From ef59eee1385855715907ff77c96b50ed1d5fc61c Mon Sep 17 00:00:00 2001
From: Johannes Middeke <j-middeke@t-online.de>
Date: Fri, 6 May 2016 14:40:13 -0400
Subject: [PATCH] Documentation for polynomials now mentions Zarith; added
 LaTeX and ASCII printer for polynomials.

---
 polys_over_GF2.ml | 42 +++++++++++++++++++++++++++++++++++-------
 test.ml           |  1 +
 2 files changed, 36 insertions(+), 7 deletions(-)

diff --git a/polys_over_GF2.ml b/polys_over_GF2.ml
index b215fe4..14fb8d8 100644
--- a/polys_over_GF2.ml
+++ b/polys_over_GF2.ml
@@ -1,10 +1,12 @@
 (* This module contains an implementation of polynomials over GF(2)
-   using integers (ie, bit-vectors) to represent the polynomials. Note
-   that this restricts the degrees to at most 63. *)
+   using integers (ie, bit-vectors) to represent the polynomials. We
+   use the Zarith package for big integers (the module [Z]) because
+   otherwise we would be restricted to polynomials of degree at most
+   63. *)
 
-(* As mentioned above, we use integers to represent polynomials. The
-   [n]-th bit will correspond to the [n]-th coefficient. We define
-   some constants, too. *)
+(* As mentioned above, we use (big) integers to represent
+   polynomials. The [n]-th bit will correspond to the [n]-th
+   coefficient. We define some constants, too. *)
 
 type t = Polynom of Z.t
 
@@ -19,7 +21,7 @@ let eql (Polynom a) (Polynom b) = Z.equal a b
 (* This function converts polynomials to strings using Maple
    notation. *)
   
-let show (Polynom a) =
+let string_of_polynomial exponent (Polynom a) =
   let rec loop accu a n =
     if Z.equal a Z.zero
     then
@@ -30,7 +32,7 @@ let show (Polynom a) =
       let accu' = match (Z.to_int (Z.logand a Z.one), n) with
 	| (1,0) -> "1" :: accu
 	| (1,1) -> "x" :: accu
-	| (1,n) -> ("x^" ^ string_of_int n) :: accu
+	| (1,n) -> ("x" ^ exponent n) :: accu
 	| _     -> accu
       in
       loop accu' (Z.shift_right a 1) (n+1)
@@ -38,6 +40,32 @@ let show (Polynom a) =
   loop [] a 0
 
 
+
+(* These functions converts polynomials to strings using Maple, LaTeX
+   and ASCII notation. *)
+
+let show = string_of_polynomial (fun i -> "^" ^ string_of_int i)
+and show_latex =
+  let expt n =
+    if n < 10
+    then "^" ^ string_of_int n
+    else "^{" ^ string_of_int n ^ "}"
+  in
+  string_of_polynomial expt
+and show_ascii =
+  let digit = function
+    | 0 -> "⁰" | 1 -> "¹" | 2 -> "²" | 3 -> "³" | 4 -> "⁴"
+    | 5 -> "⁵" | 6 -> "⁶" | 7 -> "⁷" | 8 -> "⁸" | 9 -> "⁹"
+    | _ -> failwith "Digit too large!"
+  in
+  let rec ascii_expt x = 
+    if x < 10
+    then digit x
+    else ascii_expt (x / 10) ^ digit (x mod 10)
+  in
+  string_of_polynomial ascii_expt
+  
+
 (* Use the conversion above, we can define a printer for polynomials
    at the toplevel. (Install with [#install_printer fprintf;;].) *)
     
diff --git a/test.ml b/test.ml
index 2db4727..ae28460 100644
--- a/test.ml
+++ b/test.ml
@@ -193,3 +193,4 @@ let main () =
 
 
 let () = main ()
+
-- 
2.1.4