Combining and defining units
****************************

Units and quantities can be combined together using the regular Python
numeric operators.  For example::

  >>> from astropy import units as u
  >>> fluxunit = u.erg / (u.cm ** 2 * u.s)
  >>> fluxunit
  Unit("erg / (cm2 s)")
  >>> 52.0 * fluxunit  # doctest: +FLOAT_CMP
  <Quantity  52. erg / (cm2 s)>
  >>> 52.0 * fluxunit / u.s  # doctest: +FLOAT_CMP
  <Quantity  52. erg / (cm2 s2)>

Units support fractional powers, which retain their precision through
complex operations.  To do this, it is recommended to use
`fractions.Fraction` objects.  For example::

  >>> from fractions import Fraction
  >>> Franklin = u.g ** Fraction(1, 2) * u.cm ** Fraction(3, 2) * u.s ** -1

.. note::

    Floating-point powers that are effectively the same as fractions
    with a denominator less than 10 are implicitly converted to
    `~fractions.Fraction` objects under the hood.  Therefore the
    following are equivalent::

        >>> x = u.m ** Fraction(1, 3)
        >>> x.powers
        [Fraction(1, 3)]
        >>> x = u.m ** (1. / 3.)
        >>> x.powers
        [Fraction(1, 3)]

Users are free to define new units, either fundamental or compound
using the `~astropy.units.def_unit` function.  For example::

  >>> bakers_fortnight = u.def_unit('bakers_fortnight', 13 * u.day)

The addition of a string gives the new unit a name that will show up
when the unit is printed::

  >>> 10. * bakers_fortnight  # doctest: +FLOAT_CMP
  <Quantity  10. bakers_fortnight>

Creating a new fundamental unit is simple::

  >>> titter = u.def_unit('titter')
  >>> chuckle = u.def_unit('chuckle', 5 * titter)
  >>> laugh = u.def_unit('laugh', 4 * chuckle)
  >>> guffaw = u.def_unit('guffaw', 3 * laugh)
  >>> rofl = u.def_unit('rofl', 4 * guffaw)
  >>> death_by_laughing = u.def_unit('death_by_laughing', 10 * rofl)
  >>> (1. * rofl).to(titter)  # doctest: +FLOAT_CMP
  <Quantity  240. titter>

One can see the definition of a unit and its :ref:`decomposition <decomposing>`
via::

  >>> rofl.represents
  Unit("4 guffaw")
  >>> rofl.decompose()
  Unit("240 titter")

By default, custom units are not searched by methods such as
`~astropy.units.core.UnitBase.find_equivalent_units`.  However, they
can be enabled by calling `~astropy.units.add_enabled_units`::

  >>> kmph = u.def_unit('kmph', u.km / u.h)
  >>> (u.m / u.s).find_equivalent_units()
  []
  >>> u.add_enabled_units([kmph])
  <astropy.units.core._UnitContext object at ...>
  >>> (u.m / u.s).find_equivalent_units()
    Primary name | Unit definition | Aliases
  [
    kmph         | 0.277778 m / s  |         ,
  ]