Vehicle-cpp/hkpc/software/sympy/physics/units/systems/length_weight_time.py

from sympy.core.singleton import S

from sympy.core.numbers import pi

from sympy.physics.units import DimensionSystem, hertz, kilogram
from sympy.physics.units.definitions import (
    G, Hz, J, N, Pa, W, c, g, kg, m, s, meter, gram, second, newton,
    joule, watt, pascal)
from sympy.physics.units.definitions.dimension_definitions import (
    acceleration, action, energy, force, frequency, momentum,
    power, pressure, velocity, length, mass, time)
from sympy.physics.units.prefixes import PREFIXES, prefix_unit
from sympy.physics.units.prefixes import (
    kibi, mebi, gibi, tebi, pebi, exbi
)
from sympy.physics.units.definitions import (
    cd, K, coulomb, volt, ohm, siemens, farad, henry, tesla, weber, dioptre,
    lux, katal, gray, becquerel, inch, hectare, liter, julian_year,
    gravitational_constant, speed_of_light, elementary_charge, planck, hbar,
    electronvolt, avogadro_number, avogadro_constant, boltzmann_constant,
    stefan_boltzmann_constant, 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, kelvin,
    mol, mole, candela, electric_constant, boltzmann, angstrom
)


dimsys_length_weight_time = DimensionSystem([
    # Dimensional dependencies for MKS base dimensions
    length,
    mass,
    time,
], dimensional_dependencies={
    # Dimensional dependencies for derived dimensions
    "velocity": {"length": 1, "time": -1},
    "acceleration": {"length": 1, "time": -2},
    "momentum": {"mass": 1, "length": 1, "time": -1},
    "force": {"mass": 1, "length": 1, "time": -2},
    "energy": {"mass": 1, "length": 2, "time": -2},
    "power": {"length": 2, "mass": 1, "time": -3},
    "pressure": {"mass": 1, "length": -1, "time": -2},
    "frequency": {"time": -1},
    "action": {"length": 2, "mass": 1, "time": -1},
    "area": {"length": 2},
    "volume": {"length": 3},
})


One = S.One


# Base units:
dimsys_length_weight_time.set_quantity_dimension(meter, length)
dimsys_length_weight_time.set_quantity_scale_factor(meter, One)

# gram; used to define its prefixed units
dimsys_length_weight_time.set_quantity_dimension(gram, mass)
dimsys_length_weight_time.set_quantity_scale_factor(gram, One)

dimsys_length_weight_time.set_quantity_dimension(second, time)
dimsys_length_weight_time.set_quantity_scale_factor(second, One)

# derived units

dimsys_length_weight_time.set_quantity_dimension(newton, force)
dimsys_length_weight_time.set_quantity_scale_factor(newton, kilogram*meter/second**2)

dimsys_length_weight_time.set_quantity_dimension(joule, energy)
dimsys_length_weight_time.set_quantity_scale_factor(joule, newton*meter)

dimsys_length_weight_time.set_quantity_dimension(watt, power)
dimsys_length_weight_time.set_quantity_scale_factor(watt, joule/second)

dimsys_length_weight_time.set_quantity_dimension(pascal, pressure)
dimsys_length_weight_time.set_quantity_scale_factor(pascal, newton/meter**2)

dimsys_length_weight_time.set_quantity_dimension(hertz, frequency)
dimsys_length_weight_time.set_quantity_scale_factor(hertz, One)

# Other derived units:

dimsys_length_weight_time.set_quantity_dimension(dioptre, 1 / length)
dimsys_length_weight_time.set_quantity_scale_factor(dioptre, 1/meter)

# Common volume and area units

dimsys_length_weight_time.set_quantity_dimension(hectare, length**2)
dimsys_length_weight_time.set_quantity_scale_factor(hectare, (meter**2)*(10000))

dimsys_length_weight_time.set_quantity_dimension(liter, length**3)
dimsys_length_weight_time.set_quantity_scale_factor(liter, meter**3/1000)


# Newton constant
# REF: NIST SP 959 (June 2019)

dimsys_length_weight_time.set_quantity_dimension(gravitational_constant, length ** 3 * mass ** -1 * time ** -2)
dimsys_length_weight_time.set_quantity_scale_factor(gravitational_constant, 6.67430e-11*m**3/(kg*s**2))

# speed of light

dimsys_length_weight_time.set_quantity_dimension(speed_of_light, velocity)
dimsys_length_weight_time.set_quantity_scale_factor(speed_of_light, 299792458*meter/second)


# Planck constant
# REF: NIST SP 959 (June 2019)

dimsys_length_weight_time.set_quantity_dimension(planck, action)
dimsys_length_weight_time.set_quantity_scale_factor(planck, 6.62607015e-34*joule*second)

# Reduced Planck constant
# REF: NIST SP 959 (June 2019)

dimsys_length_weight_time.set_quantity_dimension(hbar, action)
dimsys_length_weight_time.set_quantity_scale_factor(hbar, planck / (2 * pi))


__all__ = [
    'mmHg', 'atmosphere', 'newton', 'meter', 'vacuum_permittivity', 'pascal',
    'magnetic_constant', 'angular_mil', 'julian_year', 'weber', 'exbibyte',
    'liter', 'molar_gas_constant', 'faraday_constant', 'avogadro_constant',
    'planck_momentum', 'planck_density', 'gee', 'mol', 'bit', 'gray', 'kibi',
    'bar', 'curie', 'prefix_unit', 'PREFIXES', 'planck_time', 'gram',
    'candela', 'force', 'planck_intensity', 'energy', 'becquerel',
    'planck_acceleration', 'speed_of_light', 'dioptre', 'second', 'frequency',
    'Hz', 'power', 'lux', 'planck_current', 'momentum', 'tebibyte',
    'planck_power', 'degree', 'mebi', 'K', 'planck_volume',
    'quart', 'pressure', 'W', 'joule', 'boltzmann_constant', 'c', 'g',
    'planck_force', 'exbi', 's', 'watt', 'action', 'hbar', 'gibibyte',
    'DimensionSystem', 'cd', 'volt', 'planck_charge', 'angstrom',
    'dimsys_length_weight_time', 'pebi', 'vacuum_impedance', 'planck',
    'farad', 'gravitational_constant', 'u0', 'hertz', 'tesla', 'steradian',
    'josephson_constant', 'planck_area', 'stefan_boltzmann_constant',
    'astronomical_unit', 'J', 'N', 'planck_voltage', 'planck_energy',
    'atomic_mass_constant', 'rutherford', 'elementary_charge', 'Pa',
    'planck_mass', 'henry', 'planck_angular_frequency', 'ohm', 'pound',
    'planck_pressure', 'G', 'avogadro_number', 'psi', 'von_klitzing_constant',
    'planck_length', 'radian', 'mole', 'acceleration',
    'planck_energy_density', 'mebibyte', 'length',
    'acceleration_due_to_gravity', 'planck_temperature', 'tebi', 'inch',
    'electronvolt', 'coulomb_constant', 'kelvin', 'kPa', 'boltzmann',
    'milli_mass_unit', 'gibi', 'planck_impedance', 'electric_constant', 'kg',
    'coulomb', 'siemens', 'byte', 'atomic_mass_unit', 'm', 'kibibyte',
    'kilogram', 'lightyear', 'mass', 'time', 'pebibyte', 'velocity',
    'ampere', 'katal',
]