> On Nov 6, 2015, at 9:07 PM, dyrueta <[email protected]> wrote:
>
> Hi All --
>
> I'm hoping the answer to the question below will serve as an intro to macros,
> a subject I've been interested in for awhile but haven't had time to look
> into much. Here goes, fingers crossed:
>
> Given a list of constants (a0, a1… an) and a list of x-values (x0, x1,….xn),
> I want to design a function in Racket that produces an interpolating
> polynomial in Newton form, or p(x) = a0 + a1(x - x0) + a2(x - x0)(x - x1) +
> a3(x - x0)(x - x1) (x - x2) + ….+ an(x - x0)(x - x1)…(x - xn). My
> understanding of functions that produce functions is limited to what’s in
> HtDP, and this example (I think) goes beyond that (and hopefully into
> macros).
>
> Any tips or advice would be much appreciated!
Let’s assume I don’t know what you’re talking about. But we do know together
that HtDP requests examples for problems that you’re not quite familiar with.
So we work through 3 instances of this problem:
#lang racket
(require plot)
(define ((make-p-0 a0 a1) x0 x1)
(define (p x)
(+ a0
(* a1 (- x x0))))
p)
[plot (function ((make-p-0 1 2) 3 4)) #:x-min -10 #:x-max +10]
(define ((make-p-1 a0 a1 a2) x0 x1 x2)
(define (p x)
(+ a0
(* a1 (- x x0))
(* a2 (- x x0) (- x x1))))
p)
[plot (function ((make-p-1 1 2 3) 3 4 5)) #:x-min -10 #:x-max +10]
(define ((make-p-2 a0 a1 a2 a3) x0 x1 x2 x3)
(define (p x)
(+ a0
(* a1 (- x x0))
(* a2 (- x x0) (- x x1))
(* a3 (- x x0) (- x x1) (- x x2))))
p)
[plot (function ((make-p-2 1 2 3 4) 3 4 5 6)) #:x-min -10 #:x-max +10]
I threw in the plots for fun. Now I think one of two things is wrong:
— your description (making the a-sequence as long as the x-sequence)
— or my understanding of your description.
Correct me.
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