def test_doit(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecCross(vn1, vn2).doit() - vn1.cross(vn2) == Vector.zero
assert VecCross(nabla, vn2).doit() - curl(vn2) == Vector.zero
vn3 = C.x * C.y * C.z * C.i + C.x * C.y * C.z * C.j + C.x * C.y * C.z * C.k
assert VecCross(nabla, vn3).doit() - curl(vn3) == Vector.zero
expr = VecCross(v2 * VecDot(vn1, vn2), v1).doit()
assert isinstance(expr.args[0].args[0], Add)
expr = VecCross(v2 * VecDot(vn1, vn2), v1).doit(deep=False)
assert isinstance(expr.args[0], VecMul)
def test_reverse(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecDot(v1, v2).reverse == VecDot(v2, v1)
assert VecDot(vn1, v2).reverse == VecDot(v2, vn1)
assert VecDot(v1, vn2).reverse == VecDot(vn2, v1)
assert VecDot(vn1, vn2).reverse == VecDot(vn2, vn1)
def test_doit(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
expr = VecAdd(v1, v2, v1, evaluate=False)
assert not self._check_args(expr, VecAdd(VecMul(2, v1), v2))
assert self._check_args(expr.doit(), VecAdd(VecMul(2, v1), v2))
expr = VecAdd(v1, v2, VecAdd(v1, v2, evaluate=False), evaluate=False)
assert not self._check_args(expr, VecAdd(VecMul(2, v1), VecMul(2, v2)))
assert self._check_args(expr.doit(),
VecAdd(VecMul(2, v1), VecMul(2, v2)))
r = vn1 + vn2
assert VecAdd(vn1, vn2).doit() == r
expr = VecAdd(v1.mag, VecDot(vn1, vn2))
assert self._check_args(expr.doit(deep=False), expr)
assert self._check_args(expr.doit(), VecAdd(v1.mag, vn1 & vn2))
# test the rule default_sort_key used into VecAdd.doit
assert VecAdd(v1, one, v2).doit().args == (one, v1, v2)
assert VecAdd(v1, VecCross(v1, v2),
one).doit().args == (VecCross(v1, v2), one, v1)
# test the rule merge_explicit used into VecAdd.doit
assert VecAdd(vn1, vn2).doit() == vn1 + vn2
assert self._check_args(
VecAdd(vn1, vn2, one).doit(), VecAdd(one, vn1 + vn2))
def test_doit(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
expr = VecPow(VecDot(vn1, vn2), v1.mag)
assert isinstance(expr, VecPow)
assert isinstance(expr.doit(deep=False), VecPow)
assert isinstance(expr.doit(), Pow)
def test_doit(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
v = C.x * C.y * C.z
assert gradient(v) == Grad(v).doit()
expr = v * (VecDot(vn1, vn2))
assert isinstance(Grad(expr).doit(deep=False), Grad)
assert isinstance(Grad(expr).doit(), Vector)
def test_is_vector(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
# one argument
assert not VecMul(1).is_Vector
assert not VecMul(x).is_Vector
assert VecMul(one).is_Vector
assert VecMul(v1).is_Vector
# two arguments
assert VecMul(one, x).is_Vector
assert VecMul(0, one).is_Vector
assert not VecMul(0, x).is_Vector
assert VecMul(v1, 2).is_Vector
assert not VecMul(v1.mag, 2).is_Vector
assert VecMul(v1.mag, v2).is_Vector
assert VecMul(v1 + v2, v2.mag).is_Vector
assert VecMul(v1 + v2, 3).is_Vector
assert VecMul(v1 + v2, (v1 + v2).mag).is_Vector
# with dot product and nested mul/dot
assert not VecMul(3, VecDot(v1, v2)).is_Vector
assert VecMul(3, VecMul(v1, VecDot(v1, v2))).is_Vector
assert VecMul(3, v1 + v2, VecMul(VecDot(v1, v2), x)).is_Vector
# with cross product and nested mul/cross
assert VecMul(3, VecCross(v1, v2)).is_Vector
assert VecMul(3, v1.mag, VecMul(x, VecCross(v1, v2))).is_Vector
# with cross and dot products
assert VecMul(3, VecDot(v1, v2), VecMul(x, VecCross(v1, v2))).is_Vector
assert not VecMul(3, VecDot(v1, v2),
VecDot(VecMul(x, VecCross(v1, v2)), v1)).is_Vector
def test_is_vector(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert not VecDot(v1, zero).is_Vector
assert VecDot(v1, zero).is_scalar
assert not VecDot(v1, v2).is_Vector
assert not VecDot(vn1, vn2).is_Vector
assert not VecDot(v1, vn1).is_Vector
assert not VecDot(v1 ^ v2, v1).is_Vector
def test_creation(self):
v1, v2, zero, one, nabla, C, vn1, vn2 = self._get_vars()
assert isinstance(Normalize(v1), Normalize)
assert isinstance(Normalize(one), Normalize)
assert Normalize(zero) == zero
assert isinstance(Normalize(x * v1), Normalize)
def func(arg):
with self.assertRaises(TypeError) as context:
Normalize(arg)
assert isinstance(Normalize(v1 + v2), Normalize)
assert isinstance(Normalize(vn1), Normalize)
args = [nabla, 1, v1.mag, VecDot(v1, v2)]
for a in args:
func(a)
assert isinstance(Normalize(v1.norm), Normalize)
def func(*args):
with self.assertRaises(TypeError):
VecDot(*args)
def test_creation(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecDot(v1, zero) == S.Zero
assert VecDot(zero, v1) == S.Zero
assert isinstance(VecDot(v1, v1), VecDot)
assert isinstance(VecDot(v1, v2), VecDot)
assert isinstance(VecDot(v1, v1.norm), VecDot)
assert isinstance(VecDot(v1.norm, v1), VecDot)
assert isinstance(VecDot(nabla, v1), VecDot)
assert isinstance(VecDot(v1, vn1), VecDot)
assert isinstance(VecDot(vn1, v1), VecDot)
assert isinstance(VecDot(v1 + v2, v1), VecDot)
assert isinstance(VecDot(v1.mag * v2, v1), VecDot)
assert isinstance(VecDot(v1 ^ v2, v1), VecDot)
assert isinstance(VecDot((v1 ^ v2) * v1.mag, v1), VecDot)
def func(*args):
with self.assertRaises(TypeError):
VecDot(*args)
func(x, v1)
func(v1, x)
func(v1, v1.mag)
func(zero, 0)
func(nabla, nabla)
func(v1, nabla)