
from math import sqrt

import numpy as np
from sympy import symbols

# Coefficient
# Speed of light (m/s)
__lowerCamelCase				=			2_99_79_24_58

# Symbols
__lowerCamelCase				=			symbols("""ct x y z""")


def      UpperCamelCase   (       __lowerCamelCase	:					float       ):

       if velocity > c:
              raise ValueError("Speed must not exceed light speed 299,792,458 [m/s]!"       )
       elif velocity < 1:
              # Usually the speed should be much higher than 1 (c order of magnitude)
              raise ValueError("Speed must be greater than or equal to 1!"       )

       return velocity / c


def      UpperCamelCase   (       __lowerCamelCase	:					float       ):
       return 1 / sqrt(1 - beta(__a       ) ** 2       )


def      UpperCamelCase   (       __lowerCamelCase	:					float       ):
       return np.array(
           [
               [gamma(__a       ), -gamma(__a       ) * beta(__a       ), 0, 0],
               [-gamma(__a       ) * beta(__a       ), gamma(__a       ), 0, 0],
               [0, 0, 1, 0],
               [0, 0, 0, 1],
           ]       )


def      UpperCamelCase   (       __lowerCamelCase	:					float							,   __lowerCamelCase	:					np.ndarray | None = None       ):

       if event is None:
              snake_case			:  Tuple     							= np.array([ct, x, y, z]       )  # Symbolic four vector
       else:
              event[0] *= c  # x0 is ct (speed of light * time)

       return transformation_matrix(__a       ) @ event


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   # Example of symbolic vector:
   __lowerCamelCase				=			transform(29_97_92_45)
   print("""Example of four vector: """)
   print(F'ct\' = {four_vector[0]}')
   print(F'x\' = {four_vector[1]}')
   print(F'y\' = {four_vector[2]}')
   print(F'z\' = {four_vector[3]}')

   # Substitute symbols with numerical values
   __lowerCamelCase				=			{ct: c, x: 1, y: 1, z: 1}
   __lowerCamelCase				=			[four_vector[i].subs(sub_dict) for i in range(4)]

   print(F'\n{numerical_vector}')












def   __lowerCamelCase   (				__a  :Dict       )						->							Optional[int]:






		"""simple docstring"""

		A__     =  []
		A__     =  []
		A__     =  {
		    """^""": 3,
		    """*""": 2,
		    """/""": 2,
		    """%""": 2,
		    """+""": 1,
		    """-""": 1,
		}  # Priority of each operator
		A__     =  len(__a       ) if (len(__a       ) > 7) else 7

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

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

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

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

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







def   __lowerCamelCase   (				__a  :List[str]       )						->							Union[str, Any]:






		"""simple docstring"""

		A__     =  list(infix[::-1]       )  # reverse the infix equation

		for i in range(len(__a       )       ):
				if infix[i] == "(":
						A__     =  """)"""  # change "(" to ")"
				elif infix[i] == ")":
						A__     =  """("""  # change ")" to "("

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


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



