Merge pull request #179 from mileslucas/refactor

Abstracting Polynomials

Author: jverzani

.github/workflows/compat.yml

@@ -0,0 +1,24 @@
+name: CompatHelper
+
+on:
+  schedule:
+    - cron: "0 0 * * *"
+
+jobs:
+  CompatHelper:
+    runs-on: ${{ matrix.os }}
+    strategy:
+      matrix:
+        julia-version: [1.3.0]
+        julia-arch: [x86]
+        os: [ubuntu-latest]
+    steps:
+      - uses: julia-actions/setup-julia@latest
+        with:
+          version: ${{ matrix.julia-version }}
+      - name: Pkg.add("CompatHelper")
+        run: julia -e 'using Pkg; Pkg.add("CompatHelper")'
+      - name: CompatHelper.main()
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+        run: julia -e 'using CompatHelper; CompatHelper.main()'

.travis.yml

@@ -19,7 +19,7 @@ matrix:
 notifications:
   email: false
 
-coveralls: true
+codecov: true
 
 jobs:
   include:

Project.toml

@@ -2,15 +2,18 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "0.6.1"
+version = "0.7.0"
 
 [deps]
+Intervals = "d8418881-c3e1-53bb-8760-2df7ec849ed5"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 
 [compat]
-julia = "1.0"
+Intervals = "0.5.0"
 RecipesBase = "0.7, 0.8"
+julia = "1"
+
 
 [extras]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

README.md

@@ -1,180 +1,167 @@
-# Polynomials
+# Polynomials.jl
 
 Basic arithmetic, integration, differentiation, evaluation, and root finding over dense univariate polynomials.
 
-[![Polynomials](http://pkg.julialang.org/badges/Polynomials_0.6.svg)](http://pkg.julialang.org/?pkg=Polynomials)
-
-Master branch:
+[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/Polynomials.jl/stable)
+[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMath.github.io/Polynomials.jl/dev)
 [![Build Status](https://travis-ci.org/JuliaMath/Polynomials.jl.svg?branch=master)](https://travis-ci.org/JuliaMath/Polynomials.jl)
-[![Coverage Status](https://coveralls.io/repos/github/JuliaMath/Polynomials.jl/badge.svg)](https://coveralls.io/github/JuliaMath/Polynomials.jl)
+[![codecov](https://codecov.io/gh/JuliaMath/Polynomials.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaMath/Polynomials.jl)
 
-Documentation:
-[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/Polynomials.jl/stable)
-[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMath.github.io/Polynomials.jl/latest)
 
-#### Poly(a::Vector) where {T<:Number}
+## Installation
+
+```julia
+(v1.2) pkg> add Polynomials
+
+julia> using Polynomials
+```
+
+## Usage
+
+#### Available Polynomials
+
+* `Polynomial` - Standard polynomials
+* `ChebyshevT` - Chebyshev polynomials of the first kind
+
+#### Construction and Evaluation
 
 Construct a polynomial from its coefficients, lowest order first.
 
 ```julia
-julia> Poly([1,0,3,4])
-Poly(1 + 3x^2 + 4x^3)
+julia> Polynomial([1,0,3,4])
+Polynomial(1 + 3x^2 + 4x^3)
 ```
 
 An optional variable parameter can be added.
 
 ```julia
-julia> Poly([1,2,3], :s)
-Poly(1 + 2s + 3s^2)
+julia> Polynomial([1,2,3], :s)
+Polynomial(1 + 2s + 3s^2)
 ```
 
-#### poly(r::AbstractVector)
+Construct a polynomial from its roots.
 
