def test_where():
    X = Geometric('X', S(1)/5)
    Y = Poisson('Y', 4)
    assert where(X**2 > 4).set == Range(3, S.Infinity, 1)
    assert where(X**2 >= 4).set == Range(2, S.Infinity, 1)
    assert where(Y**2 < 9).set == Range(0, 3, 1)
    assert where(Y**2 <= 9).set == Range(0, 4, 1)

def test_domains():
    X, Y = Die('x', 6), Die('y', 6)
    x, y = X.symbol, Y.symbol
    # Domains
    d = where(X > Y)
    assert d.condition == (x > y)
    d = where(And(X > Y, Y > 3))
    assert d.as_boolean() == Or(And(Eq(x, 5), Eq(y, 4)), And(Eq(x, 6),
        Eq(y, 5)), And(Eq(x, 6), Eq(y, 4)))
    assert len(d.elements) == 3

    assert len(pspace(X + Y).domain.elements) == 36

    Z = Die('x', 4)

    raises(ValueError, lambda: P(X > Z))  # Two domains with same internal symbol

    pspace(X + Y).domain.set == FiniteSet(1, 2, 3, 4, 5, 6)**2

    assert where(X > 3).set == FiniteSet(4, 5, 6)
    assert X.pspace.domain.dict == FiniteSet(
        *[Dict({X.symbol: i}) for i in range(1, 7)])

    assert where(X > Y).dict == FiniteSet(*[Dict({X.symbol: i, Y.symbol: j})
            for i in range(1, 7) for j in range(1, 7) if i > j])

def test_ContinuousDomain():
    X = Normal('x', 0, 1)
    assert where(X**2 <= 1).set == Interval(-1, 1)
    assert where(X**2 <= 1).symbol == X.symbol
    where(And(X**2 <= 1, X >= 0)).set == Interval(0, 1)
    raises(ValueError, lambda: where(sin(X) > 1))

    Y = given(X, X >= 0)

    assert Y.pspace.domain.set == Interval(0, oo)

def test_latex_RandomDomain():
    from sympy.stats import Normal, Die, Exponential, pspace, where
    X = Normal(0, 1, symbol=Symbol('x1'))
    assert latex(where(X>0)) == "Domain: 0 < x_{1}"

    D = Die(6, symbol=Symbol('d1'))
    assert latex(where(D>4)) == r"Domain: d_{1} = 5 \vee d_{1} = 6"

    A = Exponential(1, symbol=Symbol('a'))
    B = Exponential(1, symbol=Symbol('b'))
    assert latex(pspace(Tuple(A,B)).domain) =="Domain: 0 \leq a \wedge 0 \leq b"

def test_RandomDomain():
    from sympy.stats import Normal, Die, Exponential, pspace, where
    X = Normal('x1', 0, 1)
    assert str(where(X > 0)) == "Domain: 0 < x1"

    D = Die('d1', 6)
    assert str(where(D > 4)) == "Domain: Or(d1 == 5, d1 == 6)"

    A = Exponential('a', 1)
    B = Exponential('b', 1)
    assert str(pspace(Tuple(A, B)).domain) == "Domain: And(0 <= a, 0 <= b)"

def test_latex_RandomDomain():
    from sympy.stats import Normal, Die, Exponential, pspace, where
    X = Normal('x1', 0, 1)
    assert latex(where(X > 0)) == "Domain: x_{1} > 0"

    D = Die('d1', 6)
    assert latex(where(D > 4)) == r"Domain: d_{1} = 5 \vee d_{1} = 6"

    A = Exponential('a', 1)
    B = Exponential('b', 1)
    assert latex(
        pspace(Tuple(A, B)).domain) == "Domain: a \geq 0 \wedge b \geq 0"

def test_latex_RandomDomain():
    from sympy.stats import Normal, Die, Exponential, pspace, where

    X = Normal("x1", 0, 1)
    assert latex(where(X > 0)) == "Domain: 0 < x_{1}"

    D = Die("d1", 6)
    assert latex(where(D > 4)) == r"Domain: d_{1} = 5 \vee d_{1} = 6"

    A = Exponential("a", 1)
    B = Exponential("b", 1)
    assert latex(pspace(Tuple(A, B)).domain) == "Domain: 0 \leq a \wedge 0 \leq b"

def test_exponential():
    rate = Symbol('lambda', positive=True, real=True, bounded=True)
    X = Exponential('x', rate)

    assert E(X) == 1/rate
    assert variance(X) == 1/rate**2
    assert skewness(X) == 2
    assert P(X > 0) == S(1)
    assert P(X > 1) == exp(-rate)
    assert P(X > 10) == exp(-10*rate)

    assert where(X <= 1).set == Interval(0, 1)

def test_exponential():
    rate = Symbol('lambda', positive=True, real=True, finite=True)
    X = Exponential('x', rate)

    assert E(X) == 1/rate
    assert variance(X) == 1/rate**2
    assert skewness(X) == 2
    assert skewness(X) == smoment(X, 3)
    assert smoment(2*X, 4) == smoment(X, 4)
    assert moment(X, 3) == 3*2*1/rate**3
    assert P(X > 0) == S(1)
    assert P(X > 1) == exp(-rate)
    assert P(X > 10) == exp(-10*rate)

    assert where(X <= 1).set == Interval(0, 1)

