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1 ;;; cal-mayan.el --- calendar functions for the Mayan calendars.
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2
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3 ;; Copyright (C) 1992, 1993 Free Software Foundation, Inc.
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4
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5 ;; Author: Stewart M. Clamen <clamen@cs.cmu.edu>
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6 ;; Edward M. Reingold <reingold@cs.uiuc.edu>
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7 ;; Keywords: calendar
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8 ;; Human-Keywords: Mayan calendar, Maya, calendar, diary
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9
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10 ;; This file is part of XEmacs.
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11
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12 ;; XEmacs is free software; you can redistribute it and/or modify it
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13 ;; under the terms of the GNU General Public License as published by
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14 ;; the Free Software Foundation; either version 2, or (at your option)
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15 ;; any later version.
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16
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17 ;; XEmacs is distributed in the hope that it will be useful, but
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18 ;; WITHOUT ANY WARRANTY; without even the implied warranty of
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19 ;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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20 ;; General Public License for more details.
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21
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22 ;; You should have received a copy of the GNU General Public License
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70
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23 ;; along with XEmacs; see the file COPYING. If not, write to the Free
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24 ;; Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA.
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25
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26 ;;; Commentary:
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27
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28 ;; This collection of functions implements the features of calendar.el and
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29 ;; diary.el that deal with the Mayan calendar. It was written jointly by
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30
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31 ;; Stewart M. Clamen School of Computer Science
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32 ;; clamen@cs.cmu.edu Carnegie Mellon University
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33 ;; 5000 Forbes Avenue
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34 ;; Pittsburgh, PA 15213
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35
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36 ;; and
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37
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38 ;; Edward M. Reingold Department of Computer Science
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39 ;; (217) 333-6733 University of Illinois at Urbana-Champaign
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40 ;; reingold@cs.uiuc.edu 1304 West Springfield Avenue
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41 ;; Urbana, Illinois 61801
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42
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43 ;; Comments, improvements, and bug reports should be sent to Reingold.
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44
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45 ;; Technical details of the Mayan calendrical calculations can be found in
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46 ;; ``Calendrical Calculations, Part II: Three Historical Calendars''
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47 ;; by E. M. Reingold, N. Dershowitz, and S. M. Clamen,
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48 ;; Software--Practice and Experience, Volume 23, Number 4 (April, 1993),
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49 ;; pages 383-404.
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50
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51 ;;; Code:
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52
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53 (require 'calendar)
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54
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55 (defun mayan-adjusted-mod (m n)
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56 "Non-negative remainder of M/N with N instead of 0."
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57 (1+ (mod (1- m) n)))
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58
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59 (defconst calendar-mayan-days-before-absolute-zero 1137140
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60 "Number of days of the Mayan calendar epoch before absolute day 0.
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61 According to the Goodman-Martinez-Thompson correlation. This correlation is
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62 not universally accepted, as it still a subject of astro-archeological
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63 research. Using 1232041 will give you Spinden's correlation; using
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64 1142840 will give you Hochleitner's correlation.")
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65
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66 (defconst calendar-mayan-haab-at-epoch '(8 . 18)
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67 "Mayan haab date at the epoch.")
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68
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69 (defconst calendar-mayan-haab-month-name-array
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70 ["Pop" "Uo" "Zip" "Zotz" "Tzec" "Xul" "Yaxkin" "Mol" "Chen" "Yax"
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71 "Zac" "Ceh" "Mac" "Kankin" "Muan" "Pax" "Kayab" "Cumku"])
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72
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73 (defconst calendar-mayan-tzolkin-at-epoch '(4 . 20)
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74 "Mayan tzolkin date at the epoch.")
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75
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76 (defconst calendar-mayan-tzolkin-names-array
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77 ["Imix" "Ik" "Akbal" "Kan" "Chicchan" "Cimi" "Manik" "Lamat" "Muluc" "Oc"
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78 "Chuen" "Eb" "Ben" "Ix" "Men" "Cib" "Caban" "Etznab" "Cauac" "Ahau"])
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79
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80 (defun calendar-mayan-long-count-from-absolute (date)
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81 "Compute the Mayan long count corresponding to the absolute DATE."
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82 (let ((long-count (+ date calendar-mayan-days-before-absolute-zero)))
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83 (let* ((baktun (/ long-count 144000))
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84 (remainder (% long-count 144000))
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85 (katun (/ remainder 7200))
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86 (remainder (% remainder 7200))
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87 (tun (/ remainder 360))
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88 (remainder (% remainder 360))
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89 (uinal (/ remainder 20))
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90 (kin (% remainder 20)))
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91 (list baktun katun tun uinal kin))))
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92
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93 (defun calendar-mayan-long-count-to-string (mayan-long-count)
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94 "Convert MAYAN-LONG-COUNT into traditional written form."
