Thanks for the sleuthing and ideas, John.  Yes, I should have used a
monic polynomial in my example since the original problem I have is
with factors of a characteristic polynomial (and get similar
behavior).

I also get

sage: M._gens is None
True

The eigenspace code (and probably eigenvalues, too) assume the root
field has just one generator, so there is more to do there perhaps.

Is that indicative of anything?  I'll dig deeper and see if I can get
to the bottom of this.  Maybe at Bug Days 32.  ;-)

Rob

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