增加练习2-87.

Author: ramsayleung

chapter2/exercise2-87.rkt

@@ -0,0 +1,11 @@
+#lang racket
+(require "poly.rkt")
+;;; 练习2-87
+(define (=zero-poly? poly)
+  (define (all-coeff-zero? term-list)
+    (if (empty-termlist? term-list)
+        #t
+        (and (=zero? (coeff (first-term term-list)))
+             (all-coeff-zero? (rest-terms term-list)))))
+  (all-coeff-zero? (term-list poly)))
+

chapter2/poly.rkt

@@ -6,17 +6,17 @@
 (define (same-variable? v1 v2)
   (and (variable? v1) (variable? v2) (eq? v1 v2)))
 
+(define (variable p) (car p))
+
+(define (term-list p) (cdr p))
+
 (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))
-
   (define (add-poly p1 p2)
     (if (same-variable? (variable p1) (variable p2))
         (make-poly (variable p1)
@@ -41,3 +41,65 @@
   (put 'make 'polynomial (lambda (var terms) (tag (make-poly var terms))))
 
   'done)
+
+(define (empty-termlist? term-list)
+  (null? term-list))
+
+(define (first-term term-list)
+  (car term-list))
+
+(define (=zero? term)
+  (or (empty-termlist? term)
+      (= (coeff term) 0)))
+
+(define (adjoin-term term term-list)
+  (if (=zero? (coeff term))
+      term-list
+      (cons term term-list)))
+
+(define (rest-terms term-list)
+  (cdr term-list))
+
+(define (make-term order coeff) (list order coeff))
+
+(define (order term) (car term))
+
+(define (coeff term) (cadr term))
+
+(define (the-empty-termlist)
+  '())
+
+(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 (adjoin-term (rest-terms t1) t2)))
+                 ((< (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))))))
+
+(provide empty-termlist? =zero? first-term rest-terms coeff term-list)