Invert-unit-series procedure
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 + SR
where
SR
is the part of
S
after the constant term. Then we can solve for
X
as follows:
In other words,
X
is the power series whose constant term is
1
and whose higher-order terms are given by the negative of
SR
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