; - Program 5.6, pg. 144 -

(define zero-poly?
  (lambda (poly)
    (and (zero? (degree poly)) (zero? (leading-coef poly)))))

; - End Program -

; - Program 5.7, pg. 145 -

(define make-term
  (lambda (deg coef)
    (poly-cons deg coef the-zero-poly))) 

; - End Program -

; - Program 5.8, pg. 145 -

(define leading-term
  (lambda (poly)
    (make-term (degree poly) (leading-coef poly))))

; - End Program -

; - Program 5.9, pg. 146 -

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

; - End Program -

; - Program 5.10, pg. 148 -

(define p* 
  (letrec 
    ((t* (lambda (trm poly)
           (if (zero-poly? poly)
               the-zero-poly
               (poly-cons 
                 (+ (degree trm) (degree poly))
                 (* (leading-coef trm) (leading-coef poly))
                 (t* trm (rest-of-poly poly)))))))
    (lambda (poly1 poly2)
      (letrec
        ((p*-helper (lambda (p1)
                      (if (zero-poly? p1)
                          the-zero-poly
                          (p+ (t* (leading-term p1) poly2)
                              (p*-helper (rest-of-poly p1)))))))
        (p*-helper poly1)))))

; - End Program -

; - Program 5.11, pg. 148 -

(define negative-poly
  (lambda (poly) 
    (let ((poly-negative-one (make-term 0 -1)))
      (p* poly-negative-one poly))))

; - End Program -

; - Program 5.12, pg. 148 -

(define p-
  (lambda (poly1 poly2)
    (p+ poly1 (negative-poly poly2))))  

; - End Program -

; - Program 5.13, pg. 150 -

(define poly-value
  (lambda (poly num)
    (letrec 
      ((pvalue (lambda (p)
                 (let ((n (degree p)))
                   (if (zero? n) 
                       (leading-coef p)
                       (let ((rest (rest-of-poly p)))
                         (if (< (degree rest) (sub1 n))
                             (pvalue (poly-cons
                                       (sub1 n)
                                       (* num (leading-coef p))
                                       rest))
                             (pvalue (poly-cons 
                                       (sub1 n)
                                       (+ (* num (leading-coef p))
                                          (leading-coef rest))
                                       (rest-of-poly rest))))))))))
      (pvalue poly))))

; - End Program -