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from sympy.core.numbers import (Float, pi)
from sympy.core.symbol import symbols
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
from sympy.physics.vector import ReferenceFrame, dynamicsymbols, outer
from sympy.physics.vector.dyadic import _check_dyadic
from sympy.testing.pytest import raises
A = ReferenceFrame('A')
def test_dyadic():
d1 = A.x | A.x
d2 = A.y | A.y
d3 = A.x | A.y
assert d1 * 0 == 0
assert d1 != 0
assert d1 * 2 == 2 * A.x | A.x
assert d1 / 2. == 0.5 * d1
assert d1 & (0 * d1) == 0
assert d1 & d2 == 0
assert d1 & A.x == A.x
assert d1 ^ A.x == 0
assert d1 ^ A.y == A.x | A.z
assert d1 ^ A.z == - A.x | A.y
assert d2 ^ A.x == - A.y | A.z
assert A.x ^ d1 == 0
assert A.y ^ d1 == - A.z | A.x
assert A.z ^ d1 == A.y | A.x
assert A.x & d1 == A.x
assert A.y & d1 == 0
assert A.y & d2 == A.y
assert d1 & d3 == A.x | A.y
assert d3 & d1 == 0
assert d1.dt(A) == 0
q = dynamicsymbols('q')
qd = dynamicsymbols('q', 1)
B = A.orientnew('B', 'Axis', [q, A.z])
assert d1.express(B) == d1.express(B, B)
assert d1.express(B) == ((cos(q)**2) * (B.x | B.x) + (-sin(q) * cos(q)) *
(B.x | B.y) + (-sin(q) * cos(q)) * (B.y | B.x) + (sin(q)**2) *
(B.y | B.y))
assert d1.express(B, A) == (cos(q)) * (B.x | A.x) + (-sin(q)) * (B.y | A.x)
assert d1.express(A, B) == (cos(q)) * (A.x | B.x) + (-sin(q)) * (A.x | B.y)
assert d1.dt(B) == (-qd) * (A.y | A.x) + (-qd) * (A.x | A.y)
assert d1.to_matrix(A) == Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
assert d1.to_matrix(A, B) == Matrix([[cos(q), -sin(q), 0],
[0, 0, 0],
[0, 0, 0]])
assert d3.to_matrix(A) == Matrix([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
a, b, c, d, e, f = symbols('a, b, c, d, e, f')
v1 = a * A.x + b * A.y + c * A.z
v2 = d * A.x + e * A.y + f * A.z
d4 = v1.outer(v2)
assert d4.to_matrix(A) == Matrix([[a * d, a * e, a * f],
[b * d, b * e, b * f],
[c * d, c * e, c * f]])
d5 = v1.outer(v1)
C = A.orientnew('C', 'Axis', [q, A.x])
for expected, actual in zip(C.dcm(A) * d5.to_matrix(A) * C.dcm(A).T,
d5.to_matrix(C)):
assert (expected - actual).simplify() == 0
raises(TypeError, lambda: d1.applyfunc(0))
def test_dyadic_simplify():
x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')
N = ReferenceFrame('N')
dy = N.x | N.x
test1 = (1 / x + 1 / y) * dy
assert (N.x & test1 & N.x) != (x + y) / (x * y)
test1 = test1.simplify()
assert (N.x & test1 & N.x) == (x + y) / (x * y)
test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * dy
test2 = test2.simplify()
assert (N.x & test2 & N.x) == (A**2 * s**4 / (4 * pi * k * m**3))
test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * dy
test3 = test3.simplify()
assert (N.x & test3 & N.x) == 0
test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * dy
test4 = test4.simplify()
assert (N.x & test4 & N.x) == -2 * y
def test_dyadic_subs():
N = ReferenceFrame('N')
s = symbols('s')
a = s*(N.x | N.x)
assert a.subs({s: 2}) == 2*(N.x | N.x)
def test_check_dyadic():
raises(TypeError, lambda: _check_dyadic(0))
def test_dyadic_evalf():
N = ReferenceFrame('N')
a = pi * (N.x | N.x)
assert a.evalf(3) == Float('3.1416', 3) * (N.x | N.x)
s = symbols('s')
a = 5 * s * pi* (N.x | N.x)
assert a.evalf(2) == Float('5', 2) * Float('3.1416', 2) * s * (N.x | N.x)
assert a.evalf(9, subs={s: 5.124}) == Float('80.48760378', 9) * (N.x | N.x)
def test_dyadic_xreplace():
x, y, z = symbols('x y z')
N = ReferenceFrame('N')
D = outer(N.x, N.x)
v = x*y * D
assert v.xreplace({x : cos(x)}) == cos(x)*y * D
assert v.xreplace({x*y : pi}) == pi * D
v = (x*y)**z * D
assert v.xreplace({(x*y)**z : 1}) == D
assert v.xreplace({x:1, z:0}) == D
raises(TypeError, lambda: v.xreplace())
raises(TypeError, lambda: v.xreplace([x, y]))
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