2c:null 2d:["$","title",null,{"children":"Julian Calendar | Enrico Spinielli | Observable"}] 32:T4c0,function roman_from_fixed(date) { // """Return the Roman name corresponding to fixed date ’date’.""" const j_date = julian_from_fixed(date); const month = standard_month(j_date); const day = standard_day(j_date); const year = standard_year(j_date); const month_prime = amod(1 + month, 12); const year_prime = month_prime != 1 ? year : year != -1 ? year + 1 : 1; const kalends1 = fixed_from_roman( roman_date(year_prime, month_prime, KALENDS, 1, false) ); let res; if (day == 1) { res = roman_date(year, month, KALENDS, 1, false); } else if (day <= nones_of_month(month)) { res = roman_date( year, month, NONES, nones_of_month(month) - day + 1, false ); } else if (day <= ides_of_month(month)) { res = roman_date(year, month, IDES, ides_of_month(month) - day + 1, false); } else if (month != FEBRUARY || !is_julian_leap_year(year)) { res = roman_date( year_prime, month_prime, KALENDS, kalends1 - date + 1, false ); } else if (day < 25) { res = roman_date(year, MARCH, KALENDS, 30 - day, false); } else { res = roman_date(year, MARCH, KALENDS, 31 - day, day == 25); } return res; }33:[] 30:{"id":"3de1ce000e4812f6","slug":"calcal-julian","title":"Julian Calendar","thumbnail":"171ec207b5b591d898c113ccddf01f11befc2edc608b1fe3694b6e8304bbb12e","access_level":"public","create_time":"$D2021-01-02T14:39:54.114Z","update_time":"$D2021-01-09T14:49:37.824Z","view_time":null,"first_public_time":"$D2021-01-08T14:48:08.060Z","has_unpublished_edits":null,"fork":true,"stars":0,"starred":false,"owner":{"type":"team","id":"7df7767074068af4","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":"starter_2024"},"version":1166,"publish_version":1166,"role":null,"authored":false,"authors":[{"type":"individual","id":"c2f17e4031105178","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":null}],"members":[{"type":"individual","id":"c2f17e4031105178","login":"espinielli","name":"Enrico Spinielli","avatar_url":"https://avatars-next.observableusercontent.com/2bf5259d0c49a57cec6acc725062bdc41374a518de8772a2a051315f6be64567","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"7b8e3cfdf35afbc5","slug":"calendrical-calculations","title":"Calendrical Calculations","owner":{"id":"7df7767074068af4","login":"espinielli","name":"Enrico Spinielli"}},"type":"notebook","body":{"titling":"auto","title":"Julian Calendar","cells":[{"id":878,"value":"md`# Julian Calendar\n\nThe functions defined in this notebook are all derived from [PyCalCal](https://github.com/espinielli/pycalcal) the Python implementation of the Calendrical Calculation as described in \n\n> Nachum Dershowitz, Edward M. Reingold \"Calendrical Calculations\"\n> Cambridge University Press; 3rd edition (December 10, 2007)\n> Paperback; ISBN-13: 9780521702386\n\n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1164,"value":"md`Notebook's image: Menologium Rusticum Colotianum (ca. 19–65 AD), discovered by Angelo Colocci in XVI century, near Campo di Marte, Rome, Italy. Now held by the National Archaeological Museum, Naples, Italy`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":881,"value":"function julian_date(year, month, day) {\n // \"\"\"Return the Julian date data structure.\"\"\"\n return [year, month, day];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":887,"value":"function bce(n) {\n // \"\"\"Retrun a negative value to indicate a BCE Julian year.\"\"\"\n return -n;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":891,"value":"function ce(n) {\n // \"\"\"Return a positive value to indicate a CE Julian year.\"\"\"\n return n;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":894,"value":"function is_julian_leap_year(j_year) {\n // \"\"\"Return True if Julian year ’j_year’ is a leap year in\n // the Julian calendar.\"\"\"\n return mod(j_year, 4) == (j_year > 0 ? 0 : 3);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":897,"value":"function fixed_from_julian(j_date) {\n // \"\"\"Return the fixed date equivalent to the Julian date ’j_date’.\"\"\"\n const month = standard_month(j_date);\n const day = standard_day(j_date);\n const year = standard_year(j_date);\n const y = year < 0 ? year + 1 : year;\n return (\n JULIAN_EPOCH -\n 1 +\n 365 * (y - 1) +\n quotient(y - 1, 4) +\n quotient(367 * month - 362, 12) +\n (month <= 2 ? 0 : is_julian_leap_year(year) ? -1 : -2) +\n day\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":901,"value":"function julian_from_fixed(date) {\n // \"\"\"Return the Julian date corresponding to fixed date ’date’.\"\"\"\n const approx = quotient(4 * (date - JULIAN_EPOCH) + 1464, 1461);\n const year = approx <= 0 ? approx - 1 : approx;\n const prior_days = date - fixed_from_julian(julian_date(year, JANUARY, 1));\n const correction =\n date < fixed_from_julian(julian_date(year, MARCH, 1))\n ? 0\n : is_julian_leap_year(year)\n ? 