#12600: machine epsilon for RR, RDF, ...
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       Reporter:  dkrenn             |        Owner:  jason, jkantor
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.4
      Component:  numerical          |   Resolution:
       Keywords:  machine epsilon    |    Merged in:
        Authors:  Jeroen Demeyer     |    Reviewers:
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jdemeyer/ticket/12600            |  5e83b95e5161797bddc676156e9d629d839e3670
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by mmezzarobba):

 * status:  needs_review => needs_work


Comment:

 This breaks the usual doctest in `coercion_and_categories.rst`.

 {{{
 Failed example:
     [p for p in dir(Field) if p not in dir(Parent)]
 Expected:
     ['__div__', '__fraction_field', '__ideal_monoid', '__iter__',
      '__pow__', '__rdiv__', '__rpow__', '__rxor__', '__xor__',
      '_an_element', '_an_element_c', '_an_element_impl', '_coerce_',
      '_coerce_c', '_coerce_impl', '_coerce_self', '_coerce_try',
      '_default_category', '_gens', '_gens_dict',
      '_has_coerce_map_from', '_ideal_class_', '_latex_names', '_list',
      '_one_element', '_pseudo_fraction_field',
      '_random_nonzero_element', '_richcmp', '_unit_ideal',
      '_zero_element', '_zero_ideal', 'algebraic_closure',
      'base_extend', 'cardinality', 'class_group', 'coerce_map_from_c',
      'coerce_map_from_impl', 'content', 'divides', 'extension',
      'fraction_field', 'frobenius_endomorphism', 'gcd', 'gen', 'gens',
      'get_action_c', 'get_action_impl', 'has_coerce_map_from_c',
      'has_coerce_map_from_impl', 'ideal', 'ideal_monoid',
      'integral_closure', 'is_commutative', 'is_field', 'is_finite',
      'is_integral_domain', 'is_integrally_closed', 'is_noetherian',
      'is_prime_field', 'is_ring', 'is_subring',
      'krull_dimension', 'list', 'ngens', 'one', 'one_element',
      'order', 'prime_subfield', 'principal_ideal', 'quo', 'quotient',
      'quotient_ring', 'random_element', 'unit_ideal', 'zero',
      'zero_element', 'zero_ideal', 'zeta', 'zeta_order']
 Got:
     ['__div__',
      '__fraction_field',
      '__ideal_monoid',
      '__iter__',
      '__pow__',
      '__rdiv__',
      '__rpow__',
      '__rxor__',
      '__xor__',
      '_an_element',
      '_an_element_c',
      '_an_element_impl',
      '_coerce_',
      '_coerce_c',
      '_coerce_impl',
      '_coerce_self',
      '_coerce_try',
      '_default_category',
      '_gens',
      '_gens_dict',
      '_has_coerce_map_from',
      '_ideal_class_',
      '_latex_names',
      '_list',
      '_one_element',
      '_pseudo_fraction_field',
      '_random_nonzero_element',
      '_richcmp',
      '_unit_ideal',
      '_zero_element',
      '_zero_ideal',
      'algebraic_closure',
      'base_extend',
      'cardinality',
      'class_group',
      'coerce_map_from_c',
      'coerce_map_from_impl',
      'content',
      'divides',
      ***'epsilon',***
      'extension',
      'fraction_field',
      'frobenius_endomorphism',
      'gcd',
      'gen',
      'gens',
      'get_action_c',
      'get_action_impl',
      'has_coerce_map_from_c',
      'has_coerce_map_from_impl',
      'ideal',
      'ideal_monoid',
      'integral_closure',
      'is_commutative',
      'is_field',
      'is_finite',
      'is_integral_domain',
      'is_integrally_closed',
      'is_noetherian',
      'is_prime_field',
      'is_ring',
      'is_subring',
      'krull_dimension',
      'list',
      'ngens',
      'one',
      'one_element',
      'order',
      'prime_subfield',
      'principal_ideal',
      'quo',
      'quotient',
      'quotient_ring',
      'random_element',
      'unit_ideal',
      'zero',
      'zero_element',
      'zero_ideal',
      'zeta',
      'zeta_order']
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/12600#comment:10>
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