# `Calendrical.Julian.Sept1`

Proleptic Julian calendar whose year begins on 1 September (the
*Byzantine* year, used by the Byzantine Empire and in the Eastern
Orthodox liturgical year).

The year begins four months before 1 January of the same number: year
1700 runs from 1 September 1699 to 31 August 1700, so September to
December carry the number of the year to come. Months are counted
from the new-year day: month 1 is September and month 12 August.

    iex> Date.convert!(~D[1699-09-01 Calendrical.Julian], Calendrical.Julian.Sept1)
    ~D[1700-01-01 Calendrical.Julian.Sept1]

    iex> Date.convert!(~D[1700-08-31 Calendrical.Julian], Calendrical.Julian.Sept1)
    ~D[1700-12-31 Calendrical.Julian.Sept1]

A Byzantine year of the world is 5509 more than the Julian year from
September to December and 5508 more from January to August, which is
5508 more than the year here throughout: the year of the world 7208
began on 1 September 1699, the first day of 1700 above.

See `Calendrical.Julian` for the calendar's structure, leap-year
rule and the full public API.

# `add`

Adds whole years, quarters or months to the fields of a naive
datetime, keeping its time of day: the `add/9` callback
[`CalendarInterval`](https://hexdocs.pm/calendar_interval) steps an
interval of a year or a month with. The date moves as `shift/6`
moves it, clamping the day into a shorter month.

### Arguments

* `year`, `month` and `day` are the date's fields in this calendar.

* `hour`, `minute`, `second` and `microsecond` are the time of day,
  returned unchanged.

* `precision` is `:year`, `:quarter` or `:month`.

* `step` is the number of years, quarters or months to add, which
  may be negative.

### Returns

* `{year, month, day, hour, minute, second, microsecond}`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day, 12, 30, 0, {0, 0}} =
    ...>   Calendrical.Julian.Sept1.add(date.year, date.month, date.day, 12, 30, 0, {0, 0}, :month, 1)
    iex> {year, month, day} == Calendrical.Julian.Sept1.shift(date.year, date.month, date.day, :months, 1, [])
    true

# `base`

Returns the base calendar this calendar's years are cut from.

### Returns

* The base calendar module.

### Examples

    iex> Calendrical.Julian.Sept1.base() |> Code.ensure_loaded?()
    true

# `base_date`

Returns the base calendar's date of a date of this calendar.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{year, month, day}` in the base calendar. For a partial date,
  a field that depends on a missing one is `nil`: the base month
  needs the month, the base day the month and the day, and the
  base year all three.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.base_date(today.year, today.month, today.day)
    iex> Calendrical.Julian.Sept1.date_from_base_date(year, month, day)
    {today.year, today.month, today.day}

    iex> Calendrical.Julian.Sept1.base_date(2024, nil, nil)
    {nil, nil, nil}

# `calendar_base`

Returns what this calendar's year is built of, `:month` or `:week`,
as its `info/0` states.

### Returns

* `:week` for a calendar whose year is built of weeks.

* `:month` otherwise.

### Examples

    iex> Calendrical.Julian.Sept1.calendar_base() in [:month, :week]
    true

# `calendar_from_cldr_calendar_type`

Returns the calendar module whose CLDR calendar type is the one
given, whichever calendar is asked
(`Calendrical.calendar_from_cldr_calendar_type/1`).

### Arguments

* `calendar_type` is a CLDR calendar type as an atom or a string.

### Returns

* `{:ok, calendar_module}`, or

* `{:error, exception}` for a calendar type no calendar module has.

