401 lines
14 KiB
Python
401 lines
14 KiB
Python
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from sympy.physics.units.definitions.dimension_definitions import current, temperature, amount_of_substance, \
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luminous_intensity, angle, charge, voltage, impedance, conductance, capacitance, inductance, magnetic_density, \
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magnetic_flux, information
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from sympy.core.numbers import (Rational, pi)
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from sympy.core.singleton import S as S_singleton
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from sympy.physics.units.prefixes import kilo, mega, milli, micro, deci, centi, nano, pico, kibi, mebi, gibi, tebi, pebi, exbi
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from sympy.physics.units.quantities import PhysicalConstant, Quantity
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One = S_singleton.One
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#### UNITS ####
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# Dimensionless:
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percent = percents = Quantity("percent", latex_repr=r"\%")
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percent.set_global_relative_scale_factor(Rational(1, 100), One)
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permille = Quantity("permille")
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permille.set_global_relative_scale_factor(Rational(1, 1000), One)
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# Angular units (dimensionless)
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rad = radian = radians = Quantity("radian", abbrev="rad")
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radian.set_global_dimension(angle)
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deg = degree = degrees = Quantity("degree", abbrev="deg", latex_repr=r"^\circ")
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degree.set_global_relative_scale_factor(pi/180, radian)
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sr = steradian = steradians = Quantity("steradian", abbrev="sr")
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mil = angular_mil = angular_mils = Quantity("angular_mil", abbrev="mil")
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# Base units:
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m = meter = meters = Quantity("meter", abbrev="m")
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# gram; used to define its prefixed units
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g = gram = grams = Quantity("gram", abbrev="g")
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# NOTE: the `kilogram` has scale factor 1000. In SI, kg is a base unit, but
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# nonetheless we are trying to be compatible with the `kilo` prefix. In a
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# similar manner, people using CGS or gaussian units could argue that the
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# `centimeter` rather than `meter` is the fundamental unit for length, but the
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# scale factor of `centimeter` will be kept as 1/100 to be compatible with the
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# `centi` prefix. The current state of the code assumes SI unit dimensions, in
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# the future this module will be modified in order to be unit system-neutral
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# (that is, support all kinds of unit systems).
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kg = kilogram = kilograms = Quantity("kilogram", abbrev="kg")
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kg.set_global_relative_scale_factor(kilo, gram)
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s = second = seconds = Quantity("second", abbrev="s")
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A = ampere = amperes = Quantity("ampere", abbrev='A')
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ampere.set_global_dimension(current)
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K = kelvin = kelvins = Quantity("kelvin", abbrev='K')
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kelvin.set_global_dimension(temperature)
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mol = mole = moles = Quantity("mole", abbrev="mol")
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mole.set_global_dimension(amount_of_substance)
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cd = candela = candelas = Quantity("candela", abbrev="cd")
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candela.set_global_dimension(luminous_intensity)
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# derived units
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newton = newtons = N = Quantity("newton", abbrev="N")
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joule = joules = J = Quantity("joule", abbrev="J")
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watt = watts = W = Quantity("watt", abbrev="W")
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pascal = pascals = Pa = pa = Quantity("pascal", abbrev="Pa")
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hertz = hz = Hz = Quantity("hertz", abbrev="Hz")
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# CGS derived units:
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dyne = Quantity("dyne")
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dyne.set_global_relative_scale_factor(One/10**5, newton)
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erg = Quantity("erg")
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erg.set_global_relative_scale_factor(One/10**7, joule)
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# MKSA extension to MKS: derived units
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coulomb = coulombs = C = Quantity("coulomb", abbrev='C')
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coulomb.set_global_dimension(charge)
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volt = volts = v = V = Quantity("volt", abbrev='V')
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volt.set_global_dimension(voltage)
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ohm = ohms = Quantity("ohm", abbrev='ohm', latex_repr=r"\Omega")
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ohm.set_global_dimension(impedance)
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siemens = S = mho = mhos = Quantity("siemens", abbrev='S')
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siemens.set_global_dimension(conductance)
