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Unit-safe computations with quantities (including money)

## Project description

The package quantity provides classes for unit-safe computations with quantities, including money.

### Defining a quantity class

A basic type of quantity is declared just by sub-classing Quantity:

>>> class Length(Quantity):
...     pass
...


But, as long as there is no unit defined for that class, you can not create any instance for the new quantity class:

>>> l = Length(1)
Traceback (most recent call last):
ValueError: A unit must be given.


If there is a reference unit, the simplest way to define it is giving a name and a symbol for it as keywords. The meta-class of Quantity will then create a unit automatically:

>>> class Mass(Quantity,
...            ref_unit_name='Kilogram',
...            ref_unit_symbol='kg'):
...     pass
...
>>> Mass.ref_unit
Unit('kg')
>>> class Length(Quantity,
...              ref_unit_name='Metre',
...              ref_unit_symbol='m'):
...     pass
...
>>> Length.ref_unit
Unit('m')


Now, this unit can be given to create a quantity:

>>> METRE = Length.ref_unit
>>> print(Length(15, METRE))
15 m


If no unit is given, the reference unit is used:

>>> print(Length(15))
15 m


Other units can be derived from the reference unit (or another unit), giving a definition by multiplying a scaling factor with that unit:

>>> a_thousandth = Decimal("0.001")
>>> KILOGRAM = Mass.ref_unit
>>> GRAM = Mass.new_unit('g', 'Gram', a_thousandth * KILOGRAM)
>>> MILLIMETRE = Length.new_unit('mm', 'Millimetre', a_thousandth * METRE)
>>> MILLIMETRE
Unit('mm')
>>> KILOMETRE = Length.new_unit('km', 'Kilometre', 1000 * METRE)
>>> KILOMETRE
Unit('km')
>>> CENTIMETRE = Length.new_unit('cm', 'Centimetre', 10 * MILLIMETRE)
>>> CENTIMETRE
Unit('cm')


Instead of a number a SI prefix can be used as scaling factor. SI prefixes are provided in a sub-module:

>>> from quantity.si_prefixes import *
>>> NANO.abbr, NANO.name, NANO.factor
('n', 'Nano', Decimal('0.000000001'))

>>> NANOMETRE = Length.new_unit('nm', 'Nanometre', NANO * METRE)
>>> NANOMETRE
Unit('nm')


Using one unit as a reference and defining all other units by giving a scaling factor is only possible if the units have the same scale. Otherwise, units can just be instantiated without giving a definition:

>>> class Temperature(Quantity):
...     pass
...
>>> CELSIUS = Temperature.new_unit('°C', 'Degree Celsius')
>>> FAHRENHEIT = Temperature.new_unit('°F', 'Degree Fahrenheit')
>>> KELVIN = Temperature.new_unit('K', 'Kelvin')


Derived types of quantities are declared by giving a definition based on more basic types of quantities:

>>> class Volume(Quantity,
...              define_as=Length ** 3,
...              ref_unit_name='Cubic Metre'):
...     pass
...
>>> class Duration(Quantity,
...                ref_unit_name='Second',
...                ref_unit_symbol='s'):
...     pass
...
>>> class Velocity(Quantity,
...                define_as=Length / Duration,
...                ref_unit_name='Metre per Second'):
...     pass
...


If no symbol for the reference unit is given with the class declaration, a symbol is generated from the definition, as long as all types of quantities in that definition have a reference unit.

>>> Volume.ref_unit.symbol
'm³'
>>> Velocity.ref_unit.symbol
'm/s'


Other units have to be defined explicitly. This can be done either as shown above or by deriving them from units of the base quantities:

>>> CUBIC_CENTIMETRE = Volume.derive_unit_from(CENTIMETRE,
...                                            name='Cubic Centimetre')
>>> CUBIC_CENTIMETRE
Unit('cm³')
>>> HOUR = Duration.new_unit('h', 'Hour', 3600 * Duration.ref_unit)
>>> KILOMETRE_PER_HOUR = Velocity.derive_unit_from(KILOMETRE, HOUR)
>>> KILOMETRE_PER_HOUR
Unit('km/h')


