Yes, I can see at least two significant errors in my description. The first is in the sequence definitions. They should be
list of constants (a0, a1… an) and a list of x-values (x0, x1,….x(n-1)) Similarly, the def of p(x) should read p(x) = a0 + a1(x - x0) + a2(x - x0)(x - x1) + a3(x - x0)(x - x1) (x - x2) + ….+ an(x - x0)(x - x1)…(x - x(n-1)), not 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). Thank you for correcting me! Here are some examples: Data Defs: x is a real number lox is (listof x) ;;NewtonPx : (lox lox -> (x -> x) ;; accepts two list of numbers, returns a function equivalent to the interpolating polynomial in Netwton form that accepts a number and returns a number (define (NewtonPx lox loa) ….) Ex #1 (define lox1 ‘(1 2)) (define loa1 (4 5 6)) (NewtonPx lox1 loa1) -> (lambda (x) (+ 4 (* 5(- x 1)) (* 6 (- x 1) (- x 2)))) and ( (NewtonPx lox1 loa1) 2) -> 9 Ex. #2 (define lox2 '(4 2 7)) (define loa2 ‘(9 8 6 3)) (NewtonPx lox1 loa1) -> (lambda (x) (+ 9 (* 8 (- x 4)) (* 6 (- x 4) (- x 2)) (* 3 (- x 4) (- x 2) (- x 7)))) and ( (NewtonPx lox2 loa2) 2) -> -7 I realize now that the function I’m after doesn’t require anything as fancy as macros — judicious use of loops should do. Still, I’m wondering if there is a macro-based solution that I can use to study as an entry point to this subject. Cheers, DY > On Nov 6, 2015, at 6:43 PM, Matthias Felleisen <[email protected]> wrote: > > >> 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. -- You received this message because you are subscribed to the Google Groups "Racket Users" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
