SICP Workout (1.40) Resolution summary

SICP workout 1.40 is a casual job very easy, but it looks very complex, single problem.

The topic of the original question is as follows:

Define a procedure cubic, which is used with the Newtons-method process in the following form of expression:

(Newtons-method (cubic a b c) 1)

Can force three of times into the equation.

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of 0 points.

The problem is very easy, asked us to do a cubic process, but it involves Newtons-method and three of the equation 0 points, assuming only to see the topic of the words really do not know where to start.

To finish this problem, we have to go back to the book to Newtons-method once again, the book's newtons-method definition such as the following:

(Define (Newtons-method g guess)  (Fixed-point (Newton-transform g) guess))

In fact, it is to seek the fixed point of newton-transform.

So what is this newton-transform, Newton's transformation?

The Newton-transform definitions in the book are as follows:

(Define (Newton-transform g)  (Lambda (x)    (-X (/(g x) ((Deriv g) x))))

Its function is to derive f (x) so that f (x) such as the following:

f (x) = X-g (x)/Dg (x)

As described in the book 1.3.4 describes the description of Newton's Law:

Assuming that x-> g (x) is a micro function, then a solution of the equation g (x) =0 is a fixed point of the function x->f (x). Middle F (x) = X-g (x)/Dg (x)

Well, back to our topic, we have a function

G (x) =

We're going to push into the 0 point of the function g (x), which is to ask for a solution of the G (x) =0.

As described above, we request (Newtons-method <g (x) > 1). Note that this is not a valid scheme statement.

The g (x) Here is the return value of the cubic process we are going to do.

The problem is very easy here, just to use the cubic process to generate a lambda process that represents a three-second equation, cubic process definitions such as the following:

(Define (cubic a B c)   (Lambda (x)    (+ (* x x x) (* a x x) (* b x) c))

Is the result a little bit unexpectedly simple?

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SICP Workout (1.40) Resolution summary