#12026: root finding misses a root over QQbar
---------------------------+------------------------------------------------
Reporter: was | Owner: AlexGhitza
Type: defect | Status: positive_review
Priority: critical | Milestone: sage-4.8
Component: algebra | Keywords:
Work_issues: | Upstream: N/A
Reviewer: Keshav Kini | Author: William Stein
Merged: | Dependencies:
---------------------------+------------------------------------------------
Changes (by kini):
* status: needs_review => positive_review
Old description:
> {{{
> sage: A = matrix(QQ, 8, lambda i, j: 1/(i + j + 1))
> sage: f = A.charpoly()
> sage: f.degree()
> 8
> sage: f.is_squarefree() # so f must have 8 roots over the algebraic
> closure.
> True
> sage: len(f.roots(QQbar)) # VERY BAD
> 7
> }}}
> At least the roots that are found are really roots:
> {{{
> sage: [f(a[0])==0 for a in f.roots(QQbar)]
> [True, True, True, True, True, True, True]
> }}}
New description:
{{{
sage: A = matrix(QQ, 8, lambda i, j: 1/(i + j + 1))
sage: f = A.charpoly()
sage: f.degree()
8
sage: f.is_squarefree() # so f must have 8 roots over the algebraic
closure.
True
sage: len(f.roots(QQbar)) # VERY BAD
7
}}}
At least the roots that are found are really roots:
{{{
sage: [f(a[0])==0 for a in f.roots(QQbar)]
[True, True, True, True, True, True, True]
}}}
----
Apply:
1. [attachment:trac_12026.patch]
1. [attachment:trac_12026.reviewer.patch]
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/12026#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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