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| """ | |
| SI unit system. | |
| Based on MKSA, which stands for "meter, kilogram, second, ampere". | |
| Added kelvin, candela and mole. | |
| """ | |
| from __future__ import annotations | |
| from sympy.physics.units import DimensionSystem, Dimension, dHg0 | |
| from sympy.physics.units.quantities import Quantity | |
| from sympy.core.numbers import (Rational, pi) | |
| from sympy.core.singleton import S | |
| from sympy.functions.elementary.miscellaneous import sqrt | |
| from sympy.physics.units.definitions.dimension_definitions import ( | |
| acceleration, action, current, impedance, length, mass, time, velocity, | |
| amount_of_substance, temperature, information, frequency, force, pressure, | |
| energy, power, charge, voltage, capacitance, conductance, magnetic_flux, | |
| magnetic_density, inductance, luminous_intensity | |
| ) | |
| from sympy.physics.units.definitions import ( | |
| kilogram, newton, second, meter, gram, cd, K, joule, watt, pascal, hertz, | |
| coulomb, volt, ohm, siemens, farad, henry, tesla, weber, dioptre, lux, | |
| katal, gray, becquerel, inch, liter, julian_year, gravitational_constant, | |
| speed_of_light, elementary_charge, planck, hbar, electronvolt, | |
| avogadro_number, avogadro_constant, boltzmann_constant, electron_rest_mass, | |
| stefan_boltzmann_constant, Da, atomic_mass_constant, molar_gas_constant, | |
| faraday_constant, josephson_constant, von_klitzing_constant, | |
| acceleration_due_to_gravity, magnetic_constant, vacuum_permittivity, | |
| vacuum_impedance, coulomb_constant, atmosphere, bar, pound, psi, mmHg, | |
| milli_mass_unit, quart, lightyear, astronomical_unit, planck_mass, | |
| planck_time, planck_temperature, planck_length, planck_charge, planck_area, | |
| planck_volume, planck_momentum, planck_energy, planck_force, planck_power, | |
| planck_density, planck_energy_density, planck_intensity, | |
| planck_angular_frequency, planck_pressure, planck_current, planck_voltage, | |
| planck_impedance, planck_acceleration, bit, byte, kibibyte, mebibyte, | |
| gibibyte, tebibyte, pebibyte, exbibyte, curie, rutherford, radian, degree, | |
| steradian, angular_mil, atomic_mass_unit, gee, kPa, ampere, u0, c, kelvin, | |
| mol, mole, candela, m, kg, s, electric_constant, G, boltzmann | |
| ) | |
| from sympy.physics.units.prefixes import PREFIXES, prefix_unit | |
| from sympy.physics.units.systems.mksa import MKSA, dimsys_MKSA | |
| derived_dims = (frequency, force, pressure, energy, power, charge, voltage, | |
| capacitance, conductance, magnetic_flux, | |
| magnetic_density, inductance, luminous_intensity) | |
| base_dims = (amount_of_substance, luminous_intensity, temperature) | |
| units = [mol, cd, K, lux, hertz, newton, pascal, joule, watt, coulomb, volt, | |
| farad, ohm, siemens, weber, tesla, henry, candela, lux, becquerel, | |
| gray, katal] | |
| all_units: list[Quantity] = [] | |
| for u in units: | |
| all_units.extend(prefix_unit(u, PREFIXES)) | |
| all_units.extend(units) | |
| all_units.extend([mol, cd, K, lux]) | |
| dimsys_SI = dimsys_MKSA.extend( | |
| [ | |
| # Dimensional dependencies for other base dimensions: | |
| temperature, | |
| amount_of_substance, | |
| luminous_intensity, | |
| ]) | |
| dimsys_default = dimsys_SI.extend( | |
| [information], | |
| ) | |
| SI = MKSA.extend(base=(mol, cd, K), units=all_units, name='SI', dimension_system=dimsys_SI, derived_units={ | |
| power: watt, | |
| magnetic_flux: weber, | |
| time: second, | |
| impedance: ohm, | |
| pressure: pascal, | |
| current: ampere, | |
| voltage: volt, | |
| length: meter, | |
| frequency: hertz, | |
| inductance: henry, | |
| temperature: kelvin, | |
| amount_of_substance: mole, | |
| luminous_intensity: candela, | |
| conductance: siemens, | |
| mass: kilogram, | |
| magnetic_density: tesla, | |
| charge: coulomb, | |