def test_dice():
    # TODO: Make iid method!
    X, Y, Z = Die('X', 6), Die('Y', 6), Die('Z', 6)
    a, b = symbols('a b')

    assert E(X) == 3 + S.Half
    assert variance(X) == S(35)/12
    assert E(X + Y) == 7
    assert E(X + X) == 7
    assert E(a*X + b) == a*E(X) + b
    assert variance(X + Y) == variance(X) + variance(Y) == cmoment(X + Y, 2)
    assert variance(X + X) == 4 * variance(X) == cmoment(X + X, 2)
    assert cmoment(X, 0) == 1
    assert cmoment(4*X, 3) == 64*cmoment(X, 3)
    assert covariance(X, Y) == S.Zero
    assert covariance(X, X + Y) == variance(X)
    assert density(Eq(cos(X*S.Pi), 1))[True] == S.Half
    assert correlation(X, Y) == 0
    assert correlation(X, Y) == correlation(Y, X)
    assert smoment(X + Y, 3) == skewness(X + Y)
    assert smoment(X, 0) == 1
    assert P(X > 3) == S.Half
    assert P(2*X > 6) == S.Half
    assert P(X > Y) == S(5)/12
    assert P(Eq(X, Y)) == P(Eq(X, 1))

    assert E(X, X > 3) == 5 == moment(X, 1, 0, X > 3)
    assert E(X, Y > 3) == E(X) == moment(X, 1, 0, Y > 3)
    assert E(X + Y, Eq(X, Y)) == E(2*X)
    assert moment(X, 0) == 1
    assert moment(5*X, 2) == 25*moment(X, 2)

    assert P(X > 3, X > 3) == S.One
    assert P(X > Y, Eq(Y, 6)) == S.Zero
    assert P(Eq(X + Y, 12)) == S.One/36
    assert P(Eq(X + Y, 12), Eq(X, 6)) == S.One/6

    assert density(X + Y) == density(Y + Z) != density(X + X)
    d = density(2*X + Y**Z)
    assert d[S(22)] == S.One/108 and d[S(4100)] == S.One/216 and S(3130) not in d

    assert pspace(X).domain.as_boolean() == Or(
        *[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]])

    assert where(X > 3).set == FiniteSet(4, 5, 6)

def test_dice():
    X, Y, Z = Die(6), Die(6), Die(6)
    a, b = symbols("a b")

    assert E(X) == 3 + S.Half
    assert variance(X) == S(35) / 12
    assert E(X + Y) == 7
    assert E(X + X) == 7
    assert E(a * X + b) == a * E(X) + b
    assert variance(X + Y) == variance(X) + variance(Y)
    assert variance(X + X) == 4 * variance(X)
    assert covariance(X, Y) == S.Zero
    assert covariance(X, X + Y) == variance(X)
    assert density(Eq(cos(X * S.Pi), 1))[True] == S.Half

    assert P(X > 3) == S.Half
    assert P(2 * X > 6) == S.Half
    assert P(X > Y) == S(5) / 12
    assert P(Eq(X, Y)) == P(Eq(X, 1))

    assert E(X, X > 3) == 5
    assert E(X, Y > 3) == E(X)
    assert E(X + Y, Eq(X, Y)) == E(2 * X)
    assert E(X + Y - Z, 2 * X > Y + 1) == S(49) / 12

    assert P(X > 3, X > 3) == S.One
    assert P(X > Y, Eq(Y, 6)) == S.Zero
    assert P(Eq(X + Y, 12)) == S.One / 36
    assert P(Eq(X + Y, 12), Eq(X, 6)) == S.One / 6

    assert density(X + Y) == density(Y + Z) != density(X + X)
    d = density(2 * X + Y ** Z)
    assert d[S(22)] == S.One / 108 and d[S(4100)] == S.One / 216 and S(3130) not in d

    assert pspace(X).domain.as_boolean() == Or(*[Eq(X.symbol, i) for i in [1, 2, 3, 4, 5, 6]])

    assert where(X > 3).set == FiniteSet(4, 5, 6)

def test_where():
    X, Y = Die(), Die()
    Z = Normal(0, 1)

    assert where(Z**2<=1).set == Interval(-1, 1)
    assert where(Z**2<=1).as_boolean() == Interval(-1,1).as_relational(Z.symbol)
    assert where(And(X>Y, Y>4)).as_boolean() == And(
            Eq(X.symbol, 6), Eq(Y.symbol, 5))

    assert len(where(X<3).set) == 2
    assert 1 in where(X<3).set

    X, Y = Normal(0, 1), Normal(0, 1)
    assert where(And(X**2 <= 1, X >= 0)).set == Interval(0, 1)
    XX = given(X, And(X**2 <= 1, X >= 0))
    assert XX.pspace.domain.set == Interval(0, 1)
    assert XX.pspace.domain.as_boolean() == And(0 <= X.symbol, X.symbol**2 <= 1)

    raises(TypeError, "XX = given(X, X+3)")

def test_given():
    X = Die(6)
    density(X, X > 5) == {S(6): S(1)}
    where(X > 2, X > 5).as_boolean() == Eq(X.symbol, 6)
    sample(X, X > 5) == 6

def test_given():
    X = Die('X', 6)
    assert density(X, X > 5) == {S(6): S(1)}
    assert where(X > 2, X > 5).as_boolean() == Eq(X.symbol, 6)
    assert sample(X, X > 5) == 6