### Examples

    iex> Calendrical.Julian.Sept1.calendar_from_cldr_calendar_type(:gregorian)
    {:ok, Calendrical.Gregorian}

    iex> {:error, %Localize.UnknownCalendarError{}} =
    ...>   Calendrical.Julian.Sept1.calendar_from_cldr_calendar_type(:not_a_calendar)

# `cardinal_day`

Returns the day a date is written with: the day of its
`written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The day of the date's `written_date/3`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {_year, _month, written_day} = Calendrical.Julian.Sept1.written_date(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.cardinal_day(date.year, date.month, date.day) == written_day
    true

# `cardinal_month`

Returns the CLDR month a month of the year names without a year
(`Calendrical.Month.cldr_month/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* The CLDR month the month is named in the year that holds
  1 January 2000, the month itself in the Hebrew calendar, whose
  names depend on the year, and the month itself where the
  reference year has no such month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2000-01-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.cardinal_month(1) == Calendrical.Julian.Sept1.cldr_month(date.year, 1)
    true

# `cardinal_year`

Returns the year a date is written with: the year of its
`written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The year of the date's `written_date/3`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {written_year, _month, _day} = Calendrical.Julian.Sept1.written_date(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.cardinal_year(date.year, date.month, date.day) == written_year
    true

# `cldr_calendar_type`

Returns the CLDR calendar type whose data names this calendar's
months, days and quarters, as its `info/0` states.

### Returns

* A CLDR calendar type such as `:gregorian` or `:hebrew`.

### Examples

    iex> Calendrical.Julian.Sept1.cldr_calendar_type() == Calendrical.Julian.Sept1.info().cldr_calendar_type
    true

# `cldr_calendar_type`

Returns the CLDR calendar type whose data names a date's months and
days: the member in effect on the date in a composite calendar, and
this calendar's own otherwise (`Calendrical.Info.cldr_calendar_type/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* A CLDR calendar type.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> in_effect = Calendrical.Info.in_effect(Calendrical.Julian.Sept1, date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.cldr_calendar_type(date.year, date.month, date.day) == in_effect.cldr_calendar_type()
    true

# `cldr_month`

Returns the CLDR month of a month of a year
(`Calendrical.Month.cldr_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A CLDR month number, or `{month, :leap}` where the month's name
  has a leap form, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> cldr_month = Calendrical.Julian.Sept1.cldr_month(date.year, date.month)
    iex> Calendrical.Julian.Sept1.written_month_from_cldr_month(date.year, cldr_month) ==
    ...>   Calendrical.Julian.Sept1.numeric_month(date.year, date.month, date.day)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.cldr_month(date.year, 99)

# `cyclic_year`

Returns the cyclic year of a date (`Calendrical.Era.cyclic_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The date's place in the sexagenary cycle, `1` to `60`, in an East
  Asian calendar, and its year in a calendar whose years run in no
  such cycle, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> cyclic_year = Calendrical.Julian.Sept1.cyclic_year(date.year, date.month, date.day)
    iex> cyclic_year in 1..60 or cyclic_year == date.year
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Julian.Sept1.cyclic_year(nil, 1, 1)

# `date_from_base_date`

Returns the date of this calendar that names a date of the base
calendar.

### Arguments

* `year`, `month` and `day` are a date of the base calendar.

### Returns

* `{year, month, day}` in this calendar. For a partial date, whose
  counted month, day and year each depend on the base month and
  day, every field is `nil` unless all three are given.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.base_date(today.year, today.month, today.day)
    iex> Calendrical.Julian.Sept1.date_from_base_date(year, month, day)
    {today.year, today.month, today.day}

    iex> Calendrical.Julian.Sept1.date_from_base_date(2024, nil, 1)
    {nil, nil, nil}

# `date_from_cardinal_date`

Returns the date of this calendar that written figures name
(`date_from_written_date/3`), as fields.

### Arguments

* `year`, `month` and `day` are the figures a date is written with,
  as `written_date/3` returns them.

### Returns

* `{year, month, day}`, the date of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` where the figures name no date.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.written_date(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.date_from_cardinal_date(year, month, day) == {date.year, date.month, date.day}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.date_from_cardinal_date(date.year, 0, 1)

# `date_from_day_of_year`

Returns the date of a day of a year, counted from the year's first
day.

### Arguments

* `year` is a year of this calendar.

* `day_of_year` is the day of the year, counted from 1.

### Returns

* A `t:Date.t/0` of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` for a day the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> day_of_year = Calendrical.Julian.Sept1.day_of_year(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.date_from_day_of_year(date.year, day_of_year) == date
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.date_from_day_of_year(date.year, 1000)

# `date_from_iso_days`

Returns the date of this calendar of an ISO day number.

### Arguments

* `iso_days` is an ISO day number.

