id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
15411,is_nilpotent on multivariate power series gives baloney,darij,,"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?",defect,new,minor,sage-6.4,algebra,,"multivariate power series, rings, nilpotent",hivert chapoton nthiery jakobkroeker,,,,N/A,,,,#14814,