from sympy.core import Rational
from sympy.simplify import simplify, trigsimp
from sympy import pi, sqrt, symbols, ImmutableMatrix as Matrix, \
     sin, cos, Function, Integral, Derivative, diff
from sympy.vector.vector import Vector, BaseVector, VectorAdd, \
     VectorMul, VectorZero
from sympy.vector.coordsysrect import CoordSys3D
from sympy.vector.vector import Cross, Dot, cross
from sympy.utilities.pytest import raises

C = CoordSys3D('C')

i, j, k = C.base_vectors()
a, b, c = symbols('a b c')


def test_cross():
    v1 = C.x * i + C.z * C.z * j
    v2 = C.x * i + C.y * j + C.z * k
    assert Cross(v1, v2) == Cross(C.x*C.i + C.z**2*C.j, C.x*C.i + C.y*C.j + C.z*C.k)
    assert Cross(v1, v2).doit() == C.z**3*C.i + (-C.x*C.z)*C.j + (C.x*C.y - C.x*C.z**2)*C.k
    assert cross(v1, v2) == C.z**3*C.i + (-C.x*C.z)*C.j + (C.x*C.y - C.x*C.z**2)*C.k
    assert Cross(v1, v2) == -Cross(v2, v1)
    assert Cross(v1, v2) + Cross(v2, v1) == Vector.zero


def test_dot():
    v1 = C.x * i + C.z * C.z * j
    v2 = C.x * i + C.y * j + C.z * k
    assert Dot(v1, v2) == Dot(C.x*C.i + C.z**2*C.j, C.x*C.i + C.y*C.j + C.z*C.k)
    assert Dot(v1, v2).doit() == C.x**2 + C.y*C.z**2
    assert Dot(v1, v2).doit() == C.x**2 + C.y*C.z**2
    assert Dot(v1, v2) == Dot(v2, v1)


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
    assert k != i
    assert i - i == Vector.zero
    assert i + Vector.zero == i
    assert i - Vector.zero == i
    assert Vector.zero != 0
    assert -Vector.zero == Vector.zero

    v1 = a*i + b*j + c*k
    v2 = a**2*i + b**2*j + c**2*k
    v3 = v1 + v2
    v4 = 2 * v1
    v5 = a * i

    assert isinstance(v1, VectorAdd)
    assert v1 - v1 == Vector.zero
    assert v1 + Vector.zero == v1
    assert v1.dot(i) == a
    assert v1.dot(j) == b
    assert v1.dot(k) == c
    assert i.dot(v2) == a**2
    assert j.dot(v2) == b**2
    assert k.dot(v2) == c**2
    assert v3.dot(i) == a**2 + a
    assert v3.dot(j) == b**2 + b
    assert v3.dot(k) == c**2 + c

    assert v1 + v2 == v2 + v1
    assert v1 - v2 == -1 * (v2 - v1)
    assert a * v1 == v1 * a

    assert isinstance(v5, VectorMul)
    assert v5.base_vector == i
    assert v5.measure_number == a
    assert isinstance(v4, Vector)
    assert isinstance(v4, VectorAdd)
    assert isinstance(v4, Vector)
    assert isinstance(Vector.zero, VectorZero)
    assert isinstance(Vector.zero, Vector)
    assert isinstance(v1 * 0, VectorZero)

    assert v1.to_matrix(C) == Matrix([[a], [b], [c]])

    assert i.components == {i: 1}
    assert v5.components == {i: a}
    assert v1.components == {i: a, j: b, k: c}

    assert VectorAdd(v1, Vector.zero) == v1
    assert VectorMul(a, v1) == v1*a
    assert VectorMul(1, i) == i
    assert VectorAdd(v1, Vector.zero) == v1
    assert VectorMul(0, Vector.zero) == Vector.zero
    raises(TypeError, lambda: v1.outer(1))
    raises(TypeError, lambda: v1.dot(1))


def test_vector_magnitude_normalize():
    assert Vector.zero.magnitude() == 0
    assert Vector.zero.normalize() == Vector.zero

    assert i.magnitude() == 1
    assert j.magnitude() == 1
    assert k.magnitude() == 1
    assert i.normalize() == i
    assert j.normalize() == j
    assert k.normalize() == k

