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README.md

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# ApproxFunFourier.jl
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Support for orthogonal polyFouriernomial-based spaces in ApproxFun
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[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaApproximation.github.io/ApproxFun.jl/stable)
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[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaApproximation.github.io/ApproxFun.jl/latest)
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[![Build Status](https://travis-ci.org/JuliaApproximation/ApproxFun.jl.svg?branch=master)](https://travis-ci.org/JuliaApproximation/ApproxFunFourier.jl)
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[![Build status](https://ci.appveyor.com/api/projects/status/q3e3ihfbxnrjn7ji?svg=true)](https://ci.appveyor.com/project/dlfivefifty/approxfunfourier-jl)
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[![Coverage Status](https://img.shields.io/coveralls/JuliaApproximation/ApproxFunFourier.jl.svg)](https://coveralls.io/r/JuliaApproximation/ApproxFunFourier.jl?branch=master)
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[![Join the chat at https://gitter.im/JuliaApproximation/ApproxFun.jl](https://badges.gitter.im/JuliaApproximation/ApproxFun.jl.svg)](https://gitter.im/JuliaApproximation/ApproxFun.jl?utm_source=badge&utm_medium=badge&utm_campaign=pr-badge&utm_content=badge)
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[ApproxFun.jl](https://github.com/JuliaApproximation/ApproxFun.jl) is a package for approximating functions. This package implements Fourier based spaces to ApproxFun.

REQUIRE

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ApproxFunBase
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FastGaussQuadrature 0.3.2
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FastTransforms 0.4.2
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RecipesBase 0.5
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DualNumbers 0.4
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ToeplitzMatrices 0.4
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Calculus 0.1.15
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DomainSets 0.0.1
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IntervalSets 0.3.1
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StaticArrays 0.8.3
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BlockArrays 0.8
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BlockBandedMatrices 0.3.5
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BlockBandedMatrices 0.4
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BandedMatrices 0.9
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AbstractFFTs 0.3.1
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FFTW 0.2.4

src/ApproxFunFourier.jl

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toeplitz_getindex, toeplitz_axpy!, ToeplitzOperator, hankel_getindex,
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SpaceOperator, ZeroOperator, InterlaceOperator,
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interlace!, reverseeven!, negateeven!, cfstype, pad!,
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extremal_args, hesseneigvals, chebyshev_clenshaw, recA, recB, recC, roots, chebmult_getindex, intpow, alternatingsum
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extremal_args, hesseneigvals, chebyshev_clenshaw, recA, recB, recC, roots, chebmult_getindex, intpow, alternatingsum,
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affine_setdiff, complexroots
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import DomainSets: Domain, indomain, UnionDomain, ProductDomain, FullSpace, Point, elements, DifferenceDomain,

src/Domains/PeriodicCurve.jl

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export PeriodicCurve
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struct PeriodicCurve{S<:Space,T,VT} <: PeriodicDomain{T}
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curve::Fun{S,T,VT}

src/Domains/PeriodicSegment.jl

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union_rule(A::SumSpace{<:Any,<:PeriodicSegment}, B::Space{<:IntervalOrSegment}) =
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union(Space(Interval(domain(A))), B)
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Base.setdiff(d::PeriodicSegment, ptsin::UnionDomain{AS}) where {AS <: AbstractVector{P}} where {P <: Point} =
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affine_setdiff(d, ptsin)

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