From b8bb0df5850845ed9efc911ef891c4b916462fe6 Mon Sep 17 00:00:00 2001
From: Felix Martin <mail@felixm.de>
Date: Sun, 3 Jan 2021 07:59:39 -0500
Subject: [PATCH] Implement till 3.62

---
 ex-3_50-xx.scm => ex-3_50-62.scm | 75 ++++++++++++++++++++++++++++++++
 ex-3_63-xx.scm                   |  4 ++
 2 files changed, 79 insertions(+)
 rename ex-3_50-xx.scm => ex-3_50-62.scm (70%)
 create mode 100644 ex-3_63-xx.scm

diff --git a/ex-3_50-xx.scm b/ex-3_50-62.scm
similarity index 70%
rename from ex-3_50-xx.scm
rename to ex-3_50-62.scm
index 042f5da..0bbf4ae 100644
--- a/ex-3_50-xx.scm
+++ b/ex-3_50-62.scm
@@ -187,4 +187,79 @@
         '(1 2 3 4 5 6 8 9 10 12))
 
 (display "\nex-3.57\n")
+(display "[answered]\n")
+
+; With memoizing only one addition is required per number. So the complexity is
+; O(n). With memoizing the previous numbers have to be calculated recursively
+; which leads to exponential growth.
+
+(display "\nex-3.58 - expand\n")
+
+(define (expand num den radix)
+  (cons-stream
+   (quotient (* num radix) den)
+   (expand (remainder (* num radix) den) den radix)))
+
+(assert (take 5 (expand 1 7 10))
+        '(1 4 2 8 5))
+
+(assert (take 5 (expand 3 8 10))
+        '(3 7 5 0 0))
+
+; The procedure expands a fraction (num/dem) into the rational value to base
+; radix.
+
+(display "\nex-3.59 - sine/cosine series\n")
+
+(define (integrate-series xs)
+  (define (iter n xs)
+    (cons-stream (* (/ 1 n) (stream-car xs))
+                 (iter (+ n 1) (stream-cdr xs))))
+  (iter 1 xs))
+
+(define (integrate-series xs)
+  (stream-map * (stream-map / ones integers) xs))
+
+(assert (take 5 (integrate-series integers))
+        '(1 1 1 1 1))
+
+(define exp-series
+  (cons-stream 1 (integrate-series exp-series)))
+
+(define (sum xs)
+  (if (null? xs)
+    0
+    (+ (car xs) (sum (cdr xs)))))
+
+(assert (sum (take 5 exp-series))
+        (/ 65 24))
+
+(define cosine-series
+  (cons-stream 1 (stream-map - (integrate-series sine-series))))
+
+(define sine-series
+  (cons-stream 0 (integrate-series cosine-series)))
+
+(assert (sum (take 10 sine-series))
+        (/ 305353 362880))
+
+(display "\nex-3.60 - mul-series\n")
+
+(define add-series add-streams)
+
+(define (mul-series s1 s2)
+  (cons-stream (* (stream-car s1) (stream-car s2))
+               (add-streams (scale-stream (stream-cdr s2) (stream-car s1))
+                            (mul-series (stream-cdr s1) s2)))))
+
+(assert (sum (take 10 (add-series (mul-series cosine-series cosine-series)
+                                  (mul-series sine-series sine-series))))
+        1)
+
+(display "\nex-3.61 - invert-unit-series\n")
+
+(define (invert-unit-series s) 0)
+
+
+(display "\nex-3.62\n")
 
diff --git a/ex-3_63-xx.scm b/ex-3_63-xx.scm
new file mode 100644
index 0000000..a5aa85c
--- /dev/null
+++ b/ex-3_63-xx.scm
@@ -0,0 +1,4 @@
+(load "util.scm")
+
+(display "\nex-3.63\n")
+