import sys




def    lowerCAmelCase_  (		lowercase:				str		)     ->					Dict:







 '''simple docstring'''
 _UpperCamelCase:  Dict    						=			len(lowercase		)
 _UpperCamelCase:  Optional[Any]    						=			[[0 for x in range(lowercase		)] for x in range(lowercase		)]
 _UpperCamelCase:  int    						=			[[0 for x in range(lowercase		)] for x in range(lowercase		)]

 for chain_length in range(2	,       lowercase		):
  for a in range(1	,       n - chain_length + 1		):
   _UpperCamelCase:  Union[str, Any]    						=			a + chain_length - 1

   _UpperCamelCase:  List[str]    						=			sys.maxsize
   for c in range(lowercase	,       lowercase		):
    _UpperCamelCase:  List[Any]    						=			(
        matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
    )
    if cost < matrix[a][b]:
     _UpperCamelCase:  Dict    						=			cost
     _UpperCamelCase:  Tuple    						=			c
 return matrix, sol




def    lowerCAmelCase_  (		lowercase:				Tuple	,       lowercase:				List[str]	,       lowercase:				Dict		)     ->					Optional[int]:







 '''simple docstring'''
 if i == j:
  print('''A''' + str(lowercase		)	,       end=''' '''		)
 else:
  print('''('''	,       end=''' '''		)
  print_optiomal_solution(lowercase	,       lowercase	,       optimal_solution[i][j]		)
  print_optiomal_solution(lowercase	,       optimal_solution[i][j] + 1	,       lowercase		)
  print(''')'''	,       end=''' '''		)




def    lowerCAmelCase_  (		)     ->					Any:







 '''simple docstring'''
 _UpperCamelCase:  int    						=			[30, 35, 15, 5, 10, 20, 25]
 _UpperCamelCase:  Dict    						=			len(lowercase		)
 # Size of matrix created from above array will be
 # 30*35 35*15 15*5 5*10 10*20 20*25
 _UpperCamelCase						,				_UpperCamelCase:  Optional[Any]    						=			matrix_chain_order(lowercase		)

 print('''No. of Operation required: ''' + str(matrix[1][n - 1]		)		)
 print_optiomal_solution(lowercase	,       1	,       n - 1		)


if __name__ == "__main__":
  main()
from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def    lowerCAmelCase_  (		lowercase:				str	,       lowercase:				complex	,       lowercase:				str = "x"	,       lowercase:				float = 10**-10	,       lowercase:				int = 1	,       )     ->					complex:







 '''simple docstring'''
 _UpperCamelCase:  Any    						=			symbols(lowercase		)
 _UpperCamelCase:  str    						=			lambdify(lowercase	,       lowercase		)
 _UpperCamelCase:  str    						=			lambdify(lowercase	,       diff(lowercase	,       lowercase		)		)

 _UpperCamelCase:  Optional[int]    						=			starting_point

 while True:
  if diff_function(lowercase		) != 0:
   _UpperCamelCase:  int    						=			prev_guess - multiplicity * func(lowercase		) / diff_function(
       lowercase		)
  else:
   raise ZeroDivisionError('''Could not find root'''		) from None

  # Precision is checked by comparing the difference of consecutive guesses
  if abs(next_guess - prev_guess		) < precision:
   return next_guess

  _UpperCamelCase:  Any    						=			next_guess


# Let's Execute
if __name__ == "__main__":
  # Find root of trigonometric function
  # Find value of pi
  print(f"""The root of sin(x) = 0 is {newton_raphson('sin(x)', 2)}""")

  # Find root of polynomial
  # Find fourth Root of 5
  print(f"""The root of x**4 - 5 = 0 is {newton_raphson('x**4 -5', 0.4 +5J)}""")

  # Find value of e
  print(
      '''The root of log(y) - 1 = 0 is ''',
      f"""{newton_raphson('log(y) - 1', 2, variable='y')}""",
  )

  # Exponential Roots
  print(
      '''The root of exp(x) - 1 = 0 is''',
      f"""{newton_raphson('exp(x) - 1', 1_0, precision=0.0_0_5)}""",
  )

  # Find root of cos(x)
  print(f"""The root of cos(x) = 0 is {newton_raphson('cos(x)', 0)}""")