def test_lame_coefficients():
a = CoordSysCartesian('a')
a._set_lame_coefficient_mapping('spherical')
assert a.lame_coefficients() == (1, a.x, sin(a.y) * a.x)
a = CoordSysCartesian('a')
assert a.lame_coefficients() == (1, 1, 1)
a = CoordSysCartesian('a')
a._set_lame_coefficient_mapping('cartesian')
assert a.lame_coefficients() == (1, 1, 1)
a = CoordSysCartesian('a')
a._set_lame_coefficient_mapping('cylindrical')
assert a.lame_coefficients() == (1, a.y, 1)
def test_transformation_equations():
from sympy import symbols
x, y, z = symbols('x y z')
a = CoordSysCartesian('a')
# Str
a._connect_to_standard_cartesian('spherical')
assert a._transformation_equations() == (a.x * sin(a.y) * cos(a.z),
a.x * sin(a.y) * sin(a.z),
a.x * cos(a.y))
assert a.lame_coefficients() == (1, a.x, a.x * sin(a.y))
a._connect_to_standard_cartesian('cylindrical')
assert a._transformation_equations() == (a.x * cos(a.y), a.x * sin(a.y),
a.z)
assert a.lame_coefficients() == (1, a.y, 1)
a._connect_to_standard_cartesian('cartesian')
assert a._transformation_equations() == (a.x, a.y, a.z)
assert a.lame_coefficients() == (1, 1, 1)
# Variables and expressions
a._connect_to_standard_cartesian(((x, y, z), (x, y, z)))
assert a._transformation_equations() == (a.x, a.y, a.z)
assert a.lame_coefficients() == (1, 1, 1)
a._connect_to_standard_cartesian(
((x, y, z), ((x * cos(y), x * sin(y), z))))
assert a._transformation_equations() == (a.x * cos(a.y), a.x * sin(a.y),
a.z)
assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)
a._connect_to_standard_cartesian(
((x, y, z), (x * sin(y) * cos(z), x * sin(y) * sin(z), x * cos(y))))
assert a._transformation_equations() == (a.x * sin(a.y) * cos(a.z),
a.x * sin(a.y) * sin(a.z),
a.x * cos(a.y))
assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2),
sqrt(sin(a.y)**2 * a.x**2))
# Equations
a._connect_to_standard_cartesian(
(a.x * sin(a.y) * cos(a.z), a.x * sin(a.y) * sin(a.z), a.x * cos(a.y)))
assert a._transformation_equations() == (a.x * sin(a.y) * cos(a.z),
a.x * sin(a.y) * sin(a.z),
a.x * cos(a.y))
assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2),
sqrt(sin(a.y)**2 * a.x**2))
a._connect_to_standard_cartesian((a.x, a.y, a.z))
assert a._transformation_equations() == (a.x, a.y, a.z)
assert simplify(a.lame_coefficients()) == (1, 1, 1)
a._connect_to_standard_cartesian((a.x * cos(a.y), a.x * sin(a.y), a.z))
assert a._transformation_equations() == (a.x * cos(a.y), a.x * sin(a.y),
a.z)
assert simplify(a.lame_coefficients()) == (1, sqrt(a.x**2), 1)
