Arithmetic/Rational: Difference between revisions

=={{header|Ol}}==

Otus Lisp has rational numbers built-in and integrated with all other number types.

<lang scheme>

(define x 3/7)

(define y 9/11)

(define z -2/5)

; demonstrate builtin functions:

(print "(abs " z ") = " (abs z))

(print "- " z " = " (- z))

(print x " + " y " = " (+ x y))

(print x " - " y " = " (- x y))

(print x " * " y " = " (* x y))

(print x " / " y " = " (/ x y))

(print x " < " y " = " (< x y))

(print x " > " y " = " (> x y))

; introduce new functions:

(define (+:= x) (+ x 1))

(define (-:= x) (- x 1))

(print "+:= " z " = " (+:= z))

(print "-:= " z " = " (-:= z))

; finally, find all perfect numbers less than 2^15:

(lfor-each (lambda (candidate)

(let ((sum (lfold (lambda (sum factor)

(if (= 0 (modulo candidate factor))

(+ sum (/ 1 factor) (/ factor candidate))

sum))

(/ 1 candidate)

(liota 2 1 (+ (isqrt candidate) 1)))))

(if (= 1 (denominator sum))

(print candidate (if (eq? sum 1) ", perfect" "")))))

(liota 2 1 (expt 2 15)))

</lang>

{{Out}}

<pre>

(abs -2/5) = 2/5

- -2/5 = 2/5

3/7 + 9/11 = 96/77

3/7 - 9/11 = -30/77

3/7 * 9/11 = 27/77

3/7 / 9/11 = 11/21

3/7 < 9/11 = #true

3/7 > 9/11 = #false

+:= -2/5 = 3/5

-:= -2/5 = -7/5

6, perfect

28, perfect

120

496, perfect

672

8128, perfect

30240

32760

</pre>