#13054: Pernicious bug for algebraic numbers
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Reporter: rbeezer | Owner: davidloeffler
Type: defect | Status: new
Priority: major | Milestone: sage-5.1
Component: number fields | Keywords: sd40.5
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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I hit this bug '''all''' the time when doing linear algebra over `QQbar` -
just as soon as matrices get to be about 10 x 10. David Roe helped locate
the problem, I have no ideas about solutions.
Line 1563 (5.1.beta0) of sage/rings/qqbar.py:
{{{
rev = parent(best_elt.Mod(pari_poly).modreverse().lift())
}}}
Bug results in the situation when {{{best_elt.Mod(pari_poly)}}} is not
square free, in contrast to the PARI docs, which say:
{{{
Help: modreverse(a): reverse polymod of the polmod a, if it exists
Doc: $a$ being a polmod $A(X)$ modulo $T(X)$, finds
the ``reverse polmod'' $B(X)$ modulo $Q(X)$, where $Q$ is the minimal
polynomial of $a$, which must be equal to the degree of $T$, and such
that if
$\theta$ is a root of $T$ then $\theta=B(\alpha)$ for a certain root
$\alpha$
of $Q$.
}}}
So the assumption of the equality of the degrees is violated. This causes
a trap in PARI.
It would make a lot of exact linear algebra '''much''' more reliable if
this was resolved.
I'll try to find a reproducible example.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13054>
Sage <http://www.sagemath.org>
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