96d1400654
* bernoulli -> bernoulli-number * farey -> farey-sequence * fibonacci/mod -> modular-fibonacci * order -> unit-group-order * orders -> unit-group-orders Documented `make-fibonacci' and `make-modular-fibonacci' Reworked text about loading external libraries in docs for `math/bigfloat' Removed type aliases like Z, Q, Prime (I like them, but TR was printing them in unexpected places like array return types)
23 lines
764 B
Racket
23 lines
764 B
Racket
#lang typed/racket/base
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(require "types.rkt")
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(provide farey-sequence mediant)
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(: mediant : Exact-Rational Exact-Rational -> Exact-Rational)
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(define (mediant x y)
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(/ (+ (numerator x) (numerator y))
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(+ (denominator x) (denominator y))))
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(: farey-sequence : Integer -> (Listof Exact-Rational))
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(define (farey-sequence n)
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(cond [(n . <= . 0) (raise-argument-error 'farey-sequence "Positive-Integer" n)]
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[else
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(let loop ([a 1] [b 1] [c (sub1 n)] [d n] [#{fs : (Listof Exact-Rational)} '()])
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(let ([fs (cons (/ a b) fs)])
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(cond [(positive? a)
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(define k (quotient (+ n b) d))
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(loop c d (- (* k c) a) (- (* k d) b) fs)]
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[else
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fs])))]))
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