Coverage for /usr/lib/python3/dist-packages/sympy/physics/units/systems/si.py: 99%

1"""

2SI unit system.

3Based on MKSA, which stands for "meter, kilogram, second, ampere".

4Added kelvin, candela and mole.

6"""

8from __future__ import annotations

10from sympy.physics.units import DimensionSystem, Dimension, dHg0

12from sympy.physics.units.quantities import Quantity

14from sympy.core.numbers import (Rational, pi)

15from sympy.core.singleton import S

16from sympy.functions.elementary.miscellaneous import sqrt

17from sympy.physics.units.definitions.dimension_definitions import (

18 acceleration, action, current, impedance, length, mass, time, velocity,

19 amount_of_substance, temperature, information, frequency, force, pressure,

20 energy, power, charge, voltage, capacitance, conductance, magnetic_flux,

21 magnetic_density, inductance, luminous_intensity

22)

23from sympy.physics.units.definitions import (

24 kilogram, newton, second, meter, gram, cd, K, joule, watt, pascal, hertz,

25 coulomb, volt, ohm, siemens, farad, henry, tesla, weber, dioptre, lux,

26 katal, gray, becquerel, inch, liter, julian_year, gravitational_constant,

27 speed_of_light, elementary_charge, planck, hbar, electronvolt,

28 avogadro_number, avogadro_constant, boltzmann_constant, electron_rest_mass,

29 stefan_boltzmann_constant, Da, atomic_mass_constant, molar_gas_constant,

30 faraday_constant, josephson_constant, von_klitzing_constant,

31 acceleration_due_to_gravity, magnetic_constant, vacuum_permittivity,

32 vacuum_impedance, coulomb_constant, atmosphere, bar, pound, psi, mmHg,

33 milli_mass_unit, quart, lightyear, astronomical_unit, planck_mass,

34 planck_time, planck_temperature, planck_length, planck_charge, planck_area,

35 planck_volume, planck_momentum, planck_energy, planck_force, planck_power,

36 planck_density, planck_energy_density, planck_intensity,

37 planck_angular_frequency, planck_pressure, planck_current, planck_voltage,

38 planck_impedance, planck_acceleration, bit, byte, kibibyte, mebibyte,

39 gibibyte, tebibyte, pebibyte, exbibyte, curie, rutherford, radian, degree,

40 steradian, angular_mil, atomic_mass_unit, gee, kPa, ampere, u0, c, kelvin,

41 mol, mole, candela, m, kg, s, electric_constant, G, boltzmann

42)

43from sympy.physics.units.prefixes import PREFIXES, prefix_unit

44from sympy.physics.units.systems.mksa import MKSA, dimsys_MKSA

46derived_dims = (frequency, force, pressure, energy, power, charge, voltage,

47 capacitance, conductance, magnetic_flux,

48 magnetic_density, inductance, luminous_intensity)

49base_dims = (amount_of_substance, luminous_intensity, temperature)

51units = [mol, cd, K, lux, hertz, newton, pascal, joule, watt, coulomb, volt,

52 farad, ohm, siemens, weber, tesla, henry, candela, lux, becquerel,

53 gray, katal]

55all_units: list[Quantity] = []

56for u in units:

57 all_units.extend(prefix_unit(u, PREFIXES))

59all_units.extend(units)

60all_units.extend([mol, cd, K, lux])

63dimsys_SI = dimsys_MKSA.extend(

64 [

65 # Dimensional dependencies for other base dimensions:

66 temperature,

67 amount_of_substance,

68 luminous_intensity,

69 ])

71dimsys_default = dimsys_SI.extend(

72 [information],

73)

75SI = MKSA.extend(base=(mol, cd, K), units=all_units, name='SI', dimension_system=dimsys_SI, derived_units={

76 power: watt,

77 magnetic_flux: weber,

78 time: second,

79 impedance: ohm,

80 pressure: pascal,

81 current: ampere,

82 voltage: volt,

83 length: meter,

84 frequency: hertz,

85 inductance: henry,

86 temperature: kelvin,

87 amount_of_substance: mole,

88 luminous_intensity: candela,

89 conductance: siemens,

90 mass: kilogram,

91 magnetic_density: tesla,

92 charge: coulomb,

93 force: newton,

94 capacitance: farad,

95 energy: joule,

96 velocity: meter/second,

97})

99One = S.One

100

101SI.set_quantity_dimension(radian, One)

102

103SI.set_quantity_scale_factor(ampere, One)

104

105SI.set_quantity_scale_factor(kelvin, One)

106

107SI.set_quantity_scale_factor(mole, One)

