#7736: factor returns a reducible factor,
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Reporter: syazdani | Owner: tbd
Type: defect | Status: new
Priority: critical | Milestone:
Component: factorization | Keywords:
Work_issues: | Author:
Upstream: N/A | Reviewer:
Merged: |
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Here is a result that confuses me (appologies for not having a simpler
example for this):
{{{
sage: E = EllipticCurve('1728z');
sage: Et = E.mod5family();
sage: f=Et.discriminant().numerator().factor()[0][0];
sage: K.<alpha> = NumberField(f);
sage: f.change_ring(K).factor()[1][0].is_irreducible()
False
}}}
Here f turns out to be a degree 12 polynomial, and when you factor it over
K, you get a linear factor and a degree 11 factor. However, degree 11
factor in this case is not irreducible. In fact, if you continue with
{{{
sage: g = f.change_ring(K).factor()[1][0];
sage: g.factor()
}}}
you get a linear factor and a degree 10 factor, where both are
irreducible.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7736>
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