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farad = farads = F = Quantity("farad", abbrev='F')
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farad.set_global_dimension(capacitance)
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henry = henrys = H = Quantity("henry", abbrev='H')
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henry.set_global_dimension(inductance)
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tesla = teslas = T = Quantity("tesla", abbrev='T')
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tesla.set_global_dimension(magnetic_density)
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weber = webers = Wb = wb = Quantity("weber", abbrev='Wb')
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weber.set_global_dimension(magnetic_flux)
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# CGS units for electromagnetic quantities:
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statampere = Quantity("statampere")
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statcoulomb = statC = franklin = Quantity("statcoulomb", abbrev="statC")
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statvolt = Quantity("statvolt")
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gauss = Quantity("gauss")
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maxwell = Quantity("maxwell")
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debye = Quantity("debye")
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oersted = Quantity("oersted")
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# Other derived units:
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optical_power = dioptre = diopter = D = Quantity("dioptre")
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lux = lx = Quantity("lux", abbrev="lx")
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# katal is the SI unit of catalytic activity
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katal = kat = Quantity("katal", abbrev="kat")
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# gray is the SI unit of absorbed dose
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gray = Gy = Quantity("gray")
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# becquerel is the SI unit of radioactivity
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becquerel = Bq = Quantity("becquerel", abbrev="Bq")
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# Common mass units
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mg = milligram = milligrams = Quantity("milligram", abbrev="mg")
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mg.set_global_relative_scale_factor(milli, gram)
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ug = microgram = micrograms = Quantity("microgram", abbrev="ug", latex_repr=r"\mu\text{g}")
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ug.set_global_relative_scale_factor(micro, gram)
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# Atomic mass constant
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Da = dalton = amu = amus = atomic_mass_unit = atomic_mass_constant = PhysicalConstant("atomic_mass_constant")
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t = metric_ton = tonne = Quantity("tonne", abbrev="t")
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tonne.set_global_relative_scale_factor(mega, gram)
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# Electron rest mass
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me = electron_rest_mass = Quantity("electron_rest_mass", abbrev="me")
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# Common length units
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km = kilometer = kilometers = Quantity("kilometer", abbrev="km")
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km.set_global_relative_scale_factor(kilo, meter)
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dm = decimeter = decimeters = Quantity("decimeter", abbrev="dm")
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dm.set_global_relative_scale_factor(deci, meter)
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cm = centimeter = centimeters = Quantity("centimeter", abbrev="cm")
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cm.set_global_relative_scale_factor(centi, meter)
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mm = millimeter = millimeters = Quantity("millimeter", abbrev="mm")
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mm.set_global_relative_scale_factor(milli, meter)
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um = micrometer = micrometers = micron = microns = \
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Quantity("micrometer", abbrev="um", latex_repr=r'\mu\text{m}')
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um.set_global_relative_scale_factor(micro, meter)
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nm = nanometer = nanometers = Quantity("nanometer", abbrev="nm")
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nm.set_global_relative_scale_factor(nano, meter)
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pm = picometer = picometers = Quantity("picometer", abbrev="pm")
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pm.set_global_relative_scale_factor(pico, meter)
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ft = foot = feet = Quantity("foot", abbrev="ft")
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ft.set_global_relative_scale_factor(Rational(3048, 10000), meter)
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inch = inches = Quantity("inch")
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inch.set_global_relative_scale_factor(Rational(1, 12), foot)
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yd = yard = yards = Quantity("yard", abbrev="yd")
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yd.set_global_relative_scale_factor(3, feet)
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mi = mile = miles = Quantity("mile")
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mi.set_global_relative_scale_factor(5280, feet)
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nmi = nautical_mile = nautical_miles = Quantity("nautical_mile")
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nmi.set_global_relative_scale_factor(6076, feet)
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angstrom = angstroms = Quantity("angstrom", latex_repr=r'\r{A}')
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angstrom.set_global_relative_scale_factor(Rational(1, 10**10), meter)
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# Common volume and area units
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ha = hectare = Quantity("hectare", abbrev="ha")
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l = L = liter = liters = Quantity("liter")
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dl = dL = deciliter = deciliters = Quantity("deciliter")