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95 (apply 'format (cons "%s.%s.%s.%s.%s" mayan-long-count)))
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96
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97 (defun calendar-string-to-mayan-long-count (str)
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98 "Given STR, a string of format \"%d.%d.%d.%d.%d\", return list of nums."
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99 (let ((rlc nil)
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100 (c (length str))
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101 (cc 0))
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102 (condition-case condition
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103 (progn
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104 (while (< cc c)
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105 (let* ((start (string-match "[0-9]+" str cc))
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106 (end (match-end 0))
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107 datum)
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108 (setq datum (read (substring str start end)))
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109 (setq rlc (cons datum rlc))
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110 (setq cc end)))
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111 (if (not (= (length rlc) 5)) (signal 'invalid-read-syntax nil)))
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112 (invalid-read-syntax nil))
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113 (reverse rlc)))
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114
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115 (defun calendar-mayan-haab-from-absolute (date)
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116 "Convert absolute DATE into a Mayan haab date (a pair)."
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117 (let* ((long-count (+ date calendar-mayan-days-before-absolute-zero))
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118 (day-of-haab
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119 (% (+ long-count
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120 (car calendar-mayan-haab-at-epoch)
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121 (* 20 (1- (cdr calendar-mayan-haab-at-epoch))))
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122 365))
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123 (day (% day-of-haab 20))
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124 (month (1+ (/ day-of-haab 20))))
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125 (cons day month)))
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126
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127 (defun calendar-mayan-haab-difference (date1 date2)
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128 "Number of days from Mayan haab DATE1 to next occurrence of haab date DATE2."
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129 (mod (+ (* 20 (- (cdr date2) (cdr date1)))
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130 (- (car date2) (car date1)))
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131 365))
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132
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133 (defun calendar-mayan-haab-on-or-before (haab-date date)
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134 "Absolute date of latest HAAB-DATE on or before absolute DATE."
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135 (- date
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136 (% (- date
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137 (calendar-mayan-haab-difference
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138 (calendar-mayan-haab-from-absolute 0) haab-date))
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139 365)))
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140
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141 (defun calendar-next-haab-date (haab-date &optional noecho)
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142 "Move cursor to next instance of Mayan HAAB-DATE.
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143 Echo Mayan date if NOECHO is t."
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144 (interactive (list (calendar-read-mayan-haab-date)))
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145 (calendar-goto-date
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146 (calendar-gregorian-from-absolute
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147 (calendar-mayan-haab-on-or-before
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148 haab-date
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149 (+ 365
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150 (calendar-absolute-from-gregorian (calendar-cursor-to-date))))))
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151 (or noecho (calendar-print-mayan-date)))
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152
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153 (defun calendar-previous-haab-date (haab-date &optional noecho)
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154 "Move cursor to previous instance of Mayan HAAB-DATE.
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155 Echo Mayan date if NOECHO is t."
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156 (interactive (list (calendar-read-mayan-haab-date)))
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157 (calendar-goto-date
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158 (calendar-gregorian-from-absolute
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159 (calendar-mayan-haab-on-or-before
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160 haab-date
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161 (1- (calendar-absolute-from-gregorian (calendar-cursor-to-date))))))
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162 (or noecho (calendar-print-mayan-date)))
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163
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164 (defun calendar-mayan-haab-to-string (haab)
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165 "Convert Mayan haab date (a pair) into its traditional written form."
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166 (let ((month (cdr haab))
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167 (day (car haab)))
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168 ;; 19th month consists of 5 special days
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169 (if (= month 19)
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170 (format "%d Uayeb" day)
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171 (format "%d %s"
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172 day
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173 (aref calendar-mayan-haab-month-name-array (1- month))))))
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174
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175 (defun calendar-mayan-tzolkin-from-absolute (date)
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176 "Convert absolute DATE into a Mayan tzolkin date (a pair)."
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177 (let* ((long-count (+ date calendar-mayan-days-before-absolute-zero))
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178 (day (mayan-adjusted-mod
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179 (+ long-count (car calendar-mayan-tzolkin-at-epoch))
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180 13))
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181 (name (mayan-adjusted-mod
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182 (+ long-count (cdr calendar-mayan-tzolkin-at-epoch))
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183 20)))
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184 (cons day name)))
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185
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186 (defun calendar-mayan-tzolkin-difference (date1 date2)
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187 "Number of days from Mayan tzolkin DATE1 to next occurrence of tzolkin DATE2."
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188 (let ((number-difference (- (car date2) (car date1)))
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189 (name-difference (- (cdr date2) (cdr date1))))
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190 (mod (+ number-difference
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191 (* 13 (mod (* 3 (- number-difference name-difference))
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192 20)))
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193 260)))
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194
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195 (defun calendar-mayan-tzolkin-on-or-before (tzolkin-date date)
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196 "Absolute date of latest TZOLKIN-DATE on or before absolute DATE."
