Exercise 1.25 · 习题

Exercise 1.25: Alyssa P. Hacker complains that
we went to a lot of extra work in writing expmod. After all, she says,
since we already know how to compute exponentials, we could have simply written

(define (expmod base exp m)
(remainder (fast-expt base exp) m))

Is she correct? Would this procedure serve as well for our fast prime tester?

Explain.

练习 1.25：Alyssa P. Hacker 抱怨说，我们在编写 expmod 时做了很多多余的工作。她说，既然我们已经知道如何计算乘幂，完全可以直接写成

(define (expmod base exp m)
(remainder (fast-expt base exp) m))

她说得对吗？这个过程在我们的快速素性检验中同样适用吗？请解释。