vm.fail
symbolic mathematics engine in OCaml with differentiation, integration, simplification, and numerical methods
1open Expr
2open Simplify
3open Diff
4open Substitute
5
6type direction = FromLeft | FromRight | Bidirectional
7
8let rec limit expr var point direction =
9 let try_direct_sub () =
10 try
11 let substituted = substitute var point expr in
12 let simplified = simplify substituted in
13 match simplified with
14 | Const c when not (Float.is_nan c || Float.is_infinite c) -> Some simplified
15 | _ -> None
16 with _ -> None
17 in
18
19 let try_lhopital () =
20 let numerator, denominator = match expr with
21 | Div (n, d) -> (n, d)
22 | _ -> (expr, Const 1.0)
23 in
24
25 let num_at_point = substitute var point numerator |> simplify in
26 let den_at_point = substitute var point denominator |> simplify in
27
28 match (num_at_point, den_at_point) with
29 | (Const 0.0, Const 0.0) ->
30 let num_deriv = diff var numerator in
31 let den_deriv = diff var denominator in
32 let new_expr = Div (num_deriv, den_deriv) in
33 limit new_expr var point direction
34 | _ -> None
35 in
36
37 let try_series_expansion () =
38 None
39 in
40
41 match try_direct_sub () with
42 | Some result -> Some result
43 | None ->
44 match try_lhopital () with
45 | Some result -> Some result
46 | None -> try_series_expansion ()
47
48let limit_at_infinity expr var =
49 let rec find_highest_power = function
50 | Pow (Var v, Const n) when v = var -> Some (int_of_float n)
51 | Div (num, den) ->
52 let num_pow = find_highest_power num |> Option.value ~default:0 in
53 let den_pow = find_highest_power den |> Option.value ~default:0 in
54 Some (num_pow - den_pow)
55 | Add (e1, e2) | Sub (e1, e2) ->
56 let p1 = find_highest_power e1 |> Option.value ~default:0 in
57 let p2 = find_highest_power e2 |> Option.value ~default:0 in
58 Some (max p1 p2)
59 | Mul (e1, e2) ->
60 let p1 = find_highest_power e1 |> Option.value ~default:0 in
61 let p2 = find_highest_power e2 |> Option.value ~default:0 in
62 Some (p1 + p2)
63 | _ -> None
64 in
65
66 match find_highest_power expr with
67 | Some p when p > 0 -> Some (SymConst E)
68 | Some p when p < 0 -> Some (Const 0.0)
69 | Some _ -> Some (Const 1.0)
70 | None -> None