This package has been deprecated in favour of https://github.com/Keno/Polynomials.jl (which started out as a fork of this package with the coefficient order reversed)

Polynomial

Basic arithmetic, integration, differentiation, evaluation, and root finding over dense polynomials.

Poly{T<:Number}(a::Vector)

Construct a polynomial from its coefficients, highest order first.

julia> Poly([1,0,3,4])
Poly(1x^3 + 3x^1 + 4)

Leading zeros are stripped.

julia> Poly([0,1,2,3])
Poly(1x^2 + 2x^1 + 3)

An optional variable parameter can be added.

julia> Poly([1,2,3], 's')
Poly(s^2 + 2 s + 3)

poly(r::AbstractVector)

Construct a polynomial from its roots. This is in contrast to the Poly constructor, which constructs a polynomial from its coefficients.

// Represents (x - 1)*(x-2)*(x-3)
julia> poly([1,2,3])
Poly(1x^3 + -6x^2 + 11x^1 + -6)

+, -, *, /, ==

The usual arithmetic operators are overloaded to work on polynomials, and combinations of polynomials and scalars.

julia> a = Poly([1,2])
Poly(1x^1 + 2)

julia> b = Poly([1, 0, -1])
Poly(1x^2 + -1)

julia> 2*a
Poly(2x^1 + 4)

julia> 2 + a
Poly(1x^1 + 4)

julia> a - b
Poly(-1x^2 + 1x^1 + 3)

julia> a*b
Poly(1x^3 + 2x^2 + -1x^1 + -2)

julia> b/2
Poly(0.5x^2 + -0.5)

Note that operations involving polynomials with different variables will error.

julia> a = Poly([1,2,3], 'x');
julia> b = Poly([1,2,3], 's');
julia> a + b
ERROR: Polynomials must have same variable.

polyval(p::Poly, x::Number)

Evaluate the polynomial p at x.

julia> polyval(Poly([1, 0, -1]), 0.1)
-0.99

polyint(p::Poly, k::Number=0)

Integrate the polynomial p term by term, optionally adding constant term k. The order of the resulting polynomial is one higher than the order of p.

julia> polyint(Poly([1, 0, -1]))
Poly(0.3333333333333333x^3 + -1.0x^1)

julia> polyint(Poly([1, 0, -1]), 2)
Poly(0.3333333333333333x^3 + -1.0x^1 + 2.0)

polyder(p::Poly)

Differentiate the polynomial p term by term. The order of the resulting polynomial is one lower than the order of p.

julia> polyder(Poly([1, 3, -1]))
Poly(2x^1 + 3)

roots(p::Poly)

Return the roots (zeros) of p, with multiplicity. The number of roots returned is equal to the order of p. The returned roots may be real or complex.

julia> roots(Poly([1, 0, -1]))
2-element Array{Float64,1}:
 -1.0
  1.0

julia> roots(Poly([1, 0, 1]))
2-element Array{Complex{Float64},1}:
 0.0-1.0im
 0.0+1.0im

julia> roots(Poly([1, 0, 0]))
2-element Array{Float64,1}:
 0.0
 0.0