open Leibniz

let () =
  print_endline "basic differentiation and simplification\n";

  let f = Parser.parse "x^3 + 2x^2 + x" in
  print_endline ("f(x) = " ^ Expr.to_string f);

  let df = Diff.diff "x" f in
  print_endline ("f'(x) = " ^ Expr.to_string df);

  let ddf = Diff.diff "x" df in
  print_endline ("f''(x) = " ^ Expr.to_string ddf);

  print_endline "\nsimplification\n";

  let expr = Parser.parse "(x + 0) * 1 + x * 0" in
  print_endline ("before: " ^ Expr.to_string expr);
  let simplified = Simplify.simplify expr in
  print_endline ("after: " ^ Expr.to_string simplified);

  print_endline "\nimplicit multiplication\n";

  let expr2 = Parser.parse "2x + 3sin(x)" in
  print_endline ("parsed: " ^ Expr.to_string expr2);

  print_endline "\ntrigonometric functions\n";

  let trig = Parser.parse "sin(x)^2 + cos(x)^2" in
  print_endline ("trig identity: " ^ Expr.to_string trig);
  let dtrig = Diff.diff "x" trig in
  print_endline ("derivative: " ^ Expr.to_string dtrig)