| force: newton, | |
| capacitance: farad, | |
| energy: joule, | |
| velocity: meter/second, | |
| }) | |
| One = S.One | |
| SI.set_quantity_dimension(radian, One) | |
| SI.set_quantity_scale_factor(ampere, One) | |
| SI.set_quantity_scale_factor(kelvin, One) | |
| SI.set_quantity_scale_factor(mole, One) | |
| SI.set_quantity_scale_factor(candela, One) | |
| # MKSA extension to MKS: derived units | |
| SI.set_quantity_scale_factor(coulomb, One) | |
| SI.set_quantity_scale_factor(volt, joule/coulomb) | |
| SI.set_quantity_scale_factor(ohm, volt/ampere) | |
| SI.set_quantity_scale_factor(siemens, ampere/volt) | |
| SI.set_quantity_scale_factor(farad, coulomb/volt) | |
| SI.set_quantity_scale_factor(henry, volt*second/ampere) | |
| SI.set_quantity_scale_factor(tesla, volt*second/meter**2) | |
| SI.set_quantity_scale_factor(weber, joule/ampere) | |
| SI.set_quantity_dimension(lux, luminous_intensity / length ** 2) | |
| SI.set_quantity_scale_factor(lux, steradian*candela/meter**2) | |
| # katal is the SI unit of catalytic activity | |
| SI.set_quantity_dimension(katal, amount_of_substance / time) | |
| SI.set_quantity_scale_factor(katal, mol/second) | |
| # gray is the SI unit of absorbed dose | |
| SI.set_quantity_dimension(gray, energy / mass) | |
| SI.set_quantity_scale_factor(gray, meter**2/second**2) | |
| # becquerel is the SI unit of radioactivity | |
| SI.set_quantity_dimension(becquerel, 1 / time) | |
| SI.set_quantity_scale_factor(becquerel, 1/second) | |
| #### CONSTANTS #### | |
| # elementary charge | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(elementary_charge, charge) | |
| SI.set_quantity_scale_factor(elementary_charge, 1.602176634e-19*coulomb) | |
| # Electronvolt | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(electronvolt, energy) | |
| SI.set_quantity_scale_factor(electronvolt, 1.602176634e-19*joule) | |
| # Avogadro number | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(avogadro_number, One) | |
| SI.set_quantity_scale_factor(avogadro_number, 6.02214076e23) | |
| # Avogadro constant | |
| SI.set_quantity_dimension(avogadro_constant, amount_of_substance ** -1) | |
| SI.set_quantity_scale_factor(avogadro_constant, avogadro_number / mol) | |
| # Boltzmann constant | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(boltzmann_constant, energy / temperature) | |
| SI.set_quantity_scale_factor(boltzmann_constant, 1.380649e-23*joule/kelvin) | |
| # Stefan-Boltzmann constant | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(stefan_boltzmann_constant, energy * time ** -1 * length ** -2 * temperature ** -4) | |
| SI.set_quantity_scale_factor(stefan_boltzmann_constant, pi**2 * boltzmann_constant**4 / (60 * hbar**3 * speed_of_light ** 2)) | |
| # Atomic mass | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(atomic_mass_constant, mass) | |
| SI.set_quantity_scale_factor(atomic_mass_constant, 1.66053906660e-24*gram) | |
| # Molar gas constant | |
| # REF: NIST SP 959 (June 2019) | |
| SI.set_quantity_dimension(molar_gas_constant, energy / (temperature * amount_of_substance)) | |
| SI.set_quantity_scale_factor(molar_gas_constant, boltzmann_constant * avogadro_constant) | |
| # Faraday constant | |
| SI.set_quantity_dimension(faraday_constant, charge / amount_of_substance) | |
| SI.set_quantity_scale_factor(faraday_constant, elementary_charge * avogadro_constant) | |
| # Josephson constant | |
| SI.set_quantity_dimension(josephson_constant, frequency / voltage) | |
| SI.set_quantity_scale_factor(josephson_constant, 0.5 * planck / elementary_charge) | |
| # Von Klitzing constant | |
| SI.set_quantity_dimension(von_klitzing_constant, voltage / current) | |
| SI.set_quantity_scale_factor(von_klitzing_constant, hbar / elementary_charge ** 2) | |
| # Acceleration due to gravity (on the Earth surface) | |
| SI.set_quantity_dimension(acceleration_due_to_gravity, acceleration) | |
