019f8fd211
git-subtree-dir: users/wpcarro git-subtree-mainline:464bbcb15cgit-subtree-split:24f5a642afChange-Id: I6105b3762b79126b3488359c95978cadb3efa789
93 lines
2.6 KiB
EmacsLisp
93 lines
2.6 KiB
EmacsLisp
;;; series.el --- Hosting common series of numbers -*- lexical-binding: t -*-
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;; Author: William Carroll <wpcarro@gmail.com>
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;; Version: 0.0.1
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;; URL: https://git.wpcarro.dev/wpcarro/briefcase
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;; Package-Requires: ((emacs "24"))
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;;; Commentary:
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;; Encoding number series as I learn about them.
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;;
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;; These are the following series I'm interested in supporting:
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;; - Fibonacci
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;; - Catalan numbers
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;; - Figurate number series
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;; - Triangular
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;; - Square
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;; - Pentagonal
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;; - Hexagonal
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;; - Lazy-caterer
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;; - Magic square
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;; - Look-and-say
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;;; Code:
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Dependencies
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(require 'number)
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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;; Library
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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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(defun series-range (beg end)
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"Create a list of numbers from `BEG' to `END'.
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This is an inclusive number range."
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(if (< end beg)
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(list-reverse
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(number-sequence end beg))
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(number-sequence beg end)))
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(defun series-fibonacci-number (i)
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"Return the number in the fibonacci series at `I'."
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(cond
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((= 0 i) 0)
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((= 1 i) 1)
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(t (+ (series-fibonacci-number (- i 1))
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(series-fibonacci-number (- i 2))))))
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(defun series-fibonacci (n)
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"Return the first `N' numbers of the fibonaccci series starting at zero."
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(if (= 0 n)
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'()
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(list-reverse
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(list-cons (series-fibonacci-number (number-dec n))
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(list-reverse
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(series-fibonacci (number-dec n)))))))
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;; TODO: Consider memoization.
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(defun series-triangular-number (i)
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"Return the number in the triangular series at `I'."
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(if (= 0 i)
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0
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(+ i (series-triangular-number (number-dec i)))))
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;; TODO: Improve performance.
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;; TODO: Consider creating a stream protocol with `stream/next' and implement
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;; this using that.
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(defun series-triangular (n)
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"Return the first `N' numbers of a triangular series starting at 0."
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(if (= 0 n)
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'()
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(list-reverse
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(list-cons (series-triangular-number (number-dec n))
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(list-reverse
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(series-triangular (number-dec n)))))))
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(defun series-catalan-number (i)
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"Return the catalan number in the series at `I'."
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(if (= 0 i)
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1
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(/ (number-factorial (* 2 i))
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(* (number-factorial (number-inc i))
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(number-factorial i)))))
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(defun series-catalan (n)
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"Return the first `N' numbers in a catalan series."
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(->> (series-range 0 (number-dec n))
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(list-map #'series-catalan-number)))
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(provide 'series)
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;;; series.el ends here
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