Complete up to 2.86

We now have complex numbers with arbitrary number coefficients (ie
integer, rational or real).

2_78.rkt

@@ -1,9 +1,6 @@
 #lang sicp
 
 
-;;;from chapter 1
-(define (square x) (* x x))
-
 ;;;from section 1.2.5, for Section 2.1.1
 (define (gcd a b)
   (if (= b 0)
@@ -153,15 +150,28 @@
 (define (install-integer-package)
   (define (tag x)
     (attach-tag 'integer x))
+  (define (raise-int x)
+    (make-rational x 1))
  
   (put 'add '(integer integer)
        (lambda (x y)
          (make-integer (+ x y))))
+  (put 'mul '(integer integer)
+       (lambda (x y)
+         (make-integer (* x y))))
+  (put 'sine '(integer)
+       (lambda (x) (sine (raise-int x))))
+  (put 'cosine '(integer)
+       (lambda (x) (cosine (raise-int x))))
+  (put 'square-root '(integer)
+       (lambda (x) (square-root (raise-int x))))
+  (put 'arctan '(integer integer)
+       (lambda (x y) (arctan (raise-int x)
+                             (raise-int y))))
   (put 'equ? '(integer integer)
        (lambda (x y)
          (= x y)))
-  (put 'raise '(integer)
-       (lambda (x) (make-rational x 1)))
+  (put 'raise '(integer) raise-int)
   (put 'project '(integer)
        (lambda (x) '()))
   (put 'make 'integer
@@ -177,6 +187,17 @@
   (put 'add '(real real)
        (lambda (x y)
          (make-real (+ x y))))
+  (put 'mul '(real real)
+       (lambda (x y)
+         (make-real (* x y))))
+  (put 'sine '(real)
+       (lambda (x) (make-real (sin x))))
+  (put 'cosine '(real)
+       (lambda (x) (make-real (cos x))))
+  (put 'square-root '(real)
+       (lambda (x) (make-real (sqrt x))))
+  (put 'arctan '(real real)
+       (lambda (x y) (make-real (atan x y))))
   (put 'equ? '(real real)
        (lambda (x y)
          (= x y)))
@@ -216,6 +237,8 @@
   (define (eq-rat x y)
     (and (= (numer x) (numer y))
          (= (denom x) (denom y))))
+  (define (raise-rat x)
+    (make-real (/ (numer x) (denom x))))
   ;; interface to rest of the system
   (define (tag x) (attach-tag 'rational x))
   (put 'add '(rational rational)
@@ -228,12 +251,19 @@
        (lambda (x y) (tag (mul-rat x y))))
   (put 'div '(rational rational)
        (lambda (x y) (tag (div-rat x y))))
+  (put 'sine '(rational)
+       (lambda (x) (sine (raise-rat x))))
+  (put 'cosine '(rational)
+       (lambda (x) (cosine (raise-rat x))))
+  (put 'square-root '(rational)
+       (lambda (x) (square-root (raise-rat x))))
+  (put 'arctan '(rational rational)
+       (lambda (x y) (arctan (raise-rat x)
+                             (raise-rat y))))
   (put 'equ? '(rational rational) eq-rat)
   (put '=zero? '(rational)
        (lambda (x) (= (numer x) 0)))
-  (put 'raise '(rational)
-       (lambda (x)
-         (make-real (/ (numer x) (denom x)))))
+  (put 'raise '(rational) raise-rat)
   (put 'project '(rational)
        (lambda (x)
          (make-integer
@@ -254,12 +284,13 @@
   (define (imag-part z) (cdr z))
   (define (make-from-real-imag x y) (cons x y))
   (define (magnitude z)
-    (sqrt (+ (square (real-part z))
-             (square (imag-part z)))))
+    (square-root (add (square (real-part z))
+                      (square (imag-part z)))))
   (define (angle z)
-    (atan (imag-part z) (real-part z)))
+    (arctan (imag-part z) (real-part z)))
   (define (make-from-mag-ang r a) 
-    (cons (* r (cos a)) (* r (sin a))))
+    (cons (mul r (cosine a))
+          (mul r (sine a))))
 
   ;; interface to the rest of the system
   (define (tag x) (attach-tag 'rectangular x))
@@ -279,12 +310,12 @@
   (define (angle z) (cdr z))
   (define (make-from-mag-ang r a) (cons r a))
   (define (real-part z)
-    (* (magnitude z) (cos (angle z))))
+    (mul (magnitude z) (cosine (angle z))))
   (define (imag-part z)
-    (* (magnitude z) (sin (angle z))))
+    (mul (magnitude z) (sine (angle z))))
   (define (make-from-real-imag x y) 
-    (cons (sqrt (+ (square x) (square y)))
-          (atan y x)))
+    (cons (square-root (add (square x) (square y)))
+          (arctan y x)))
 
   ;; interface to the rest of the system
   (define (tag x) (attach-tag 'polar x))
@@ -386,6 +417,11 @@
 (define (sub x y) (apply-generic 'sub x y))
 (define (mul x y) (apply-generic 'mul x y))
 (define (div x y) (apply-generic 'div x y))
+(define (sine x) (apply-generic 'sine x))
+(define (cosine x) (apply-generic 'cosine x))
+(define (square-root x) (apply-generic 'square-root x))
+(define (arctan x y) (apply-generic 'arctan x y))
+(define (square x) (mul x x))
 
 (define (equ? x y) (apply-generic 'equ? x y))
 ;;(put 'equ? '(complex complex) equ?)