crash with coredump in `crt` for polynomials over finite rings

[Georgi Guninski]

def testcrtcrash1():
"""
crash with coredump in `crt` for polynomials over finite rings
author: Georgi Guninski
"""
A=13
Kx.<x>=Integers(A**2)[]
mods=[x^2+A,x^4+A]
resi=[x,x^2]
g=crt(resi,mods)
return g


Aborted (core dumped)

[Nils Bruin]

In case someone wants to follow up, the crash is due to an unsurprising:

Flint exception (Impossible inverse):
    Cannot invert modulo 13*13

so perhaps a bit more extensive error catching/processing needs to happen in the flint wrapper.

[Georgi Guninski]

This is offtopic: P != NP implies you can't work efficiently with many
nilpotent elements over commutative ring or algebra even on a
quantum computer.

The reduction is from counting hamiltonian cycles in a graph
via powers of nilpotent matrix.

For reference, check:

https://mathoverflow.net/q/364267/12481