#11890: Sage cannot factor polynomials over number fields with unfactorable
discriminant
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Reporter: jdemeyer | Owner: davidloeffler
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7.2
Component: number fields | Keywords: nffactor PARI nfinit pari_nf
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Description changed by jdemeyer:
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)
> }}}
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 avoid calling `nfinit()`.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11890#comment:1>
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