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update Documenter version (#539)
* update Documenter version * work on bumping to Documenter v1.0
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docs/Project.toml

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SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
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[compat]
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Documenter = "0.27"
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Documenter = "1"
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GR_jll = "< 0.58"

docs/make.jl

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],
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"Extending" => "extending.md",
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],
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warnonly = [:cross_references, :missing_docs],
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)
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deploydocs(repo = "github.com/JuliaMath/Polynomials.jl.git")

docs/src/extending.md

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# Extending Polynomials
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The [`AbstractUnivaeriatePolynomial`](@ref) type was made to be extended.
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The [`AbstractUnivariatePolynomial`](@ref) type was made to be extended.
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A polynomial's coefficients are relative to some *basis*. The `Polynomial` type relates coefficients `[a0, a1, ..., an]`, say, to the polynomial ``a_0 + a_1\cdot x + a_2\cdot x^2 + \cdots + a_n\cdot x^n``, through the standard basis ``1, x, x^2, ..., x^n``. New polynomial types typically represent the polynomial through a different basis. For example, `CheyshevT` uses a basis ``T_0=1, T_1=x, T_2=2x^2-1, \cdots, T_n = 2xT_{n-1} - T_{n-2}``. For this type the coefficients `[a0,a1,...,an]` are associated with the polynomial ``a0\cdot T_0 + a_1 \cdot T_1 + \cdots + a_n\cdot T_n`.
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src/common.jl

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## large degree
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For fitting with a large degree, the Vandermonde matrix is exponentially ill-conditioned. The [`ArnoldiFit`](@ref) type introduces an Arnoldi orthogonalization that fixes this problem.
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For fitting with a large degree, the Vandermonde matrix is exponentially ill-conditioned. The `ArnoldiFit` type introduces an Arnoldi orthogonalization that fixes this problem.
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"""

src/polynomials/ngcd.jl

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"""
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ngcd(p, q, [k]; kwargs...)
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Find numerical GCD of polynomials `p` and `q`. Refer to [`NGCD.ngcd(p,q)`](@ref) for details.
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Find numerical GCD of polynomials `p` and `q`. Refer to `NGCD.ngcd` for details.
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The main entry point for this function is `gcd(p, q, method=:numerical)`, but `ngcd` outputs the gcd factorization -- `u, v, w` with `u*v ≈ p` and `u*w ≈ q` -- along with `Θ`, an estimate on how close `p`,`q` is to a gcd factorization of degree `k` and `κ` the GCD condition number.
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src/polynomials/standard-basis/laurent-polynomial.jl

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This satisfies for *imaginary* `s`: `conj(p(s)) = p̃(s) = (conj ∘ p)(s) = cconj(p)(s) `
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[ref](https://github.com/hurak/PolynomialEquations.jl#symmetrix-conjugate-equation-continuous-time-case)
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[reference](https://github.com/hurak/PolynomialEquations.jl#symmetrix-conjugate-equation-continuous-time-case)
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Examples:
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```jldoctest laurent

src/polynomials/standard-basis/standard-basis.jl

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Passing `method=:noda_sasaki` uses scaling to circumvent some of these.
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Passing `method=:numerical` will call the internal method `NGCD.ngcd` for the numerical gcd. See the help page of [`Polynomials.NGCD.ngcd(p,q)`](@ref) for details.
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Passing `method=:numerical` will call the internal method `NGCD.ngcd` for the numerical gcd. See the docstring of `NGCD.ngcd` for details.
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"""
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function Base.gcd(p1::P, p2::Q, args...;
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method=:euclidean,

src/rational-functions/fit.jl

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"""
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fit(::Type{RationalFunction}, r::Polynomial, m, n; var=:x)
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Fit a Pade approximant ([`pade_fit`](@ref)) to `r`.
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Fit a Pade approximant (cf docstring for `Polynomials.pade_fit`) to `r`.
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Examples:
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src/rational-functions/rational-function.jl

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Create a rational expression (`p//q`) from the two polynomials.
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Common factors are not cancelled by the constructor, as they are for
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the base `Rational` type. The [`lowest_terms(pq)`](@ref) function attempts
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the base `Rational` type. The [`lowest_terms`](@ref) function attempts
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that operation.
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For purposes of iteration, a rational function is treated like a two-element container.

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