
"""simple docstring"""




def  _lowerCAmelCase		(		_UpperCamelCase						):






  """simple docstring"""



  _lowercase:			List[str]       =     []
  _lowercase:			List[Any]       =     []
  _lowercase:			Any       =     {
      '''^''': 3,
      '''*''': 2,
      '''/''': 2,
      '''%''': 2,
      '''+''': 1,
      '''-''': 1,
  }  # Priority of each operator
  _lowercase:			Tuple       =     len(_UpperCamelCase						) if (len(_UpperCamelCase						) > 7) else 7

  # Print table header for output
  print(
      '''Symbol'''.center(8						) ,				'''Stack'''.center(_UpperCamelCase						) ,				'''Postfix'''.center(_UpperCamelCase						) ,				sep=''' | ''' ,				)
  print('''-''' * (print_width * 3 + 7)						)

  for x in infix:
    if x.isalpha() or x.isdigit():
      post_fix.append(_UpperCamelCase						)  # if x is Alphabet / Digit, add it to Postfix
    elif x == "(":
      stack.append(_UpperCamelCase						)  # if x is "(" push to Stack
    elif x == ")":  # if x is ")" pop stack until "(" is encountered
      while stack[-1] != "(":
        post_fix.append(stack.pop()						)  # Pop stack & add the content to Postfix
      stack.pop()
    else:
      if len(_UpperCamelCase						) == 0:
        stack.append(_UpperCamelCase						)  # If stack is empty, push x to stack
      else:  # while priority of x is not > priority of element in the stack
        while len(_UpperCamelCase						) > 0 and priority[x] <= priority[stack[-1]]:
          post_fix.append(stack.pop()						)  # pop stack & add to Postfix
        stack.append(_UpperCamelCase						)  # push x to stack

    print(
        x.center(8						) ,				(''''''.join(_UpperCamelCase						)).ljust(_UpperCamelCase						) ,				(''''''.join(_UpperCamelCase						)).ljust(_UpperCamelCase						) ,				sep=''' | ''' ,				)  # Output in tabular format

  while len(_UpperCamelCase						) > 0:  # while stack is not empty
    post_fix.append(stack.pop()						)  # pop stack & add to Postfix
    print(
        ''' '''.center(8						) ,				(''''''.join(_UpperCamelCase						)).ljust(_UpperCamelCase						) ,				(''''''.join(_UpperCamelCase						)).ljust(_UpperCamelCase						) ,				sep=''' | ''' ,				)  # Output in tabular format

  return "".join(_UpperCamelCase						)  # return Postfix as str




def  _lowerCAmelCase		(		_UpperCamelCase						):






  """simple docstring"""



  _lowercase:			Union[str, Any]       =     list(infix[::-1]						)  # reverse the infix equation

  for i in range(len(_UpperCamelCase						)						):
    if infix[i] == "(":
      _lowercase:			int       =     ''')'''  # change "(" to ")"
    elif infix[i] == ")":
      _lowercase:			Union[str, Any]       =     '''('''  # change ")" to "("

  return (infix_2_postfix(''''''.join(_UpperCamelCase						)						))[
      ::-1
  ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
  A__							=   input('\nEnter an Infix Equation = ')  # Input an Infix equation
  A__							=   ''.join(Infix.split())  # Remove spaces from the input
  print('\n\t', Infix, '(Infix) -> ', infix_2_prefix(Infix), '(Prefix)')


"""simple docstring"""




from typing import Any

import numpy as np




def  _lowerCAmelCase		(		_UpperCamelCase						):






  """simple docstring"""



  return np.array_equal(_UpperCamelCase ,				matrix.conjugate().T						)




def  _lowerCAmelCase		(		_UpperCamelCase ,				_UpperCamelCase						):






  """simple docstring"""



  _lowercase:			str       =     v.conjugate().T
  _lowercase:			List[Any]       =     v_star.dot(_UpperCamelCase						)
  assert isinstance(_UpperCamelCase ,				np.ndarray						)
  return (v_star_dot.dot(_UpperCamelCase						)) / (v_star.dot(_UpperCamelCase						))




def  _lowerCAmelCase		(		):






  """simple docstring"""



  _lowercase:			int       =     np.array([[2, 2 + 1j, 4], [2 - 1j, 3, 1j], [4, -1j, 1]]						)
  _lowercase:			str       =     np.array([[1], [2], [3]]						)
  assert is_hermitian(_UpperCamelCase						), f'''{a} is not hermitian.'''
  print(rayleigh_quotient(_UpperCamelCase ,				_UpperCamelCase						)						)

  _lowercase:			Any       =     np.array([[1, 2, 4], [2, 3, -1], [4, -1, 1]]						)
  assert is_hermitian(_UpperCamelCase						), f'''{a} is not hermitian.'''
  assert rayleigh_quotient(_UpperCamelCase ,				_UpperCamelCase						) == float(3						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  tests()
