vm.fail
symbolic mathematics engine in OCaml with differentiation, integration, simplification, and numerical methods
1open Leibniz
2
3let () =
4 print_endline "root finding\n";
5
6 let f = Parser.parse "x^2 - 4" in
7 print_endline ("finding roots of f(x) = " ^ Expr.to_string f);
8
9 (match Numerical.bisection f "x" 0.0 3.0 0.0001 100 with
10 | Some root -> Printf.printf "bisection: root ≈ %.6f\n" root
11 | None -> print_endline "bisection failed");
12
13 (match Numerical.newton_raphson f "x" 1.0 0.0001 100 with
14 | Some root -> Printf.printf "newton-raphson: root ≈ %.6f\n" root
15 | None -> print_endline "newton-raphson failed");
16
17 print_endline "\nnumerical integration\n";
18
19 let g = Parser.parse "sin(x)" in
20 print_endline ("integrating g(x) = " ^ Expr.to_string g);
21
22 let trap = Numerical.trapezoidal g "x" 0.0 3.14159265 100 in
23 Printf.printf "trapezoidal rule: %.6f\n" trap;
24
25 let simp = Numerical.simpsons g "x" 0.0 3.14159265 100 in
26 Printf.printf "simpson's rule: %.6f\n" simp