108

109SI.set_quantity_scale_factor(candela, One)

110

111# MKSA extension to MKS: derived units

112

113SI.set_quantity_scale_factor(coulomb, One)

114

115SI.set_quantity_scale_factor(volt, joule/coulomb)

116

117SI.set_quantity_scale_factor(ohm, volt/ampere)

118

119SI.set_quantity_scale_factor(siemens, ampere/volt)

120

121SI.set_quantity_scale_factor(farad, coulomb/volt)

122

123SI.set_quantity_scale_factor(henry, volt*second/ampere)

124

125SI.set_quantity_scale_factor(tesla, volt*second/meter**2)

126

127SI.set_quantity_scale_factor(weber, joule/ampere)

128

129

130SI.set_quantity_dimension(lux, luminous_intensity / length ** 2)

131SI.set_quantity_scale_factor(lux, steradian*candela/meter**2)

132

133# katal is the SI unit of catalytic activity

134

135SI.set_quantity_dimension(katal, amount_of_substance / time)

136SI.set_quantity_scale_factor(katal, mol/second)

137

138# gray is the SI unit of absorbed dose

139

140SI.set_quantity_dimension(gray, energy / mass)

141SI.set_quantity_scale_factor(gray, meter**2/second**2)

142

143# becquerel is the SI unit of radioactivity

144

145SI.set_quantity_dimension(becquerel, 1 / time)

146SI.set_quantity_scale_factor(becquerel, 1/second)

147

148#### CONSTANTS ####

149

150# elementary charge

151# REF: NIST SP 959 (June 2019)

152

153SI.set_quantity_dimension(elementary_charge, charge)

154SI.set_quantity_scale_factor(elementary_charge, 1.602176634e-19*coulomb)

155

156# Electronvolt

157# REF: NIST SP 959 (June 2019)

158

159SI.set_quantity_dimension(electronvolt, energy)

160SI.set_quantity_scale_factor(electronvolt, 1.602176634e-19*joule)

161

162# Avogadro number

163# REF: NIST SP 959 (June 2019)

164

165SI.set_quantity_dimension(avogadro_number, One)

166SI.set_quantity_scale_factor(avogadro_number, 6.02214076e23)

167

168# Avogadro constant

169

170SI.set_quantity_dimension(avogadro_constant, amount_of_substance ** -1)

171SI.set_quantity_scale_factor(avogadro_constant, avogadro_number / mol)

172

173# Boltzmann constant

174# REF: NIST SP 959 (June 2019)

175

176SI.set_quantity_dimension(boltzmann_constant, energy / temperature)

177SI.set_quantity_scale_factor(boltzmann_constant, 1.380649e-23*joule/kelvin)

178

179# Stefan-Boltzmann constant

180# REF: NIST SP 959 (June 2019)

181

182SI.set_quantity_dimension(stefan_boltzmann_constant, energy * time ** -1 * length ** -2 * temperature ** -4)

183SI.set_quantity_scale_factor(stefan_boltzmann_constant, pi**2 * boltzmann_constant**4 / (60 * hbar**3 * speed_of_light ** 2))

184

185# Atomic mass

186# REF: NIST SP 959 (June 2019)

187

188SI.set_quantity_dimension(atomic_mass_constant, mass)

189SI.set_quantity_scale_factor(atomic_mass_constant, 1.66053906660e-24*gram)

190

191# Molar gas constant

192# REF: NIST SP 959 (June 2019)

193

194SI.set_quantity_dimension(molar_gas_constant, energy / (temperature * amount_of_substance))

195SI.set_quantity_scale_factor(molar_gas_constant, boltzmann_constant * avogadro_constant)

196

197# Faraday constant

198

199SI.set_quantity_dimension(faraday_constant, charge / amount_of_substance)

200SI.set_quantity_scale_factor(faraday_constant, elementary_charge * avogadro_constant)

201

202# Josephson constant

203

204SI.set_quantity_dimension(josephson_constant, frequency / voltage)

205SI.set_quantity_scale_factor(josephson_constant, 0.5 * planck / elementary_charge)

206

207# Von Klitzing constant

208

209SI.set_quantity_dimension(von_klitzing_constant, voltage / current)

210SI.set_quantity_scale_factor(von_klitzing_constant, hbar / elementary_charge ** 2)

211

212# Acceleration due to gravity (on the Earth surface)

213

214SI.set_quantity_dimension(acceleration_due_to_gravity, acceleration)

215SI.set_quantity_scale_factor(acceleration_due_to_gravity, 9.80665*meter/second**2)

216

217# magnetic constant:

