sympy/physics/units.py

   1 """
   2 Physical units and dimensions.
   3
   4 The base class is Unit, where all here defined units (~200) inherit from.
   5 """
   6
   7 from sympy import Rational, pi
   8 from sympy.core.basic import Basic, Atom
   9
  10 class Unit(Atom):
  11     """
  12     Base class for all physical units.
  13
  14     Create own units like:
  15     m = Unit("meter", "m")
  16     """
  17     is_positive = True    # make (m**2)**Rational(1,2) --> m
  18     is_commutative = True
  19
  20     __slots__ = ["name", "abbrev"]
  21
  22     def __new__(cls, name, abbrev, **assumptions):
  23         obj = Basic.__new__(cls, **assumptions)
  24         assert isinstance(name, str),`type(name)`
  25         assert isinstance(abbrev, str),`type(abbrev)`
  26         obj.name = name
  27         obj.abbrev = abbrev
  28         return obj
  29
  30     def __eq__(self, other):
  31         return isinstance(other, Unit) and self.name == other.name
  32
  33     def _hashable_content(self):
  34         return (self.name,self.abbrev)
  35
  36 # Delete this so it doesn't pollute the namespace
  37 del Atom
  38
  39 def defunit(value, *names):
  40     u = value
  41     g = globals()
  42     for name in names:
  43         g[name] = u
  44
  45
  46 # Dimensionless
  47
  48 percent = percents = Rational(1,100)
  49 permille = permille = Rational(1,1000)
  50
  51 ten = Rational(10)
  52
  53 yotta = ten**24
  54 zetta = ten**21
  55 exa   = ten**18
  56 peta  = ten**15
  57 tera  = ten**12
  58 giga  = ten**9
  59 mega  = ten**6
  60 kilo  = ten**3
  61 deca  = ten**1
  62 deci  = ten**-1
  63 centi = ten**-2
  64 milli = ten**-3
  65 micro = ten**-6
  66 nano  = ten**-9
  67 pico  = ten**-12
  68 femto = ten**-15
  69 atto  = ten**-18
  70 zepto = ten**-21
  71 yocto = ten**-24
  72
  73 rad = radian = radians = 1
  74 deg = degree = degrees = pi/180
  75
  76
  77 # Base units
  78
  79 defunit(Unit('meter', 'm'), 'm', 'meter', 'meters')
  80 defunit(Unit('kilogram', 'kg'), 'kg', 'kilogram', 'kilograms')
  81 defunit(Unit('second', 's'), 's', 'second', 'seconds')
  82 defunit(Unit('ampere', 'A'), 'A', 'ampere', 'amperes')
  83 defunit(Unit('kelvin', 'K'), 'K', 'kelvin', 'kelvins')
  84 defunit(Unit('mole', 'mol'), 'mol', 'mole', 'moles')
  85 defunit(Unit('candela', 'cd'), 'cd', 'candela', 'candelas')
  86
  87
  88 # Derived units
  89
  90 defunit(1/s, 'Hz', 'hz', 'hertz')
  91 defunit(m*kg/s**2, 'N', 'newton', 'newtons')
  92 defunit(N*m, 'J', 'joule', 'joules')
  93 defunit(J/s, 'W', 'watt', 'watts')
  94 defunit(N/m**2, 'Pa', 'pa', 'pascal', 'pascals')
  95 defunit(s*A, 'C', 'coulomb', 'coulombs')
  96 defunit(W/A, 'v', 'V', 'volt', 'volts')
  97 defunit(V/A, 'ohm', 'ohms')
  98 defunit(A/V, 'S', 'siemens', 'mho', 'mhos')
  99 defunit(C/V, 'F', 'farad', 'farads')
 100 defunit(J/A, 'Wb', 'wb', 'weber', 'webers')
 101 defunit(V*s/m**2, 'T', 'tesla', 'teslas')
 102 defunit(V*s/A, 'H', 'henry', 'henrys')
 103
 104
 105 # Common length units
 106
 107 defunit(kilo*m, 'km', 'kilometer', 'kilometers')
 108 defunit(deci*m, 'dm', 'decimeter', 'decimeters')
 109 defunit(centi*m, 'cm', 'centimeter', 'centimeters')
 110 defunit(milli*m, 'mm', 'millimeter', 'millimeters')
 111 defunit(micro*m, 'um', 'micrometer', 'micrometers', 'micron', 'microns')
 112 defunit(nano*m, 'nm', 'nanometer', 'nanometers')
 113 defunit(pico*m, 'pm', 'picometer', 'picometers')
 114
 115 defunit(Rational('0.3048')*m, 'ft', 'foot', 'feet')
 116 defunit(Rational('25.4')*mm, 'inch', 'inches')
 117 defunit(3*ft, 'yd', 'yard', 'yards')
 118 defunit(5280*ft, 'mi', 'mile', 'miles')
 119
 120
 121 # Common volume and area units
 122
 123 defunit(m**3 / 1000, 'l', 'liter', 'liters')
 124 defunit(deci*l, 'dl', 'deciliter', 'deciliters')
 125 defunit(centi*l, 'cl', 'centiliter', 'centiliters')
 126 defunit(milli*l, 'ml', 'milliliter', 'milliliters')
 127
 128
 129 # Common time units
 130
 131 defunit(milli*s, 'ms', 'millisecond', 'milliseconds')
 132 defunit(micro*s, 'us', 'microsecond', 'microseconds')
 133 defunit(nano*s, 'ns', 'nanosecond', 'nanoseconds')
 134 defunit(pico*s, 'ps', 'picosecond', 'picoseconds')
 135
 136 defunit(60*s, 'minute', 'minutes')
 137 defunit(60*minute, 'h', 'hour', 'hours')
 138 defunit(24*hour, 'day', 'days')
 139
 140 defunit(Rational('31558149.540')*s, 'sidereal_year', 'sidereal_years')
 141 defunit(Rational('365.24219')*day, 'tropical_year', 'tropical_years')
 142 defunit(Rational('365')*day, 'common_year', 'common_years')
 143 defunit(Rational('365.25')*day, 'julian_year', 'julian_years')
 144
 145 year = years = tropical_year
 146
 147
 148 # Common mass units
 149
 150 defunit(kilogram / kilo, 'g', 'gram', 'grams')
 151 defunit(milli * g, 'mg', 'milligram', 'milligrams')
 152 defunit(micro * g, 'ug', 'microgram', 'micrograms')
 153
 154
 155
 156 #----------------------------------------------------------------------------
 157 # Physical constants
 158 #
 159
 160 c = speed_of_light = 299792458 * m/s
 161 G = gravitational_constant = Rational('6.67428') * ten**-11 * m**3 / kg / s**2
 162 u0 = magnetic_constant = 4*pi * ten**-7 * N/A**2
 163 e0 = electric_constant = 1/(u0 * c**2)
 164 Z0 = vacuum_impedance = u0 * c
 165
 166 planck = Rational('6.2606896') * ten**-34 * J*s
 167 hbar = planck / (2*pi)
 168
 169 avogadro = (Rational('6.02214179') * 10**23) / mol
 170 boltzmann = Rational('1.3806505') * ten**-23 * J / K
 171
 172 gee = gees = Rational('9.80665') * m/s**2
 173 atmosphere = atmospheres = atm = 101325 * pascal
 174
 175
 176 # Other convenient units and magnitudes
 177
 178 defunit(c*julian_year, 'ly', 'lightyear', 'lightyears')
 179 defunit(149597870691*m, 'au', 'astronomical_unit', 'astronomical_units')
 180
 181 # Delete this so it doesn't pollute the namespace
 182 del Rational, pi