;Term format: (deg coef)

(define p+
  (lambda (poly1 poly2)
    (cond
      ((zero-poly? poly1) poly2)
      ((zero-poly? poly2) poly1)
      (else
        (let 
          ( (n1 (degree poly1))
            (n2 (degree poly2))
          )
          (cond
            ((> n1 n2) 
              (let 
                ( (a1 (leading-coef poly1))
                  (rest1 (rest-of-poly poly1))
                )
                (poly-cons n1 a1 (p+ rest1 poly2))
              )
            )
            ((< n1 n2) 
              (let 
                ( (a2 (leading-coef poly2))
                  (rest2 (rest-of-poly poly2))
                )
                (poly-cons n2 a2 (p+ rest2 poly1))
              )
            )
            (else
              (let 
                ( (a1 (leading-coef poly1))
                  (a2 (leading-coef poly2))
                  (rest1 (rest-of-poly poly1))
                  (rest2 (rest-of-poly poly2))
                )
                (poly-cons n1 (+ a1 a2) (p+ rest1 rest2))
              )
            )
          )
        )
      )
    )
  )
)



;============== Unit Tests ======================
(load "test.scm")
(load "poly-basic.scm")
(define msg "poly-add")

(test  msg (p+ '((4 5)) '((1 2))) 
               '((4 5) (1 2))) 

(test  msg (p+ '((1 2)) '((4 5))) 
               '((4 5) (1 2))) 

(test  msg (p+ '((4 5) (3 -7) (1  2) (0 -4)) 
                     '((3 1) (2  6) (1 -3)))
                     '((4 5) (3 -6) (2  6) (1 -1) (0 -4)))