text: ##      -*-   coding: utf-8   -*-     ##
  ##          Sage Doctest File         ##
  #**************************************#
  #*    Generated from PreTeXt source   *#
  #*    on 2017-08-24T11:43:34-07:00    *#
  #*                                    *#
  #*   http://mathbook.pugetsound.edu   *#
  #*                                    *#
  #**************************************#
  ##
  """
  Please contact Rob Beezer (beezer@ups.edu) with
  any test failures here that need to be changed
  as a result of changes accepted into Sage.  You
  may edit/change this file in any sensible way, so
  that development work may procede.  Your changes
  may later be replaced by the authors of "Abstract
  Algebra: Theory and Applications" when the text is
  updated, and a replacement of this file is proposed
  for review.
  """
  ##
  ## To execute doctests in these files, run
  ##   $ $SAGE_ROOT/sage -t <directory-of-these-files>
  ## or
  ##   $ $SAGE_ROOT/sage -t <a-single-file>
  ##
  ## Replace -t by "-tp n" for parallel testing,
  ##   "-tp 0" will use a sensible number of threads
  ##
  ## See: http://www.sagemath.org/doc/developer/doctesting.html
  ##   or run  $ $SAGE_ROOT/sage --advanced  for brief help
  ##
  ## Generated at 2017-08-24T11:43:34-07:00
  ## From "Abstract Algebra"
  ## At commit 26d3cac0b4047f4b8d6f737542be455606e2c4b4
  ##
  ## Exercises 6.6 Sage Exercises
  ##
  r"""
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: a = 5
      sage: b = 10
      sage: c = 6
      sage: d = 13
      sage: a.divides(b)
      True
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: not (b in [c,d])
      True
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: a.divides(b) and not (b in [c,d])
      True
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: a = 20
      sage: b = 6
      sage: a.mod(b)
      2
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: prime_range(50, 100)
      [53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: all([True, True, True, True])
      True
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: all([True, True, False, True])
      False
  
  ~~~~~~~~~~~~~~~~~~~~~~ ::
  
      sage: [a/b for a in srange(9) for b in srange(1,a) if gcd(a,b)==1]
      [2, 3, 3/2, 4, 4/3, 5, 5/2, 5/3, 5/4, 6, 6/5,
       7, 7/2, 7/3, 7/4, 7/5, 7/6, 8, 8/3, 8/5, 8/7]
  
  """
  