1\n : 2;\n const month = quotient(12 * (prior_days + correction) + 373, 367);\n const day = 1 + (date - fixed_from_julian(julian_date(year, month, 1)));\n return julian_date(year, month, day);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":884,"value":"JULIAN_EPOCH = fixed_from_gregorian(gregorian_date(0, DECEMBER, 30))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":915,"value":"md`## Roman Nomenclature`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":927,"value":"function roman_date(year, month, event, count, leap) {\n // \"\"\"Return the Roman date data structure.\"\"\"\n return [year, month, event, count, leap];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":930,"value":"function roman_year(date) {\n // \"\"\"Return the year of Roman date ’date’.\"\"\"\n return date[0];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":933,"value":"function roman_month(date) {\n // \"\"\"Return the month of Roman date ’date’.\"\"\"\n return date[1];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":936,"value":"function roman_event(date) {\n // \"\"\"Return the event of Roman date ’date’.\"\"\"\n return date[2];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":939,"value":"function roman_count(date) {\n // \"\"\"Return the count of Roman date ’date’.\"\"\"\n return date[3];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":942,"value":"function roman_leap(date) {\n // \"\"\"Return the leap indicator of Roman date ’date’.\"\"\"\n return date[4];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":945,"value":"function ides_of_month(month) {\n // \"\"\"Return the date of the Ides in Roman month ’month’.\"\"\"\n return [MARCH, MAY, JULY, OCTOBER].includes(month) ? 15 : 13;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":952,"value":"function nones_of_month(month) {\n // \"\"\"Return the date of Nones in Roman month ’month’.\"\"\"\n return ides_of_month(month) - 8;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":955,"value":"function fixed_from_roman(r_date) {\n // \"\"\"Return the fixed date corresponding to Roman date ’r_date’.\"\"\"\n const leap = roman_leap(r_date);\n const count = roman_count(r_date);\n const event = roman_event(r_date);\n const month = roman_month(r_date);\n const year = roman_year(r_date);\n let rm = [];\n rm[KALENDS] = fixed_from_julian(julian_date(year, month, 1));\n rm[NONES] = fixed_from_julian(\n julian_date(year, month, nones_of_month(month))\n );\n rm[IDES] = fixed_from_julian(julian_date(year, month, ides_of_month(month)));\n return (\n rm[event] -\n count +\n (is_julian_leap_year(year) &&\n month == MARCH &&\n event == KALENDS &&\n 16 >= count >= 6\n ? 0\n : 1) +\n (leap ? 1 : 0)\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":960,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":972,"value":"function julian_year_from_auc_year(year) {\n // \"\"\"Return the Julian year equivalent to AUC year ’year’.\"\"\"\n return 1 <= year <= year - YEAR_ROME_FOUNDED\n ? year + YEAR_ROME_FOUNDED - 1\n : year + YEAR_ROME_FOUNDED;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":976,"value":"function auc_year_from_julian_year(year) {\n // \"\"\"Return the AUC year equivalent to Julian year ’year’.\"\"\"\n return YEAR_ROME_FOUNDED <= year <= -1\n ? year - YEAR_ROME_FOUNDED - 1\n : year - YEAR_ROME_FOUNDED;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":969,"value":"YEAR_ROME_FOUNDED = bce(753)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":918,"value":"KALENDS = 1","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":921,"value":"NONES = 2","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":924,"value":"IDES = 3","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":979,"value":"md`### Holidays and Helper Functions`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":982,"value":"function julian_in_gregorian(j_month, j_day, g_year) {\n // \"\"\"Return the list of the fixed dates of Julian month ’j_month’, day\n // ’j_day’ that occur in Gregorian year ’g_year’.\"\"\"\n const jan1 = gregorian_new_year(g_year);\n const y = standard_year(julian_from_fixed(jan1));\n const y_prime = y == -1 ? 1 : y + 1;\n const date1 = fixed_from_julian(julian_date(y, j_month, j_day));\n const date2 = fixed_from_julian(julian_date(y_prime, j_month, j_day));\n return list_range([date1, date2], gregorian_year_range(g_year));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":985,"value":"function eastern_orthodox_christmas(g_year) {\n // \"\"\"Return the list of zero or one fixed dates of Eastern Orthodox Christmas\n // in Gregorian year ’g_year’.\"\"\"\n return julian_in_gregorian(DECEMBER, 25, g_year);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1118,"value":"md`## Technical details`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1125,"value":"import {\n fixed_from_gregorian,\n gregorian_date,\n gregorian_new_year,\n gregorian_year_range,\n JANUARY,\n FEBRUARY,\n MARCH,\n APRIL,\n MAY,\n JUNE,\n JULY,\n OCTOBER,\n NOVEMBER,\n DECEMBER,\n SUNDAY,\n MONDAY,\n TURSDAY,\n WEDNESDAY,\n THURSDAY,\n FRIDAY,\n SATURDAY\n} from \"@espinielli/calcal-gregorian\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1117,"value":"import {\n amod,\n list_range,\n mod,\n quotient,\n standard_year,\n standard_month,\n standard_day\n} from \"@espinielli/calcal-foundation\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W33","stdlib":"1"}} 31:"$30:body"