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Typos (#405)
* bump SymPy * adjust p.toml * readjust * add spell check to CI * format adjustments * fix typos
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.github/workflows/SpellCheck.yml

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name: Spell Check
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on: [pull_request]
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jobs:
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typos-check:
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name: Spell Check with Typos
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runs-on: ubuntu-latest
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steps:
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- name: Checkout Actions Repository
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uses: actions/checkout@v4
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- name: Check spelling
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uses: crate-ci/typos@master

Project.toml

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@@ -19,9 +19,10 @@ SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c"
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ChainRulesCore = "1"
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CommonSolve = "0.1, 0.2"
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ForwardDiff = "0.10"
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SymPy = "1"
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SymPyPythonCall = "0.1,1"
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SymPy = "1,2"
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SymPyPythonCall = "0.1, 0.2, 1"
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Setfield = "0.7, 0.8, 1"
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Printf = "1"
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julia = "1.0"
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docs/src/roots.md

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julia> below = accumulate((x,y) -> prevfloat(x), 1:10, init=1/3);
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julia> ns = sort([below...,1/3, above...]); # floating point numbers aroudn 1/3
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julia> ns = sort([below...,1/3, above...]); # floating point numbers around 1/3
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julia> maximum(abs.(f.(ns) - f1.(ns))) < 1e-14
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true

src/Bracketing/alefeld_potra_shi.jl

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"""
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const AlefeldPotraShi = A2425{2}
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# Algorith 5.7 is parameterized by K
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# Algorithm 5.7 is parameterized by K
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# 4.1 -> K=1; 4.2 -> K=2
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struct A57{K} <: AbstractAlefeldPotraShi end
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fncalls_per_step(::A57{K}) where {K} = K - 1

src/Bracketing/bisection.jl

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val, stopped = :not_converged, false
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ctr = 1
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log_step(l, M, state; init=true)
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T,S = TS(state)
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T, S = TS(state)
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while !stopped
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a::T, b::T = state.xn0, state.xn1
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a::T, b::T = state.xn0, state.xn1
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fa::S, fb::S = state.fxn0, state.fxn1
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## assess_convergence

src/Derivative/lith.jl

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@@ -148,7 +148,7 @@ function evalf(F::Callable_Function{S,T,𝑭,P}, x) where {N,S<:Val{N},T<:Val{tr
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end
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#specializations for N = 1,2,3,4,5,6
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## lmm(::Roots.LithBoonkkampIJzerman{1, D}) is defined up unitl D = 6, so specialize those
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## lmm(::Roots.LithBoonkkampIJzerman{1, D}) is defined up until D = 6, so specialize those
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function evalf(F::Callable_Function{S,T,𝑭,P}, x) where {S<:Val{1},T<:Val{false},𝑭,P}
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F(x)

src/DerivativeFree/esser.jl

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Esser, H. Computing (1975) 14: 367. DOI: [10.1007/BF02253547](https://doi.org/10.1007/BF02253547)
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Eine stets quadratisch konvergente Modifikation des Steffensen-Verfahrens
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Eine stets quadratisch konvergente Modification des Steffensen-Verfahrens
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## Examples

src/alternative_interfaces.jl

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Keyword arguments are passed to `find_zero` using the `Roots.Halley()` method.
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"""
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=#
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halley(f, fp, fpp, x0; kwargs...) = find_zero((f, fp, fpp), x0, Halley(); kwargs...)
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Searches for all zeros of `f` within an interval `(a,b)`. Assume neither `a` or `b` is a zero.
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Compatability interface for [`find_zeros`](@ref).
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Compatibility interface for [`find_zeros`](@ref).
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"""
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function fzeros(f, a::Number, b::Number; kwargs...)
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find_zeros(FnWrapper(f), float(a), float(b); kwargs...)

src/simple.jl

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"""
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Roots.a42(f, ab; atol=nothing, rtol=nothing, λ=0.7, μ = 0.5)
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Direct implemenation of Alefeld, Potra, and Shi's Algorithm 4.2. See also [`A42()`](@ref).
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Direct implementation of Alefeld, Potra, and Shi's Algorithm 4.2. See also [`A42()`](@ref).
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* `f`: function to find zero of. (If `f` is 4-times continuously differentiable, convergence to a simple root will be like ``(2 + 7^{1/2})^{1/3} = 1.6686...``
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* `ab`: a *bracketing interval
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* `atol`, `rtol`: optional tolerances. These are `0` and `eps` respectively by default.
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Not exported
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"""
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=#

src/state.jl

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fxn0::S
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end
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TS(::AbstractUnivariateZeroState{T,S}) where {T,S} = T,S
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TS(::AbstractUnivariateZeroState{T,S}) where {T,S} = T, S
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# simple helper to set main properties of a state object
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function _set(state, xf1)

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