"""Tests for noncommutative symbols and expressions."""

from sympy import (
    adjoint,
    cancel,
    collect,
    combsimp,
    conjugate,
    cos,
    expand,
    factor,
    posify,
    radsimp,
    ratsimp,
    rcollect,
    sin,
    simplify,
    symbols,
    transpose,
    trigsimp,
    I,
)
from sympy.abc import x, y, z
from sympy.utilities.pytest import XFAIL

A, B, C = symbols("A B C", commutative=False)
X = symbols("X", commutative=False, hermitian=True)
Y = symbols("Y", commutative=False, antihermitian=True)


def test_adjoint():
    assert adjoint(A).is_commutative is False
    assert adjoint(A*A) == adjoint(A)**2
    assert adjoint(A*B) == adjoint(B)*adjoint(A)
    assert adjoint(A*B**2) == adjoint(B)**2*adjoint(A)
    assert adjoint(A*B - B*A) == adjoint(B)*adjoint(A) - adjoint(A)*adjoint(B)
    assert adjoint(A + I*B) == adjoint(A) - I*adjoint(B)

    assert adjoint(X) == X
    assert adjoint(-I*X) == I*X
    assert adjoint(Y) == -Y
    assert adjoint(-I*Y) == -I*Y

    assert adjoint(X) == conjugate(transpose(X))
    assert adjoint(Y) == conjugate(transpose(Y))
    assert adjoint(X) == transpose(conjugate(X))
    assert adjoint(Y) == transpose(conjugate(Y))


def test_cancel():
    assert cancel(A*B - B*A) == A*B - B*A
    assert cancel(A*B*(x - 1)) == A*B*(x - 1)
    assert cancel(A*B*(x**2 - 1)/(x + 1)) == A*B*(x - 1)
    assert cancel(A*B*(x**2 - 1)/(x + 1) - B*A*(x - 1)) == A*B*(x - 1) + (1 - x)*B*A


@XFAIL
def test_collect():
    assert collect(A*B - B*A, A) == A*B - B*A
    assert collect(A*B - B*A, B) == A*B - B*A
    assert collect(A*B - B*A, x) == A*B - B*A


def test_combsimp():
    assert combsimp(A*B - B*A) == A*B - B*A


def test_conjugate():
    assert conjugate(A).is_commutative is False
    assert (A*A).conjugate() == conjugate(A)**2
    assert (A*B).conjugate() == conjugate(A)*conjugate(B)
    assert (A*B**2).conjugate() == conjugate(A)*conjugate(B)**2
    assert (A*B - B*A).conjugate() == \
        conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A)
    assert (A*B).conjugate() - (B*A).conjugate() == \
        conjugate(A)*conjugate(B) - conjugate(B)*conjugate(A)
    assert (A + I*B).conjugate() == conjugate(A) - I*conjugate(B)


def test_expand():
    assert expand((A*B)**2) == A*B*A*B
    assert expand(A*B - B*A) == A*B - B*A
    assert expand((A*B/A)**2) == A*B*B/A
    assert expand(B*A*(A + B)*B) == B*A**2*B + B*A*B**2
    assert expand(B*A*(A + C)*B) == B*A**2*B + B*A*C*B


def test_factor():
    assert factor(A*B - B*A) == A*B - B*A


def test_posify():
    assert posify(A)[0].is_commutative is False
    for q in (A*B/A, (A*B/A)**2, (A*B)**2, A*B - B*A):
        p = posify(q)
        assert p[0].subs(p[1]) == q


def test_radsimp():
    assert radsimp(A*B - B*A) == A*B - B*A


@XFAIL
def test_ratsimp():
    assert ratsimp(A*B - B*A) == A*B - B*A


@XFAIL
def test_rcollect():
    assert rcollect(A*B - B*A, A) == A*B - B*A
    assert rcollect(A*B - B*A, B) == A*B - B*A
    assert rcollect(A*B - B*A, x) == A*B - B*A


def test_simplify():
    assert simplify(A*B - B*A) == A*B - B*A


def test_subs():
    assert (x*y*A).subs(x*y, z) == A*z
    assert (x*A*B).subs(x*A, C) == C*B
    assert (x*A*x*x).subs(x**2*A, C) == x*C
    assert (x*A*x*B).subs(x**2*A, C) == C*B
    assert (A**2*B**2).subs(A*B**2, C) == A*C
    assert (A*A*A + A*B*A).subs(A*A*A, C) == C + A*B*A


def test_transpose():
    assert transpose(A).is_commutative is False
    assert transpose(A*A) == transpose(A)**2
    assert transpose(A*B) == transpose(B)*transpose(A)
    assert transpose(A*B**2) == transpose(B)**2*transpose(A)
    assert transpose(A*B - B*A) == \
        transpose(B)*transpose(A) - transpose(A)*transpose(B)
    assert transpose(A + I*B) == transpose(A) + I*transpose(B)

    assert transpose(X) == conjugate(X)
    assert transpose(-I*X) == -I*conjugate(X)
    assert transpose(Y) == -conjugate(Y)
    assert transpose(-I*Y) == I*conjugate(Y)


def test_trigsimp():
    assert trigsimp(A*sin(x)**2 + A*cos(x)**2) == A