    v1 = a * i
    assert v1.normalize() == (a/sqrt(a**2))*i
    assert v1.magnitude() == sqrt(a**2)

    v2 = a*i + b*j + c*k
    assert v2.magnitude() == sqrt(a**2 + b**2 + c**2)
    assert v2.normalize() == v2 / v2.magnitude()

    v3 = i + j
    assert v3.normalize() == (sqrt(2)/2)*C.i + (sqrt(2)/2)*C.j


def test_vector_simplify():
    A, s, k, m = symbols('A, s, k, m')

    test1 = (1 / a + 1 / b) * i
    assert (test1 & i) != (a + b) / (a * b)
    test1 = simplify(test1)
    assert (test1 & i) == (a + b) / (a * b)
    assert test1.simplify() == simplify(test1)

    test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * i
    test2 = simplify(test2)
    assert (test2 & i) == (A**2 * s**4 / (4 * pi * k * m**3))

    test3 = ((4 + 4 * a - 2 * (2 + 2 * a)) / (2 + 2 * a)) * i
    test3 = simplify(test3)
    assert (test3 & i) == 0

    test4 = ((-4 * a * b**2 - 2 * b**3 - 2 * a**2 * b) / (a + b)**2) * i
    test4 = simplify(test4)
    assert (test4 & i) == -2 * b

    v = (sin(a)+cos(a))**2*i - j
    assert trigsimp(v) == (2*sin(a + pi/4)**2)*i + (-1)*j
    assert trigsimp(v) == v.trigsimp()

    assert simplify(Vector.zero) == Vector.zero


def test_vector_dot():
    assert i.dot(Vector.zero) == 0
    assert Vector.zero.dot(i) == 0
    assert i & Vector.zero == 0

    assert i.dot(i) == 1
    assert i.dot(j) == 0
    assert i.dot(k) == 0
    assert i & i == 1
    assert i & j == 0
    assert i & k == 0

    assert j.dot(i) == 0
    assert j.dot(j) == 1
    assert j.dot(k) == 0
    assert j & i == 0
    assert j & j == 1
    assert j & k == 0

    assert k.dot(i) == 0
    assert k.dot(j) == 0
    assert k.dot(k) == 1
    assert k & i == 0
    assert k & j == 0
    assert k & k == 1

    raises(TypeError, lambda: k.dot(1))


def test_vector_cross():
    assert i.cross(Vector.zero) == Vector.zero
    assert Vector.zero.cross(i) == Vector.zero

    assert i.cross(i) == Vector.zero
    assert i.cross(j) == k
    assert i.cross(k) == -j
    assert i ^ i == Vector.zero
    assert i ^ j == k
    assert i ^ k == -j

    assert j.cross(i) == -k
    assert j.cross(j) == Vector.zero
    assert j.cross(k) == i
    assert j ^ i == -k
    assert j ^ j == Vector.zero
    assert j ^ k == i

    assert k.cross(i) == j
    assert k.cross(j) == -i
    assert k.cross(k) == Vector.zero
    assert k ^ i == j
    assert k ^ j == -i
    assert k ^ k == Vector.zero

    assert k.cross(1) == Cross(k, 1)


def test_projection():
    v1 = i + j + k
    v2 = 3*i + 4*j
    v3 = 0*i + 0*j
    assert v1.projection(v1) == i + j + k
    assert v1.projection(v2) == Rational(7, 3)*C.i + Rational(7, 3)*C.j + Rational(7, 3)*C.k
    assert v1.projection(v1, scalar=True) == 1
    assert v1.projection(v2, scalar=True) == Rational(7, 3)
    assert v3.projection(v1) == Vector.zero


def test_vector_diff_integrate():
    f = Function('f')
    v = f(a)*C.i + a**2*C.j - C.k
    assert Derivative(v, a) == Derivative((f(a))*C.i +
                                          a**2*C.j + (-1)*C.k, a)
    assert (diff(v, a) == v.diff(a) == Derivative(v, a).doit() ==
            (Derivative(f(a), a))*C.i + 2*a*C.j)
    assert (Integral(v, a) == (Integral(f(a), a))*C.i +
            (Integral(a**2, a))*C.j + (Integral(-1, a))*C.k)


def test_vector_args():
    raises(ValueError, lambda: BaseVector(3, C))
    raises(TypeError, lambda: BaseVector(0, Vector.zero))
