(* polynomials in ML *)

datatype termType = pair of real * int;

fun termAdd(pair(c1,e1), pair(c2,e2)) = 
   if e1 = e2 then pair(c1+c2, e1)
   else (print "error, terms don't match"; pair(0.0, 0));

fun termPlusPoly(termIt:termType, []) = [termIt] |
    termPlusPoly((termIt as pair(tc, te)):termType, 
                 (x as pair(firstc, firste))::xs) = 
    if te = firste then
       termAdd(termIt, x)::xs
    else x::termPlusPoly(termIt, xs);

fun polyPlusPoly([], y) = y |
    polyPlusPoly(x, []) = x |
    polyPlusPoly((x as pair(xc,xe))::xs, (y as pair(yc,ye))::ys) = 
         if xe > ye then x::polyPlusPoly(xs, y::ys)
    else if xe < ye then y::polyPlusPoly(x::xs, ys)
    else termAdd(x,y)::polyPlusPoly(xs,ys);

fun isZero([]) = true |
    isZero((x as pair(xc, xe))::xs) = 
       if (xc <= 0.0 andalso xc >= 0.0) andalso isZero(xs) then true 
       else false;

fun printTerm(pair(coeff,expo)) =
         if expo = 0 then print (Real.toString(coeff))
    else if expo = 1 then print (Real.toString(coeff)^"X")
    else print (Real.toString(coeff)^"X^"^Int.toString(expo));

fun printPoly([]) = print "\n" |
    printPoly(x::[]) = (printTerm(x); print("\n")) |
    printPoly(x::(pair(tc, te)::xs)) = ( 
       printTerm(x);
       if tc > 0.0 then print "+" (* print the connecting plus *)
       else print "" (* nothing *);
       printPoly((pair(tc, te)::xs)));

(*   p1 = ((3,4),(5,3),(1,2),(4,0)) which is 3x^4+5x^3+x^2+4
     p2 = ((4,5),(2,1)) which is 4x^5+2x
     p3 = ((-2,2),(3,1),(6,0)) which is -2x^2+3x+6, and
     p4 = ((0,0)) i.e. the zero polynomial.                     *)

val poly1 = [pair(3.0,4), pair(5.0,3), pair(1.0,2), pair(4.0,0)];
printPoly(poly1);
val poly2 = [pair(4.0,5), pair(2.0,1)];
printPoly(poly2);
val poly3 = [pair(~2.0,2), pair(3.0,1), pair(6.0, 0)];
printPoly(poly3);
val poly4 = [pair(0.0,0)];
printPoly(poly4);

print "p1+p2 is"; printPoly(polyPlusPoly(poly1, poly2));
print "p3+p4 is"; printPoly(polyPlusPoly(poly3, poly4));
print "p2+p3 is"; printPoly(polyPlusPoly(poly2, poly3));

print "is poly1 zero?"; isZero(poly1);
print "is poly2 zero?"; isZero(poly2);
print "is poly3 zero?"; isZero(poly3);
print "is poly4 zero?"; isZero(poly4);