b3342afbfa
After attempting to package some of my Elisp libraries using Nix, I exposed circular dependencies between modules that has existed for awhile. I'm temporarily disabling this code since I do not have time to refactor everything. When I get around to packaging everything, I'll need to resolve these issues. For now, I must carry on.
89 lines
2.5 KiB
EmacsLisp
89 lines
2.5 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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;;; 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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