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_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_is_vector(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecCross(v1, zero).is_Vector
assert VecCross(v1, v2).is_Vector
assert VecCross(vn1, vn2).is_Vector
assert VecCross(v1, vn1).is_Vector
assert VecCross((v1 & v2) * one, v2).is_Vector
def test_doit(self):
v1, v2, zero, one, nabla, C, vn1, vn2 = self._get_vars()
assert Magnitude(VecAdd(v1, zero, evaluate=False)).doit() == v1.mag
assert Magnitude(vn1).doit() == sqrt(14)
assert Magnitude(vn2).doit() == sqrt(x**2 + y**2 + z**2)
assert isinstance(
Magnitude(VecCross(vn1, vn2)).doit(deep=False), Magnitude)
assert isinstance(Magnitude(VecCross(vn1, vn2)).doit(), Pow)
def test_creation(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecCross(v1, zero) == zero
assert VecCross(zero, v1) == zero
assert VecCross(v1, v1) == zero
assert VecCross(vn1, vn1) == Vector.zero
assert VecCross(v1, v1.norm)
assert VecCross(vn1, v1.norm)
assert VecCross(nabla, v1)
assert VecCross(v1, vn1)
assert VecCross(vn1, v1)
def func(*args):
with self.assertRaises(TypeError) as context:
VecCross(*args)
func(x, v1)
func(v1, x)
func(v1, v1.mag)
func(v1 & v2, v1.mag)
func(v1 & v2, v1)
func(0, v1)
func(nabla, nabla)
func(v1, nabla)
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_veccross(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
expr = VecCross(v1, v2)
assert isinstance(expr.diff(x), VecAdd)
assert isinstance(expr.diff(x, evaluate=False), D)
assert self._check_args(
expr.diff(x),
(v1.diff(x) ^ v2) + (v1 ^ v2.diff(x))
)
expr = v1.cu.diff(x, 2)
assert isinstance(expr, D)
def test_reverse(self):
v1, v2, zero, one, nabla, C, vn1, vn2, x, y, z = self._get_vars()
assert VecCross(v1, v2).reverse == -VecCross(v2, v1)
assert VecCross(vn1, v2).reverse == -VecCross(v2, vn1)
assert VecCross(v1, vn2).reverse == -VecCross(vn2, v1)
assert VecCross(vn1, vn2).reverse == -VecCross(vn2, vn1)
def func(*args):
with self.assertRaises(TypeError) as context:
VecCross(*args)