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from sympy.core.containers import Tuple
from sympy.core.numbers import pi
from sympy.core.power import Pow
from sympy.core.symbol import symbols
from sympy.core.sympify import sympify
from sympy.printing.str import sstr
from sympy.physics.units import (
G, centimeter, coulomb, day, degree, gram, hbar, hour, inch, joule, kelvin,
kilogram, kilometer, length, meter, mile, minute, newton, planck,
planck_length, planck_mass, planck_temperature, planck_time, radians,
second, speed_of_light, steradian, time, km)
from sympy.physics.units.util import convert_to, check_dimensions
from sympy.testing.pytest import raises
from sympy.functions.elementary.miscellaneous import sqrt
def NS(e, n=15, **options):
return sstr(sympify(e).evalf(n, **options), full_prec=True)
L = length
T = time
def test_dim_simplify_add():
# assert Add(L, L) == L
assert L + L == L
def test_dim_simplify_mul():
# assert Mul(L, T) == L*T
assert L*T == L*T
def test_dim_simplify_pow():
assert Pow(L, 2) == L**2
def test_dim_simplify_rec():
# assert Mul(Add(L, L), T) == L*T
assert (L + L) * T == L*T
def test_convert_to_quantities():
assert convert_to(3, meter) == 3
assert convert_to(mile, kilometer) == 25146*kilometer/15625
assert convert_to(meter/second, speed_of_light) == speed_of_light/299792458
assert convert_to(299792458*meter/second, speed_of_light) == speed_of_light
assert convert_to(2*299792458*meter/second, speed_of_light) == 2*speed_of_light
assert convert_to(speed_of_light, meter/second) == 299792458*meter/second
assert convert_to(2*speed_of_light, meter/second) == 599584916*meter/second
assert convert_to(day, second) == 86400*second
assert convert_to(2*hour, minute) == 120*minute
assert convert_to(mile, meter) == 201168*meter/125
assert convert_to(mile/hour, kilometer/hour) == 25146*kilometer/(15625*hour)
assert convert_to(3*newton, meter/second) == 3*newton
assert convert_to(3*newton, kilogram*meter/second**2) == 3*meter*kilogram/second**2
assert convert_to(kilometer + mile, meter) == 326168*meter/125
assert convert_to(2*kilometer + 3*mile, meter) == 853504*meter/125
assert convert_to(inch**2, meter**2) == 16129*meter**2/25000000
assert convert_to(3*inch**2, meter) == 48387*meter**2/25000000
assert convert_to(2*kilometer/hour + 3*mile/hour, meter/second) == 53344*meter/(28125*second)
assert convert_to(2*kilometer/hour + 3*mile/hour, centimeter/second) == 213376*centimeter/(1125*second)
assert convert_to(kilometer * (mile + kilometer), meter) == 2609344 * meter ** 2
assert convert_to(steradian, coulomb) == steradian
assert convert_to(radians, degree) == 180*degree/pi
assert convert_to(radians, [meter, degree]) == 180*degree/pi
assert convert_to(pi*radians, degree) == 180*degree
assert convert_to(pi, degree) == 180*degree
# https://github.com/sympy/sympy/issues/26263
assert convert_to(sqrt(meter**2 + meter**2.0), meter) == sqrt(meter**2 + meter**2.0)
assert convert_to((meter**2 + meter**2.0)**2, meter) == (meter**2 + meter**2.0)**2
def test_convert_to_tuples_of_quantities():
from sympy.core.symbol import symbols
alpha, beta = symbols('alpha beta')
assert convert_to(speed_of_light, [meter, second]) == 299792458 * meter / second
assert convert_to(speed_of_light, (meter, second)) == 299792458 * meter / second
assert convert_to(speed_of_light, Tuple(meter, second)) == 299792458 * meter / second
assert convert_to(joule, [meter, kilogram, second]) == kilogram*meter**2/second**2
assert convert_to(joule, [centimeter, gram, second]) == 10000000*centimeter**2*gram/second**2
assert convert_to(299792458*meter/second, [speed_of_light]) == speed_of_light
assert convert_to(speed_of_light / 2, [meter, second, kilogram]) == meter/second*299792458 / 2
# This doesn't make physically sense, but let's keep it as a conversion test:
assert convert_to(2 * speed_of_light, [meter, second, kilogram]) == 2 * 299792458 * meter / second
assert convert_to(G, [G, speed_of_light, planck]) == 1.0*G
assert NS(convert_to(meter, [G, speed_of_light, hbar]), n=7) == '6.187142e+34*gravitational_constant**0.5000000*hbar**0.5000000/speed_of_light**1.500000'
assert NS(convert_to(planck_mass, kilogram), n=7) == '2.176434e-8*kilogram'
assert NS(convert_to(planck_length, meter), n=7) == '1.616255e-35*meter'
assert NS(convert_to(planck_time, second), n=6) == '5.39125e-44*second'
assert NS(convert_to(planck_temperature, kelvin), n=7) == '1.416784e+32*kelvin'
assert NS(convert_to(convert_to(meter, [G, speed_of_light, planck]), meter), n=10) == '1.000000000*meter'
