本节主要讲述无穷流。
3.53，显然
3.54，定义阶乘组成的无穷序列：
3.55解答，比较有趣，也是不难的题目，列出来找出规律就成了，就是将(stream-car s)加到生成的序列中的每个元素上，通过stream-map，最后的结果就是每个元素都是前n个元素累积的结果，我的解答：
3.56，有了merge就好办了，根据条件合并起3种情况来就好：
3.57,略过
3.58，观察到，num每次都与radix相乘并且radix保持不变，那么radix可以认为是一个基数，den也保持不变作为除数，那么这个序列就是以radix为基数对den求整数商的序列，不明白num为什么每次要变换成余数？这个序列有啥特别的用途呢？未解。
a)只要将序列通过前面定义的mul-streams与整数的倒数序列相乘：
b)照着定义来了，cons的级数注意使用scale-stream乘以-1：
3.64解答：
习题3.65：
3.53，显然
(define s (cons
-
stream
1
(add
-
stream s s)))
定义是2的n次方组成的无穷数列，2,4,8,16,32...
3.54，定义阶乘组成的无穷序列：
(define (mul
-
streams s1 s2)
(stream - map * s1 s2))
(define factorials (cons - stream 1 (mul - streams factorials (stream - cdr integers))))
(stream - map * s1 s2))
(define factorials (cons - stream 1 (mul - streams factorials (stream - cdr integers))))
3.55解答，比较有趣，也是不难的题目，列出来找出规律就成了，就是将(stream-car s)加到生成的序列中的每个元素上，通过stream-map，最后的结果就是每个元素都是前n个元素累积的结果，我的解答：
(define (partial
-
sums s)
(cons - stream (stream - car s) (stream - map ( lambda (x) ( + x (stream - car s))) (partial - sums (stream - cdr s)))))
(cons - stream (stream - car s) (stream - map ( lambda (x) ( + x (stream - car s))) (partial - sums (stream - cdr s)))))
3.56，有了merge就好办了，根据条件合并起3种情况来就好：
(define S (cons
-
stream
1
(merge (scale
-
stream s
2
) (merge (scale
-
stream s
3
) (scale
-
stream s
5
)))))
3.57,略过
3.58，观察到，num每次都与radix相乘并且radix保持不变，那么radix可以认为是一个基数，den也保持不变作为除数，那么这个序列就是以radix为基数对den求整数商的序列，不明白num为什么每次要变换成余数？这个序列有啥特别的用途呢？未解。
(expand 1 7 10)3.59解答：
=> 1 4 2 8 5 7 1 4 2 8
(expand 3 8 10)
=> 3 7 5 0 0 0 0 0 0 0
a)只要将序列通过前面定义的mul-streams与整数的倒数序列相乘：
(define (integrate
-
series s)
(mul - streams (stream - map ( lambda (x) ( / 1 x)) integers) s))
(mul - streams (stream - map ( lambda (x) ( / 1 x)) integers) s))
b)照着定义来了，cons的级数注意使用scale-stream乘以-1：
(define sine
-
series
(cons - stream 0 (integrate - series cosine - series)))
(define cosine - series
(cons - stream 1
(scale - stream
(integrate - series sine - series)
- 1 )))
(cons - stream 0 (integrate - series cosine - series)))
(define cosine - series
(cons - stream 1
(scale - stream
(integrate - series sine - series)
- 1 )))
3.64解答：
(define (stream
-
limit s tolerance)
(define (stream - limit - iter stream current)
(cond (( or (stream - null? stream) (null? (stream - car stream))) # f)
( else
(let ((next (stream - car stream)))
( if ( < (abs ( - next current)) tolerance)
next
(stream - limit - iter (stream - cdr stream) next))))))
(stream - limit - iter (stream - cdr s) (stream - car s)))
(define (stream - limit - iter stream current)
(cond (( or (stream - null? stream) (null? (stream - car stream))) # f)
( else
(let ((next (stream - car stream)))
( if ( < (abs ( - next current)) tolerance)
next
(stream - limit - iter (stream - cdr stream) next))))))
(stream - limit - iter (stream - cdr s) (stream - car s)))
习题3.65：
(define (ln
-
summands n)
(cons - stream ( / 1.0 n)
(stream - map - (ln - summands ( + n 1 )))))
(define ln - stream (partial - sums (ln - summands 1 )))
(define ln - stream2 (euler - transform ln - stream))
(define ln - stream3 (accelerated - sequence euler - transform ln - stream))
(cons - stream ( / 1.0 n)
(stream - map - (ln - summands ( + n 1 )))))
(define ln - stream (partial - sums (ln - summands 1 )))
(define ln - stream2 (euler - transform ln - stream))
(define ln - stream3 (accelerated - sequence euler - transform ln - stream))
经过欧拉变换加速过的级数收敛的很快，测测就知道
文章转自庄周梦蝶 ，原文发布时间2008-05-13