| SI.set_quantity_scale_factor(acceleration_due_to_gravity, 9.80665*meter/second**2) | |
| # magnetic constant: | |
| SI.set_quantity_dimension(magnetic_constant, force / current ** 2) | |
| SI.set_quantity_scale_factor(magnetic_constant, 4*pi/10**7 * newton/ampere**2) | |
| # electric constant: | |
| SI.set_quantity_dimension(vacuum_permittivity, capacitance / length) | |
| SI.set_quantity_scale_factor(vacuum_permittivity, 1/(u0 * c**2)) | |
| # vacuum impedance: | |
| SI.set_quantity_dimension(vacuum_impedance, impedance) | |
| SI.set_quantity_scale_factor(vacuum_impedance, u0 * c) | |
| # Electron rest mass | |
| SI.set_quantity_dimension(electron_rest_mass, mass) | |
| SI.set_quantity_scale_factor(electron_rest_mass, 9.1093837015e-31*kilogram) | |
| # Coulomb's constant: | |
| SI.set_quantity_dimension(coulomb_constant, force * length ** 2 / charge ** 2) | |
| SI.set_quantity_scale_factor(coulomb_constant, 1/(4*pi*vacuum_permittivity)) | |
| SI.set_quantity_dimension(psi, pressure) | |
| SI.set_quantity_scale_factor(psi, pound * gee / inch ** 2) | |
| SI.set_quantity_dimension(mmHg, pressure) | |
| SI.set_quantity_scale_factor(mmHg, dHg0 * acceleration_due_to_gravity * kilogram / meter**2) | |
| SI.set_quantity_dimension(milli_mass_unit, mass) | |
| SI.set_quantity_scale_factor(milli_mass_unit, atomic_mass_unit/1000) | |
| SI.set_quantity_dimension(quart, length ** 3) | |
| SI.set_quantity_scale_factor(quart, Rational(231, 4) * inch**3) | |
| # Other convenient units and magnitudes | |
| SI.set_quantity_dimension(lightyear, length) | |
| SI.set_quantity_scale_factor(lightyear, speed_of_light*julian_year) | |
| SI.set_quantity_dimension(astronomical_unit, length) | |
| SI.set_quantity_scale_factor(astronomical_unit, 149597870691*meter) | |
| # Fundamental Planck units: | |
| SI.set_quantity_dimension(planck_mass, mass) | |
| SI.set_quantity_scale_factor(planck_mass, sqrt(hbar*speed_of_light/G)) | |
| SI.set_quantity_dimension(planck_time, time) | |
| SI.set_quantity_scale_factor(planck_time, sqrt(hbar*G/speed_of_light**5)) | |
| SI.set_quantity_dimension(planck_temperature, temperature) | |
| SI.set_quantity_scale_factor(planck_temperature, sqrt(hbar*speed_of_light**5/G/boltzmann**2)) | |
| SI.set_quantity_dimension(planck_length, length) | |
| SI.set_quantity_scale_factor(planck_length, sqrt(hbar*G/speed_of_light**3)) | |
| SI.set_quantity_dimension(planck_charge, charge) | |
| SI.set_quantity_scale_factor(planck_charge, sqrt(4*pi*electric_constant*hbar*speed_of_light)) | |
| # Derived Planck units: | |
| SI.set_quantity_dimension(planck_area, length ** 2) | |
| SI.set_quantity_scale_factor(planck_area, planck_length**2) | |
| SI.set_quantity_dimension(planck_volume, length ** 3) | |
| SI.set_quantity_scale_factor(planck_volume, planck_length**3) | |
| SI.set_quantity_dimension(planck_momentum, mass * velocity) | |
| SI.set_quantity_scale_factor(planck_momentum, planck_mass * speed_of_light) | |
| SI.set_quantity_dimension(planck_energy, energy) | |
| SI.set_quantity_scale_factor(planck_energy, planck_mass * speed_of_light**2) | |
| SI.set_quantity_dimension(planck_force, force) | |
| SI.set_quantity_scale_factor(planck_force, planck_energy / planck_length) | |
| SI.set_quantity_dimension(planck_power, power) | |
| SI.set_quantity_scale_factor(planck_power, planck_energy / planck_time) | |
| SI.set_quantity_dimension(planck_density, mass / length ** 3) | |
| SI.set_quantity_scale_factor(planck_density, planck_mass / planck_length**3) | |
| SI.set_quantity_dimension(planck_energy_density, energy / length ** 3) | |
| SI.set_quantity_scale_factor(planck_energy_density, planck_energy / planck_length**3) | |
| SI.set_quantity_dimension(planck_intensity, mass * time ** (-3)) | |
| SI.set_quantity_scale_factor(planck_intensity, planck_energy_density * speed_of_light) | |
| SI.set_quantity_dimension(planck_angular_frequency, 1 / time) | |