218

219SI.set_quantity_dimension(magnetic_constant, force / current ** 2)

220SI.set_quantity_scale_factor(magnetic_constant, 4*pi/10**7 * newton/ampere**2)

221

222# electric constant:

223

224SI.set_quantity_dimension(vacuum_permittivity, capacitance / length)

225SI.set_quantity_scale_factor(vacuum_permittivity, 1/(u0 * c**2))

226

227# vacuum impedance:

228

229SI.set_quantity_dimension(vacuum_impedance, impedance)

230SI.set_quantity_scale_factor(vacuum_impedance, u0 * c)

231

232# Electron rest mass

233SI.set_quantity_dimension(electron_rest_mass, mass)

234SI.set_quantity_scale_factor(electron_rest_mass, 9.1093837015e-31*kilogram)

235

236# Coulomb's constant:

237SI.set_quantity_dimension(coulomb_constant, force * length ** 2 / charge ** 2)

238SI.set_quantity_scale_factor(coulomb_constant, 1/(4*pi*vacuum_permittivity))

239

240SI.set_quantity_dimension(psi, pressure)

241SI.set_quantity_scale_factor(psi, pound * gee / inch ** 2)

242

243SI.set_quantity_dimension(mmHg, pressure)

244SI.set_quantity_scale_factor(mmHg, dHg0 * acceleration_due_to_gravity * kilogram / meter**2)

245

246SI.set_quantity_dimension(milli_mass_unit, mass)

247SI.set_quantity_scale_factor(milli_mass_unit, atomic_mass_unit/1000)

248

249SI.set_quantity_dimension(quart, length ** 3)

250SI.set_quantity_scale_factor(quart, Rational(231, 4) * inch**3)

251

252# Other convenient units and magnitudes

253

254SI.set_quantity_dimension(lightyear, length)

255SI.set_quantity_scale_factor(lightyear, speed_of_light*julian_year)

256

257SI.set_quantity_dimension(astronomical_unit, length)

258SI.set_quantity_scale_factor(astronomical_unit, 149597870691*meter)

259

260# Fundamental Planck units:

261

262SI.set_quantity_dimension(planck_mass, mass)

263SI.set_quantity_scale_factor(planck_mass, sqrt(hbar*speed_of_light/G))

264

265SI.set_quantity_dimension(planck_time, time)

266SI.set_quantity_scale_factor(planck_time, sqrt(hbar*G/speed_of_light**5))

267

268SI.set_quantity_dimension(planck_temperature, temperature)

269SI.set_quantity_scale_factor(planck_temperature, sqrt(hbar*speed_of_light**5/G/boltzmann**2))

270

271SI.set_quantity_dimension(planck_length, length)

272SI.set_quantity_scale_factor(planck_length, sqrt(hbar*G/speed_of_light**3))

273

274SI.set_quantity_dimension(planck_charge, charge)

275SI.set_quantity_scale_factor(planck_charge, sqrt(4*pi*electric_constant*hbar*speed_of_light))

276

277# Derived Planck units:

278

279SI.set_quantity_dimension(planck_area, length ** 2)

280SI.set_quantity_scale_factor(planck_area, planck_length**2)

281

282SI.set_quantity_dimension(planck_volume, length ** 3)

283SI.set_quantity_scale_factor(planck_volume, planck_length**3)

284

285SI.set_quantity_dimension(planck_momentum, mass * velocity)

286SI.set_quantity_scale_factor(planck_momentum, planck_mass * speed_of_light)

287

288SI.set_quantity_dimension(planck_energy, energy)

289SI.set_quantity_scale_factor(planck_energy, planck_mass * speed_of_light**2)

290

291SI.set_quantity_dimension(planck_force, force)

292SI.set_quantity_scale_factor(planck_force, planck_energy / planck_length)

293

294SI.set_quantity_dimension(planck_power, power)

295SI.set_quantity_scale_factor(planck_power, planck_energy / planck_time)

296

297SI.set_quantity_dimension(planck_density, mass / length ** 3)

298SI.set_quantity_scale_factor(planck_density, planck_mass / planck_length**3)

299

300SI.set_quantity_dimension(planck_energy_density, energy / length ** 3)

301SI.set_quantity_scale_factor(planck_energy_density, planck_energy / planck_length**3)

302

303SI.set_quantity_dimension(planck_intensity, mass * time ** (-3))

304SI.set_quantity_scale_factor(planck_intensity, planck_energy_density * speed_of_light)

305

306SI.set_quantity_dimension(planck_angular_frequency, 1 / time)

307SI.set_quantity_scale_factor(planck_angular_frequency, 1 / planck_time)

