#15422: factorization of non-squarefree polynomials over the p-adics
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Reporter: jdemeyer | Owner:
Type: defect | Status:
Priority: major | needs_review
Component: padics | Milestone: sage-5.13
Keywords: | Resolution:
Authors: Jeroen Demeyer | Merged in:
Report Upstream: N/A | Reviewers: Robert
Branch: | Bradshaw
Dependencies: #864, #9640, #10018, #11868 | Work issues:
| Commit:
| Stopgaps:
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Comment (by roed):
Replying to [comment:21 jdemeyer]:
> Replying to [comment:20 roed]:
> > You can '''never''' say that a p-adic polynomial has a root.
> That can't be true (or I am misunderstanding you). Using Hensel's Lemma,
you ''can'' be certain that polynomials factor in a certain way. For
example, any polynomial over `Zp` which is congruent to `(t-1)(t-2)`
modulo p, will have a single p-adic root close to 1 and a single p-adic
root close to 2. In particular, `(t-1)(t-2) + p*f` will never be
irreducible (for f in `Zp[t]`). What am I missing?...
You're right. I need to go to sleep now, but I'll think about this more
and get back to you tomorrow. Perhaps we can add an option to pass to
`factor` that allows for factoring non-squarefree polynomials.
As for the `content` comment, it was based on reading through the patch
and noting that you'd deleted that function in
`Polynomial_element_generic.pyx`. But I see now that it's defined again
in the other classes, so there's no issue.
--
Ticket URL: <http://trac.sagemath.org/ticket/15422#comment:27>
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