classes for the fields of complex and real numbers

[videlec]

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 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).

Depends on #24464
Depends on #24465
Depends on #24483
Depends on #24457

CC: @rwst @tscrim @egourgoulhon @mjungmath

Component: basic arithmetic

Work Issues: merge conflict

Author: Vincent Delecroix

Branch/Commit: u/rws/24456 @ febfe35

Issue created by migration from https://trac.sagemath.org/ticket/24456

[tscrim]

comment:2

+1

[videlec]

comment:3

:-) pushing in a minute...

[videlec]

Author: Vincent Delecroix

[videlec]

Description changed:

--- 
+++ 
@@ -1 +1,9 @@
 We create a (mostly abstract) class to model the set of real numbers.
+
+We also fix
+
+```
+sage: ZZ.completion(oo, 53)
+Real Field with 53 bits of precision
+```
+as `ZZ` is complete (for the usual absolute value)!

[videlec]

Commit: 78f677e

[videlec]

New commits:

78f677e

24456: class for the field of real numbers

[videlec]

Branch: u/vdelecroix/24456

[videlec]

Description changed:

--- 
+++ 
@@ -7,3 +7,7 @@
 Real Field with 53 bits of precision
 ```
 as `ZZ` is complete (for the usual absolute value)!
+
+follow-ups:
+- #24457: rename `sage.rings.real_mpfr.RealField`
+- #24458: a useful real lazy field