vm.fail
symbolic mathematics engine in OCaml with differentiation, integration, simplification, and numerical methods
1open Leibniz
2
3let () =
4 print_endline "polynomial expansion and collection\n";
5
6 let expr = Parser.parse "(x + 1)^3" in
7 let expanded = Polynomial.expand expr in
8 print_endline ("expanded: " ^ Expr.to_string expanded);
9
10 print_endline "\ncommon subexpression elimination\n";
11
12 let complex_expr = Parser.parse "sin(x + y) * cos(x + y) + sin(x + y)" in
13 let cse_result = Cse.common_subexpression_elimination complex_expr in
14 print_endline ("original: " ^ Expr.to_string complex_expr);
15 List.iter (fun (name, e) ->
16 print_endline (Printf.sprintf "%s = %s" name (Expr.to_string e))
17 ) cse_result.subexpressions;
18 print_endline ("final: " ^ Expr.to_string cse_result.final_expr);
19
20 print_endline "\ncode generation to C\n";
21
22 let f = Parser.parse "x^2 + sin(y) * cos(z)" in
23 let c_code = Codegen.compile_to_c f ["x"; "y"; "z"] in
24 print_endline c_code;
25
26 print_endline "horner form optimization\n";
27
28 let poly = Parser.parse "x^4 + 2x^3 + 3x^2 + 4x + 5" in
29 let horner = Cse.horner_form poly "x" in
30 print_endline ("horner form: " ^ Expr.to_string horner);
31
32 print_endline "\nlimits computation\n";
33
34 let limit_expr = Parser.parse "(sin(x)) / x" in
35 (match Limits.limit limit_expr "x" (Expr.Const 0.0) Limits.Bidirectional with
36 | Some result -> print_endline ("lim (sin(x)/x) as x→0 = " ^ Expr.to_string result)
37 | None -> print_endline "limit could not be computed");
38
39 print_endline "\nsymbolic matrix operations\n";
40
41 let m = Matrix.create 2 2 (fun i j ->
42 if i = j then Expr.Var (Printf.sprintf "a%d%d" i j)
43 else Expr.Var (Printf.sprintf "a%d%d" i j)
44 ) in
45
46 let det_m = Matrix.det m in
47 print_endline ("det = " ^ Expr.to_string det_m);
48
49 let trace_m = Matrix.trace m in
50 print_endline ("trace = " ^ Expr.to_string trace_m)