + O(q^1000)).is_zero()
True
"""
return not not self.polynomial()
Why?
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