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Taylor-mode automatic differentiation for higher-order derivatives

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Feature request: Based on the package design, it seems like it is probably possible to calculate the first n derivatives of a function at once (with one call). Right now...

TaylorDiff.jl seems to throw an error when I try to differentiate a fairly simple ODE solver. There is an error on the MTK side, but even after the workaround there...

Bumps [julia-actions/cache](https://github.com/julia-actions/cache) from 1 to 2. Release notes Sourced from julia-actions/cache's releases. v2.0.0 Breaking Changes ⚠️ v2.0.0 requires node20. This is a breaking change, because node20 does not support the...

dependencies

I brought up this as an issue in the `Zygote.jl` repository, but it might belong here: `Zygote` fails to use `rrule`s defined by `TaylorDiff` when run with `Julia 1.10+` In...

The derivative function behaves really odd for simple user defined function. If I define two simple functions as follows ```julia julia> f(x) = x*x julia> h(x) = x^2 ``` then...

TaylorDiff is depending on a lot of stuff it should not, which tanks my TTFX. As already noted in https://github.com/JuliaDiff/TaylorDiff.jl/issues/52#issuecomment-1707801903_ , It would be very beneficial to leverage package preferences...

Hey, The following behaviors are really annoying: ```julia julia> t = TaylorScalar{Float64, 3}((Inf, 1.0, 0.0)) TaylorScalar{Float64, 3}((Inf, 1.0, 0.0)) julia> t+1 TaylorScalar{Float64, 3}((Inf, 1.0, 0.0)) ##### OK julia> t*1 TaylorScalar{Float64,...

Hey, The current implementation of `*(::TaylorScalar,::Number)` in your package promotes the scalar to a TaylorScalar as so : ````julia for op in (:+, :-, :*, :/) @eval @inline $op(a::TaylorScalar, b::Number)...

When running on an ODE solve the solver kicks a non-concrete error message, I've included a MWE of a Lotka-Volterra system demonstrating the behavior. I get the same error for...