#15519: Wrong enclosing intervals for real algebraic numbers
-----------------------------+----------------------------
Reporter: mmezzarobba | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.1
Component: number fields | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
-----------------------------+----------------------------
Consider a polynomial with two close roots:
{{{
sage: x = polygen(QQ); pol = x^7-2*(10^20*x-1)^2
sage: pol.roots(RIF)
[(9.999999999999999999999999999999999999999999999999999999999999999999999?e-21,
1),
(1.000000000000000000000000000000000000000000000000000000000000000000001?e-20,
1),
(1.14869835499703500680?e8, 1)]
}}}
and represent one of these roots as an element of `AA`:
{{{
sage: a = AA.polynomial_root(pol, RIF((0.9e-20,1.0e-20)))
}}}
Then the upper bound stored internally is smaller than the actual root:
{{{
sage: a._descr._interval.upper()
9.99999999999999946e-21
}}}
and indeed we have:
{{{
sage: pol(a._descr._interval.lower().exact_rational()).sign()
-1
sage: pol(a._descr._interval.lower().exact_rational()).sign()
-1
sage: sage: a.n(50)
...
ValueError: Refining interval that does not bound unique root!
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15519>
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