### Returns

* `{year, month, day}` in this calendar.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.date_from_iso_days(Date.to_gregorian_days(~D[2024-06-01]))
    {today.year, today.month, today.day}

# `date_from_week_date`

Returns the date of a day of a week of a week-year
(`Calendrical.Week.date_from_week_date/4`).

### Arguments

* `week_year` is a week-year of this calendar.

* `week` is a week of the week-year.

* `day` is the day of the week, numbered from 1 for the day the
  calendar's weeks begin on.

### Returns

* A `t:Date.t/0` of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` where the week has no such day.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week, day} = Calendrical.Julian.Sept1.week_date_from_date(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.date_from_week_date(week_year, week, day) == date
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.date_from_week_date(date.year, 1, 8)

# `date_from_written_date`

Returns the date of this calendar that written figures name: the
inverse of `written_date/3`.

### Arguments

* `year`, `month` and `day` are the written figures of a date.

### Returns

* `{:ok, {year, month, day}}` in this calendar.

* `{:error, :invalid_date}` for figures that name no date, an atom
  as `c:Calendrical.date_from_written_date/3` answers.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.written_date(today.year, today.month, today.day)
    iex> Calendrical.Julian.Sept1.date_from_written_date(year, month, day)
    {:ok, {today.year, today.month, today.day}}

# `date_to_iso_days`

Returns the ISO day number of a date of this calendar.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The ISO day number.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.date_to_iso_days(today.year, today.month, today.day) ==
    ...>   Date.to_gregorian_days(~D[2024-06-01])
    true

# `dates_in_gregorian_year`

Returns the dates of this calendar, earliest first, whose month and
day are those given and that fall in a Gregorian year.

### Arguments

* `gregorian_year` is the Gregorian year to search within.

* `month` and `day` are a month and a day of this calendar.

### Returns

* A list of zero, one or two `t:Date.t/0` of this calendar, earliest
  first, since this calendar's years and the Gregorian years drift.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> date in Calendrical.Julian.Sept1.dates_in_gregorian_year(2024, date.month, date.day)
    true

# `day_numbers`

Returns the days a month of a year has, as runs of their numbers
(`Calendrical.Month.day_numbers/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A list of ranges: one from 1 in every month of every calendar but
  a composite, whose month a change of calendar falls in has the
  days that are left, and `[]` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.day_numbers(date.year, date.month) ==
    ...>   [1..Calendrical.Julian.Sept1.days_in_month(date.year, date.month)//1]
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.day_numbers(date.year, 99)
    []

# `day_of_era`

Returns the day of era of a date: counted from the first day of this
calendar's year 1, and back from the day before it for the era
before.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{day, era}`.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {day, 1} = Calendrical.Julian.Sept1.day_of_era(today.year, today.month, today.day)
    iex> day > 0
    true

# `day_of_week`

Returns the day of the week of a date (`Calendrical.Week.day_of_week/5`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `starting_on` is `:default` for the day this calendar's weeks
  begin on, or the name of a weekday, `:monday` to `:sunday`.

### Returns

* `{day_of_week, 1, 7}`, the day numbered from the day the week
  begins on, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing field.

### Examples

    # 1 June 2024 is a Saturday
    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.day_of_week(date.year, date.month, date.day, :monday)
    {6, 1, 7}

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.day_of_week(date.year, date.month, 0, :monday)

# `day_of_year`

Returns the day of the year of a date (`Calendrical.Period.day_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The day of the year, counted from 1 for its first day, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing field.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> first_day = Calendrical.Julian.Sept1.year(date.year).first
    iex> Calendrical.Julian.Sept1.day_of_year(date.year, date.month, date.day) == Date.diff(date, first_day) + 1
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.day_of_year(date.year, date.month, 0)

# `days_in_month`

Returns the number of days in a month without a year
(`Calendrical.Month.days_in_month/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* The number of days where the month has as many in every year, or

* `{:ambiguous, lengths}` where its length depends on the year, the
  lengths a range or, where they are not consecutive, a list, or

