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;;; series.el --- Hosting common series of numbers -*- lexical-binding: t -*-
;; Author: William Carroll <wpcarro@gmail.com>
;;; Commentary:
;; Encoding number series as I learn about them.
;;
;; These are the following series I'm interested in supporting:
;; - Fibonacci
;; - Catalan numbers
;; - Figurate number series
;; - Triangular
;; - Square
;; - Pentagonal
;; - Hexagonal
;; - Lazy-caterer
;; - Magic square
;; - Look-and-say
;;; Code:
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Dependencies
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(require 'number)
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Library
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(defun series/range (beg end)
"Create a list of numbers from `BEG' to `END'.
This is an inclusive number range."
(if (< end beg)
(list/reverse
(number-sequence end beg))
(number-sequence beg end)))
(defun series/fibonacci-number (i)
"Return the number in the fibonacci series at `I'."
(cond
((= 0 i) 0)
((= 1 i) 1)
(t (+ (series/fibonacci-number (- i 1))
(series/fibonacci-number (- i 2))))))
(defun series/fibonacci (n)
"Return the first `N' numbers of the fibonaccci series starting at zero."
(if (= 0 n)
'()
(list/reverse
(list/cons (series/fibonacci-number (number/dec n))
(list/reverse
(series/fibonacci (number/dec n)))))))
;; TODO: Consider memoization.
(defun series/triangular-number (i)
"Return the number in the triangular series at `I'."
(if (= 0 i)
0
(+ i (series/triangular-number (number/dec i)))))
;; TODO: Improve performance.
;; TODO: Consider creating a stream protocol with `stream/next' and implement
;; this using that.
(defun series/triangular (n)
"Return the first `N' numbers of a triangular series starting at 0."
(if (= 0 n)
'()
(list/reverse
(list/cons (series/triangular-number (number/dec n))
(list/reverse
(series/triangular (number/dec n)))))))
(defun series/catalan-number (i)
"Return the catalan number in the series at `I'."
(if (= 0 i)
1
(/ (number/factorial (* 2 i))
(* (number/factorial (number/inc i))
(number/factorial i)))))
(defun series/catalan (n)
"Return the first `N' numbers in a catalan series."
(->> (series/range 0 (number/dec n))
(list/map #'series/catalan-number)))
(provide 'series)
;;; series.el ends here
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