Units of measurement

This is the units package. It contains information about many units and conversions between them.

TUTORIAL:

To return a unit:

sage: units.length.meter
meter

This unit acts exactly like a symbolic variable:

sage: s = units.length.meter
sage: s^2
meter^2
sage: s + var('x')
meter + x

Units have additional information in their docstring:

sage: # You would type: units.force.dyne?
sage: print units.force.dyne._sage_doc_()
CGS unit for force defined to be gram*centimeter/second^2.
Equal to 10^-5 newtons.

You may call the convert function with units:

sage: t = units.mass.gram*units.length.centimeter/units.time.second^2
sage: t.convert(units.mass.pound*units.length.foot/units.time.hour^2)
5400000000000/5760623099*foot*pound/hour^2
sage: t.convert(units.force.newton)
1/100000*newton

Calling the convert function with no target returns base SI units:

sage: t.convert()
1/100000*kilogram*meter/second^2

Giving improper units to convert to raises a ValueError:

sage: t.convert(units.charge.coulomb)
...
ValueError: Incompatible units

Converting temperatures works as well:

sage: s = 68*units.temperature.fahrenheit
sage: s.convert(units.temperature.celsius)
20*celsius
sage: s.convert()
293.150000000000*kelvin

Trying to multiply temperatures by another unit then converting raises a ValueError:

sage: wrong = 50*units.temperature.celsius*units.length.foot
sage: wrong.convert()
...
ValueError: Cannot convert

AUTHORS:

• David Ackerman
• William Stein

class sage.symbolic.units.UnitExpression

Bases: sage.symbolic.expression.Expression

A symbolic unit.

EXAMPLES:

sage: acre = units.area.acre
sage: type(acre)
<class 'sage.symbolic.units.UnitExpression'>

TESTS:

sage: bool(loads(dumps(acre)) == acre)
True
sage: type(loads(dumps(acre)))
<class 'sage.symbolic.units.UnitExpression'>

class sage.symbolic.units.Units(data, name='')

A collection of units of a some type.

EXAMPLES:

sage: units.power
Collection of units of power: cheval_vapeur horsepower watt

trait_names()

Return completions of this unit objects. This is used by the Sage command line and notebook to create the list of method names.

EXAMPLES:

sage: units.area.trait_names()
['acre', 'are', 'barn', 'hectare', 'rood', 'section', 'square_chain', 'square_meter', 'township']

sage.symbolic.units.base_units(unit)

Converts unit to base SI units.

INPUT:

• unit

OUTPUT:

• 

EXAMPLES:

sage: sage.symbolic.units.base_units(units.length.foot)
381/1250*meter

If unit is already a base unit, it just returns that unit:

sage: sage.symbolic.units.base_units(units.length.meter)
meter

Derived units get broken down into their base parts:

sage: sage.symbolic.units.base_units(units.force.newton)
kilogram*meter/second^2
sage: sage.symbolic.units.base_units(units.volume.liter)
1/1000*meter^3

Returns variable if ‘unit’ is not a unit:

sage: sage.symbolic.units.base_units(var('x'))
x

sage.symbolic.units.convert(expr, target)

Converts units between expr and target. If target is None then converts to SI base units.

INPUT:

• – the symbolic expression converting from
• – (default None) the symbolic expression converting to

OUTPUT:

• 

EXAMPLES:

sage: sage.symbolic.units.convert(units.length.foot, None)
381/1250*meter
sage: sage.symbolic.units.convert(units.mass.kilogram, units.mass.pound)
100000000/45359237*pound

Raises ValueError if expr and target are not convertible:

sage: sage.symbolic.units.convert(units.mass.kilogram, units.length.foot)
...
ValueError: Incompatible units
sage: sage.symbolic.units.convert(units.length.meter^2, units.length.foot)
...
ValueError: Incompatible units

Recognizes derived unit relationships to base units and other derived units:

sage: sage.symbolic.units.convert(units.length.foot/units.time.second^2, units.acceleration.galileo)
762/25*galileo
sage: sage.symbolic.units.convert(units.mass.kilogram*units.length.meter/units.time.second^2, units.force.newton)
newton
sage: sage.symbolic.units.convert(units.length.foot^3, units.area.acre*units.length.inch)
1/3630*acre*inch
sage: sage.symbolic.units.convert(units.charge.coulomb, units.current.ampere*units.time.second)
ampere*second
sage: sage.symbolic.units.convert(units.pressure.pascal*units.si_prefixes.kilo, units.pressure.pounds_per_square_inch)
1290320000000/8896443230521*pounds_per_square_inch

For decimal answers multiply 1.0:

sage: sage.symbolic.units.convert(units.pressure.pascal*units.si_prefixes.kilo, units.pressure.pounds_per_square_inch)*1.0
0.145037737730209*pounds_per_square_inch

sage.symbolic.units.convert_temperature(expr, target)

Function for converting between temperatures.