* `{:error, %Calendrical.NotDefinedError{}}` for a month the calendar has in no year, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, where
  the month is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {fewest, most} = Calendrical.Julian.Sept1.days_in_month_bounds(date.month)
    iex> case Calendrical.Julian.Sept1.days_in_month(date.month) do
    ...>   days when is_integer(days) -> fewest == days and most == days
    ...>   {:ambiguous, lengths} -> Enum.min(lengths) == fewest and Enum.max(lengths) == most
    ...> end
    true

    iex> {:error, %Calendrical.NotDefinedError{}} = Calendrical.Julian.Sept1.days_in_month(99)

# `days_in_month`

```elixir
@spec days_in_month(Calendar.year(), Calendar.month()) ::
  Calendar.day() | {:error, Exception.t()}
```

Returns the number of days in a month of a year: the base month's,
and a part of it for the two months a year begun within a base month
splits it into.

### Arguments

* `year` is a year of this calendar.

* `month` is a month of the year.

### Returns

* The number of days, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month the year
  does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  month is `nil`.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.days_in_month(today.year, today.month) >= today.day
    true

# `days_in_month_bounds`

Returns the fewest and the most days a month has in any year
(`Calendrical.Month.days_in_month_bounds/2`).

### Arguments

* `month` is a month of this calendar.

### Returns

* `{fewest, most}`, or

* `{:error, exception}` for a month the calendar has in no year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {fewest, most} = Calendrical.Julian.Sept1.days_in_month_bounds(date.month)
    iex> Calendrical.Julian.Sept1.days_in_month(date.year, date.month) in fewest..most
    true

    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.days_in_month_bounds(99)

# `days_in_week`

Returns the number of days in a week.

### Returns

* `7`.

### Examples

    iex> Calendrical.Julian.Sept1.days_in_week()
    7

# `days_in_year`

Returns the number of days in a year (`Calendrical.Period.days_in_year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of days, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.days_in_year(date.year) == Enum.count(Calendrical.Julian.Sept1.year(date.year))
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Julian.Sept1.days_in_year(nil)

# `diff`

Returns the number of whole units between two dates, counted
positionally.

### Arguments

* `from` and `to` are dates of this calendar as `{year, month, day}`
  tuples.

* `date_part` is one of `:years`, `:quarters`, `:months`, `:weeks`
  or `:days`.

### Returns

* The largest number of `date_part`s that can be added to `from`
  without passing `to`, negative where `to` is before `from`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a `from` or `to`
  the calendar does not have, `{:error, %Calendrical.MissingFieldsError{}}`
  for one missing a field, or `{:error, %Calendrical.InvalidPartError{}}`
  for a `date_part` other than the five.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> from = {date.year, date.month, date.day}
    iex> Calendrical.Julian.Sept1.diff(from, {date.year + 1, date.month, date.day}, :years)
    1

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> later = Date.add(date, 10)
    iex> Calendrical.Julian.Sept1.diff({later.year, later.month, later.day}, {date.year, date.month, date.day}, :days)
    -10

# `era_calendar_type`

Returns the CLDR calendar type that names this calendar's eras, as
its `info/0` states.

### Returns

* A CLDR calendar type such as `:gregorian` or `:japanese`.

### Examples

    iex> Calendrical.Julian.Sept1.era_calendar_type() == Calendrical.Julian.Sept1.info().era_calendar_type
    true

# `extended_year`

Returns the extended year of a date (`Calendrical.Era.extended_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The year numbered without a gap at 0, so that in a calendar with
  no year 0 the year before 1 is 0, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.extended_year(date.year, date.month, date.day) == date.year
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Julian.Sept1.extended_year(nil, 1, 1)

# `info`

Returns the static facts about this calendar, as
`t:Calendrical.Info.t/0`.

### Returns

* A `t:Calendrical.Info.t/0` describing this calendar.

### Examples

    iex> Calendrical.Julian.Sept1.info().calendar
    Calendrical.Julian.Sept1

# `iso_week_of_year`

Returns the ISO 8601 week-year and week of the day a date names
(`Calendrical.Week.iso_week_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week}` of ISO 8601, or

* `{:error, exception}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.iso_week_of_year(date.year, date.month, date.day)
    {2024, 22}

# `leap_month`

Returns the position of a year's leap month, or `nil` where the
year has none.

