Unable to invert Toeplitz matrices

[ParadaCarleton]

julia> using FFTW

julia> using ToeplitzMatrices

julia> y = SymmetricToeplitz([1, 2, 3])
3×3 SymmetricToeplitz{Int64}:
 1  2  3
 2  1  2
 3  2  1

julia> inv(y)
ERROR: MethodError: no method matching ldiv!(::ToeplitzMatrices.ToeplitzFactorization{Float64, SymmetricToeplitz{Float64}, ComplexF64, FFTW.cFFTWPlan{ComplexF64, -1, true, 1, UnitRange{Int64}}}, ::Matrix{Float64})
Closest candidates are:
  ldiv!(::Any, ::ChainRulesCore.AbstractThunk) at ~/.julia/packages/ChainRulesCore/ctmSK/src/tangent_types/thunks.jl:90
  ldiv!(::LinearAlgebra.SymTridiagonal, ::AbstractVecOrMat; shift) at /usr/share/julia/stdlib/v1.8/LinearAlgebra/src/tridiag.jl:280
  ldiv!(::LinearAlgebra.Diagonal, ::AbstractVecOrMat) at /usr/share/julia/stdlib/v1.8/LinearAlgebra/src/diagonal.jl:425
  ...
Stacktrace:
 [1] inv(A::SymmetricToeplitz{Int64})
   @ LinearAlgebra /usr/share/julia/stdlib/v1.8/LinearAlgebra/src/generic.jl:1039
 [2] top-level scope
   @ REPL[6]:1

This is pretty weird; inversion should be able to fall back on the generic algorithm, even if the Toeplitz-specific algorithms haven't been implemented yet.

[bonStats]

I'm not a developer of this package but since cholesky() is implemented you can do this inv(cholesky(y)).
Perhaps that should be the fallback for SymmetricToeplitz, though there might be more considerations happening from #64 (comment)

[dlfivefifty]

Only would work for positive definite… we’d want an LDLt factorisation