def test_R3():
a, b, c = symbols('a b c', positive=True)
m = Matrix([[a], [b], [c]])
assert m == R3_c.coord_tuple_transform_to(R3_r, R3_r.coord_tuple_transform_to(R3_c, m)).applyfunc(simplify)
#TODO assert m == R3_r.coord_tuple_transform_to(R3_c, R3_c.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify)
assert m == R3_s.coord_tuple_transform_to(R3_r, R3_r.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify)
#TODO assert m == R3_r.coord_tuple_transform_to(R3_s, R3_s.coord_tuple_transform_to(R3_r, m)).applyfunc(simplify)
assert m == R3_s.coord_tuple_transform_to(R3_c, R3_c.coord_tuple_transform_to(R3_s, m)).applyfunc(simplify)
def main():
a, b, c = symbols('a b c', real=True)
x, y, z = R3_r.coord_functions()
dx, dy, dz = R3_r.base_oneforms()
ex, ey, ez = R3_r.base_vectors()
fx = a* x * y * z
fy = b * x ** 2 * z
fz = -3 * x**2 * y
omega = fx * dx + fy * dy + fz * dz
print_latex(omega)
domega = Differential(omega)
print_latex(domega)
print_latex(domega(ey, ez)) # for WedgeProduct(dy, dz)
print_latex(domega(ez, ex)) # for WedgeProduct(dz, dx)
print_latex(domega(ex, ey)) # for WedgeProduct(dx, dy)