### Arguments

* `year` is a year of this calendar.

### Returns

* The leap month's position in the year, or

* `nil` where the year has no leap month, as for anything but an
  integer year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> leap_month = Calendrical.Julian.Sept1.leap_month(date.year)
    iex> is_nil(leap_month) or leap_month in 1..Calendrical.Julian.Sept1.months_in_year(date.year)
    true

# `leap_year?`

Returns whether a year is a leap year: whether it holds 366 days.

### Arguments

* `year` is a year of this calendar.

### Returns

* `true` if the year holds 366 days, otherwise `false`.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.leap_year?(today.year) in [true, false]
    true

# `lunar_month_of_year`

Returns the traditional month at a position in a year
(`Calendrical.Month.traditional_month/3`), or an error for a place
the year does not have.

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* The month's traditional number, or `{month, :leap}` for a leap
  month, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.lunar_month_of_year(date.year, date.month) ==
    ...>   Calendrical.Julian.Sept1.traditional_month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.lunar_month_of_year(date.year, 99)

# `month`

Returns the days of a month of a year (`Calendrical.Period.month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a month the year does not have, or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing year or month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> date in Calendrical.Julian.Sept1.month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.month(date.year, 99)

# `month_from_traditional`

Returns the position of a traditional month in a year
(`Calendrical.Month.month_from_traditional/3`).

### Arguments

* `year` is a year of this calendar.

* `traditional_month` is a month's traditional number, or
  `{month, :leap}` for a leap month.

### Returns

* The month's position in the year, or

* `{:error, exception}` where the year has no such month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> traditional_month = Calendrical.Julian.Sept1.traditional_month(date.year, date.month)
    iex> Calendrical.Julian.Sept1.month_from_traditional(date.year, traditional_month) == date.month
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.month_from_traditional(date.year, 99)

# `month_numbers`

Returns the months a year has, as runs of their numbers
(`Calendrical.Month.month_numbers/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A list of ranges: one from 1 in every year of every calendar but a
  composite, whose year a change of calendar falls in has the months
  that are left, and `[]` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.month_numbers(date.year) == [1..Calendrical.Julian.Sept1.months_in_year(date.year)//1]
    true

# `month_of_year`

Returns the CLDR month of a month of a year: the index of its name
in this calendar's CLDR data, with `{month, :leap}` where the name
has a leap form (`Calendrical.Month.cldr_month/3`).

### Arguments

* `year`, `month` and `day` are a date of this calendar. The year
  and the day may be `nil`: a month's name needs only the month.

### Returns

* A CLDR month number, or `{month, :leap}`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a day the month does not have, or

* `{:error, exception}` for a month the year does not have, or a
  `Calendrical.MissingFieldsError` where the month is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.month_of_year(date.year, date.month, date.day) == Calendrical.Julian.Sept1.cldr_month(date.year, date.month)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.month_of_year(date.year, date.month, 0)

# `months_in_leap_year`

Returns the number of months in a leap year: the most months a year
of this calendar has.

### Returns

* A positive integer.

### Examples

    iex> Calendrical.Julian.Sept1.months_in_leap_year() >= Calendrical.Julian.Sept1.months_in_ordinary_year()
    true

# `months_in_ordinary_year`

Returns the number of months in an ordinary year: the fewest months
a year of this calendar has.

### Returns

* A positive integer.

### Examples

    iex> Calendrical.Julian.Sept1.months_in_ordinary_year() <= Calendrical.Julian.Sept1.months_in_leap_year()
    true

# `months_in_year`

Returns the number of months in a year without a year: the count
where every year has as many, `{:ambiguous, range}` where a leap
year has more, and `{:error, %Calendrical.NotDefinedError{}}` for a composite calendar
(`Calendrical.Info.months_in_year/1`).

### Returns

* The number of months where every year has as many, or

* `{:ambiguous, fewest..most}` where a leap year has more, or

* `{:error, %Calendrical.NotDefinedError{}}` for a composite calendar, whose bounds
  `months_in_year_bounds/0` gives.

