new_contents: """Tests for noncommutative symbols and expressions."""
  
  from sympy import (
      conjugate,
      expand,
      factor,
      radsimp,
      simplify,
      symbols,
      I,
  )
  from sympy.abc import x, y, z
  
  A, B, C = symbols("A B C", commutative=False)
  X, Y = symbols("X Y", commutative=False, real=True)
  Z = X + I*Y
  
  def test_complex():
      assert Z.conjugate() == X - I*Y
      assert (Z*Z.conjugate()).expand() == X**2 + Y**2 + I*Y*X - I*X*Y
  
  def test_conjugate():
      assert conjugate(A).is_commutative == 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)
  
  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_radsimp():
      assert radsimp(A*B - B*A) == 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
  
subject: Add tests for noncommutative symbols.