/polynomial

Implementation of class: Polynomial

Primary LanguageJupyter Notebook

Creation of class Polynomial

The Polynomial class is a Python implementation that represents polynomials and provides various operations on polynomials. It allows you to create, evaluate, manipulate, approximate roots and plot polynomials easily.

Where a polynomial in a single indeterminate $x$ can be written in the form, $a_n x^n+a_{n-1} x^{n-1}+\cdots+a_2 x^2+a_1 x+a_0, n \in \mathbb{Z}^+$

poly_dict.py contains a function decompose_polynomial which takes a polynomial expression as a string and extracts the coefficients of each term.

decompose_polynomial function

Creates a dictionary representation of a polynomial.

Usage
def decompose_polynomial(formula: str):
    """
    Polynomial exponents are natural numbers.
    If exponents are rationals or negative integers, the formula will not parse
    :return Polynomial dictionary; {exponent: coefficient, ... }
    """
# Example usage:
formula = "x^3 + 2*x^2 - 3*x - 1"
polynomial = decompose_polynomial(formula)
print(polynomial)

# Output
{3: 1.0, 2: 2.0, 1: -3.0, 0: -1.0}

Polynomial Class

Features
  • Creation using a dictionary format for coefficients.
  • Evaluation for a given value of x.
  • String representation.
  • Approximating roots numerically by the Newton-Raphson method
  • Addition, subtraction and multiplication
  • Computation of the derivative.
  • Plotting using matplotlib.
Usage
# Create a Polynomial object with coefficients {3: 2, 2: -1, 0: 1}:
p = Polynomial({3: 2, 2: -1, 0: 1})

# Evaluate the polynomial for x = 2:
result = p(2)

# Print the string representation of the polynomial:
print(p)

# Add two polynomials:
p1 = Polynomial({2: 3, 1: 1})
p2 = Polynomial({3: 2, 2: -1, 0: 1})
p3 = p1 + p2

# Subtract two polynomials:
p4 = p1 + p2

# Multiply two polynomials:
p5 = p1 * p2

# Compute the derivative of the polynomial:
dp = p.derivative()

# Plot the polynomial:
p.plot()
Installation

Uses; Python 3.9 matplotlib 3.6.2 numpy 1.23.4 sympy 1.11.1

Install the required dependencies from the requirements.txt file:

pip install -r requirements.txt