#17379: Add a 'all' option to the .nth_root() method of algebraic numbers
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   Reporter:  tmonteil       |            Owner:
       Type:  enhancement    |           Status:  new
   Priority:  major          |        Milestone:  sage-6.5
  Component:  number fields  |         Keywords:
  Merged in:                 |          Authors:
  Reviewers:                 |  Report Upstream:  N/A
Work issues:                 |           Branch:
     Commit:                 |     Dependencies:
   Stopgaps:                 |
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 There is currently no `all` option for the .nth_root() method of algebraic
 numbers:

 {{{
 sage: a = QQbar(-1)
 sage: a.nth_root(3)
 0.500000000000000? + 0.866025403784439?*I
 sage: a.nth_root(3, all=True)
 ...
 TypeError: nth_root() got an unexpected keyword argument 'all'
 }}}

 while such an option exists for other representations of complex numbers:

 {{{
 sage: a = CDF(-1)
 sage: sage: a.nth_root(3)
 0.5000000000000001 + 0.8660254037844386*I
 sage: sage: a.nth_root(3, all=True)
 [0.5000000000000001 + 0.8660254037844386*I,
  -1.0 + 3.4393603416671414e-16*I,
  0.49999999999999933 - 0.8660254037844389*I]
 }}}

 The aim of this ticket is to provide one.

--
Ticket URL: <http://trac.sagemath.org/ticket/17379>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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