def test_differential_operators_curvilinear_system():
A = CoordSysCartesian('A')
A._set_lame_coefficient_mapping('spherical')
B = CoordSysCartesian('B')
B._set_lame_coefficient_mapping('cylindrical')
# Test for spherical coordinate system and gradient
assert gradient(3 * A.x + 4 * A.y) == 3 * A.i + 4 / A.x * A.j
assert gradient(
3 * A.x * A.z +
4 * A.y) == 3 * A.z * A.i + 4 / A.x * A.j + (3 / sin(A.y)) * A.k
assert gradient(0 * A.x + 0 * A.y + 0 * A.z) == Vector.zero
assert gradient(
A.x * A.y *
A.z) == A.y * A.z * A.i + A.z * A.j + (A.y / sin(A.y)) * A.k
# Test for spherical coordinate system and divergence
assert divergence(A.x * A.i + A.y * A.j + A.z * A.k) == \
(sin(A.y)*A.x + cos(A.y)*A.x*A.y)/(sin(A.y)*A.x**2) + 3 + 1/(sin(A.y)*A.x)
assert divergence(3*A.x*A.z*A.i + A.y*A.j + A.x*A.y*A.z*A.k) == \
(sin(A.y)*A.x + cos(A.y)*A.x*A.y)/(sin(A.y)*A.x**2) + 9*A.z + A.y/sin(A.y)
assert divergence(Vector.zero) == 0
assert divergence(0 * A.i + 0 * A.j + 0 * A.k) == 0
# Test for cylindrical coordinate system and divergence
assert divergence(B.x * B.i + B.y * B.j + B.z * B.k) == 2 + 1 / B.y
assert divergence(B.x * B.j + B.z * B.k) == 1
# Test for spherical coordinate system and divergence
assert curl(A.x*A.i + A.y*A.j + A.z*A.k) == \
(cos(A.y)*A.z/(sin(A.y)*A.x))*A.i + (-A.z/A.x)*A.j + A.y/A.x*A.k
assert curl(A.x * A.j + A.z *
A.k) == (cos(A.y) * A.z /
(sin(A.y) * A.x)) * A.i + (-A.z / A.x) * A.j + 2 * A.k
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)