308

309SI.set_quantity_dimension(planck_pressure, pressure)

310SI.set_quantity_scale_factor(planck_pressure, planck_force / planck_length**2)

311

312SI.set_quantity_dimension(planck_current, current)

313SI.set_quantity_scale_factor(planck_current, planck_charge / planck_time)

314

315SI.set_quantity_dimension(planck_voltage, voltage)

316SI.set_quantity_scale_factor(planck_voltage, planck_energy / planck_charge)

317

318SI.set_quantity_dimension(planck_impedance, impedance)

319SI.set_quantity_scale_factor(planck_impedance, planck_voltage / planck_current)

320

321SI.set_quantity_dimension(planck_acceleration, acceleration)

322SI.set_quantity_scale_factor(planck_acceleration, speed_of_light / planck_time)

323

324# Older units for radioactivity

325

326SI.set_quantity_dimension(curie, 1 / time)

327SI.set_quantity_scale_factor(curie, 37000000000*becquerel)

328

329SI.set_quantity_dimension(rutherford, 1 / time)

330SI.set_quantity_scale_factor(rutherford, 1000000*becquerel)

331

332

333# check that scale factors are the right SI dimensions:

334for _scale_factor, _dimension in zip(

335 SI._quantity_scale_factors.values(),

336 SI._quantity_dimension_map.values()

337):

338 dimex = SI.get_dimensional_expr(_scale_factor)

339 if dimex != 1:

340 # XXX: equivalent_dims is an instance method taking two arguments in

341 # addition to self so this can not work:

342 if not DimensionSystem.equivalent_dims(_dimension, Dimension(dimex)): # type: ignore

343 raise ValueError("quantity value and dimension mismatch")

344del _scale_factor, _dimension

345

346__all__ = [

347 'mmHg', 'atmosphere', 'inductance', 'newton', 'meter',

348 'vacuum_permittivity', 'pascal', 'magnetic_constant', 'voltage',

349 'angular_mil', 'luminous_intensity', 'all_units',

350 'julian_year', 'weber', 'exbibyte', 'liter',

351 'molar_gas_constant', 'faraday_constant', 'avogadro_constant',

352 'lightyear', 'planck_density', 'gee', 'mol', 'bit', 'gray',

353 'planck_momentum', 'bar', 'magnetic_density', 'prefix_unit', 'PREFIXES',

354 'planck_time', 'dimex', 'gram', 'candela', 'force', 'planck_intensity',

355 'energy', 'becquerel', 'planck_acceleration', 'speed_of_light',

356 'conductance', 'frequency', 'coulomb_constant', 'degree', 'lux', 'planck',

357 'current', 'planck_current', 'tebibyte', 'planck_power', 'MKSA', 'power',

358 'K', 'planck_volume', 'quart', 'pressure', 'amount_of_substance',

359 'joule', 'boltzmann_constant', 'Dimension', 'c', 'planck_force', 'length',

360 'watt', 'action', 'hbar', 'gibibyte', 'DimensionSystem', 'cd', 'volt',

361 'planck_charge', 'dioptre', 'vacuum_impedance', 'dimsys_default', 'farad',

362 'charge', 'gravitational_constant', 'temperature', 'u0', 'hertz',

363 'capacitance', 'tesla', 'steradian', 'planck_mass', 'josephson_constant',

364 'planck_area', 'stefan_boltzmann_constant', 'base_dims',

365 'astronomical_unit', 'radian', 'planck_voltage', 'impedance',

366 'planck_energy', 'Da', 'atomic_mass_constant', 'rutherford', 'second', 'inch',

367 'elementary_charge', 'SI', 'electronvolt', 'dimsys_SI', 'henry',

368 'planck_angular_frequency', 'ohm', 'pound', 'planck_pressure', 'G', 'psi',

369 'dHg0', 'von_klitzing_constant', 'planck_length', 'avogadro_number',

370 'mole', 'acceleration', 'information', 'planck_energy_density',

371 'mebibyte', 's', 'acceleration_due_to_gravity', 'electron_rest_mass',

372 'planck_temperature', 'units', 'mass', 'dimsys_MKSA', 'kelvin', 'kPa',

373 'boltzmann', 'milli_mass_unit', 'planck_impedance', 'electric_constant',

374 'derived_dims', 'kg', 'coulomb', 'siemens', 'byte', 'magnetic_flux',

375 'atomic_mass_unit', 'm', 'kibibyte', 'kilogram', 'One', 'curie', 'u',

376 'time', 'pebibyte', 'velocity', 'ampere', 'katal',

377]