Implement 2.91 division

ex-2_77-97.scm

@@ -609,13 +609,17 @@
         (error "Polys not in same var -- ADD-POLY"
                (list p1 p2))))
 
+  (define (negate-term term)
+    (make-term (order term) (negate (coeff term))))
+
+  (define (negate-terms terms)
+    (map negate-term terms))
+
   (define (sub-poly p1 p2)
-    (define (negate-term term)
-      (make-term (order term) (negate (coeff term))))
     (if (same-variable? (variable p1) (variable p2))
         (make-poly (variable p1)
                    (add-terms (term-list p1)
-                              (map negate-term (term-list p2))))
+                              (negate-terms (term-list p2))))
         (error "Polys not in same var -- ADD-POLY"
                (list p1 p2))))
 
@@ -778,7 +782,8 @@
       (attach-tag term-type (cdr terms))))
 
   (define (empty-termlist? term-list) (null? (contents term-list)))
-  (define (make-term order coeff) (list order coeff))
+  (define (make-term order coeff)
+    (list order coeff))
   (define (order term) (car term))
   (define (coeff term) (cadr term))
 
@@ -843,53 +848,48 @@
 
   (define (div-poly p1 p2)
     (if (same-variable? (variable p1) (variable p2))
-        (make-poly (variable p1)
-                   (div-terms (term-list p1)
-                              (term-list p2)))
+      (let ((result (div-terms (term-list p1) (term-list p2)))
+            (var (variable p1)))
+        (list
+          (tag (make-poly var (car result)))
+          (tag (make-poly var (cadr result)))))
         (error "Polys not in same var -- MUL-POLY"
                (list p1 p2))))
 
-; Division can be performed via long division. That is, divide the highest-order
-; term of the dividend by the highest-order term of the divisor. The result is
-; the first term of the quotient. Next, multiply the result by the divisor,
-; subtract that from the dividend, and produce the rest of the answer by
-; recursively dividing the difference by the divisor. Stop when the order of the
-; divisor exceeds the order of the dividend and declare the dividend to be the
-; remainder. Also, if the dividend ever becomes zero, return zero as both
-; quotient and remainder.
-;
-; We can design a div-poly procedure on the model of add-poly and mul-poly. The
-; procedure checks to see if the two polys have the same variable. If so,
-; div-poly strips off the variable and passes the problem to div-terms, which
-; performs the division operation on term lists. Div-poly finally reattaches the
-; variable to the result supplied by div-terms. It is convenient to design
-; div-terms to compute both the quotient and the remainder of a division.
-; Div-terms can take two term lists as arguments and return a list of the
-; quotient term list and the remainder term list.
-;
-; dividend
-; --------
-; divisor
-;
-; Complete the following definition of div-terms by filling in the missing
-; expressions. Use this to implement div-poly, which takes two polys as arguments
-; and returns a list of the quotient and remainder polys.
-
+  ; Division can be performed via long division. That is, divide the
+  ; highest-order term of the dividend by the highest-order term of the
+  ; divisor. The result is the first term of the quotient. Next, multiply the
+  ; result by the divisor, subtract that from the dividend, and produce the
+  ; rest of the answer by recursively dividing the difference by the divisor.
+  ; Stop when the order of the divisor exceeds the order of the dividend and
+  ; declare the dividend to be the remainder. Also, if the dividend ever
+  ; becomes zero, return zero as both quotient and remainder.
   (define (div-terms L1 L2)
+    (define (negate-term t)
+      (make-term (order t) (negate (coeff t))))
+    (define (negate-terms terms)
+      (let ((term-type (type-tag terms))
+            (term-list (contents terms)))
+        (cons term-type (map negate-term term-list))))
     (if (empty-termlist? L1)
         (list L1 L2)
-        (let ((t1 (first-term L1))
-              (t2 (first-term L2)))
+        (let ((t1 (first-term L1)) ; dividend
+              (t2 (first-term L2))) ; divisor
          (if (> (order t2) (order t1))
              (list (empty-termlist L2) L1)
              (let ((new-c (div (coeff t1) (coeff t2)))
                    (new-o (- (order t1) (order t2)))
                    (new-term (make-term (- (order t1) (order t2))
                                         (div (coeff t1) (coeff t2)))))
-               ; XXX: continue here
-               (let ((rest-of-result (div-terms (empty-termlist L1) L2)))
-                 (list (adjoin-term new-term (car rest-of-result))
-                       (cadr rest-of-result))))))))
+               (let ((new-dividend (add-terms
+                                     L1
+                                     (negate-terms
+                                       (mul-terms
+                                         (adjoin-term new-term (empty-termlist L1))
+                                         L2)))))
+                 (let ((rest-of-result (div-terms new-dividend L2)))
+                   (list (adjoin-term new-term (car rest-of-result))
+                         (cadr rest-of-result)))))))))
 
   (define (=zero?-poly p)
     (define (=zero?-terms terms)
@@ -953,10 +953,10 @@
 (define p2 (make-poly-dense 'x '((2 1) (0 -1))))
 (assert (mul p1 p1) (make-poly-dense 'x '((10 1) (5 -2) (0 1))))
 (assert (mul p1 p2) (make-poly-dense 'x '((7 1) (5 -1) (2 -1) (0 1))))
-(display p1) (newline)
-(display p2) (newline)
-(display (div p1 p2)) (newline)
+(let ((result (div p1 p2)))
+  (assert (car result) (make-poly-dense 'x '((3 1) (1 1))))
+  (assert (cadr result) (make-poly-dense 'x '((1 1) (0 -1)))))
+
 
 (display "\nex-2.92\n")
 
-;(display "\nex-2.93\n")