Hi,

The algorithm used doesn't need to be specific to the p-adics,
but shouldn't apply an algorithm for fields or integral domains.

Rather than the matrix code, it looks like this is the source of
the problem:

sage: M.parent().base_ring()
101-adic Ring with capped relative precision 2
sage: R.is_integral_domain()
True

With such a result, the wrong linear algebra is applied.

One could possibly identify which algorithms to apply for real
complex fields, p-adics, and power series rings from this:

sage: R.is_exact()
False

Inexact rings are only approximations to mathematical
objects.  However, in this case the intended ring is the
quotient ring Z/p^nZ (= Z_p/p^n Z_p), which is 'exact'
(i.e. a well-defined ring) but is not an integral domain.

I would hope that the matrix code would then pick up a
valid algorithm to apply, even if not the most efficient.

--David

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