is_nilpotent on multivariate power series gives baloney

[darijgr]

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?

Depends on #14814

CC: @hivert @fchapoton @nthiery @sagetrac-jakobkroeker

Component: algebra

Keywords: multivariate power series, rings, nilpotent

Issue created by migration from https://trac.sagemath.org/ticket/15411