false_position.py

# -*- coding: utf-8 -*-
"""false_position.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1v-3ibHQTF_oadzBLf0hdRyO44ulT6ucL
"""

import random

def evaluate_polynomial(coefficients, x):
    result = 0
    power = len(coefficients) - 1
    for coeff in coefficients:
        result += coeff * (x ** power)
        power -= 1
    return result

def false_position(array,x,y,epsilon=1e-6, max_iterations=100):
    if evaluate_polynomial(array, x) * evaluate_polynomial(array, y) >= 0 or x >= y:
        while evaluate_polynomial(array, x) * evaluate_polynomial(array, y) >= 0 or x >= y:
            x = random.randint(-9, 9)
            y = random.randint(-9, 9)
    f_x = evaluate_polynomial(array, x)
    f_y = evaluate_polynomial(array, y)
    iterations = 0
    while abs(f_y - f_x) >= epsilon and iterations < max_iterations:
        x_new = (x * f_y - y * f_x) / (f_y - f_x)
        f_new = evaluate_polynomial(array, x_new)

        if f_new == 0:
            break

        if f_new * f_x < 0:
            y = x_new
            f_y = f_new
        else:
            x = x_new
            f_x = f_new

        iterations += 1

    if iterations == max_iterations:
        print("Maximum iterations reached. The method may not have converged.")

    return x_new

print("\tFalse position method\t")
d = int(input("Enter the highest degree of the polynomial: "))
array = []
for i in range(d + 1):
    f = d - i
    c = int(input("Enter the coefficient of x ^"+str(f)+" : "))
    array.append(int(c))
a = int(input("Enter a value for a: "))
b = int(input("Enter a value for b: "))
result = evaluate_polynomial(array, a)
res = evaluate_polynomial(array, b)
print(f"The result of the polynomial with x = {a} is {result}")
print(f"The result of the polynomial with x = {b} is {res}")
root = false_position(array, a, b)
print(f"The root of the polynomial is {root}")