Polynomial long division: Difference between revisions
Translate Ocaml into F#
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</pre>
=={{header|F_Sharp|F#}}==
{{trans|Ocaml}}
<lang fsharp>
let rec shift n l = if n <= 0 then l else shift (n-1) (l @ [0.0])
let rec pad n l = if n <= 0 then l else pad (n-1) (0.0 :: l)
let rec norm = function | 0.0 :: tl -> norm tl | x -> x
let deg l = List.length (norm l) - 1
let zip op p q =
let d = (List.length p) - (List.length q) in
List.map2 op (pad (-d) p) (pad d q)
let polydiv f g =
let rec aux f s q =
let ddif = (deg f) - (deg s) in
if ddif < 0 then (q, f) else
let k = (List.head f) / (List.head s) in
let ks = List.map ((*) k) (shift ddif s) in
let q' = zip (+) q (shift ddif [k])
let f' = norm (List.tail (zip (-) f ks)) in
aux f' s q' in
aux (norm f) (norm g) []
let str_poly l =
let term v p = match (v, p) with
| ( _, 0) -> string v
| (1.0, 1) -> "x"
| ( _, 1) -> (string v) + "*x"
| (1.0, _) -> "x^" + (string p)
| _ -> (string v) + "*x^" + (string p) in
let rec terms = function
| [] -> []
| h :: t ->
if h = 0.0 then (terms t) else (term h (List.length t)) :: (terms t) in
String.concat " + " (terms l)
let _ =
let f,g = [1.0; -4.0; 6.0; 5.0; 3.0], [1.0; 2.0; 1.0] in
let q, r = polydiv f g in
Printf.printf
" (%s) div (%s)\ngives\nquotient:\t(%s)\nremainder:\t(%s)\n"
(str_poly f) (str_poly g) (str_poly q) (str_poly r)
</lang>
{{out}}
<pre>
(x^4 + -4*x^3 + 6*x^2 + 5*x + 3) div (x^2 + 2*x + 1)
gives
quotient: (x^2 + -6*x + 17)
remainder: (-23*x + -14)
</pre>
=={{header|Factor}}==
<lang factor>USE: math.polynomials
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