
from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403


def 							__A(lowerCAmelCase						,  lowerCAmelCase						,  lowerCAmelCase = "x"						,  lowerCAmelCase = 1_0**-1_0						,  lowerCAmelCase = 1						,  )		->				complex:

		"""simple docstring"""






		_UpperCamelCase						    =	symbols(lowerCAmelCase )
		_UpperCamelCase						    =	lambdify(lowerCAmelCase						,  lowerCAmelCase )
		_UpperCamelCase						    =	lambdify(lowerCAmelCase						,  diff(lowerCAmelCase						,  lowerCAmelCase ) )

		_UpperCamelCase						    =	starting_point

		while True:
				if diff_function(lowerCAmelCase ) != 0:
						_UpperCamelCase						    =	prev_guess - multiplicity * func(lowerCAmelCase ) / diff_function(
						    lowerCAmelCase )
				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						    =	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", 10, precision=0.0_05)}""",
		)

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





def 							__A(lowerCAmelCase						,  lowerCAmelCase )		->				tuple[float, float]:

		"""simple docstring"""






		if not len(lowerCAmelCase ) == len(lowerCAmelCase ) == 3:
				raise ValueError("""Please enter a valid equation.""" )
		if equationa[0] == equationa[1] == equationa[0] == equationa[1] == 0:
				raise ValueError("""Both a & b of two equations can't be zero.""" )

		# Extract the coefficients
		_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	equationa
		_UpperCamelCase    ,	_UpperCamelCase    ,	_UpperCamelCase						    =	equationa

		# Calculate the determinants of the matrices
		_UpperCamelCase						    =	aa * ba - aa * ba
		_UpperCamelCase						    =	ca * ba - ca * ba
		_UpperCamelCase						    =	aa * ca - aa * ca

		# Check if the system of linear equations has a solution (using Cramer's rule)
		if determinant == 0:
				if determinant_x == determinant_y == 0:
						raise ValueError("""Infinite solutions. (Consistent system)""" )
				else:
						raise ValueError("""No solution. (Inconsistent system)""" )
		else:
				if determinant_x == determinant_y == 0:
						# Trivial solution (Inconsistent system)
						return (0.0, 0.0)
				else:
						_UpperCamelCase						    =	determinant_x / determinant
						_UpperCamelCase						    =	determinant_y / determinant
						# Non-Trivial Solution (Consistent system)
						return (x, y)



