Generation of multivariate polynomial basis with given degree

[JinraeKim]

Notes

• The original post can be found here.

Questions

• I would like to make a multivariate polynomial with given degree.
  For example, the bivariate polynomial basis of a vector x = [x1, y2] with degree of 2 would be
  [1, x1, x1^2, x2, x2^2, x1*x2].

It seems that there are some nice packages for handling multivariate polynomials such as MultivariatePolynomials.jl but I don’t know how to create a polynomial basis functions easily.

Is there any method for this? Or, an example code?

[JinraeKim]

I found a way:

using Combinatorics, Transducers


"""
n ∈ N: length of array, i.e., x ∈ Rⁿ
d ∈ N: degree
"""
function polynomial_basis(n, d; with_bias=true)
    _n = with_bias ? n+1 : n
    exponents = multiexponents(_n, d)
    return function (x)
        _x = with_bias ? [x..., 1] : x
        exponents |> Map(exponent -> prod(_x.^exponent)) |> collect
    end
end