(* 2008 Jonathan Dehan *)
(* CSE307 Fall w/Stark *)
(* polynomial functions *)

(*
Besides readability, writability, and reliability, a programming language can be judged on it's built in library of functions / integration with tools.
Although these seem like they would fall in the categories of writability, since a writable language lets a programmer quickly fill in the blanks for necessary functions, when a good
editor is made aware of the common libraries advanced debugging  is easier.
*)
type poly = real list

val pn = []
val p0 = [0.0]
val p1 = [1.0,2.0,3.0]
val p2 = [1.0,1.0]
val p4 = [3.0,5.0,0.0,3.0]

fun degree(p)= if length(p)-1 < 0 then 0 else length(p)-1;

fun add (nil: real list, nil: real list) = nil
  | add (nil: real list, q: real list) = q
  | add (p:real list, nil:real list) = p
  | add (h::t,h'::t') = (h+h')::add(t,t');

(*
fun scale ( r: real, p: real list) = map( fn x: real=>(x*r): real, p: real list);
*)


fun scale ( r: real, nil: real list) = nil
  | scale ( r: real, (h::t): real list ) = r*h::scale(r,t);

fun mul ( [], _ ) = []
  | mul ( _, [] ) = []
  | mul ( h::t, p) = add(scale(h, p), 0.0::mul(t, p));

fun toString ( [] ) = ""
  | toString (h::t) =
	    ( if
		    ( Real.toString(h)="0.0" )
		  then
		    ( "" )
		  else Real.toString(h) ^ (
		   case degree(t)+1 of
	           0 => ""
	         | 1 => "x + "
	         | r => "x^" ^ Int.toString(r) ^ " + " )
	   )
	   ^ toString(t);

 (*
fun eval (r: real, []) = []
  | eval (r: real, (h::t): real list) =
*)

fun map f l

degree(pn) = 0;
degree(p0) = 1;
degree(p1) = 3;
degree(p2) = 2;
degree(p4) = 4;

add(pn, p0);
add(p1, p2);
add(p2, p4);
add(p1, p4);
add(p2, p0);

scale(5.0, pn);
scale(3.0, p0);
scale(1.0, p1);
scale(0.0, p2);
scale(~4.0, p4);

mul(pn,p0);
mul(pn,p2);
mul(p0,p4);
mul(p1,p2);
mul(p2,p4);

toString(pn);
toString(p0);
toString(p1);
toString(p2);
toString(p4);