def test_R2():
x0, y0, r0, theta0 = symbols('x0, y0, r0, theta0', real=True)
point_r = R2_r.point([x0, y0])
point_p = R2_p.point([r0, theta0])
# r**2 = x**2 + y**2
assert (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_r) == 0
assert trigsimp( (R2.r**2 - R2.x**2 - R2.y**2).rcall(point_p) ) == 0
assert trigsimp(R2.e_r(R2.x**2 + R2.y**2).rcall(point_p).doit()) == 2*r0
# polar->rect->polar == Id
a, b = symbols('a b', positive=True)
m = Matrix([[a], [b]])
#TODO assert m == R2_r.transform(R2_p, R2_p.transform(R2_r, [a, b])).applyfunc(simplify)
assert m == R2_p.transform(R2_r, R2_r.transform(R2_p, m)).applyfunc(simplify)
# deprecated method
with warns_deprecated_sympy():
assert m == R2_p.coord_tuple_transform_to(
R2_r, R2_r.coord_tuple_transform_to(R2_p, m)).applyfunc(simplify)
