from sympy.vector import CoordSys3D, Gradient, Divergence, Curl, VectorZero, Laplacian
from sympy.printing.repr import srepr

R = CoordSys3D('R')
s1 = R.x*R.y*R.z
s2 = R.x + 3*R.y**2
s3 = R.x**2 + R.y**2 + R.z**2
v1 = R.x*R.i + R.z*R.z*R.j
v2 = R.x*R.i + R.y*R.j + R.z*R.k
v3 = R.x**2*R.i + R.y**2*R.j + R.z**2*R.k


def test_Gradient():
    assert Gradient(s1) == Gradient(R.x*R.y*R.z)
    assert Gradient(s2) == Gradient(R.x + 3*R.y**2)
    assert Gradient(s1).doit() == R.y*R.z*R.i + R.x*R.z*R.j + R.x*R.y*R.k
    assert Gradient(s2).doit() == R.i + 6*R.y*R.j


def test_Divergence():
    assert Divergence(v1) == Divergence(R.x*R.i + R.z*R.z*R.j)
    assert Divergence(v2) == Divergence(R.x*R.i + R.y*R.j + R.z*R.k)
    assert Divergence(v1).doit() == 1
    assert Divergence(v2).doit() == 3


def test_Curl():
    assert Curl(v1) == Curl(R.x*R.i + R.z*R.z*R.j)
    assert Curl(v2) == Curl(R.x*R.i + R.y*R.j + R.z*R.k)
    assert Curl(v1).doit() == (-2*R.z)*R.i
    assert Curl(v2).doit() == VectorZero()


def test_Laplacian():
    assert Laplacian(s3) == Laplacian(R.x**2 + R.y**2 + R.z**2)
    assert Laplacian(v3) == Laplacian(R.x**2*R.i + R.y**2*R.j + R.z**2*R.k)
    assert Laplacian(s3).doit() == 6
    assert Laplacian(v3).doit() == 2*R.i + 2*R.j + 2*R.k
    assert srepr(Laplacian(s3)) == \
            'Laplacian(Add(Pow(R.x, Integer(2)), Pow(R.y, Integer(2)), Pow(R.z, Integer(2))))'
