Exercise 3.61: Let S be a power series
(Exercise 3.59) whose constant term is 1. Suppose we want to find the
power series 1
/
S, that is, the series X such that S
X
=
1.
Write S
=
1
+
S
R where S
R is the part of S after the
constant term. Then we can solve for X as follows:
S
⋅
X
=
1
,
(
1
+
S
R
)
⋅
X
=
1
,
X
+
S
R
⋅
X
=
1
,
X
=
1
−
S
R
⋅
X
.
In other words, X is the power series whose constant term is 1 and whose
higher-order terms are given by the negative of S
R times X. Use
this idea to write a procedure invert-unit-series that computes 1
/
S
for a power series S with constant term 1. You will need to use
mul-series from Exercise 3.60.
练习 3.61：设 S 是一个常数项为 1 的幂级数（练习 3.59）。假设我们想求幂级数 1/S，即满足 S·X = 1 的级数 X。写 S = 1 + Sᴿ，其中 Sᴿ 是 S 去掉常数项后的部分。则可按如下方式求解 X：S·X = 1，(1 + Sᴿ)·X = 1，X + Sᴿ·X = 1，X = 1 − Sᴿ·X。换言之，X 是常数项为 1、高次项由 −Sᴿ 乘以 X 给出的幂级数。利用这一思路，写一个过程 invert-unit-series，它对常数项为 1 的幂级数 S 计算 1/S。你需要用到练习 3.60 中的 mul-series。