open Expr
open Diff
open Substitute
open Simplify

let rec factorial n =
  if n <= 1 then 1.0
  else float_of_int n *. factorial (n - 1)

let taylor var expr center order =
  let rec build_terms n acc =
    if n > order then acc
    else
      let derivative = diff_n var n expr in
      let deriv_at_center = substitute var center derivative in
      let coeff = Div (deriv_at_center, Const (factorial n)) in
      let h = Sub (Var var, center) in
      let term = Mul (coeff, Pow (h, Const (float_of_int n))) in
      build_terms (n + 1) (term :: acc)
  in
  let terms = List.rev (build_terms 0 []) in
  let series = List.fold_left (fun acc t -> Add (acc, t)) (Const 0.0) terms in
  simplify series

let maclaurin var expr order =
  taylor var expr (Const 0.0) order