-Construct a polynomial from its roots. This is in contrast to the
-`Poly` constructor, which constructs a polynomial from its
-coefficients.
+```julia
+julia> fromroots([1,2,3]) # (x-1)*(x-2)*(x-3)
+Polynomial(-6 + 11x - 6x^2 + x^3)
+```
+
+Evaluate the polynomial `p` at `x`.
 
 ```julia
-// Represents (x-1)*(x-2)*(x-3)
-julia> poly([1,2,3])
-Poly(-6 + 11x - 6x^2 + x^3)
+julia> p = Polynomial([1, 0, -1])
+julia> p(0.1)
+0.99
 ```
 
-#### +, -, *, /, div, ==
+#### Arithmetic
 
 The usual arithmetic operators are overloaded to work on polynomials, and combinations of polynomials and scalars.
+
 ```julia
-julia> p = Poly([1,2])
-Poly(1 + 2x)
+julia> p = Polynomial([1,2])
+Polynomial(1 + 2x)
 
-julia> q = Poly([1, 0, -1])
-Poly(1 - x^2)
+julia> q = Polynomial([1, 0, -1])
+Polynomial(1 - x^2)
 
 julia> 2p
-Poly(2 + 4x)
+Polynomial(2 + 4x)
 
 julia> 2+p
-Poly(3 + 2x)
+Polynomial(3 + 2x)
 
 julia> p - q
 Poly(2x + x^2)
 
 julia> p * q
-Poly(1 + 2x - x^2 - 2x^3)
+Polynomial(1 + 2x - x^2 - 2x^3)
 
 julia> q / 2
-Poly(0.5 - 0.5x^2)
+Polynomial(0.5 - 0.5x^2)
 
-julia> q ÷ p      # `div`, also `rem` and `divrem`
-Poly(0.25 - 0.5x)
+julia> q ÷ p  # `div`, also `rem` and `divrem`
+Polynomial(0.25 - 0.5x)
 ```
 
 Note that operations involving polynomials with different variables will error.
 
 ```julia
-julia> p = Poly([1, 2, 3], :x)
-julia> q = Poly([1, 2, 3], :s)
+julia> p = Polynomial([1, 2, 3], :x)
+julia> q = Polynomial([1, 2, 3], :s)
 julia> p + q
 ERROR: Polynomials must have same variable.
 ```
 
-To get the degree of the polynomial use the `degree` method
-
-```
-julia> degree(p)
-2
-
-julia> degree(p^2)
-4
-
-julia> degree(p-p)
--1
-```
-
-#### polyval(p::Poly, x::Number)
-
-Evaluate the polynomial `p` at `x`.
-
-```julia
-julia> p = Poly([1, 0, -1])
-julia> polyval(p, 0.1)
-0.99
-```
-
-A call method is also available:
-
-```julia
-julia> p(0.1)
-0.99
-```
-
-
-#### polyint(p::Poly, k::Number=0)
+#### Integrals and Derivatives
 
 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
-julia> polyint(Poly([1, 0, -1]))
-Poly(x - 0.3333333333333333x^3)
+julia> integrate(Polynomial([1, 0, -1]))
+Polynomial(x - 0.3333333333333333x^3)
 
-julia> polyint(Poly([1, 0, -1]), 2)
-Poly(2.0 + x - 0.3333333333333333x^3)
+julia> integrate(Polynomial([1, 0, -1]), 2)
+Polynomial(2.0 + x - 0.3333333333333333x^3)
 ```
 
-#### 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
-julia> polyder(Poly([1, 3, -1]))
-Poly(3 - 2x)
+julia> derivative(Polynomial([1, 3, -1]))
+Polynomial(3 - 2x)
 ```
 
-#### roots(p::Poly)
+#### Root-finding
+
 
 Return the roots (zeros) of `p`, with multiplicity. The number of
 roots returned is equal to the order of `p`. By design, this is not type-stable,
 the returned roots may be real or complex.
 
 ```julia
-julia> roots(Poly([1, 0, -1]))
+julia> roots(Polynomial([1, 0, -1]))
 2-element Array{Float64,1}:
  -1.0
   1.0
 
-julia> roots(Poly([1, 0, 1]))
+julia> roots(Polynomial([1, 0, 1]))
 2-element Array{Complex{Float64},1}:
  0.0+1.0im
  0.0-1.0im
 
-julia> roots(Poly([0, 0, 1]))
+julia> roots(Polynomial([0, 0, 1]))
 2-element Array{Float64,1}:
  0.0
  0.0
 ```
 
