julia> using CoDa

julia> b = rand(Composition{3}, 10)
10-element Vector{Composition{3, PARTS} where PARTS}:
 "0.610 : 0.296 : 0.094"
 "0.608 : 0.264 : 0.128"
 "0.510 : 0.016 : 0.473"
 "0.165 : 0.192 : 0.643"
 "0.007 : 0.963 : 0.030"
 "0.698 : 0.255 : 0.048"
 "0.679 : 0.004 : 0.316"
 "0.039 : 0.695 : 0.266"
 "0.763 : 0.097 : 0.140"
 "0.212 : 0.202 : 0.586"

julia> A = rand(10,10)
10×10 Matrix{Float64}:
 0.760859    0.104603   0.823341   0.705046   0.600313    0.916079  0.791862   0.632603    0.778659  0.473457
 0.00990181  0.329258   0.0765397  0.68822    0.536604    0.127633  0.411928   0.659145    0.909937  0.612008
 0.805942    0.498786   0.517988   0.0988711  0.00978311  0.958379  0.322744   0.944924    0.257193  0.970391
 0.212351    0.0373405  0.311988   0.712594   0.30764     0.721235  0.581307   0.00426507  0.681214  0.474252
 0.835093    0.88451    0.832915   0.778178   0.661449    0.139439  0.375395   0.301075    0.289008  0.960027
 0.258823    0.441132   0.268645   0.596426   0.331703    0.675858  0.685603   0.318803    0.812066  0.669362
 0.638684    0.0211262  0.68885    0.0161966  0.309542    0.148414  0.319035   0.866017    0.379569  0.199479
 0.0585245   0.477418   0.886183   0.269309   0.489928    0.750661  0.881117   0.192531    0.234592  0.554885
 0.625465    0.51341    0.157735   0.927946   0.961164    0.390173  0.0871444  0.753436    0.365655  0.100547
 0.102124    0.929157   0.868679   0.234841   0.624787    0.312557  0.0458109  0.440861    0.20748   0.92118

julia> A'A \ A'b # doesn't compile because A'b is a vector of Composition objects (objects in a vector space)
ERROR: MethodError: no method matching one(::Type{Composition})
Closest candidates are:
  one(::Union{Type{T}, T}) where T<:AbstractString at strings/basic.jl:262
  one(::Union{Type{P}, P}) where P<:Dates.Period at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/Dates/src/periods.jl:54
  one(::LinearAlgebra.Tridiagonal{T, V} where V<:AbstractVector{T}) where T at /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/special.jl:307
  ...
Stacktrace:
 [1] oneunit(#unused#::Type{Composition})
   @ Base ./number.jl:319
 [2] \(F::LinearAlgebra.LU{Float64, Matrix{Float64}}, B::Vector{Composition})
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/factorization.jl:101
 [3] \(A::Matrix{Float64}, B::Vector{Composition})
   @ LinearAlgebra /buildworker/worker/package_linux64/build/usr/share/julia/stdlib/v1.6/LinearAlgebra/src/generic.jl:1136
 [4] top-level scope
   @ REPL[37]:1

julia> (A'A \ A') * b # manually fix the issue by changing the order of operations
10-element Vector{Composition}:
 "0.000 : 1.000 : 0.000"
 "0.000 : 0.000 : 1.000"
 "0.000 : 0.000 : 1.000"
 "0.000 : 0.000 : 1.000"
 "0.000 : 1.000 : 0.000"
 "0.000 : 1.000 : 0.000"
 "0.000 : 1.000 : 0.000"
 "0.000 : 0.000 : 1.000"
 "0.992 : 0.008 : 0.000"
 "0.000 : 1.000 : 0.000"