#15411: is_nilpotent on multivariate power series gives baloney
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Reporter: darij | Owner:
Type: defect | Status: new
Priority: minor | Milestone: sage-5.13
Component: algebra | Keywords: multivariate power series,
Merged in: | rings, nilpotent
Reviewers: | Authors:
Work issues: | Report Upstream: N/A
Commit: | Branch:
Stopgaps: | Dependencies: #14814
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From `sage/rings/multi_power_series_ring_element.py` (I added the
warning/todo in #14814):
{{{
def is_nilpotent(self):
"""
Return ``True`` if ``self`` is nilpotent. This occurs if
- ``self`` has finite precision and positive valuation, or
- ``self`` is constant and nilpotent in base ring.
Otherwise, return ``False``.
.. WARNING::
This is so far just a sufficient condition, so don't trust
a ``False`` output to be legit!
.. TODO::
What should we do about this method? Is nilpotency of a
power series even decidable (assuming a nilpotency oracle
in the base ring)? And I am not sure that returning
``True`` just because the series has finite precision and
zero constant term is a good idea.
}}}
How shall we fix this?
Notice that `is_nilpotent` is NotImplemented for univariate power series.
Maybe we can just follow that example -- or does something rely on this
method?
--
Ticket URL: <http://trac.sagemath.org/ticket/15411>
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