#10369: Yet another bug in factorization over number fields
-----------------------------+----------------------------------------------
Reporter: lftabera | Owner: tbd
Type: defect | Status: new
Priority: critical | Milestone: sage-4.6.2
Component: factorization | Keywords: factorization, number fields
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Changes (by fwclarke):
* cc: jdemeyer (added)
Comment:
I think this is very likely a pari bug, and is the same one
([http://pari.math.u-bordeaux.fr/cgi-bin/bugreport.cgi?bug=1132]) that was
fixed in response to #10279. If I'm right, it would be solved by #10430.
This is the simplest example (of the first problem) that I have found:
{{{
trousseau-bash% sage-4.6/sage
----------------------------------------------------------------------
| Sage Version 4.6, Release Date: 2010-10-30 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: L.<a> = QuadraticField(3)
sage: PL.<y> = L[]
sage: (y*(y^2 - (1 + a)/3)*(y^2 - a/2)^2).factor()
y^3 * (y^4 + (-5/6*a - 1/3)*y^2 + 1/6*a + 1/2)
}}}
This is the equivalent in pari (producing the same erroneous result):
{{{
trousseau-bash% sage-4.6/sage -gp
GP/PARI CALCULATOR Version 2.4.3 (development
svn-12577:12605)
i386 running darwin (x86-64/GMP-4.2.1 kernel) 64-bit
version
...
parisize = 8000000, primelimit = 500509
? K = nfinit(a^2 - 3);
? f = x*(x^2 + Mod(-(a + 1)/3, a^2 - 3))*(x^2 + Mod(-a/2, a^2 - 3))^2;
? nffactor(K, f)
%1 =
[x 3]
[x^4 + Mod(-5/6*a - 1/3, a^2 - 3)*x^2 + Mod(1/6*a + 1/2, a^2 - 3) 1]
}}}
But with the version of pari in sage 4.5.3 the result is correct:
{{{
trousseau-bash% sage-4.5.3/sage -gp
GP/PARI CALCULATOR Version 2.3.5 (released)
i386 running darwin (x86-64/GMP-4.2.1 kernel) 64-bit
version
...
parisize = 8000000, primelimit = 500000
? K = nfinit(a^2 - 3);
? f = x*(x^2 + Mod(-(a + 1)/3, a^2 - 3))*(x^2 + Mod(-a/2, a^2 - 3))^2;
? nffactor(K, f)
%1 =
[x 1]
[x^2 + Mod(-1/2*a, a^2 - 3) 2]
[x^2 + Mod(-1/3*a - 1/3, a^2 - 3) 1]
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10369#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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