Source code for sympy.physics.units

"""
Physical units and dimensions.

The base class is Unit, where all here defined units (~200) inherit from.

The find_unit function can help you find units for a given quantity:

    >>> import sympy.physics.units as u
    >>> u.find_unit('coul')
    ['coulomb', 'coulombs']
    >>> u.find_unit(u.charge)
    ['C', 'charge', 'coulomb', 'coulombs']
    >>> u.coulomb
    A*s

Units are always given in terms of base units that have a name and
an abbreviation:

    >>> u.A.name
    'ampere'
    >>> u.ampere.abbrev
    'A'

The generic name for a unit (like 'length', 'mass', etc...)
can help you find units:

    >>> u.find_unit('magnet')
    ['magnetic_flux', 'magnetic_constant', 'magnetic_flux_density']
    >>> u.find_unit(u.magnetic_flux)
    ['Wb', 'wb', 'weber', 'webers', 'magnetic_flux']

If, for a given session, you wish to add a unit you may do so:

    >>> u.find_unit('gal')
    []
    >>> u.gal = 4*u.quart
    >>> u.gal/u.inch**3
    924

To see a given quantity in terms of some other unit, divide by the desired
unit:

    >>> mph = u.miles/u.hours
    >>> (u.m/u.s/mph).n(2)
    2.2

The units are defined in terms of base units, so when you divide similar
units you will obtain a pure number. This means, for example, that if you
divide a real-world mass (like grams) by the atomic mass unit (amu) you
will obtain Avogadro's number. To obtain the answer in moles you
should divide by the unit ``avogadro``:

    >>> u.grams/u.amu
    602214179000000000000000
    >>> _/u.avogadro
    mol

For chemical calculations the unit ``mmu`` (molar mass unit) has been
defined so this conversion is handled automatically. For example, the
number of moles in 1 kg of water might be calculated as:

    >>> u.kg/(18*u.mmu).n(3)
    55.5*mol

If you need the number of atoms in a mol as a pure number you can use
``avogadro_number`` but if you need it as a dimensional quantity you should use
``avogadro_constant``. (``avogadro`` is a shorthand for the dimensional
quantity.)

    >>> u.avogadro_number
    602214179000000000000000
    >>> u.avogadro_constant
    602214179000000000000000/mol
"""

