from sympy.core.add import Add
from sympy.core.function import Function
from sympy.core.numbers import Float, I, oo, pi, Rational
from sympy.core.singleton import S
from sympy.core.symbol import Symbol
from sympy.functions.elementary.miscellaneous import sqrt, cbrt, root, Min, Max, real_root
from sympy.functions.elementary.trigonometric import cos, sin
from sympy.functions.special.delta_functions import Heaviside

from sympy.utilities.pytest import raises

def test_Min():
    from sympy.abc import x, y, z
    n = Symbol('n', negative=True)
    n_ = Symbol('n_', negative=True)
    nn = Symbol('nn', nonnegative=True)
    nn_ = Symbol('nn_', nonnegative=True)
    p = Symbol('p', positive=True)
    p_ = Symbol('p_', positive=True)
    np = Symbol('np', nonpositive=True)
    np_ = Symbol('np_', nonpositive=True)

    assert Min(5, 4) == 4
    assert Min(-oo, -oo) == -oo
    assert Min(-oo, n) == -oo
    assert Min(n, -oo) == -oo
    assert Min(-oo, np) == -oo
    assert Min(np, -oo) == -oo
    assert Min(-oo, 0) == -oo
    assert Min(0, -oo) == -oo
    assert Min(-oo, nn) == -oo
    assert Min(nn, -oo) == -oo
    assert Min(-oo, p) == -oo
    assert Min(p, -oo) == -oo
    assert Min(-oo, oo) == -oo
    assert Min(oo, -oo) == -oo
    assert Min(n, n) == n
    assert Min(n, np) == Min(n, np)
    assert Min(np, n) == Min(np, n)
    assert Min(n, 0) == n
    assert Min(0, n) == n
    assert Min(n, nn) == n
    assert Min(nn, n) == n
    assert Min(n, p) == n
    assert Min(p, n) == n
    assert Min(n, oo) == n
    assert Min(oo, n) == n
    assert Min(np, np) == np
    assert Min(np, 0) == np
    assert Min(0, np) == np
    assert Min(np, nn) == np
    assert Min(nn, np) == np
    assert Min(np, p) == np
    assert Min(p, np) == np
    assert Min(np, oo) == np
    assert Min(oo, np) == np
    assert Min(0, 0) == 0
    assert Min(0, nn) == 0
    assert Min(nn, 0) == 0
    assert Min(0, p) == 0
    assert Min(p, 0) == 0
    assert Min(0, oo) == 0
    assert Min(oo, 0) == 0
    assert Min(nn, nn) == nn
    assert Min(nn, p) == Min(nn, p)
    assert Min(p, nn) == Min(p, nn)
    assert Min(nn, oo) == nn
    assert Min(oo, nn) == nn
    assert Min(p, p) == p
    assert Min(p, oo) == p
    assert Min(oo, p) == p
    assert Min(oo, oo) == oo

    assert Min(n, n_).func is Min
    assert Min(nn, nn_).func is Min
    assert Min(np, np_).func is Min
    assert Min(p, p_).func is Min

    # lists
    raises(ValueError, lambda: Min())
    assert Min(x, y) == Min(y, x)
    assert Min(x, y, z) == Min(z, y, x)
    assert Min(x, Min(y, z)) == Min(z, y, x)
    assert Min(x, Max(y, -oo)) == Min(x, y)
    assert Min(p, oo, n, p, p, p_) == n
    assert Min(p_, n_, p) == n_
    assert Min(n, oo, -7, p, p, 2) == Min(n, -7)
    assert Min(2, x, p, n, oo, n_, p, 2, -2, -2) == Min(-2, x, n, n_)
    assert Min(0, x, 1, y) == Min(0, x, y)
    assert Min(1000, 100, -100, x, p, n) == Min(n, x, -100)
    assert Min(cos(x), sin(x)) == Min(cos(x), sin(x))
    assert Min(cos(x), sin(x)).subs(x, 1) == cos(1)
    assert Min(cos(x), sin(x)).subs(x, S(1)/2) == sin(S(1)/2)
    raises(ValueError, lambda: Min(cos(x), sin(x)).subs(x, I))
    raises(ValueError, lambda: Min(I))
    raises(ValueError, lambda: Min(I, x))
    raises(ValueError, lambda: Min(S.ComplexInfinity, x))

    assert Min(1,x).diff(x) == Heaviside(1-x)
    assert Min(x,1).diff(x) == Heaviside(1-x)
    assert Min(0,-x,1-2*x).diff(x) == -Heaviside(x + Min(0, -2*x + 1)) \
        - 2*Heaviside(2*x + Min(0, -x) - 1)

    a, b = Symbol('a', real=True), Symbol('b', real=True)
    # a and b are both real, Min(a, b) should be real
    assert Min(a, b).is_real