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dl.set_global_relative_scale_factor(Rational(1, 10), liter)
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cl = cL = centiliter = centiliters = Quantity("centiliter")
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cl.set_global_relative_scale_factor(Rational(1, 100), liter)
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ml = mL = milliliter = milliliters = Quantity("milliliter")
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ml.set_global_relative_scale_factor(Rational(1, 1000), liter)
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# Common time units
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ms = millisecond = milliseconds = Quantity("millisecond", abbrev="ms")
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millisecond.set_global_relative_scale_factor(milli, second)
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us = microsecond = microseconds = Quantity("microsecond", abbrev="us", latex_repr=r'\mu\text{s}')
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microsecond.set_global_relative_scale_factor(micro, second)
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ns = nanosecond = nanoseconds = Quantity("nanosecond", abbrev="ns")
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nanosecond.set_global_relative_scale_factor(nano, second)
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ps = picosecond = picoseconds = Quantity("picosecond", abbrev="ps")
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picosecond.set_global_relative_scale_factor(pico, second)
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minute = minutes = Quantity("minute")
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minute.set_global_relative_scale_factor(60, second)
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h = hour = hours = Quantity("hour")
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hour.set_global_relative_scale_factor(60, minute)
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day = days = Quantity("day")
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day.set_global_relative_scale_factor(24, hour)
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anomalistic_year = anomalistic_years = Quantity("anomalistic_year")
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anomalistic_year.set_global_relative_scale_factor(365.259636, day)
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sidereal_year = sidereal_years = Quantity("sidereal_year")
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sidereal_year.set_global_relative_scale_factor(31558149.540, seconds)
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tropical_year = tropical_years = Quantity("tropical_year")
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tropical_year.set_global_relative_scale_factor(365.24219, day)
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common_year = common_years = Quantity("common_year")
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common_year.set_global_relative_scale_factor(365, day)
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julian_year = julian_years = Quantity("julian_year")
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julian_year.set_global_relative_scale_factor((365 + One/4), day)
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draconic_year = draconic_years = Quantity("draconic_year")
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draconic_year.set_global_relative_scale_factor(346.62, day)
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gaussian_year = gaussian_years = Quantity("gaussian_year")
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gaussian_year.set_global_relative_scale_factor(365.2568983, day)
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full_moon_cycle = full_moon_cycles = Quantity("full_moon_cycle")
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full_moon_cycle.set_global_relative_scale_factor(411.78443029, day)
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year = years = tropical_year
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#### CONSTANTS ####
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# Newton constant
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G = gravitational_constant = PhysicalConstant("gravitational_constant", abbrev="G")
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# speed of light
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c = speed_of_light = PhysicalConstant("speed_of_light", abbrev="c")
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# elementary charge
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elementary_charge = PhysicalConstant("elementary_charge", abbrev="e")
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# Planck constant
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planck = PhysicalConstant("planck", abbrev="h")
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# Reduced Planck constant
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hbar = PhysicalConstant("hbar", abbrev="hbar")
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# Electronvolt
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eV = electronvolt = electronvolts = PhysicalConstant("electronvolt", abbrev="eV")
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# Avogadro number
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avogadro_number = PhysicalConstant("avogadro_number")
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# Avogadro constant
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avogadro = avogadro_constant = PhysicalConstant("avogadro_constant")
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# Boltzmann constant
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boltzmann = boltzmann_constant = PhysicalConstant("boltzmann_constant")
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# Stefan-Boltzmann constant
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stefan = stefan_boltzmann_constant = PhysicalConstant("stefan_boltzmann_constant")
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# Molar gas constant
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R = molar_gas_constant = PhysicalConstant("molar_gas_constant", abbrev="R")
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# Faraday constant
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faraday_constant = PhysicalConstant("faraday_constant")
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# Josephson constant
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josephson_constant = PhysicalConstant("josephson_constant", abbrev="K_j")
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# Von Klitzing constant
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von_klitzing_constant = PhysicalConstant("von_klitzing_constant", abbrev="R_k")
