Monomials.jl

A simple apackage to generate, order, and evaluate vectors of monomials. It is designed as an alternative to the MultivariatePolynomials.jl ecosystem if all you require is monomials not fully fledged polynomials.

The core functionality is exposed through the monomials function. It generates all monomials of the given variables up to a defined maximum degree and sorts them in the requested order. Available monomial orders are:

• LexicographicOrder
• GradedLexicographicOrder
• GradedReverseLexicographicOrder

There are no concrete plans to add more features to the package.

Examples

The following returns the monomials of two variables with a maximum degree of 2 in lexicographic order.

monomials(["x","y"], 2, LexicographicOrder())

5-element Vector{Monomial}:
 y
 y²
 x
 xy
 x²

it is possible to include the zero-degree monomial by passing the include_zero=true option.

m = monomials(["x","y"], 2, LexicographicOrder(); include_zero=true)

6-element Vector{Monomial}:
 1
 y
 y²
 x
 xy
 x²

Monomials can be evaluated by passing a Vector.

    m = Monomial(["x", "y"], [1, 2])
    m([2, 3])

For convenience, a single monomial can be evaluated at multiple points by passing a Matrix. In this case, the points are expected to be the columns of the given matrix.

m = Monomial(["x", "y"], [1, 2])
m(rand(2, 5))

Finally, to evaulate all monomials in a vector for one or more points pass the Vector or Matrix directly to the vector of monomials.

m = monomials((["x", "y"], 2, LexicographicOrder())
m(rand(2, 5))