    # issue 7619
    f = Function('f')
    assert Min(1, 2*Min(f(1), 2))  # doesn't fail

    # issue 7233
    e = Min(0, x)
    assert e.evalf == e.n
    assert e.n().args == (0, x)


def test_Max():
    from sympy.abc import x, y, z
    n = Symbol('n', negative=True)
    n_ = Symbol('n_', negative=True)
    nn = Symbol('nn', nonnegative=True)
    nn_ = Symbol('nn_', nonnegative=True)
    p = Symbol('p', positive=True)
    p_ = Symbol('p_', positive=True)
    np = Symbol('np', nonpositive=True)
    np_ = Symbol('np_', nonpositive=True)

    assert Max(5, 4) == 5

    # lists

    raises(ValueError, lambda: Max())
    assert Max(x, y) == Max(y, x)
    assert Max(x, y, z) == Max(z, y, x)
    assert Max(x, Max(y, z)) == Max(z, y, x)
    assert Max(x, Min(y, oo)) == Max(x, y)
    assert Max(n, -oo, n_, p, 2) == Max(p, 2)
    assert Max(n, -oo, n_, p) == p
    assert Max(2, x, p, n, -oo, S.NegativeInfinity, n_, p, 2) == Max(2, x, p)
    assert Max(0, x, 1, y) == Max(1, x, y)
    assert Max(x, x + 1, x - 1) == 1 + x
    assert Max(1000, 100, -100, x, p, n) == Max(p, x, 1000)
    assert Max(cos(x), sin(x)) == Max(sin(x), cos(x))
    assert Max(cos(x), sin(x)).subs(x, 1) == sin(1)
    assert Max(cos(x), sin(x)).subs(x, S(1)/2) == cos(S(1)/2)
    raises(ValueError, lambda: Max(cos(x), sin(x)).subs(x, I))
    raises(ValueError, lambda: Max(I))
    raises(ValueError, lambda: Max(I, x))
    raises(ValueError, lambda: Max(S.ComplexInfinity, 1))
    # interesting:
    # Max(n, -oo, n_,  p, 2) == Max(p, 2)
    # True
    # Max(n, -oo, n_,  p, 1000) == Max(p, 1000)
    # False

    assert Max(1,x).diff(x) == Heaviside(x-1)
    assert Max(x,1).diff(x) == Heaviside(x-1)
    assert Max(x**2, 1+x, 1).diff(x) == 2*x*Heaviside(x**2 - Max(1,x+1)) \
        + Heaviside(x - Max(1,x**2) + 1)

    a, b = Symbol('a', real=True), Symbol('b', real=True)
    # a and b are both real, Max(a, b) should be real
    assert Max(a, b).is_real

    # issue 7233
    e = Max(0, x)
    assert e.evalf == e.n
    assert e.n().args == (0, x)


def test_root():
    from sympy.abc import x, y, z
    n = Symbol('n', integer=True)

    assert root(2, 2) == sqrt(2)
    assert root(2, 1) == 2
    assert root(2, 3) == 2**Rational(1, 3)
    assert root(2, 3) == cbrt(2)
    assert root(2, -5) == 2**Rational(4, 5)/2

    assert root(-2, 1) == -2

    assert root(-2, 2) == sqrt(2)*I
    assert root(-2, 1) == -2

    assert root(x, 2) == sqrt(x)
    assert root(x, 1) == x
    assert root(x, 3) == x**Rational(1, 3)
    assert root(x, 3) == cbrt(x)
    assert root(x, -5) == x**Rational(-1, 5)

    assert root(x, n) == x**(1/n)
    assert root(x, -n) == x**(-1/n)


def test_nthroot():
    assert real_root(-8, 3) == -2
    assert real_root(-16, 4) == root(-16, 4)
    r = root(-7, 4)
    assert real_root(r) == r
    r1 = root(-1, 3)
    r2 = r1**2
    r3 = root(-1, 4)
    assert real_root(r1 + r2 + r3) == -1 + r2 + r3

def test_rewrite_MaxMin_as_Heaviside():
    from sympy.abc import x, y, z
    assert Max(0, x).rewrite(Heaviside) == x*Heaviside(x)
    assert Max(3, x).rewrite(Heaviside) == x*Heaviside(x - 3) + 3*Heaviside(-x + 3)
    assert Max(0, x+2, 2*x).rewrite(Heaviside) == \
        2*x*Heaviside(2*x)*Heaviside(x - 2) + (x + 2)*Heaviside(-x + 2)*Heaviside(x + 2)


    assert Min(0, x).rewrite(Heaviside) == x*Heaviside(-x)
    assert Min(3, x).rewrite(Heaviside) == x*Heaviside(-x + 3) + 3*Heaviside(x - 3)
    assert Min(x, -x, -2).rewrite(Heaviside) == \
        x*Heaviside(-2*x)*Heaviside(-x - 2) - x*Heaviside(2*x)*Heaviside(x - 2) \
        - 2*Heaviside(-x + 2)*Heaviside(x + 2)