INPUT:

• – a unit of temperature
• – a units of temperature

OUTPUT:

• 

EXAMPLES:

sage: t = 32*units.temperature.fahrenheit
sage: t.convert(units.temperature.celsius)
0
sage: t.convert(units.temperature.kelvin)
273.150000000000*kelvin

If target is None then it defaults to kelvin:

sage: t.convert()
273.150000000000*kelvin

Raises ValueError when either input is not a unit of temperature:

sage: t.convert(units.length.foot)
...
ValueError: Cannot convert
sage: wrong = units.length.meter*units.temperature.fahrenheit
sage: wrong.convert()
...
ValueError: Cannot convert

We directly call the convert_temperature function:

sage: sage.symbolic.units.convert_temperature(37*units.temperature.celsius,  units.temperature.fahrenheit)
493/5*fahrenheit
sage: 493/5.0
98.6000000000000

sage.symbolic.units.evalunitdict()

Replace all the string values of the unitdict variable by their evaluated forms, and builds some other tables for ease of use. This function is mainly used internally, for efficiency (and flexibility) purposes, making it easier to describe the units.

EXAMPLES:

sage: sage.symbolic.units.evalunitdict()

sage.symbolic.units.is_unit(s)

Returns a boolean when asked whether the input is in the list of units.

INPUT:

• – an object

OUTPUT:

• bool

EXAMPLES:

sage: sage.symbolic.units.is_unit(1)
False
sage: sage.symbolic.units.is_unit(units.length.meter)
True

The square of a unit is not a unit:

sage: sage.symbolic.units.is_unit(units.length.meter^2)
False

You can also directly create units using var, though they won’t have a nice docstring describing the unit:

sage: sage.symbolic.units.is_unit(var('meter'))
True

sage.symbolic.units.str_to_unit(name)

Create the symbolic unit with given name. A symbolic unit is a class that derives from symbolic expression, and has a specialized docstring.

INPUT:

• name – string

OUTPUT:

• UnitExpression

EXAMPLES:

sage: sage.symbolic.units.str_to_unit('acre')
acre
sage: type(sage.symbolic.units.str_to_unit('acre'))
<class 'sage.symbolic.units.UnitExpression'>

sage.symbolic.units.unit_derivations_expr(v)

Given derived units name, returns the corresponding units expression. For example, given ‘acceleration’ output the symbolic expression length/time^2.

INPUT:

• – string, name of a unit type such as ‘area’, ‘volume’, etc.

OUTPUT:

• symbolic expression

EXAMPLES:

sage: sage.symbolic.units.unit_derivations_expr('volume')
length^3
sage: sage.symbolic.units.unit_derivations_expr('electric_potential')
length^2*mass/(current*time^3)

If the unit name is unknown, a KeyError is raised:

sage: sage.symbolic.units.unit_derivations_expr('invalid')
...
KeyError: 'invalid'

sage.symbolic.units.unitdocs(unit)

Returns docstring for the given unit.

INPUT:

• unit

OUTPUT:

• string

EXAMPLES:

sage: sage.symbolic.units.unitdocs('meter')
'SI base unit of length.\nDefined to be the distance light travels in vacuum in 1/299792458 of a second.'
sage: sage.symbolic.units.unitdocs('amu')
'Abbreviation for atomic mass unit.\nApproximately equal to 1.660538782*10^-27 kilograms.'

Units not in the list unit_docs will raise a ValueError:

sage: sage.symbolic.units.unitdocs('earth')
...
ValueError: No documentation exists for the unit earth.

sage.symbolic.units.vars_in_str(s)

Given a string like ‘mass/(length*time)’, return the list [‘mass’, ‘length’, ‘time’].

INPUT:

• – string

OUTPUT:

• list of strings (unit names)

EXAMPLES:

sage: sage.symbolic.units.vars_in_str('mass/(length*time)')
['mass', 'length', 'time']