The current sage.rings.real_mpfr deals with arbitrary precision floating-point numbers (using mpfr). This is the default "real field" in many places in Sage even though it is often wiser to use intervals or balls. We perform some cosmetic changes to sage.rings.real_mpfr to emphasize the fact that the module deals with floating-point approximations of real numbers and not genuine reals. These modifications touch a lot of files and involve deprecation of widely used names.

See also the introduction of a genuine real field class in #24456 for another motivation.

step 1

• Move create_RealField to real_field.py #24511: move the class factory create_RealField in real_field.py
• Change string representation of RealField #24523: change string representation
• rename RealField/RealNumber #24524:
  • RealField -> RealFloatingPointField_factory
  • RealField_class -> RealFloatingPointField
  • RealNumber -> RealFloatingPoint
• deprecate is_RealNumber, is_AlgebraicNumber, is_RealIntervalFieldElement, ... #24525: deprecate is_RealNumber(x) and is_RealField(x) in favour of isinstance(x, RealFloatingPoint) and isinstance(x, RealFloatingPointField)

step 2

• Deprecate RR and Reals and use RFF (or RFPF?) as the standard name for RealFloatingPointField(53)?
• more documentation.

for complex numbers, see #24489.

Component: basic arithmetic

Issue created by migration from https://trac.sagemath.org/ticket/24457