# similar to https://github.com/sympy/sympy/issues/26263
assert convert_to(sqrt(meter**2 + second**2.0), [meter, second]) == sqrt(meter**2 + second**2.0)
assert convert_to((meter**2 + second**2.0)**2, [meter, second]) == (meter**2 + second**2.0)**2
# similar to https://github.com/sympy/sympy/issues/21463
assert convert_to(1/(beta*meter + meter), 1/meter) == 1/(beta*meter + meter)
assert convert_to(1/(beta*meter + alpha*meter), 1/kilometer) == (1/(kilometer*beta/1000 + alpha*kilometer/1000))
def test_eval_simplify():
from sympy.physics.units import cm, mm, km, m, K, kilo
from sympy.core.symbol import symbols
x, y = symbols('x y')
assert (cm/mm).simplify() == 10
assert (km/m).simplify() == 1000
assert (km/cm).simplify() == 100000
assert (10*x*K*km**2/m/cm).simplify() == 1000000000*x*kelvin
assert (cm/km/m).simplify() == 1/(10000000*centimeter)
assert (3*kilo*meter).simplify() == 3000*meter
assert (4*kilo*meter/(2*kilometer)).simplify() == 2
assert (4*kilometer**2/(kilo*meter)**2).simplify() == 4
def test_quantity_simplify():
from sympy.physics.units.util import quantity_simplify
from sympy.physics.units import kilo, foot
from sympy.core.symbol import symbols
x, y = symbols('x y')
assert quantity_simplify(x*(8*kilo*newton*meter + y)) == x*(8000*meter*newton + y)
assert quantity_simplify(foot*inch*(foot + inch)) == foot**2*(foot + foot/12)/12
assert quantity_simplify(foot*inch*(foot*foot + inch*(foot + inch))) == foot**2*(foot**2 + foot/12*(foot + foot/12))/12
assert quantity_simplify(2**(foot/inch*kilo/1000)*inch) == 4096*foot/12
assert quantity_simplify(foot**2*inch + inch**2*foot) == 13*foot**3/144
def test_quantity_simplify_across_dimensions():
from sympy.physics.units.util import quantity_simplify
from sympy.physics.units import ampere, ohm, volt, joule, pascal, farad, second, watt, siemens, henry, tesla, weber, hour, newton
assert quantity_simplify(ampere*ohm, across_dimensions=True, unit_system="SI") == volt
assert quantity_simplify(6*ampere*ohm, across_dimensions=True, unit_system="SI") == 6*volt
assert quantity_simplify(volt/ampere, across_dimensions=True, unit_system="SI") == ohm
assert quantity_simplify(volt/ohm, across_dimensions=True, unit_system="SI") == ampere
assert quantity_simplify(joule/meter**3, across_dimensions=True, unit_system="SI") == pascal
assert quantity_simplify(farad*ohm, across_dimensions=True, unit_system="SI") == second
assert quantity_simplify(joule/second, across_dimensions=True, unit_system="SI") == watt
assert quantity_simplify(meter**3/second, across_dimensions=True, unit_system="SI") == meter**3/second
assert quantity_simplify(joule/second, across_dimensions=True, unit_system="SI") == watt
assert quantity_simplify(joule/coulomb, across_dimensions=True, unit_system="SI") == volt
assert quantity_simplify(volt/ampere, across_dimensions=True, unit_system="SI") == ohm
assert quantity_simplify(ampere/volt, across_dimensions=True, unit_system="SI") == siemens
assert quantity_simplify(coulomb/volt, across_dimensions=True, unit_system="SI") == farad
assert quantity_simplify(volt*second/ampere, across_dimensions=True, unit_system="SI") == henry
assert quantity_simplify(volt*second/meter**2, across_dimensions=True, unit_system="SI") == tesla
assert quantity_simplify(joule/ampere, across_dimensions=True, unit_system="SI") == weber
assert quantity_simplify(5*kilometer/hour, across_dimensions=True, unit_system="SI") == 25*meter/(18*second)
assert quantity_simplify(5*kilogram*meter/second**2, across_dimensions=True, unit_system="SI") == 5*newton
def test_check_dimensions():
x = symbols('x')
assert check_dimensions(inch + x) == inch + x
assert check_dimensions(length + x) == length + x
# after subs we get 2*length; check will clear the constant
assert check_dimensions((length + x).subs(x, length)) == length
assert check_dimensions(newton*meter + joule) == joule + meter*newton
raises(ValueError, lambda: check_dimensions(inch + 1))
raises(ValueError, lambda: check_dimensions(length + 1))
raises(ValueError, lambda: check_dimensions(length + time))
raises(ValueError, lambda: check_dimensions(meter + second))
raises(ValueError, lambda: check_dimensions(2 * meter + second))
raises(ValueError, lambda: check_dimensions(2 * meter + 3 * second))
raises(ValueError, lambda: check_dimensions(1 / second + 1 / meter))
raises(ValueError, lambda: check_dimensions(2 * meter*(mile + centimeter) + km))
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