#252: Make number fields work when polynomial not integral or not monic.
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Reporter: was | Owner: davidloeffler
Type: defect | Status: needs_work
Priority: major | Milestone: sage-6.4
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: Peter Bruin | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/pbruin/252-number_fields | d1227146064d0e4ebcaf313f6eeec5c70713dde3
Dependencies: #18740 | Stopgaps:
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Changes (by kartikv):
* status: needs_review => needs_work
Comment:
Something weird seems to be going on with factoring. This is "normal"
behavior for a number field.
{{{
sage: F.<a> = NumberField(x^3+x+1)
sage: F(2).factor()
2
sage: F(3).factor()
(a^2 + a + 2) * (-a + 1)
sage: (a^2 + a + 2).factor()
a^2 + a + 2
sage: F.factor(3)
(Fractional ideal (a^2 + a + 2)) * (Fractional ideal (-a + 1))
sage: (-a+1).factor()
-a + 1
}}}
This is not.
{{{
sage: F.<a> = NumberField(2*x^3+x+1)
sage: F(2).factor()
(-47*a^2 + 21*a - 93/2) * (-1/2*a^2 + 1/2*a)^2 * (1/2*a^2 + 1/2*a)
sage: F.factor(2)
(Fractional ideal (-1/2*a^2 + 1/2*a))^2 * (Fractional ideal (1/2*a^2 +
1/2*a))
sage: (-47*a^2 + 21*a - 93/2).norm()
-8192
sage: (-47*a^2 + 21*a - 93/2).factor()
(3718815975/16384*a^2 - 1336872061/16384*a + 7884913157/32768) * (-1/2*a^2
+ 1/2*a)^14 * (1/2*a^2 + 1/2*a)^-1
sage: (1/2*a^2 + 1/2*a).factor()
(13/512*a^2 - 11/512*a - 7/256) * (-1/2*a^2 + 1/2*a)^-4
}}}
Somehow, it's not controlling primes over the leading coefficient
properly...
--
Ticket URL: <http://trac.sagemath.org/ticket/252#comment:28>
Sage <http://www.sagemath.org>
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