open Leibniz

let () =
  print_endline "symbolic integration\n";

  let expressions = [
    ("x", "x");
    ("x^2", "x");
    ("sin(x)", "x");
    ("cos(x)", "x");
    ("e^x", "x");
  ] in

  List.iter (fun (expr_str, var) ->
    let expr = Parser.parse expr_str in
    match Integrate.integrate var expr with
    | Some result ->
        Printf.printf "∫ %s d%s = %s\n" expr_str var (Expr.to_string result)
    | None ->
        Printf.printf "∫ %s d%s = (no closed form)\n" expr_str var
  ) expressions;

  print_endline "\ntaylor series expansion\n";

  let sin_x = Parser.parse "sin(x)" in
  let series = Series.maclaurin "x" sin_x 7 in
  print_endline ("sin(x) ≈ " ^ Expr.to_string series);

  let exp_x = Parser.parse "e^x" in
  let exp_series = Series.maclaurin "x" exp_x 5 in
  print_endline ("e^x ≈ " ^ Expr.to_string exp_series)