let diffPolyMap(Poly(map)) =
        Poly((Map.ofList << List.choose (fun (pow, v) -> if pow = 0 then None else Some (pow-1, float pow*v)) << Map.toList) map)

    let newDiff map =
        Map.foldBack (fun k v acc -> if k > 0 then addToMap (k-1) (float k * v) acc else acc) map Map.empty