### Instantiating quantities

The simplest way to create an instance of a class Quantity subclass is to call the class giving an amount and a unit. If the unit is omitted, the quantity's reference unit is used (if one is defined):

>>> Length(15, MILLIMETRE)
Length(Decimal(15), Unit('mm'))


Alternatively, an amount and a unit can be multiplied:

>>> 17.5 * KILOMETRE
Length(Decimal('17.5'), Unit('km'))


Also, it's possible to create a Quantity sub-class instance from a string representation:

>>> Length('17.5 km')
Length(Decimal('17.5'), Unit('km'))


### Unit-safe computations

A quantity can be converted to a quantity using a different unit by calling the method Quantity.convert:

>>> l5cm = Length(Decimal(5), CENTIMETRE)
>>> l5cm.convert(MILLIMETRE)
Length(Decimal(50), Unit('mm'))
>>> l5cm.convert(KILOMETRE)
Length(Decimal('0.00005'), Unit('km'))


Quantities can be compared to other quantities using all comparison operators defined for numbers. Different units are taken into account automatically, as long as they are compatible, i.e. a conversion is available:

>>> Length(27) <= Length(91)
True
>>> Length(27, METRE) <= Length(91, CENTIMETRE)
False


Quantities can be added to or subtracted from other quantities …:

>>> Length(27) + Length(9)
Length(Decimal(36))
>>> Length(27) - Length(91)
Length(Decimal(-64))
>>> Length(27) + Length(12, CENTIMETER)
Length(Decimal('27.12'))
>>> Length(12, CENTIMETER) + Length(17, METER)
Length(Decimal('1712'), Length.Unit('cm'))


… as long as they are instances of the same quantity type:

>>> Length(27) + Duration(9)
Traceback (most recent call last):
IncompatibleUnitsError: Can't add a 'Length' and a 'Duration'


Quantities can be multiplied or divided by scalars, preserving the unit:

>>> 7.5 * Length(3, CENTIMETRE)
Length(Decimal('22.5'), Unit('cm'))
>>> Duration(66, MINUTE) / 11
Duration(Decimal(6), Unit('min'))


Quantities can be multiplied or divided by other quantities …:

>>> Length(15, METRE) / Duration(3, SECOND)
Velocity(Decimal(5))


… as long as the resulting type of quantity is defined …:

>>> Duration(4, SECOND) * Length(7)
Traceback (most recent call last):
UndefinedResultError: Undefined result: Duration * Length


… or the result is a scalar:

>>> Duration(2, MINUTE) / Duration(50, SECOND)
Decimal('2.4')


### Money

Money is a special type of quantity. Its unit type is known as currency.

Money differs from physical quantities mainly in two aspects:

• Money amounts are discrete. For each currency there is a smallest fraction that can not be split further.

• The relation between different currencies is not fixed, instead, it varies over time.

The sub-package quantity.money provides classes and functions to deal with these specifics.

A currency must explicitly be registered as a unit for further use. The easiest way to do this is to call Money.register_currency. The method is backed by a database of currencies defined in ISO 4217. It takes the 3-character ISO 4217 code as parameter.

Money derives from Quantity, so all operations on quantities can also be applied to instances of Money. But because there is no fixed relation between currencies, there is no implicit conversion between money amounts of different currencies. Resulting values are always quantized to the smallest fraction defined with the currency.

A conversion factor between two currencies can be defined by using the class ExchangeRate. It is given a unit currency (aka base currency), a unit multiple, a term currency (aka price currency) and a term amount, i.e. the amount in term currency equivalent to unit multiple in unit currency.

Multiplying an amount in some currency with an exchange rate with the same currency as unit currency results in the equivalent amount in term currency. Likewise, dividing an amount in some currency with an exchange rate with the same currency as term currency results in the equivalent amount in unit currency.

As Money derives from Quantity, it can be combined with other quantities in order to define a new quantity. This is, for example, useful for defining prices per quantum.

For more details see the documentation provided with the source distribution or here.

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