Let’s define a tensor product of two different types

in quantum mechanics there is this ket bra product also known as outer product

in F# we can write a function

let tensor xvect yvect =
xvect
|> Seq.map (fun x ->
yvect
|> Seq.map (fun y -> x, y))
|> Seq.concat

Now we want to introduce a contraint such that each left or right vector appears only one time

Basically we have to

- fold through the tensor
- check if a vector already exists in the accumulator
- if it is not the case, we append it into a new state

Now the problem is that we want also to do a compactification to reduce the unbalanced left and right matches to a minimum

Here it is our result

let cocycle chain =
chain
|> Seq.fold
(fun cochain cycle->
let (x: 'x, y: 'y) = cycle
let foundx =
cochain
|> Seq.exists (fun (x1: 'x option,y1: 'y option) -> (x1 = Some x) && (y1.IsSome) )
let foundy =
cochain
|> Seq.exists (fun (x1,y1) -> y1 = Some y && (x1.IsSome))
match foundx, foundy with
| true, true ->
cochain
|false, false ->
Seq.append
(cochain |> Seq.except [(Some x, None); (None, Some y)] )
[(Some x, Some y)]
|false, true ->
Seq.append
(cochain |> Seq.except [(Some x, None)] )
[(Some x, None)]
|true, false ->
Seq.append
(cochain |> Seq.except [(None, Some y)] )
[(None, Some y)]
)
Seq.empty

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