"""Tests for tools for manipulating of large commutative expressions. """

from sympy import (S, Add, sin, Mul, Symbol, oo, Integral, sqrt, Tuple, I,
                   Interval, O, symbols, simplify, collect, Sum, Basic, Dict,
                   root, exp, cos, sin, oo, Dummy, log)
from sympy.core.exprtools import (decompose_power, Factors, Term, _gcd_terms,
                                  gcd_terms, factor_terms, factor_nc,
                                  _monotonic_sign)
from sympy.core.mul import _keep_coeff as _keep_coeff
from sympy.simplify.cse_opts import sub_pre
from sympy.utilities.pytest import raises

from sympy.abc import a, b, t, x, y, z


def test_decompose_power():
    assert decompose_power(x) == (x, 1)
    assert decompose_power(x**2) == (x, 2)
    assert decompose_power(x**(2*y)) == (x**y, 2)
    assert decompose_power(x**(2*y/3)) == (x**(y/3), 2)


def test_Factors():
    assert Factors() == Factors({}) == Factors(S(1))
    assert Factors().as_expr() == S.One
    assert Factors({x: 2, y: 3, sin(x): 4}).as_expr() == x**2*y**3*sin(x)**4
    assert Factors(S.Infinity) == Factors({oo: 1})
    assert Factors(S.NegativeInfinity) == Factors({oo: 1, -1: 1})

    a = Factors({x: 5, y: 3, z: 7})
    b = Factors({      y: 4, z: 3, t: 10})

    assert a.mul(b) == a*b == Factors({x: 5, y: 7, z: 10, t: 10})

    assert a.div(b) == divmod(a, b) == \
        (Factors({x: 5, z: 4}), Factors({y: 1, t: 10}))
    assert a.quo(b) == a/b == Factors({x: 5, z: 4})
    assert a.rem(b) == a % b == Factors({y: 1, t: 10})

    assert a.pow(3) == a**3 == Factors({x: 15, y: 9, z: 21})
    assert b.pow(3) == b**3 == Factors({y: 12, z: 9, t: 30})

    assert a.gcd(b) == Factors({y: 3, z: 3})
    assert a.lcm(b) == Factors({x: 5, y: 4, z: 7, t: 10})

    a = Factors({x: 4, y: 7, t: 7})
    b = Factors({z: 1, t: 3})

    assert a.normal(b) == (Factors({x: 4, y: 7, t: 4}), Factors({z: 1}))

    assert Factors(sqrt(2)*x).as_expr() == sqrt(2)*x

    assert Factors(-I)*I == Factors()
    assert Factors({S(-1): S(3)})*Factors({S(-1): S(1), I: S(5)}) == \
        Factors(I)

    assert Factors(S(2)**x).div(S(3)**x) == \
        (Factors({S(2): x}), Factors({S(3): x}))
    assert Factors(2**(2*x + 2)).div(S(8)) == \
        (Factors({S(2): 2*x + 2}), Factors({S(8): S(1)}))

    # coverage
    # /!\ things break if this is not True
    assert Factors({S(-1): S(3)/2}) == Factors({I: S.One, S(-1): S.One})
    assert Factors({I: S(1), S(-1): S(1)/3}).as_expr() == I*(-1)**(S(1)/3)

    assert Factors(-1.) == Factors({S(-1): S(1), S(1.): 1})
    assert Factors(-2.) == Factors({S(-1): S(1), S(2.): 1})
    assert Factors((-2.)**x) == Factors({S(-2.): x})
    assert Factors(S(-2)) == Factors({S(-1): S(1), S(2): 1})
    assert Factors(S.Half) == Factors({S(2): -S.One})
    assert Factors(S(3)/2) == Factors({S(3): S.One, S(2): S(-1)})
    assert Factors({I: S(1)}) == Factors(I)
    assert Factors({-1.0: 2, I: 1}) == Factors({S(1.0): 1, I: 1})
    assert Factors({S.NegativeOne: -S(3)/2}).as_expr() == I
    A = symbols('A', commutative=False)
    assert Factors(2*A**2) == Factors({S(2): 1, A**2: 1})
    assert Factors(I) == Factors({I: S.One})
    assert Factors(x).normal(S(2)) == (Factors(x), Factors(S(2)))
    assert Factors(x).normal(S(0)) == (Factors(), Factors(S(0)))
    raises(ZeroDivisionError, lambda: Factors(x).div(S(0)))
    assert Factors(x).mul(S(2)) == Factors(2*x)
    assert Factors(x).mul(S(0)).is_zero
    assert Factors(x).mul(1/x).is_one
    assert Factors(x**sqrt(2)**3).as_expr() == x**(2*sqrt(2))
    assert Factors(x)**Factors(S(2)) == Factors(x**2)
    assert Factors(x).gcd(S(0)) == Factors(x)
    assert Factors(x).lcm(S(0)).is_zero
    assert Factors(S(0)).div(x) == (Factors(S(0)), Factors())
    assert Factors(x).div(x) == (Factors(), Factors())
    assert Factors({x: .2})/Factors({x: .2}) == Factors()
    assert Factors(x) != Factors()
    assert Factors(S(0)).normal(x) == (Factors(S(0)), Factors())
    n, d = x**(2 + y), x**2
    f = Factors(n)
    assert f.div(d) == f.normal(d) == (Factors(x**y), Factors())
    assert f.gcd(d) == Factors()
    d = x**y
    assert f.div(d) == f.normal(d) == (Factors(x**2), Factors())
    assert f.gcd(d) == Factors(d)
    n = d = 2**x
    f = Factors(n)
    assert f.div(d) == f.normal(d) == (Factors(), Factors())
    assert f.gcd(d) == Factors(d)
    n, d = 2**x, 2**y
    f = Factors(n)
    assert f.div(d) == f.normal(d) == (Factors({S(2): x}), Factors({S(2): y}))
    assert f.gcd(d) == Factors()

    # extraction of constant only
    n = x**(x + 3)
    assert Factors(n).normal(x**-3) == (Factors({x: x + 6}), Factors({}))
    assert Factors(n).normal(x**3) == (Factors({x: x}), Factors({}))
    assert Factors(n).normal(x**4) == (Factors({x: x}), Factors({x: 1}))
    assert Factors(n).normal(x**(y - 3)) == \
        (Factors({x: x + 6}), Factors({x: y}))
    assert Factors(n).normal(x**(y + 3)) == (Factors({x: x}), Factors({x: y}))
    assert Factors(n).normal(x**(y + 4)) == \
        (Factors({x: x}), Factors({x: y + 1}))

    assert Factors(n).div(x**-3) == (Factors({x: x + 6}), Factors({}))
    assert Factors(n).div(x**3) == (Factors({x: x}), Factors({}))
    assert Factors(n).div(x**4) == (Factors({x: x}), Factors({x: 1}))
    assert Factors(n).div(x**(y - 3)) == \
        (Factors({x: x + 6}), Factors({x: y}))
    assert Factors(n).div(x**(y + 3)) == (Factors({x: x}), Factors({x: y}))
    assert Factors(n).div(x**(y + 4)) == \
        (Factors({x: x}), Factors({x: y + 1}))


def test_Term():