from sympy import Rational, pi
from sympy.core import AtomicExpr

[docs]class Unit(AtomicExpr): """ Base class for base unit of physical units. >>> from sympy.physics.units import Unit >>> Unit("meter", "m") m Other units are derived from base units: >>> import sympy.physics.units as u >>> cm = u.m/100 >>> 100*u.cm m """ is_positive = True # make sqrt(m**2) --> m is_commutative = True is_number = False __slots__ = ["name", "abbrev"] def __new__(cls, name, abbrev, **assumptions): obj = AtomicExpr.__new__(cls, **assumptions) assert isinstance(name, str),repr(type(name)) assert isinstance(abbrev, str),repr(type(abbrev)) obj.name = name obj.abbrev = abbrev return obj def __getnewargs__(self): return (self.name, self.abbrev) def __eq__(self, other): return isinstance(other, Unit) and self.name == other.name def __hash__(self): return super(Unit, self).__hash__() def _hashable_content(self): return (self.name, self.abbrev) @property def free_symbols(self): return set() # Dimensionless
percent = percents = Rational(1,100) permille = permille = Rational(1,1000) ten = Rational(10) yotta = ten**24 zetta = ten**21 exa = ten**18 peta = ten**15 tera = ten**12 giga = ten**9 mega = ten**6 kilo = ten**3 deca = ten**1 deci = ten**-1 centi = ten**-2 milli = ten**-3 micro = ten**-6 nano = ten**-9 pico = ten**-12 femto = ten**-15 atto = ten**-18 zepto = ten**-21 yocto = ten**-24 rad = radian = radians = 1 deg = degree = degrees = pi/180 # Base units length = m = meter = meters = Unit('meter', 'm') mass = kg = kilogram = kilograms = Unit('kilogram', 'kg') time = s = second = seconds = Unit('second', 's') current = A = ampere = amperes = Unit('ampere', 'A') temperature = K = kelvin = kelvins = Unit('kelvin', 'K') amount = mol = mole = moles = Unit('mole', 'mol') luminosity = cd = candela = candelas = Unit('candela', 'cd') # Derived units volume = meter**3 frequency = Hz = hz = hertz = 1/s force = N = newton = newtons = m*kg/s**2 energy = J = joule = joules = N*m power = W = watt = watts = J/s pressure = Pa = pa = pascal = pascals = N/m**2 charge = C = coulomb = coulombs = s*A voltage = v = V = volt = volts = W/A resistance = ohm = ohms = V/A conductance = S = siemens = mho = mhos = A/V capacitance = F = farad = farads = C/V magnetic_flux = Wb = wb = weber = webers = J/A magnetic_flux_density = T = tesla = teslas = V*s/m**2 inductance = H = henry = henrys = V*s/A speed = m/s acceleration = m/s**2 density = kg/m**3 # Common length units km = kilometer = kilometers = kilo*m dm = decimeter = decimeters = deci*m cm = centimeter = centimeters = centi*m mm = millimeter = millimeters = milli*m um = micrometer = micrometers = micron = microns = micro*m nm = nanometer = nanometers = nano*m pm = picometer = picometers = pico*m ft = foot = feet = Rational('0.3048')*m inch = inches = Rational('25.4')*mm yd = yard = yards = 3*ft mi = mile = miles = 5280*ft # Common volume and area units l = liter = liters = m**3 / 1000 dl = deciliter = deciliters = deci*l cl = centiliter = centiliters = centi*l ml = milliliter = milliliters = milli*l # Common time units ms = millisecond = milliseconds = milli*s us = microsecond = microseconds = micro*s ns = nanosecond = nanoseconds = nano*s ps = picosecond = picoseconds = pico*s minute = minutes = 60*s h = hour = hours = 60*minute day = days = 24*hour sidereal_year = sidereal_years = Rational('31558149.540')*s tropical_year = tropical_years = Rational('365.24219')*day common_year = common_years = Rational('365')*day julian_year = julian_years = Rational('365.25')*day year = years = tropical_year # Common mass units g = gram = grams = kilogram / kilo mg = milligram = milligrams = milli * g ug = microgram = micrograms = micro * g #---------------------------------------------------------------------------- # Physical constants # c = speed_of_light = 299792458 * m/s G = gravitational_constant = Rational('6.67428') * ten**-11 * m**3 / kg / s**2 u0 = magnetic_constant = 4*pi * ten**-7 * N/A**2 e0 = electric_constant = 1/(u0 * c**2) Z0 = vacuum_impedance = u0 * c planck = Rational('6.62606896') * ten**-34 * J*s hbar = planck / (2*pi) avogadro_number = Rational('6.02214179') * 10**23 avogadro = avogadro_constant = avogadro_number / mol boltzmann = Rational('1.3806505') * ten**-23 * J / K gee = gees = Rational('9.80665') * m/s**2 atmosphere = atmospheres = atm = 101325 * pascal kPa = kilo*Pa bar = bars = 100*kPa pound = pounds = 0.45359237 * kg * gee #exact psi = pound / inch ** 2 dHg0 = 13.5951 # approx value at 0 C mmHg = dHg0 * 9.80665 * Pa amu = amus = gram / avogadro / mol mmu = mmus = gram / mol quart = quarts = 231 * inch**3 eV = 1.602176487e-19 * J # Other convenient units and magnitudes ly = lightyear = lightyears = c*julian_year au = astronomical_unit = astronomical_units = 149597870691*m
[docs]def find_unit(quantity): """ Return a list of matching units names. if quantity is a string -- units containing the string `quantity` if quantity is a unit -- units having matching base units Examples ======== >>> from sympy.physics import units as u >>> u.find_unit('charge') ['charge'] >>> u.find_unit(u.charge) ['C', 'charge', 'coulomb', 'coulombs'] >>> u.find_unit('volt') ['volt', 'volts', 'voltage'] >>> u.find_unit(u.inch**3)[:5] ['l', 'cl', 'dl', 'ml', 'liter'] """ import sympy.physics.units as u rv = [] if isinstance(quantity, str): rv = [i for i in dir(u) if quantity in i] else: units = quantity.as_coeff_Mul()[1] for i in dir(u): try: if units == eval('u.' + i).as_coeff_Mul()[1]: rv.append(str(i)) except: pass return sorted(rv, key=len) # Delete this so it doesn't pollute the namespace
del Rational, pi