wnpoly package

A package to handle webnucleo polynomials.

wnpoly.symm

This module computes various symmetric polynomials.

class wnpoly.symm.Complete

Bases: object

A class for complete homogeneous symmetric polynomials.

compute(x, n)

Method to compute complete homogeneous symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n (int): A non-negative integer giving the order to which to compute the polynomials.

Returns:

A numpy.array containing the complete homogeneous symmetric polynomials.

compute_normalized(x, n, m=0)

Method to compute normalized complete homogeneous symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n (int): A non-negative integer giving the order to which to compute the polynomials.

m (int, optional): A non-negative integer giving the normalization degree. This must be less than the length of x.

Returns:

A numpy.array containing the complete homogeneous symmetric polynomials normalized by the number of terms in the polynomial.

class wnpoly.symm.Elementary

Bases: object

A class for elementary homogeneous symmetric polynomials.

compute(x, n)

Method to compute elementary homogeneous symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n (int): A non-negative integer giving the order to which to compute the polynomials. The value must be less than or equal to the length of the input array.

Returns:

A numpy.array containing the elementary homogeneous symmetric polynomials.

compute_normalized(x, n)

Method to compute normalized elementary homogeneous symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n` (int): A non-negative integer giving the order to which to compute the polynomials. The value must be less than or equal to the length of the input array.

Returns:

A numpy.array containing the elementary homogeneous symmetric polynomials normalized by the number of terms in each polynomial.

class wnpoly.symm.PowerSum

Bases: object

A class for power sum polynomials.

compute(x, n)

Method to compute power sum symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n (int): A non-negative integer giving the order to which to compute the polynomials.

Returns:

A numpy.array containing the power sum symmetric polynomials up to order n.

compute_normalized(x, n)

Method to compute normalized power sum symmetric polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials.

n (int): A non-negative integer giving the order to which to compute the polynomials.

Returns:

A numpy.array containing the power sum polynomials up to order n normalized by the number of terms in the polynomial.

wnpoly.bell

This module computes Bell polynomials.

class wnpoly.bell.Bell

Bases: object

A class for complete Bell polynomials.

compute(x)

Method to compute Bell polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials. The first element of x, that is, x[0], must be zero.

Returns:

A numpy.array containing the Bell polynomials for the input x up to order equal to the index of the last element of x.

invert(b)

Method to invert Bell polynomials, that is, to find the x elements that will give the input Bell polynomials.

Args:

b (list or numpy.array): An array containing the Bell polynomials. The first element, b[0], must equal 1.

Returns:

A numpy.array containing the x’s giving rise to the input polynomials.

class wnpoly.bell.PartialBell

Bases: object

A class for partial Bell polynomials.

compute(x)

Method to compute partial Bell polynomials.

Args:

x (list or numpy.array): An array containing the elements from which to compute the polynomials. The first value, x[0], must equal zero.

Returns:

A 2-d numpy.array containing the partial Bell polynomials B_n,k. n equals the largest index of the input x array. k ranges from 0 to n.

invert(pb)

Method to invert the partial Bell polynomials, that is, to find the x elements that will give the input Bell polynomials.

Args:

pb (numpy.array): A 2-d array giving the partial Bell polynomials B_n,k

Returns:

A numpy.array containing the input x values that give the input partial Bell polynomials.