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# Acceleration due to gravity (on the Earth surface)
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gee = gees = acceleration_due_to_gravity = PhysicalConstant("acceleration_due_to_gravity", abbrev="g")
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# magnetic constant:
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u0 = magnetic_constant = vacuum_permeability = PhysicalConstant("magnetic_constant")
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# electric constat:
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e0 = electric_constant = vacuum_permittivity = PhysicalConstant("vacuum_permittivity")
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# vacuum impedance:
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Z0 = vacuum_impedance = PhysicalConstant("vacuum_impedance", abbrev='Z_0', latex_repr=r'Z_{0}')
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# Coulomb's constant:
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coulomb_constant = coulombs_constant = electric_force_constant = \
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PhysicalConstant("coulomb_constant", abbrev="k_e")
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atmosphere = atmospheres = atm = Quantity("atmosphere", abbrev="atm")
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kPa = kilopascal = Quantity("kilopascal", abbrev="kPa")
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kilopascal.set_global_relative_scale_factor(kilo, Pa)
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bar = bars = Quantity("bar", abbrev="bar")
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pound = pounds = Quantity("pound") # exact
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psi = Quantity("psi")
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dHg0 = 13.5951 # approx value at 0 C
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mmHg = torr = Quantity("mmHg")
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atmosphere.set_global_relative_scale_factor(101325, pascal)
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bar.set_global_relative_scale_factor(100, kPa)
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pound.set_global_relative_scale_factor(Rational(45359237, 100000000), kg)
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mmu = mmus = milli_mass_unit = Quantity("milli_mass_unit")
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quart = quarts = Quantity("quart")
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# Other convenient units and magnitudes
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ly = lightyear = lightyears = Quantity("lightyear", abbrev="ly")
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au = astronomical_unit = astronomical_units = Quantity("astronomical_unit", abbrev="AU")
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# Fundamental Planck units:
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planck_mass = Quantity("planck_mass", abbrev="m_P", latex_repr=r'm_\text{P}')
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planck_time = Quantity("planck_time", abbrev="t_P", latex_repr=r't_\text{P}')
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planck_temperature = Quantity("planck_temperature", abbrev="T_P",
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latex_repr=r'T_\text{P}')
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planck_length = Quantity("planck_length", abbrev="l_P", latex_repr=r'l_\text{P}')
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planck_charge = Quantity("planck_charge", abbrev="q_P", latex_repr=r'q_\text{P}')
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|
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# Derived Planck units:
|
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planck_area = Quantity("planck_area")
|
||
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|
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|
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planck_volume = Quantity("planck_volume")
|
||
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|
||
|
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planck_momentum = Quantity("planck_momentum")
|
||
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|
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|
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planck_energy = Quantity("planck_energy", abbrev="E_P", latex_repr=r'E_\text{P}')
|
||
|
|
|
||
|
|
planck_force = Quantity("planck_force", abbrev="F_P", latex_repr=r'F_\text{P}')
|
||
|
|
|
||
|
|
planck_power = Quantity("planck_power", abbrev="P_P", latex_repr=r'P_\text{P}')
|
||
|
|
|
||
|
|
planck_density = Quantity("planck_density", abbrev="rho_P", latex_repr=r'\rho_\text{P}')
|
||
|
|
|
||
|
|
planck_energy_density = Quantity("planck_energy_density", abbrev="rho^E_P")
|
||
|
|
|
||
|
|
planck_intensity = Quantity("planck_intensity", abbrev="I_P", latex_repr=r'I_\text{P}')
|
||
|
|
|
||
|
|
planck_angular_frequency = Quantity("planck_angular_frequency", abbrev="omega_P",
|
||
|
|
latex_repr=r'\omega_\text{P}')
|
||
|
|
|
||
|
|
planck_pressure = Quantity("planck_pressure", abbrev="p_P", latex_repr=r'p_\text{P}')
|
||
|
|
|
||
|
|
planck_current = Quantity("planck_current", abbrev="I_P", latex_repr=r'I_\text{P}')
|
||
|
|
|
||
|
|
planck_voltage = Quantity("planck_voltage", abbrev="V_P", latex_repr=r'V_\text{P}')
|
||
|
|
|
||
|
|
planck_impedance = Quantity("planck_impedance", abbrev="Z_P", latex_repr=r'Z_\text{P}')
|
||
|
|
|
||
|
|
planck_acceleration = Quantity("planck_acceleration", abbrev="a_P",
|
||
|
|
latex_repr=r'a_\text{P}')
|
||
|
|
|
||
|
|
|
||
|
|
# Information theory units:
|
||
|
|
bit = bits = Quantity("bit")
|
||
|
|
bit.set_global_dimension(information)
|
||
|
|
|
||
|
|
byte = bytes = Quantity("byte")
|
||
|
|
|
||
|
|
kibibyte = kibibytes = Quantity("kibibyte")
|
||
|
|
mebibyte = mebibytes = Quantity("mebibyte")
|
||
|
|
gibibyte = gibibytes = Quantity("gibibyte")
|
||
|
|
tebibyte = tebibytes = Quantity("tebibyte")
|
||
|
|
pebibyte = pebibytes = Quantity("pebibyte")
|
||
|
|
exbibyte = exbibytes = Quantity("exbibyte")
|
||
|
|
|
||
|
|
byte.set_global_relative_scale_factor(8, bit)
|
||
|
|
kibibyte.set_global_relative_scale_factor(kibi, byte)
|
||
|
|
mebibyte.set_global_relative_scale_factor(mebi, byte)
|
||
|
|
gibibyte.set_global_relative_scale_factor(gibi, byte)
|
||
|
|
tebibyte.set_global_relative_scale_factor(tebi, byte)
|
||
|
|
pebibyte.set_global_relative_scale_factor(pebi, byte)
|
||
|
|
exbibyte.set_global_relative_scale_factor(exbi, byte)
|
||
|
|
|
||
|
|
# Older units for radioactivity
|
||
|
|
curie = Ci = Quantity("curie", abbrev="Ci")
|
||
|
|
|
||
|
|
rutherford = Rd = Quantity("rutherford", abbrev="Rd")
|