2_87.rkt

#lang racket
#| Solution for exercise 2_87. |#

(require (only-in "../solutions/dispatch-table.rkt" get put attach-tag))
(require (only-in "../solutions/2_84.rkt" apply-generic-coercion))

(provide install-polynomial-package make-term)



(define (the-empty-termlist) '())
(define (first-term term-list) (car term-list))
(define (rest-terms term-list) (cdr term-list))
(define (empty-termlist? term-list) (null? term-list))

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

(define (install-polynomial-package)
  (define (add x y) (apply-generic-coercion 'add x y))
  (define (mul x y) (apply-generic-coercion 'mul x y))

  (define (=zero? x) (apply-generic-coercion '=zero? x))

  (define (=zero?-polynominal pol)
    (define (=zero?-termlist tl)
      (if (empty-termlist? tl)
        true
        (if (=zero? (coeff (first-term tl)))
          (=zero?-polynominal (rest-terms tl))
          false)))
    (=zero?-termlist (term-list pol)))


  (define (variable? x) (symbol? x))

  (define (same-variable? v1 v2)
    (and (variable? v1) (variable? v2) (eq? v1 v2)))

  (define (make-poly variable term-list)
    (cons variable term-list))

  (define (variable p) (car p))
  (define (term-list p) (cdr p))

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

  (define (add-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (add-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- ADD-POLY"
               (list p1 p2))))

  (define (mul-poly p1 p2)
    (if (same-variable? (variable p1) (variable p2))
        (make-poly (variable p1)
                   (mul-terms (term-list p1)
                              (term-list p2)))
        (error "Polys not in same var -- MUL-POLY"
               (list p1 p2))))


  (define (add-terms L1 L2)
    (cond ((empty-termlist? L1) L2)
          ((empty-termlist? L2) L1)
          (else
           (let ((t1 (first-term L1)) (t2 (first-term L2)))
             (cond ((> (order t1) (order t2))
                    (adjoin-term
                     t1 (add-terms (rest-terms L1) L2)))
                   ((< (order t1) (order t2))
                    (adjoin-term
                     t2 (add-terms L1 (rest-terms L2))))
                   (else
                    (adjoin-term
                     (make-term (order t1)
                                (add (coeff t1) (coeff t2)))
                     (add-terms (rest-terms L1)
                                (rest-terms L2)))))))))

  (define (mul-terms L1 L2)
    (if (empty-termlist? L1)
        (the-empty-termlist)
        (add-terms (mul-term-by-all-terms (first-term L1) L2)
                   (mul-terms (rest-terms L1) L2))))

  (define (mul-term-by-all-terms t1 L)
    (if (empty-termlist? L)
        (the-empty-termlist)
        (let ((t2 (first-term L)))
          (adjoin-term
           (make-term (+ (order t1) (order t2))
                      (mul (coeff t1) (coeff t2)))
           (mul-term-by-all-terms t1 (rest-terms L))))))

       ;; interface to rest of the system
  (define (tag p) (attach-tag 'polynomial p))
  (put '=zero? '(polynomial)
       (lambda (x) (=zero?-polynominal x)))
  (put 'add '(polynomial polynomial)
       (lambda (p1 p2) (tag (add-poly p1 p2))))
  (put 'mul '(polynomial polynomial)
       (lambda (p1 p2) (tag (mul-poly p1 p2))))

  (put 'make 'polynomial
       (lambda (var terms) (tag (make-poly var terms))))
  'install-polynomial-package-done)