#18670: Use abs() to test for accuracy of roots of complex-valued functions
------------------------------------+------------------------
       Reporter:  strogdon          |        Owner:
           Type:  defect            |       Status:  new
       Priority:  blocker           |    Milestone:  sage-6.8
      Component:  doctest coverage  |   Resolution:
       Keywords:                    |    Merged in:
        Authors:                    |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:                    |     Stopgaps:
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Comment (by strogdon):

 With sage-6.8.beta3 installed I have the following failure:
 {{{
 sage -t --long src/sage/rings/polynomial/polynomial_element.pyx
 **********************************************************************
 File "src/sage/rings/polynomial/polynomial_element.pyx", line 5577, in
 sage.rings.polynomial.polynomial_element.Polynomial.roots
 Failed example:
     f(f.roots()[0][0])  # abs tol 1e-13
 Expected:
     3.3306690738754696e-15 + 1.3704315460216776e-15*I
 Got:
     1.1102230246251565e-16*I
 **********************************************************************
 1 item had failures:
    1 of 177 in sage.rings.polynomial.polynomial_element.Polynomial.roots
     [1752 tests, 1 failure, 17.15 s]
 ----------------------------------------------------------------------
 sage -t --long src/sage/rings/polynomial/polynomial_element.pyx  # 1
 doctest failed
 ----------------------------------------------------------------------
 }}}

 There may be similar failures on other architectures. I have
 {{{
 uname -a
 Linux ledaig 3.6.11-gentoo #6 SMP Mon Aug 25 17:39:25 CDT 2014 x86_64
 Dual-Core AMD Opteron(tm) Processor 2218 AuthenticAMD GNU/Linux
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/18670#comment:1>
Sage <http://www.sagemath.org>
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