### Examples

    iex> case Calendrical.Julian.Sept1.months_in_year() do
    ...>   months when is_integer(months) -> months == Calendrical.Julian.Sept1.months_in_leap_year()
    ...>   {:ambiguous, fewest..most//1} -> {fewest, most} == Calendrical.Julian.Sept1.info().months_in_year
    ...>   {:error, %Calendrical.NotDefinedError{}} -> is_list(Calendrical.Julian.Sept1.info().members)
    ...> end
    true

# `months_in_year`

Returns the number of months in a year: the base calendar's, and one
more where the year begins within a base month.

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of months.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.months_in_year(today.year) in [12, 13]
    true

# `months_in_year_bounds`

Returns the fewest and the most months a year has
(`Calendrical.Month.months_in_year_bounds/1`).

### Returns

* `{fewest, most}`, which in a composite calendar counts the months
  left in a year a change of calendar falls in.

### Examples

    iex> {fewest, most} = Calendrical.Julian.Sept1.months_in_year_bounds()
    iex> fewest <= Calendrical.Julian.Sept1.months_in_ordinary_year() and
    ...>   most >= Calendrical.Julian.Sept1.months_in_leap_year()
    true

# `naive_datetime_from_iso_days`

Converts ISO days and a day fraction to a naive datetime of this
calendar, as `c:Calendar.naive_datetime_from_iso_days/1` asks.

### Arguments

* `iso_days` is `{days, {parts_in_day, parts_per_day}}`, a day and a
  fraction of it.

### Returns

* `{year, month, day, hour, minute, second, microsecond}` of this
  calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day, 12, 0, 0, {0, 6}} =
    ...>   Calendrical.Julian.Sept1.naive_datetime_from_iso_days({739403, {43200000000, 86400000000}})
    iex> {year, month, day} == {date.year, date.month, date.day}
    true

# `naive_datetime_to_iso_days`

Converts a naive datetime of this calendar to ISO days and a day
fraction, as `c:Calendar.naive_datetime_to_iso_days/7` asks.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

### Returns

* `{iso_days, {parts_in_day, parts_per_day}}`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.naive_datetime_to_iso_days(date.year, date.month, date.day, 12, 0, 0, {0, 6})
    {739403, {43200000000, 86400000000}}

# `named_month`

Returns the days of a named month in a year
(`Calendrical.Month.named_month/3`).

### Arguments

* `year` is a year of this calendar.

* `named_month` is the CLDR month that names the month.

### Returns

* A list of `t:Date.Range.t/0`, one for each counted month that
  carries the name, earliest first, and `[]` where none does.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> cldr_month = Calendrical.Julian.Sept1.cldr_month(date.year, date.month)
    iex> Calendrical.Julian.Sept1.named_month(date.year, cldr_month) |> Enum.any?(&(date in &1))
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.named_month(date.year, 99)
    []

# `numeric_month`

Returns the number a date's month is written with in figures: the
month of its `written_date/3`.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The month of the date's `written_date/3`: a month number, or
  `{month, :leap}` for a leap month of a lunisolar calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar
  does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {_year, written_month, _day} = Calendrical.Julian.Sept1.written_date(date.year, date.month, date.day)
    iex> Calendrical.Julian.Sept1.numeric_month(date.year, date.month, date.day) == written_month
    true

# `ordinal_month_from_traditional`

Returns the position in a year of a traditional month
(`Calendrical.Month.month_from_traditional/3`), as `{:ok, month}`.

### Arguments

* `year` is a year of this calendar.

* `traditional_month` is a month's traditional number, or
  `{month, :leap}` for a leap month.

### Returns

* `{:ok, month}`, the month's position in the year, or

* `{:error, %Calendrical.InvalidMonthError{}}` for a month or a leap
  month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> traditional_month = Calendrical.Julian.Sept1.traditional_month(date.year, date.month)
    iex> Calendrical.Julian.Sept1.ordinal_month_from_traditional(date.year, traditional_month) == {:ok, date.month}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.ordinal_month_from_traditional(date.year, 99)

# `parse_date`

Parses a date written in this calendar's own notation.

### Arguments

* `string` is a date written `YYYY-MM-DD`, with a leading `-` for a
  year before 1, or, in a calendar of weeks, `YYYY-Www-D`.

