cookbook

Farey-Cauchy sequence in Lisp

A short and simple algorithm in Common Lisp for the Farey-Cauchy sequence. Among other things (reformulating the Riemann hypothesis, etc), it helps with the "Ford's touching circles" problem.

(defun farey-cauchy (n)
(let ((a 0) (b 1) (c 1) (d n) k f e)
(format t "~a/~a " a b)
(loop while (< c n) do
(setq k (floor (/ (+ n b) d))
e (- (* k c) a)
f (- (* k d) b)
a c
b d
c e
d f)
(format t "~a/~a " a b))))

CL-USER> (farey-cauchy 7)

The Ackermann Function in LISP

The Ackermann function is a killer: It looks very simple, yet it plays a major
role in computer science and computational complexity theory. This is its
definition.


(Source and copyright: kosara.net/thoughts/ackermann.html)

Slurping a file in Common Lisp

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