-#### polyfit(x, y, n=length(x)-1)
+#### Fitting arbitrary data
 
-* `polyfit`: fits a polynomial (of order `n`) to `x` and `y` using a least-squares approximation.
+Fit a polynomial (of order `deg`) to `x` and `y` using a least-squares approximation.
 
 ```julia
-julia> xs = 1:4; ys = exp.(xs); polyfit(xs, ys)
-Poly(-7.717211620141281 + 17.9146616149694x - 9.77757245502143x^2 + 2.298404288652356x^3)
+julia> xs = 0:4; ys = @. exp(-xs) + sin(xs);
+
+julia> fit(xs, ys)
+Polynomial(1.0000000000000016 + 0.059334723072240664*x + 0.39589720602859824*x^2 - 0.2845598112184312*x^3 + 0.03867830809692903*x^4)
+
+julia> fit(ChebyshevT, xs, ys, deg=2)
+ChebyshevT([0.541280671210034, -0.8990834124779993, -0.4237852336242923])
 ```
 
 Visual example:
 
-![newplot 42](https://user-images.githubusercontent.com/3156114/41799777-9ba00582-7627-11e8-94ef-15297ec8790e.png)
+![fit example](https://user-images.githubusercontent.com/14099459/70382587-9e055500-1902-11ea-8952-3f03ae08b7dc.png)
 
 #### Other methods
 
 Polynomial objects also have other methods:
 
-* 0-based indexing is used to extract the coefficients of $a_0 + a_1
-  x + a_2 x^2 + ...$, coefficients may be changed using indexing
+* 0-based indexing is used to extract the coefficients of `[a0, a1, a2, ...]`, coefficients may be changed using indexing
   notation.
 
 * `coeffs`: returns the entire coefficient vector
@@ -187,18 +174,16 @@ Polynomial objects also have other methods:
 
 * `conj`: finds the conjugate of a polynomial over a complex fiel
 
-* `truncate`: set to 0 all small terms in a polynomial; `chop` chops off
-  any small leading values that may arise due to floating point
-  operations.
+* `truncate`: set to 0 all small terms in a polynomial; 
+* `chop` chops off any small leading values that may arise due to floating point operations.
 
 * `gcd`: greatest common divisor of two polynomials.
 
 * `Pade`: Return the
-  [Pade approximant](https://en.wikipedia.org/wiki/Pad%C3%A9_approximant)
-  of order `m/n` for a polynomial as a `Pade` object.
+  [Pade approximant](https://en.wikipedia.org/wiki/Pad%C3%A9_approximant) of order `m/n` for a polynomial as a `Pade` object.
 
 
-## See also
+## Related Packages
 
 * [MultiPoly.jl](https://github.com/daviddelaat/MultiPoly.jl) for sparse multivariate polynomials
 
@@ -207,3 +192,8 @@ Polynomial objects also have other methods:
 * [Nemo.jl](https://github.com/wbhart/Nemo.jl) for generic polynomial rings, matrix spaces, fraction fields, residue rings, power series
 
 * [PolynomialRoots.jl](https://github.com/giordano/PolynomialRoots.jl) for a fast complex polynomial root finder
+
+
+## Contributing
+
+If you are interested in contributing, feel free to open an issue or pull request to get started.

docs/Project.toml

@@ -1,5 +1,7 @@
 [deps]
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 
 [compat]
-Documenter = "0.23.3"
+Documenter = "0.24"

docs/make.jl

@@ -1,13 +1,21 @@
-using Documenter, Polynomials
+using Documenter
+using Polynomials
 
-DocMeta.setdocmeta!(Polynomials, :DocTestSetup, :(using Polynomials); recursive=true)
+DocMeta.setdocmeta!(Polynomials, :DocTestSetup, :(using Polynomials); recursive = true)
 
-makedocs(modules = [Polynomials],
+makedocs(
+    modules = [Polynomials],
     format = Documenter.HTML(prettyurls = get(ENV, "CI", nothing) == "true"),
     sitename = "Polynomials.jl",
     authors = "Jameson Nash, Keno Fischer, and other contributors",
     pages = [
-        "Manual" => "index.md",
+        "Home" => "index.md",
+        "Reference/API" => "reference.md",
+        "Polynomial Types" => [
+            "Polynomial" => "polynomials/polynomial.md",
+            "Chebyshev" => "polynomials/chebyshev.md",
+        ],
+        "Extending" => "extending.md",
     ],
 )