def test_gradient():
a = Symbol('a')
assert gradient(0, R) == Vector(0)
assert gradient(R[0], R) == R.x
assert gradient(R[0]*R[1]*R[2], R) == \
R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
assert gradient(2*R[0]**2, R) == 4*R[0]*R.x
assert gradient(a*sin(R[1])/R[0], R) == \
- a*sin(R[1])/R[0]**2*R.x + a*cos(R[1])/R[0]*R.y
assert gradient(P[0]*P[1], R) == \
(-R[0]*sin(2*q) + R[1]*cos(2*q))*R.x + \
(R[0]*cos(2*q) + R[1]*sin(2*q))*R.y
assert gradient(P[0]*R[2], P) == P[2]*P.x + P[0]*P.z
def test_gradient():
a = Symbol('a')
assert gradient(0, R) == Vector(0)
assert gradient(R[0], R) == R.x
assert gradient(R[0]*R[1]*R[2], R) == \
R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
assert gradient(2*R[0]**2, R) == 4*R[0]*R.x
assert gradient(a*sin(R[1])/R[0], R) == \
- a*sin(R[1])/R[0]**2*R.x + a*cos(R[1])/R[0]*R.y
assert gradient(P[0]*P[1], R) == \
(-R[0]*sin(2*q) + R[1]*cos(2*q))*R.x + \
(R[0]*cos(2*q) + R[1]*sin(2*q))*R.y
assert gradient(P[0]*R[2], P) == P[2]*P.x + P[0]*P.z
def test_gradient():
a = Symbol("a")
assert gradient(0, R) == Vector(0)
assert gradient(R[0], R) == R.x
assert (gradient(R[0] * R[1] * R[2], R) == R[1] * R[2] * R.x +
R[0] * R[2] * R.y + R[0] * R[1] * R.z)
assert gradient(2 * R[0]**2, R) == 4 * R[0] * R.x
assert (gradient(a * sin(R[1]) / R[0],
R) == -a * sin(R[1]) / R[0]**2 * R.x +
a * cos(R[1]) / R[0] * R.y)
assert (gradient(P[0] * P[1],
R) == ((-R[0] * sin(q) + R[1] * cos(q)) * cos(q) -
(R[0] * cos(q) + R[1] * sin(q)) * sin(q)) * R.x +
((-R[0] * sin(q) + R[1] * cos(q)) * sin(q) +
(R[0] * cos(q) + R[1] * sin(q)) * cos(q)) * R.y)
assert gradient(P[0] * R[2], P) == P[2] * P.x + P[0] * P.z
a = Symbol('a')
assert gradient(0, R) == Vector(0)
assert gradient(R[0], R) == R.x
assert gradient(R[0]*R[1]*R[2], R) == \
R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
assert gradient(2*R[0]**2, R) == 4*R[0]*R.x
assert gradient(a*sin(R[1])/R[0], R) == \
- a*sin(R[1])/R[0]**2*R.x + a*cos(R[1])/R[0]*R.y
assert gradient(P[0]*P[1], R) == \
(-R[0]*sin(2*q) + R[1]*cos(2*q))*R.x + \
(R[0]*cos(2*q) + R[1]*sin(2*q))*R.y
assert gradient(P[0]*R[2], P) == P[2]*P.x + P[0]*P.z
scalar_field = 2*R[0]**2*R[1]*R[2]
grad_field = gradient(scalar_field, R)
vector_field = R[1]**2*R.x + 3*R[0]*R.y + 5*R[1]*R[2]*R.z
curl_field = curl(vector_field, R)
def test_conservative():
assert is_conservative(0) is True
assert is_conservative(R.x) is True
assert is_conservative(2 * R.x + 3 * R.y + 4 * R.z) is True
assert is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) is \
True
assert is_conservative(R[0] * R.y) is False
assert is_conservative(grad_field) is True
assert is_conservative(curl_field) is False
assert is_conservative(4*R[0]*R[1]*R[2]*R.x + 2*R[0]**2*R[2]*R.y) is \
False
a = Symbol('a')
assert gradient(0, R) == Vector(0)
assert gradient(R[0], R) == R.x
assert gradient(R[0]*R[1]*R[2], R) == \
R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
assert gradient(2*R[0]**2, R) == 4*R[0]*R.x
assert gradient(a*sin(R[1])/R[0], R) == \
- a*sin(R[1])/R[0]**2*R.x + a*cos(R[1])/R[0]*R.y
assert gradient(P[0]*P[1], R) == \
(-R[0]*sin(2*q) + R[1]*cos(2*q))*R.x + \
(R[0]*cos(2*q) + R[1]*sin(2*q))*R.y
assert gradient(P[0]*R[2], P) == P[2]*P.x + P[0]*P.z
scalar_field = 2*R[0]**2*R[1]*R[2]
grad_field = gradient(scalar_field, R)
vector_field = R[1]**2*R.x + 3*R[0]*R.y + 5*R[1]*R[2]*R.z
curl_field = curl(vector_field, R)
def test_conservative():
assert is_conservative(0) is True
assert is_conservative(R.x) is True
assert is_conservative(2 * R.x + 3 * R.y + 4 * R.z) is True
assert is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) is \
True
assert is_conservative(R[0] * R.y) is False
assert is_conservative(grad_field) is True
assert is_conservative(curl_field) is False
assert is_conservative(4*R[0]*R[1]*R[2]*R.x + 2*R[0]**2*R[2]*R.y) is \
False