#11890: Sage cannot factor polynomials over number fields with unfactorable
discriminant
-----------------------------------------+----------------------------------
Reporter: jdemeyer | Owner: davidloeffler
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-pending
Component: number fields | Keywords: nffactor PARI
nfinit pari_nf
Work_issues: | Upstream: N/A
Reviewer: Luis Felipe Tabera Alonso | Author: Jeroen Demeyer
Merged: | Dependencies: #11891, #11130
-----------------------------------------+----------------------------------
Old description:
> Let `K` be a number field with a discriminant which cannot be factored.
> Let `f` be a polynomial in `K[x]`. Then Sage is unable to factor `f`
> because it calls PARI's `nfinit()` on `K`:
> {{{
> sage: p = next_prime(10^50); q = next_prime(10^51)
> sage: K = QuadraticField(p*q)
> sage: x = polygen(K); factor(x^2+1)
> [... takes a very long time ...]
> }}}
>
> The solution is to call `nfinit()` with the defining polynomial when the
> discriminant cannot be factored. If that fails, fall back to
> `factornf()`.
>
> See also #10910.
>
> '''Apply''' [attachment:11890.patch],
> [attachment:11890_try_nffactor.patch] and
> [attachment:11890_reviewer.patch].
New description:
Let `K` be a number field with a discriminant which cannot be factored.
Let `f` be a polynomial in `K[x]`. Then Sage is unable to factor `f`
because it calls PARI's `nfinit()` on `K`:
{{{
sage: p = next_prime(10^50); q = next_prime(10^51)
sage: K = QuadraticField(p*q)
sage: x = polygen(K); factor(x^2+1)
[... takes a very long time ...]
}}}
The solution is to call `nfinit()` with the defining polynomial when the
discriminant cannot be factored. If that fails, fall back to
`factornf()`.
See also #10910.
'''Apply''' [attachment:11890_rebased.patch],
[attachment:11890_try_nffactor.patch] and
[attachment:11890_reviewer.patch].
--
Comment(by jdemeyer):
Trivial rebase.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11890#comment:13>
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