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Formal power series: Difference between revisions
→{{header|Racket}}
m (→{{header|Perl 6}}: Make FPS a role.) |
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Line 1,455:
[1, Fraction(0, 1), Fraction(-1, 2), Fraction(0, 1), Fraction(1, 24), Fraction(0, 1), Fraction(-1, 720), Fraction(0, 1), Fraction(1, 40320), Fraction(0, 1)]
</pre>
=={{header|Racket}}==
Using '''Lasy Racket''':
<lang racket>
#lang lazy
(require racket/match)
;; element-wise addition and subtraction
(define (<+> s1 s2) (map + s1 s2))
(define (<-> s1 s2) (map - s1 s2))
;; element-wise scaling
(define (scale a s) (map (λ (x) (* a x)) s))
;; series multiplication
(define (<*> fs gs)
(match-let ([(cons f ft) (! fs)]
[(cons g gt) (! gs)])
(cons (* f g) (<+> (scale f gt) (<*> ft gs)))))
;; series division
(define (</> fs gs)
(match-letrec ([(cons f ft) (! fs)]
[(cons g gt) (! gs)]
[qs (cons (/ f g) (scale (/ g) (<-> ft (<*> qs gt))))])
qs))
;; integration and differentiation
(define (int f) (map / f (enum 1)))
(define (diff f) (map * (cdr f) (enum 1)))
;; series of natural numbers greater then n
(define (enum n) (cons n (enum (+ 1 n ))))
</lang>
Examples:
<lang racket>
(define <sin> (cons 0 (int <cos>)))
(define <cos> (cons 1 (scale -1 (int <sin>))))
-> (!! (take 10 <sin>))
'(0 1 0 -1/6 0 1/120 0 -1/5040 0 1/362880)
-> (!! (take 10 <cos>))
'(1 0 -1/2 0 1/24 0 -1/720 0 1/40320 0)
-> (!! (take 10 (diff <sin>)))
'(1 0 -1/2 0 1/24 0 -1/720 0 1/40320 0)
; sin(x)² + cos(x)² = 1
-> (!! (take 10 (<+> (<*> <cos> <cos>) (<*> <sin> <sin>))))
'(1 0 0 0 0 0 0 0 0 0)
; series of (tan x)
-> (!! (take 10 (</> <sin> <cos>)))
'(0 1 0 1/3 0 2/15 0 17/315 0 62/2835)
</lang>
=={{header|Scheme}}==
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