# python_polynomial

python_polynomial, a Python code which analyzes a variety of polynomial families, returning the polynomial values, coefficients, derivatives, integrals, roots, or other information.

### Related Data and codes:

bernstein_polynomial, a Python code which evaluates the Bernstein polynomials, useful for uniform approximation of functions;

change_polynomial, a Python code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.

chebyshev_polynomial, a Python code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.

collatz_polynomial, a Python code which implements the Collatz polynomial iteration, a polynomial analog of the numerical iteration that is also known as the 3n+1 conjecture or the hailstone sequence.

gegenbauer_polynomial, a Python code which evaluates the Gegenbauer polynomial and associated functions.

gram_polynomial, a Python code which evaluates the Gram polynomials, also known as the discrete Chebyshev polyomials, and associated functions.

legendre_polynomial, a Python code which evaluates the Legendre polynomial and associated functions.

legendre_product_polynomial, a Python code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

legendre_shifted_polynomial, a Python code which evaluates the shifted Legendre polynomial, with domain [0,1].

polynomial, a Python code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

Last revised on 18 December 2022.