Linear algebra doesn't work

[dlfivefifty]

I think we just need to overload iterate and adjoint to fix this:

julia> dot([x,y], [-y,x])
ERROR: MethodError: no method matching iterate(::@ring(ℚ[x,y]))

Closest candidates are:
  iterate(::Union{LinRange, StepRangeLen})
   @ Base range.jl:880
  iterate(::Union{LinRange, StepRangeLen}, ::Integer)
   @ Base range.jl:880
  iterate(::T) where T<:Union{Base.KeySet{<:Any, <:Dict}, Base.ValueIterator{<:Dict}}
   @ Base dict.jl:698
  ...

Stacktrace:
 [1] dot(x::@ring(ℚ[x,y]), y::@ring(ℚ[x,y]))
   @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/generic.jl:848
 [2] dot(x::Vector{@ring(ℚ[x,y])}, y::Vector{@ring(ℚ[x,y])})
   @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/generic.jl:886
 [3] top-level scope
   @ REPL[24]:1

julia> [x,y]'* [-y,x]
ERROR: MethodError: no method matching adjoint(::@ring(ℚ[x,y]))

Closest candidates are:
  adjoint(::Union{QR, LinearAlgebra.QRCompactWY, QRPivoted})
   @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/qr.jl:517
  adjoint(::Union{Cholesky, CholeskyPivoted})
   @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/cholesky.jl:556
  adjoint(::LQ)
   @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/lq.jl:138
  ...

Stacktrace:
  [1] getindex
    @ ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/adjtrans.jl:302 [inlined]
  [2] iterate
    @ ./abstractarray.jl:1220 [inlined]
  [3] iterate
    @ ./abstractarray.jl:1218 [inlined]
  [4] _zip_iterate_some
    @ ./iterators.jl:424 [inlined]
  [5] _zip_iterate_all
    @ ./iterators.jl:416 [inlined]
  [6] iterate
    @ ./iterators.jl:406 [inlined]
  [7] _foldl_impl
    @ ./reduce.jl:56 [inlined]
  [8] foldl_impl(op::Base.MappingRF{LinearAlgebra.var"#13#14", Base.BottomRF{typeof(Base.add_sum)}}, nt::Base._InitialValue, itr::Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}})
    @ Base ./reduce.jl:48
  [9] mapfoldl_impl(f::typeof(identity), op::typeof(Base.add_sum), nt::Base._InitialValue, itr::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"})
    @ Base ./reduce.jl:44
 [10] mapfoldl(f::Function, op::Function, itr::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"}; init::Base._InitialValue)
    @ Base ./reduce.jl:170
 [11] mapfoldl(f::Function, op::Function, itr::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"})
    @ Base ./reduce.jl:170
 [12] mapreduce(f::Function, op::Function, itr::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"}; kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Base ./reduce.jl:302
 [13] mapreduce(f::Function, op::Function, itr::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"})
    @ Base ./reduce.jl:302
 [14] sum(f::Function, a::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"}; kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Base ./reduce.jl:530
 [15] sum(f::Function, a::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"})
    @ Base ./reduce.jl:530
 [16] sum(a::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"}; kw::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ Base ./reduce.jl:559
 [17] sum(a::Base.Generator{Base.Iterators.Zip{Tuple{Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, Vector{@ring(ℚ[x,y])}}}, LinearAlgebra.var"#13#14"})
    @ Base ./reduce.jl:559
 [18] _dot_nonrecursive(u::Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, v::Vector{@ring(ℚ[x,y])})
    @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/adjtrans.jl:428
 [19] *(u::Adjoint{Union{}, Vector{@ring(ℚ[x,y])}}, v::Vector{@ring(ℚ[x,y])})
    @ LinearAlgebra ~/Projects/julia-1.9/usr/share/julia/stdlib/v1.9/LinearAlgebra/src/adjtrans.jl:435
 [20] top-level scope
    @ REPL[25]:1