Implement till 2.87

ex-2_77-97.scm

@@ -543,8 +543,130 @@
 (display (add cr cr)) (newline)
 (display (mul cr cr)) (newline)
 
-(display "\n\nexample - symbolic algebra\n")
+(display "\nexample - symbolic algebra\n")
 
-(display "\nex-2.87\n")
+(define (install-polynomial-package)
+  ;; internal procedures
+  ;; representation of poly
+  (define (make-poly variable term-list)
+    (cons variable term-list))
+  (define (variable p) (car p))
+  (define (term-list p) (cdr p))
+
+  ;; procedures same-variable? and variable? from section 2.3.2
+  (define (variable? x) (symbol? x))
+  (define (=number? exp num)
+    (and (number? exp) (= exp num)))
+  (define (same-variable? v1 v2)
+    (and (variable? v1) (variable? v2) (eq? v1 v2)))
+
+  ;; representation of terms and term lists
+  (define (adjoin-term term term-list)
+    (if (=zero? (coeff term))
+        term-list
+        (cons term term-list)))
+  (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 (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 (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-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))))))
+
+  (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 (=zero?-poly p)
+    (define (=zero?-terms terms)
+      (cond
+        ((empty-termlist? terms) #t)
+        ((not (=zero? (coeff (first-term terms)))) #f)
+        (else (=zero?-terms (rest-terms terms)))))
+    (=zero?-terms (term-list p)))
+
+  ;; interface to rest of the system
+  (define (tag p) (attach-tag 'polynomial p))
+  (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 '=zero? '(polynomial) =zero?-poly)
+  (put 'make 'polynomial
+       (lambda (var terms) (tag (make-poly var terms))))
+  (display "[install-polynomial-package]\n")
+  'done)
+
+(install-polynomial-package)
+
+(define (make-poly var terms)
+  ((get 'make 'polynomial) var terms))
+
+(define p (make-poly 'x '((100 2) (1 2))))
+;(display p)
+(assert (mul p p)
+        (make-poly 'x '((200 4) (101 8) (2 4))))
+
+
+(display "\nex-2.87 - =zero?\n")
+
+(assert (=zero? p) #f)
+(assert #t
+        (=zero? (make-poly 'x (list
+                        (list 10 (make-rational 0 10))
+                        (list 5 (make-complex-from-real-imag 0 0))
+                        (list 1 0)))))
+
+(define px p)
+(define py (make-poly 'y (list (list 3 px))))
+(display (add py py))
+(newline)
+
+(display "\nex-2.88 - sub\n")