def test_orthogonalize():
C = CoordSysCartesian('C')
a, b = symbols('a b', integer=True);
i, j, k = C.base_vectors()
v1 = i + 2*j
v2 = 2*i + 3*j
v3 = 3*i + 5*j
v4 = 3*i + j
v5 = 2*i + 2*j
v6 = a*i + b*j
v7 = 4*a*i + 4*b*j
assert orthogonalize(v1, v2) == [C.i + 2*C.j, 2*C.i/5 + -C.j/5]
# from wikipedia
assert orthogonalize(v4, v5, orthonormal=True) == \
[(3*sqrt(10))*C.i/10 + (sqrt(10))*C.j/10, (-sqrt(10))*C.i/10 + (3*sqrt(10))*C.j/10]
raises(ValueError, lambda: orthogonalize(v1, v2, v3))
raises(ValueError, lambda: orthogonalize(v6, v7))
def test_orthogonalize():
C = CoordSysCartesian('C')
a, b = symbols('a b', integer=True)
i, j, k = C.base_vectors()
v1 = i + 2*j
v2 = 2*i + 3*j
v3 = 3*i + 5*j
v4 = 3*i + j
v5 = 2*i + 2*j
v6 = a*i + b*j
v7 = 4*a*i + 4*b*j
assert orthogonalize(v1, v2) == [C.i + 2*C.j, 2*C.i/5 + -C.j/5]
# from wikipedia
assert orthogonalize(v4, v5, orthonormal=True) == \
[(3*sqrt(10))*C.i/10 + (sqrt(10))*C.j/10, (-sqrt(10))*C.i/10 + (3*sqrt(10))*C.j/10]
raises(ValueError, lambda: orthogonalize(v1, v2, v3))
raises(ValueError, lambda: orthogonalize(v6, v7))
from sympy.simplify import simplify, trigsimp
from sympy import pi, sqrt, symbols, ImmutableMatrix as Matrix, sin, cos
from sympy.vector.vector import Vector, BaseVector, VectorAdd, VectorMul, VectorZero
from sympy.vector.coordsysrect import CoordSysCartesian
C = CoordSysCartesian("C")
i, j, k = C.base_vectors()
a, b, c = symbols("a b c")
def test_vector_sympy():
"""
Test whether the Vector framework confirms to the hashing
and equality testing properties of SymPy.
"""
i1 = BaseVector("i1", 0, C)
assert i1 == i
assert i1.__hash__() == i.__hash__()
v1 = 3 * j
assert v1 == j * 3
assert v1.components == {j: 3}
v2 = 3 * i + 4 * j + 5 * k
v3 = 2 * i + 4 * j + i + 4 * k + k
assert v3 == v2
assert v3.__hash__() == v2.__hash__()
def test_vector():
assert isinstance(i, BaseVector)
assert i != j
from sympy.simplify import simplify, trigsimp
from sympy import pi, sqrt, symbols, ImmutableMatrix as Matrix, \
sin, cos, Function, Integral, Derivative, diff, integrate
from sympy.vector.vector import Vector, BaseVector, VectorAdd, \
VectorMul, VectorZero
from sympy.vector.coordsysrect import CoordSysCartesian
C = CoordSysCartesian('C')
i, j, k = C.base_vectors()
a, b, c = symbols('a b c')
def test_vector_sympy():
"""
Test whether the Vector framework confirms to the hashing
and equality testing properties of SymPy.
"""
v1 = 3 * j
assert v1 == j * 3
assert v1.components == {j: 3}
v2 = 3 * i + 4 * j + 5 * k
v3 = 2 * i + 4 * j + i + 4 * k + k
assert v3 == v2
assert v3.__hash__() == v2.__hash__()
def test_vector():
assert isinstance(i, BaseVector)
assert i != j
assert j != k