Opened 5 years ago

Last modified 20 months ago

#15411 new defect

is_nilpotent on multivariate power series gives baloney

Reported by: darij Owned by:
Priority: minor Milestone: sage-6.4
Component: algebra Keywords: multivariate power series, rings, nilpotent
Cc: hivert, chapoton, nthiery, jakobkroeker Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: #14814 Stopgaps:

Description

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?

Change History (4)

comment:1 Changed 5 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:2 Changed 4 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:3 Changed 4 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:4 Changed 20 months ago by jakobkroeker

  • Cc jakobkroeker added
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