### Returns

* `{:ok, {year, month, day}}`, or

* `{:error, :invalid_format}` where the text is not in that form or
  its fields are not digits, or

* `{:error, :invalid_date}` where the text names no date of this
  calendar.

The reason is an atom, not an exception, because `c:Calendar.parse_date/1`
requires one: `Date.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.parse_date(Date.to_string(date)) == {:ok, {date.year, date.month, date.day}}
    true

    iex> Calendrical.Julian.Sept1.parse_date("not a date")
    {:error, :invalid_format}

# `parse_naive_datetime`

Parses a naive datetime written in this calendar's own notation.

### Arguments

* `string` is a date as `parse_date/1` reads it, then `T` or a
  space and a time of day.

### Returns

* `{:ok, {year, month, day, hour, minute, second, microsecond}}`, or

* `{:error, reason}`, such as `:invalid_format` or `:invalid_date`,
  where the text is no such datetime.

The reason is an atom, not an exception, because
`c:Calendar.parse_naive_datetime/1` requires one:
`NaiveDateTime.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.parse_naive_datetime(Date.to_string(date) <> "T12:00:00") ==
    ...>   {:ok, {date.year, date.month, date.day, 12, 0, 0, {0, 0}}}
    true

    iex> Calendrical.Julian.Sept1.parse_naive_datetime("2024-06-01")
    {:error, :invalid_format}

# `parse_utc_datetime`

Parses a UTC datetime written in this calendar's own notation.

### Arguments

* `string` is a date as `parse_date/1` reads it, then `T` or a
  space, a time of day and an offset from UTC, `Z` or `±HH:MM`.

### Returns

* `{:ok, {year, month, day, hour, minute, second, microsecond}, offset}`,
  the datetime in UTC and the offset in seconds it was written with,
  or

* `{:error, reason}`, such as `:invalid_format`, `:invalid_date` or
  `:missing_offset`, where the text is no such datetime.

The reason is an atom, not an exception, because
`c:Calendar.parse_utc_datetime/1` requires one:
`DateTime.from_iso8601/2` reads it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.parse_utc_datetime(Date.to_string(date) <> "T12:00:00Z") ==
    ...>   {:ok, {date.year, date.month, date.day, 12, 0, 0, {0, 0}}, 0}
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.parse_utc_datetime(Date.to_string(date) <> "T12:00:00")
    {:error, :missing_offset}

# `parsing_calendar`

Returns the calendar a date written for this calendar is parsed in,
as its `info/0` states.

### Returns

* A calendar module.

### Examples

    iex> Calendrical.Julian.Sept1.parsing_calendar() == Calendrical.Julian.Sept1.info().parsing_calendar
    true

# `parsing_calendars`

Returns the calendars a date written for this calendar may be
written in: the members of a composite calendar, and this calendar
alone otherwise (`Calendrical.Info.parsing_calendars/1`).

### Returns

* A non-empty list of calendar modules, the members of a composite
  calendar in the order they take effect.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> in_effect = Calendrical.Info.in_effect(Calendrical.Julian.Sept1, date.year, date.month, date.day)
    iex> in_effect in Calendrical.Julian.Sept1.parsing_calendars()
    true

# `periods_in_year`

Returns the number of periods in a year: its months.

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of months in the year, as `months_in_year/1` returns
  it.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.periods_in_year(date.year) == Calendrical.Julian.Sept1.months_in_year(date.year)
    true

# `quadrimester`

Returns the days of a quadrimester of a year
(`Calendrical.Period.quadrimester/3`).

### Arguments

* `year` is a year of this calendar.

* `quadrimester` is the quadrimester, `1` to `3`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a quadrimester or a year the
  calendar does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  quadrimester is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.quadrimester(date.year, 1).first == Calendrical.Julian.Sept1.year(date.year).first
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.quadrimester(date.year, 4)

# `quarter`

Returns the days of a quarter of a year (`Calendrical.Period.quarter/3`).

### Arguments

* `year` is a year of this calendar.

