;Term format: (deg coef)

(define the-zero-poly '((0 0)))

(define zero-poly?
  (lambda (poly)
    (equal? poly the-zero-poly)
  )
)


(define degree
  (lambda (poly)
    (car (car poly))
  )
)

(define leading-coef
  (lambda (poly)
    (car (cdr (car poly)))
  )
)

(define rest-of-poly
  (lambda (poly)
    (if (null? (cdr poly))
        the-zero-poly  ;#t
        (cdr poly)     ;#f
    )
  )
)

;If n is a nonnegative integer,
;  a is a real number,
;  p is the-zero-poly OR 
;      a polynomial of degree less than n,
;then
;  (poly-cons n a p) is the polynomial 
;  obtained by adding the leading term 
;  ax^n to the polynomial p

(define poly-cons
  (lambda (deg coef poly)
    (let ((deg-p (degree poly)))
      (cond
        ((and (zero? deg) (equal? poly the-zero-poly))
           (list (list 0 coef))
        )
        ((>= deg-p deg)
          '("Error: Degree of poly too high")
        )
        ((zero? coef) poly)
        (else
           (cons (list deg coef) poly)
        )
      )
    ) 
  )
)


;============== Unit Tests ======================
(load "test.scm")
(define msg "poly-basic")
(test msg (zero-poly? '((0 0))) #t)
(test msg (zero-poly? '((1 4) (0 5))) #f)

(test msg (leading-coef'((1 4) (0 5))) '4)

(test msg (degree'((1 4) (0 5))) '1)

(test msg (rest-of-poly '((2 3) (1 4) (0 5))) 
                         '((1 4) (0 5)))

(test msg (poly-cons 3 1 '((2 3) (1 4) (0 5))) 
                          '((3 1) (2 3) (1 4) (0 5)))

(test msg (poly-cons 8 1 '((2 3) (1 4) (0 5))) 
                          '((8 1) (2 3) (1 4) (0 5)))

(test msg (poly-cons 1 3 '((2 3) (1 4) (0 5))) 
                 '("Error: Degree of poly too high"))