Interesting idea to write Newton's root finding method as a decorator

newt.py

"""
Traditional Newton root finding method
and Alternative using decorators...
Author: Bruce Wernick
Date: 13 August 2025
"""

def newt(f, x, **kwargs):
  maxits = kwargs.get("maxits", 48)
  tol = kwargs.get("tol", 1e-6)
  for its in range(maxits):
    xo = x
    fx, dfx = f(x)
    x -= fx/dfx
    if abs(fx) <= tol: return x
    if abs(x-xo) <= tol*(abs(x)+1): return x
    #print(f"{its:2d} {x:12.9f} {fx:12.9f}")
  return x

f = lambda x: ((x-3)*(x+5), 2*(x+1))
x = newt(f, 2.5)
#print(f"root={x:0.9g}")


# ----------------------------------
# Write Newton method as a decorator
# ----------------------------------

def newton(**kwargs):
  maxits = kwargs.get("maxits", 48)
  tol = kwargs.get("tol", 1e-6)
  def decorator(f):
    def wrapper(x):
      for its in range(maxits):
        xo = x
        fx, dfx = f(x)
        x -= fx/dfx
        if abs(fx) <= tol: return x
        if abs(x-xo) <= tol*(1+abs(x)): return x
        print(f"{its:2d} {x:12.9f} {fx:12.9f}")
      return x
    return wrapper
  return decorator


@newton(tol=1e-12)
def f(x):
  """return f(x) and slope(x)"""
  return ((x-3)*(x+5), 2*(x+1))

x = f(2.5)
#print(f"root={x:0.9g}")

I'm not sure if this has any merit!
You can write a function like this...

def f(x):
  """return f(x) and slope(x)"""
  return ((x-3)*(x+5), 2*(x+1))

and then simply decorate it with...

@newton(tol=1e-12)

to find the root.

If there were other useful decorators, then it might be worthwhile.