Add implementation of dense representation of polynomials (2.90)

2_78.rkt

@@ -681,7 +681,43 @@
 ;; It isn't possible to coerce from one to the other, so a mixed-type operator is needed, and this
 ;; approach would fail.
 
-
-
+(define (highest-order-term term-list)
+  (length term-list))
+
+(define (make-term order coeff) (list order coeff))
+(define (order term) (car term))
+(define (coeff term) (cadr term))
+(define first-term car)
+(define (rest-terms term-list)
+  (if (pair? term-list)
+      (cdr term-list)
+      the-empty-termlist))
+(define (make-termlist coeffs)
+  (cond ((null? coeffs) '())
+        ((= 0 (car coeffs))
+         (make-termlist (cdr coeffs)))
+        (else (cons (car coeffs)
+                    (make-termlist (cdr coeffs))))))
+(define the-empty-termlist '())
+(define empty-termlist? null?)
+
+(define (adjoin-term-dense term term-list)
+  (let ((term-list-order (highest-order-term term-list)))
+    (cond ((and (= (order term) 1)
+                (= term-list-order 0))
+           (make-termlist (list (coeff term))))
+          ((= (order term) term-list-order)
+           (make-termlist
+            (cons (add (coeff term)
+                       (first-term term-list))
+                  (rest-terms term-list))))
+          ((> (order term) term-list-order)
+           (make-termlist
+            (cons (coeff term)
+                  (adjoin-term-dense
+                   (make-term (- (order term) 1) 0)
+                   term-list))))
+          (else (adjoin-term-dense term (rest-terms term-list))))))
+