#
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.

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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.

laguerre_polynomial,
a Python code which
evaluates the Laguerre polynomial, the generalized Laguerre polynomials,
and the Laguerre function.

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].

lobatto_polynomial,
a Python code which
evaluates the completed Lobatto polynomial and associated functions.

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

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Last revised on 24 February 2024.
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