Polynomial

Polynomial{T<:Number}(coeffs::AbstractVector{T}, var=:x)

Construct a polynomial from its coefficients a, lowest order first, optionally in terms of the given variable x. x can be a character, symbol, or string.

If $p = a_n x^n + \ldots + a_2 x^2 + a_1 x + a_0$, we construct this through Polynomial([a_0, a_1, ..., a_n]).

The usual arithmetic operators are overloaded to work with polynomials as well as with combinations of polynomials and scalars. However, operations involving two polynomials of different variables causes an error.

Examples

DocTestSetup = quote
    using Polynomials
end

julia> Polynomial([1, 0, 3, 4])
Polynomial(1 + 3*x^2 + 4*x^3)

julia> Polynomial([1, 2, 3], :s)
Polynomial(1 + 2*s + 3*s^2)

julia> one(Polynomial)
Polynomial(1.0)

Pade(::Polynomial, m::Integer, n::Integer)
Pade(::Polynomial, ::Polynomial)

Return Pade approximation of polynomial.

References

Pade Approximant

(::Pade)(x)

Evaluate the Pade approximant at the given point.

Examples

julia> using SpecialFunctions, Polynomials

julia> p = Polynomial(@.(1 // BigInt(gamma(1:17))));


julia> pade = Pade(p, 8, 8);


julia> pade(1.0) ≈ exp(1.0)
true