Implement 2.1

ex-2_01-xx.scm

@@ -0,0 +1,55 @@
+(load "util.scm")
+
+(define (add-rat x y)
+  (make-rat (+ (* (numer x) (denom y))
+               (* (numer y) (denom x)))
+            (* (denom x) (denom y))))
+(define (sub-rat x y)
+  (make-rat (- (* (numer x) (denom y))
+               (* (numer y) (denom x)))
+            (* (denom x) (denom y))))
+(define (mul-rat x y)
+  (make-rat (* (numer x) (numer y))
+            (* (denom x) (denom y))))
+(define (div-rat x y)
+  (make-rat (* (numer x) (denom y))
+            (* (denom x) (numer y))))
+(define (equal-rat? x y)
+  (= (* (numer x) (denom y))
+     (* (numer y) (denom x))))
+
+(define (make-rat n d)
+  (let ((g (gcd n d)))
+    (cons (/ n g) (/ d g))))
+(define (numer x) (car x))
+(define (denom x) (cdr x))
+
+(define (print-rat x)
+  (newline)
+  (display (numer x))
+  (display "/")
+  (display (denom x)))
+
+; Examples
+; (define one-half (make-rat 1 2))
+; (print-rat one-half)
+; (define one-third (make-rat 1 3))
+; (print-rat (add-rat one-half one-third))
+; (print-rat (mul-rat one-half one-third))
+; (print-rat (add-rat one-third one-third))
+
+(display "ex-2.1")
+
+(define (make-rat n d)
+  (let ((g (gcd n d)))
+    (if (< (* n d) 0)
+      (cons (- (abs (/ n g))) (abs (/ d g)))
+      (cons (abs (/ n g)) (abs (/ d g))))))
+
+(print-rat (make-rat 3 9))
+(print-rat (make-rat -3 9))
+(print-rat (make-rat 3 -9))
+(print-rat (make-rat -3 -9))
+
+(display "\n\nex-2.2")
+

util.scm

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+(define (assert a b)
+  (cond ((equal? a b) (display "[ok]"))
+    (else
+      (display "[error] ")
+      (display a)
+      (display " != ")
+      (display b)))
+  (newline))
+
+(define (gcd a b)
+  (if (= b 0) (abs a) (gcd b (remainder a b))))
+
+;(assert (gcd 93 15) 3)