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197 (- date
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198 (% (- date (calendar-mayan-tzolkin-difference
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199 (calendar-mayan-tzolkin-from-absolute 0)
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200 tzolkin-date))
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201 260)))
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202
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203 (defun calendar-next-tzolkin-date (tzolkin-date &optional noecho)
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204 "Move cursor to next instance of Mayan TZOLKIN-DATE.
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205 Echo Mayan date if NOECHO is t."
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206 (interactive (list (calendar-read-mayan-tzolkin-date)))
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207 (calendar-goto-date
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208 (calendar-gregorian-from-absolute
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209 (calendar-mayan-tzolkin-on-or-before
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210 tzolkin-date
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211 (+ 260
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212 (calendar-absolute-from-gregorian (calendar-cursor-to-date))))))
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213 (or noecho (calendar-print-mayan-date)))
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214
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215 (defun calendar-previous-tzolkin-date (tzolkin-date &optional noecho)
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216 "Move cursor to previous instance of Mayan TZOLKIN-DATE.
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217 Echo Mayan date if NOECHO is t."
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218 (interactive (list (calendar-read-mayan-tzolkin-date)))
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219 (calendar-goto-date
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220 (calendar-gregorian-from-absolute
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221 (calendar-mayan-tzolkin-on-or-before
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222 tzolkin-date
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223 (1- (calendar-absolute-from-gregorian (calendar-cursor-to-date))))))
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224 (or noecho (calendar-print-mayan-date)))
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225
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226 (defun calendar-mayan-tzolkin-to-string (tzolkin)
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227 "Convert Mayan tzolkin date (a pair) into its traditional written form."
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228 (format "%d %s"
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229 (car tzolkin)
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230 (aref calendar-mayan-tzolkin-names-array (1- (cdr tzolkin)))))
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231
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232 (defun calendar-mayan-tzolkin-haab-on-or-before (tzolkin-date haab-date date)
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233 "Absolute date that is Mayan TZOLKIN-DATE and HAAB-DATE.
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234 Latest such date on or before DATE.
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235 Returns nil if such a tzolkin-haab combination is impossible."
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236 (let* ((haab-difference
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237 (calendar-mayan-haab-difference
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238 (calendar-mayan-haab-from-absolute 0)
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239 haab-date))
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240 (tzolkin-difference
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241 (calendar-mayan-tzolkin-difference
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242 (calendar-mayan-tzolkin-from-absolute 0)
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243 tzolkin-date))
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244 (difference (- tzolkin-difference haab-difference)))
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245 (if (= (% difference 5) 0)
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246 (- date
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247 (mod (- date
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248 (+ haab-difference (* 365 difference)))
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249 18980))
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250 nil)))
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251
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252 (defun calendar-read-mayan-haab-date ()
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253 "Prompt for a Mayan haab date"
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254 (let* ((completion-ignore-case t)
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255 (haab-day (calendar-read
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256 "Haab kin (0-19): "
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257 '(lambda (x) (and (>= x 0) (< x 20)))))
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258 (haab-month-list (append calendar-mayan-haab-month-name-array
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259 (and (< haab-day 5) '("Uayeb"))))
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260 (haab-month (cdr
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261 (assoc
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262 (capitalize
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263 (completing-read "Haab uinal: "
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264 (mapcar 'list haab-month-list)
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265 nil t))
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266 (calendar-make-alist
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267 haab-month-list 1 'capitalize)))))
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268 (cons haab-day haab-month)))
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269
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270 (defun calendar-read-mayan-tzolkin-date ()
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271 "Prompt for a Mayan tzolkin date"
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272 (let* ((completion-ignore-case t)
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273 (tzolkin-count (calendar-read
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274 "Tzolkin kin (1-13): "
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275 '(lambda (x) (and (> x 0) (< x 14)))))
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276 (tzolkin-name-list (append calendar-mayan-tzolkin-names-array nil))
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277 (tzolkin-name (cdr
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278 (assoc
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279 (capitalize
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280 (completing-read "Tzolkin uinal: "
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281 (mapcar 'list tzolkin-name-list)
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282 nil t))
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283 (calendar-make-alist
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284 tzolkin-name-list 1 'capitalize)))))
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285 (cons tzolkin-count tzolkin-name)))
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286
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287 (defun calendar-next-calendar-round-date
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288 (tzolkin-date haab-date &optional noecho)
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289 "Move cursor to next instance of Mayan HAAB-DATE TZOKLIN-DATE combination.
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290 Echo Mayan date if NOECHO is t."
