#21068: O(x) equals zero in PowerSeriesRing
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Reporter: dkrenn | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.3
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by pbruin):
No, it is correct. The documentation says:
{{{
sage: R.<x> = ZZ[[]]
sage: x._cmp_??
Source:
cpdef int _cmp_(self, right) except -2:
r"""
Comparison of self and ``right``.
We say two approximate power series are equal if they agree for
all coefficients up to the *minimum* of the precisions of each.
Thus, e.g., `f = 1 + q + O(q^2)` is equal to `g = 1 + O(q)`.
This is how PARI defines equality of power series, but not how
Magma defines equality. (Magma would declare `f` and `g` unequal.)
The PARI/Sage convention is consistent with the idea that
comparison should take place after coercing both elements into
a common parent. Hence, in the above example `f` is truncated
to `f + O(q)`, which is considered to be equal to `g`, even
though the coefficients of `q` are unknown for both series in
that comparison.
}}}
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Ticket URL: <https://trac.sagemath.org/ticket/21068#comment:1>
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