| SI.set_quantity_scale_factor(planck_angular_frequency, 1 / planck_time) | |
| SI.set_quantity_dimension(planck_pressure, pressure) | |
| SI.set_quantity_scale_factor(planck_pressure, planck_force / planck_length**2) | |
| SI.set_quantity_dimension(planck_current, current) | |
| SI.set_quantity_scale_factor(planck_current, planck_charge / planck_time) | |
| SI.set_quantity_dimension(planck_voltage, voltage) | |
| SI.set_quantity_scale_factor(planck_voltage, planck_energy / planck_charge) | |
| SI.set_quantity_dimension(planck_impedance, impedance) | |
| SI.set_quantity_scale_factor(planck_impedance, planck_voltage / planck_current) | |
| SI.set_quantity_dimension(planck_acceleration, acceleration) | |
| SI.set_quantity_scale_factor(planck_acceleration, speed_of_light / planck_time) | |
| # Older units for radioactivity | |
| SI.set_quantity_dimension(curie, 1 / time) | |
| SI.set_quantity_scale_factor(curie, 37000000000*becquerel) | |
| SI.set_quantity_dimension(rutherford, 1 / time) | |
| SI.set_quantity_scale_factor(rutherford, 1000000*becquerel) | |
| # check that scale factors are the right SI dimensions: | |
| for _scale_factor, _dimension in zip( | |
| SI._quantity_scale_factors.values(), | |
| SI._quantity_dimension_map.values() | |
| ): | |
| dimex = SI.get_dimensional_expr(_scale_factor) | |
| if dimex != 1: | |
| # XXX: equivalent_dims is an instance method taking two arguments in | |
| # addition to self so this can not work: | |
| if not DimensionSystem.equivalent_dims(_dimension, Dimension(dimex)): # type: ignore | |
| raise ValueError("quantity value and dimension mismatch") | |
| del _scale_factor, _dimension | |
| __all__ = [ | |
| 'mmHg', 'atmosphere', 'inductance', 'newton', 'meter', | |
| 'vacuum_permittivity', 'pascal', 'magnetic_constant', 'voltage', | |
| 'angular_mil', 'luminous_intensity', 'all_units', | |
| 'julian_year', 'weber', 'exbibyte', 'liter', | |
| 'molar_gas_constant', 'faraday_constant', 'avogadro_constant', | |
| 'lightyear', 'planck_density', 'gee', 'mol', 'bit', 'gray', | |
| 'planck_momentum', 'bar', 'magnetic_density', 'prefix_unit', 'PREFIXES', | |
| 'planck_time', 'dimex', 'gram', 'candela', 'force', 'planck_intensity', | |
| 'energy', 'becquerel', 'planck_acceleration', 'speed_of_light', | |
| 'conductance', 'frequency', 'coulomb_constant', 'degree', 'lux', 'planck', | |
| 'current', 'planck_current', 'tebibyte', 'planck_power', 'MKSA', 'power', | |
| 'K', 'planck_volume', 'quart', 'pressure', 'amount_of_substance', | |
| 'joule', 'boltzmann_constant', 'Dimension', 'c', 'planck_force', 'length', | |
| 'watt', 'action', 'hbar', 'gibibyte', 'DimensionSystem', 'cd', 'volt', | |
| 'planck_charge', 'dioptre', 'vacuum_impedance', 'dimsys_default', 'farad', | |
| 'charge', 'gravitational_constant', 'temperature', 'u0', 'hertz', | |
| 'capacitance', 'tesla', 'steradian', 'planck_mass', 'josephson_constant', | |
| 'planck_area', 'stefan_boltzmann_constant', 'base_dims', | |
| 'astronomical_unit', 'radian', 'planck_voltage', 'impedance', | |
| 'planck_energy', 'Da', 'atomic_mass_constant', 'rutherford', 'second', 'inch', | |
| 'elementary_charge', 'SI', 'electronvolt', 'dimsys_SI', 'henry', | |
| 'planck_angular_frequency', 'ohm', 'pound', 'planck_pressure', 'G', 'psi', | |
| 'dHg0', 'von_klitzing_constant', 'planck_length', 'avogadro_number', | |
| 'mole', 'acceleration', 'information', 'planck_energy_density', | |
| 'mebibyte', 's', 'acceleration_due_to_gravity', 'electron_rest_mass', | |
| 'planck_temperature', 'units', 'mass', 'dimsys_MKSA', 'kelvin', 'kPa', | |
| 'boltzmann', 'milli_mass_unit', 'planck_impedance', 'electric_constant', | |
| 'derived_dims', 'kg', 'coulomb', 'siemens', 'byte', 'magnetic_flux', | |
| 'atomic_mass_unit', 'm', 'kibibyte', 'kilogram', 'One', 'curie', 'u', | |
| 'time', 'pebibyte', 'velocity', 'ampere', 'katal', | |
| ] | |