update examples/demo.py and tutorials/tutorial4_root_finding.ipynb# On branch main

examples/demo.py

@@ -1,5 +1,6 @@
 import sys
-sys.path.append('../')
+
+sys.path.append("../")
 from numethods import *
 
 
@@ -13,6 +14,7 @@ def demo_linear_solvers():
     print("Jacobi:", Jacobi(A, b, tol=1e-12).solve())
     print("Gauss-Seidel:", GaussSeidel(A, b, tol=1e-12).solve())
 
+
 def demo_qr():
     A = Matrix([[2, -1], [1, 2], [1, 1]])
 
@@ -38,11 +40,7 @@ def demo_qr():
     print("Least squares solution:", x_ls)
 
 
-
 def demo_roots():
-    f = lambda x: x**2 - 2
-    df = lambda x: 2 * x
-
     # Newton
     steps = NewtonRoot(f, df, x0=1.0).trace()
     print("Newton Method Trace (x^2 - 2):")
@@ -74,6 +72,7 @@ def demo_interpolation():
     print("Newton interpolation at", t, "=", newt.evaluate(t))
     print("Lagrange interpolation at", t, "=", lagr.evaluate(t))
 
+
 def demo_differentiation():
     f = lambda x: x**3  # f'(x) = 3x^2, f''(x) = 6x
     x0 = 2.0
@@ -86,7 +85,6 @@ def demo_differentiation():
     print("Second derivative:", SecondDerivative(f, x0))
 
 
-
 if __name__ == "__main__":
     demo_linear_solvers()
     demo_roots()