How to resolve the algorithm Farey sequence step by step in the Racket programming language

Published on 12 May 2024 09:40 PM
#Racket

How to resolve the algorithm Farey sequence step by step in the Racket programming language

Table of Contents

Problem Statement

The   Farey sequence   Fn   of order   n   is the sequence of completely reduced fractions between   0   and   1   which, when in lowest terms, have denominators less than or equal to   n,   arranged in order of increasing size. The   Farey sequence   is sometimes incorrectly called a   Farey series.

Each Farey sequence:

The Farey sequences of orders   1   to   5   are:

The length   (the number of fractions)   of a Farey sequence asymptotically approaches:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Farey sequence step by step in the Racket programming language

Source code in the racket programming language

#lang racket
(require math/number-theory)
(define (display-farey-sequence order show-fractions?)
  (define f-s (farey-sequence order))
  (printf "-- Farey Sequence for order ~a has ~a fractions~%" order (length f-s))
  ;; racket will simplify 0/1 and 1/1 to 0 and 1 respectively, so deconstruct into numerator and
  ;; denomimator (and take the opportunity to insert commas
  (when show-fractions?
    (displayln
     (string-join
      (for/list ((f f-s))
        (format "~a/~a" (numerator f) (denominator f)))
      ", "))))

; compute and show the Farey sequence for order:
;  1   through   11   (inclusive).
(for ((order (in-range 1 (add1 11)))) (display-farey-sequence order #t))
; compute and display the number of fractions in the Farey sequence for order:
;  100   through   1,000   (inclusive)   by hundreds. 
(for ((order (in-range 100 (add1 1000) 100))) (display-farey-sequence order #f))

You may also check:How to resolve the algorithm Pythagoras tree step by step in the Nim programming language
You may also check:How to resolve the algorithm Fibonacci word/fractal step by step in the Phix programming language
You may also check:How to resolve the algorithm Day of the week step by step in the bc programming language
You may also check:How to resolve the algorithm Date format step by step in the R programming language
You may also check:How to resolve the algorithm Time a function step by step in the BaCon programming language