(define (the-empty-termlist) '())

(define (make-term order coeff) (list order coeff))

(define (order term) (car term))

(define (coeff term) (cadr term))

(define (adjoin-term-dense term-list)
  (define (adjoin-term term)
    (let ((len (- (order term) (order (first-term term-list)))))
      (define (adjoin-zero-iter term-list times)
        (if (= 0 times)
            term-list
            (adjoin-zero-iter (cons 0 term-list) (- times 1))))
      (adjoin-zero-iter term-list len)))
  adjoin-term)

(define (first-term-dense term-list)
  (let ((order (- (lenth term-list) 1))
        (coeff (car term-list)))
    (make-term order coeff))))

(define (rest-terms-dense term-list)
  (cdr term-list))

(define (empty-termlist-dense? term-list)
  (null? term-list))

(define (adjoin-term-sparse term-list)
  (define (adjoin-term term)
    (if (=zero? term)
        term-list
        (cons term term-list)))
  adjoin-term)

(define (first-term-sparse term-list)
  ((car term-list)))

(define (rest-terms-sparse term-list)
  (cdr term-list))

(define (empty-termlist-sparse? term-list)
  (null? term-list))

(put 'adjoin-term-proc 'dense adjoin-term-dense)
(put 'adjoin-term-proc 'sparse adjoin-term-sparse)
(put 'first-term 'dense first-term-dense)
(put 'first-term 'sparse first-term-sparse)
(put 'rest-terms 'dense rest-terms-dense)
(put 'rest-terms 'sparse rest-terms-sparse)
(put 'empty-termlist? 'dense empty-termlist-dense?)
(put 'empty-termlist? 'sparse empty-termlist-sparse?)

(define (adjoin-term term term-list)
  (define (adjoin-term-proc term-list)
    (apply-generic 'adjoin-term-proc term-list))
  ((adjoin-term-proc term-list) term))

(define (first-term term-list)
  (apply-generic 'first-term term-list))

(define (rest-term term-list)
  (apply-generic 'rest-term term-list))

(define (empty-termlist? term-list)
  (apply-generic 'empty-termlist? term-list))