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24456 classes for the fields of complex and real numbers vdelecroix "We create (mostly abstract) classes to model the set of complex and real numbers as `sage.rings.complex_field.ComplexField` and `sage.rings.real_field.RealField`.
See also task ticket #17713.
Use cases for this new ""real field"" object:
1. As some placeholder object to denote the field of real numbers, for example as output of `QQ.completion(oo)`, for domain/codomain of symbolic functions, in manifolds, etc. This implies that it should be a unique object.
2. As a Sage analogy to [https://www.python.org/dev/peps/pep-3141/ PEP 3141]: it should provide a way to ask ""is `x` a real number"" or ""is `X` a substructure of the reals"" or maybe ""does parent `X` represent the real numbers"". Also, we should be able to ask ""is `x` an ''exact'' or ''approximate'' real number"". Note that Sage already has partial support for PEP 3141 but only for elements (not parents).
3. As a class factory for all concrete real fields (e.g. the `create_RealField` function that is currently used for non-exact approximations)." enhancement needs_work major sage-8.2 basic arithmetic rws tscrim egourgoulhon gh-mjungmath Vincent Delecroix N/A merge conflict u/rws/24456 febfe35f9a4fd3c509e1ab4e94b9c30e77ab7359 #24464, #24465, #24483, #24457