#### Newton Raphson New

S
```# Implementing Newton Raphson method in Python
# Author: Saksham Gupta
#
# The Newton-Raphson method (also known as Newton's method) is a way to
# quickly find a good approximation for the root of a functreal-valued ion
# The method can also be extended to complex functions
#
# Newton's Method - https://en.wikipedia.org/wiki/Newton's_method

from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F401, F403

def newton_raphson(
function: str,
starting_point: complex,
variable: str = "x",
precision: float = 10**-10,
multiplicity: int = 1,
) -> complex:
"""Finds root from the 'starting_point' onwards by Newton-Raphson method
Refer to https://docs.sympy.org/latest/modules/functions/index.html
for usable mathematical functions

>>> newton_raphson("sin(x)", 2)
3.141592653589793
>>> newton_raphson("x**4 -5", 0.4 + 5j)
(-7.52316384526264e-37+1.4953487812212207j)
>>> newton_raphson('log(y) - 1', 2, variable='y')
2.7182818284590455
>>> newton_raphson('exp(x) - 1', 10, precision=0.005)
1.2186556186174883e-10
>>> newton_raphson('cos(x)', 0)
Traceback (most recent call last):
...
ZeroDivisionError: Could not find root
"""

x = symbols(variable)
func = lambdify(x, function)
diff_function = lambdify(x, diff(function, x))

prev_guess = starting_point

while True:
if diff_function(prev_guess) != 0:
next_guess = prev_guess - multiplicity * func(prev_guess) / diff_function(
prev_guess
)
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

prev_guess = 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=0.005)}",
)

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