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291 (interactive (list (calendar-read-mayan-tzolkin-date)
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292 (calendar-read-mayan-haab-date)))
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293 (let ((date (calendar-mayan-tzolkin-haab-on-or-before
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294 tzolkin-date haab-date
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295 (+ 18980 (calendar-absolute-from-gregorian
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296 (calendar-cursor-to-date))))))
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297 (if (not date)
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298 (error "%s, %s does not exist in the Mayan calendar round"
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299 (calendar-mayan-tzolkin-to-string tzolkin-date)
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300 (calendar-mayan-haab-to-string haab-date))
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301 (calendar-goto-date (calendar-gregorian-from-absolute date))
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302 (or noecho (calendar-print-mayan-date)))))
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303
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304 (defun calendar-previous-calendar-round-date
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305 (tzolkin-date haab-date &optional noecho)
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306 "Move to previous instance of Mayan TZOKLIN-DATE HAAB-DATE combination.
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307 Echo Mayan date if NOECHO is t."
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308 (interactive (list (calendar-read-mayan-tzolkin-date)
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309 (calendar-read-mayan-haab-date)))
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310 (let ((date (calendar-mayan-tzolkin-haab-on-or-before
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311 tzolkin-date haab-date
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312 (1- (calendar-absolute-from-gregorian
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313 (calendar-cursor-to-date))))))
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314 (if (not date)
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315 (error "%s, %s does not exist in the Mayan calendar round"
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316 (calendar-mayan-tzolkin-to-string tzolkin-date)
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317 (calendar-mayan-haab-to-string haab-date))
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318 (calendar-goto-date (calendar-gregorian-from-absolute date))
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319 (or noecho (calendar-print-mayan-date)))))
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320
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321 (defun calendar-absolute-from-mayan-long-count (c)
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322 "Compute the absolute date corresponding to the Mayan Long Count C.
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323 Long count is a list (baktun katun tun uinal kin)"
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324 (+ (* (nth 0 c) 144000) ; baktun
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325 (* (nth 1 c) 7200) ; katun
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326 (* (nth 2 c) 360) ; tun
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327 (* (nth 3 c) 20) ; uinal
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328 (nth 4 c) ; kin (days)
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329 (- ; days before absolute date 0
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330 calendar-mayan-days-before-absolute-zero)))
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331
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332 (defun calendar-mayan-date-string (&optional date)
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333 "String of Mayan date of Gregorian DATE.
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334 Defaults to today's date if DATE is not given."
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335 (let* ((d (calendar-absolute-from-gregorian
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336 (or date (calendar-current-date))))
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337 (tzolkin (calendar-mayan-tzolkin-from-absolute d))
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338 (haab (calendar-mayan-haab-from-absolute d))
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339 (long-count (calendar-mayan-long-count-from-absolute d)))
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340 (format "Long count = %s; tzolkin = %s; haab = %s"
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341 (calendar-mayan-long-count-to-string long-count)
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342 (calendar-mayan-tzolkin-to-string tzolkin)
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343 (calendar-mayan-haab-to-string haab))))
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344
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345 (defun calendar-print-mayan-date ()
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346 "Show the Mayan long count, tzolkin, and haab equivalents of date."
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347 (interactive)
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348 (message "Mayan date: %s"
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349 (calendar-mayan-date-string (calendar-cursor-to-date t))))
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350
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351 (defun calendar-goto-mayan-long-count-date (date &optional noecho)
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352 "Move cursor to Mayan long count DATE. Echo Mayan date unless NOECHO is t."
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353 (interactive
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354 (let (lc)
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355 (while (not lc)
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356 (let ((datum
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357 (calendar-string-to-mayan-long-count
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358 (read-string "Mayan long count (baktun.katun.tun.uinal.kin): "
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359 (calendar-mayan-long-count-to-string
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360 (calendar-mayan-long-count-from-absolute
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361 (calendar-absolute-from-gregorian
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362 (calendar-current-date))))))))
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363 (if (calendar-mayan-long-count-common-era datum)
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364 (setq lc datum))))
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365 (list lc)))
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366 (calendar-goto-date
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367 (calendar-gregorian-from-absolute
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368 (calendar-absolute-from-mayan-long-count date)))
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369 (or noecho (calendar-print-mayan-date)))
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370
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371 (defun calendar-mayan-long-count-common-era (lc)
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372 "T if long count represents date in the Common Era."
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373 (let ((base (calendar-mayan-long-count-from-absolute 1)))
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374 (while (and (not (null base)) (= (car lc) (car base)))
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375 (setq lc (cdr lc)
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376 base (cdr base)))
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377 (or (null lc) (> (car lc) (car base)))))
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378
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379 (defun diary-mayan-date ()
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380 "Show the Mayan long count, haab, and tzolkin dates as a diary entry."
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381 (format "Mayan date: %s" (calendar-mayan-date-string date)))
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382
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383 (provide 'cal-mayan)
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384
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385 ;;; cal-mayan.el ends here
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