Thank you, Nils !
Trying to pinpoint things by running a manual solution step by step, it
seems that the stumbling oint is the division on two algebraics. I'll try
to make a clear minimal example and report it.
Le lundi 31 janvier 2022 à 00:49:22 UTC+1, Nils Bruin a écrit :
> On Saturday, 29 January 2022 at 13:51:14 UTC-8 Emmanuel Charpentier wrote:
>
>> /usr/local/sage-9/local/var/lib/sage/venv-python3.9/lib/python3.9/site-packages/sage/rings/qqbar.py
>>
>> in pari_field(self)
>>
>>> 3134 if self._pari_field is None:
>>> 3135 pari_pol = self._field.pari_polynomial("y")
>>> -> 3136 self._pari_field = pari_pol.nfinit(1)
>>> 3137 return self._pari_field
>>> 3138
>>>
>>> cypari2/auto_gen.pxi in cypari2.gen.Gen_base.nfinit()
>>> KeyboardInterrupt:
>>>
>>>
>>> nf_init is a perfectly respectable place to hang. After interruption,
> can you "%debug" and see what the value of pari_pol is? I'd expect that
> nfinit determines the ring of integers, which means factoring the
> discriminant. [QQbar shouldn't need the ring of integers of element
> arithmetic, but this has been stumbled on before: QQbar often tries to find
> an "optimized" form of the number field, which for small examples is often
> quite doable and, if you end up doing a LOT of arithmetic in the same
> field, is often worth the investment. However, because of factoring of the
> discriminant, it's fully subexponential in complexity, whereas all the
> things QQbar needs to do are polynomial time. So we already know that QQbar
> will do things with the wrong theoretical asymptotic complexity. That can
> come back and bite you, when reality and asymptotics start behaving
> similarly (which happens eventually ... asymptotically speakinh)
>
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