* `quarter` is the quarter, `1` to `4`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a quarter or a year the calendar
  does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  quarter is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> quarter = Calendrical.Julian.Sept1.quarter_of_year(date.year, date.month, date.day)
    iex> date in Calendrical.Julian.Sept1.quarter(date.year, quarter)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.quarter(date.year, 5)

# `quarter_of_year`

Returns the quarter of the year a date falls in
(`Calendrical.Period.quarter_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The quarter, `1` to `4`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for a
  missing year or month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.quarter_of_year(date.year, date.month, date.day) in 1..4
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.quarter_of_year(date.year, date.month, 0)

# `related_gregorian_year`

Returns the related Gregorian year of a date
(`Calendrical.Era.related_gregorian_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* The Gregorian year the date's calendar year begins in, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:ok, first_day} = Date.convert(Calendrical.Julian.Sept1.year(date.year).first, Calendrical.Gregorian)
    iex> Calendrical.Julian.Sept1.related_gregorian_year(date.year, date.month, date.day) == first_day.year
    true

# `semester`

Returns the days of a semester of a year (`Calendrical.Period.semester/3`).

### Arguments

* `year` is a year of this calendar.

* `semester` is the semester, `1` or `2`.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a semester or a year the calendar
  does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  semester is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.semester(date.year, 1).first == Calendrical.Julian.Sept1.year(date.year).first
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.semester(date.year, 3)

# `shift`

Returns the date a number of years, quarters, months, weeks or days
from a date: the base calendar's arithmetic on the base date,
relabelled, for years, quarters and months, and a count of days
otherwise.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `date_part` is one of `:years`, `:quarters`, `:months`, `:weeks`
  or `:days`.

* `increment` is the number of units, which may be negative.

* `options` is a keyword list of options.

### Options

* `:clamp` keeps a day the month reached lacks as its last day, as
  the base calendar's `shift/6` does. The default is `true`.

### Returns

* `{year, month, day}` of this calendar, or

* `{:error, %Calendrical.InvalidDateError{}}` where `year`, `month` and
  `day` are no date of this calendar, or

* `{:error, %Calendrical.MissingFieldsError{}}` where a field is `nil`.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.shift(today.year, today.month, today.day, :days, 0)
    {today.year, today.month, today.day}

# `shift_date`

Shifts a date by a duration: its years and months together, as
`shift/6` adds months, and then its weeks and days.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `duration` is a `t:Duration.t/0`.

### Returns

* `{year, month, day}` of this calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.shift_date(date.year, date.month, date.day, Duration.new!(day: 7))
    iex> Date.new!(year, month, day, Calendrical.Julian.Sept1) == Date.add(date, 7)
    true

# `shift_naive_datetime`

Shifts a naive datetime by a duration: its date as `shift_date/4`
shifts it, and its time as `Calendar.ISO` does.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

* `duration` is a `t:Duration.t/0`.

### Returns

* `{year, month, day, hour, minute, second, microsecond}` of this
  calendar.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> next_day = Date.add(date, 1)
    iex> Calendrical.Julian.Sept1.shift_naive_datetime(date.year, date.month, date.day, 23, 0, 0, {0, 0}, Duration.new!(hour: 2)) ==
    ...>   {next_day.year, next_day.month, next_day.day, 1, 0, 0, {0, 0}}
    true

# `shift_time`

Shifts a time by a duration, as `Calendar.ISO` does.

### Arguments

* `hour`, `minute`, `second` and `microsecond` are a time of day,
  the microsecond as `{microseconds, precision}`.

* `duration` is a `t:Duration.t/0` of time units.

### Returns

* `{hour, minute, second, microsecond}`, wrapped around midnight.

### Examples

    iex> Calendrical.Julian.Sept1.shift_time(23, 0, 0, {0, 0}, Duration.new!(hour: 2))
    {1, 0, 0, {0, 0}}

# `solar_term`

Returns the day of a solar term of a Gregorian year, reckoned at the
place this calendar's `info/0` names, or at the Chinese calendar's
meridian, the traditional reference, where it names none.

### Arguments

* `index` is the solar term's number, `1` (lichun, 315° of solar
  longitude) to `24`, every 15° on.

* `gregorian_year` is a Gregorian year.

### Returns

* `{:ok, date}`, a `t:Date.t/0` in `Calendrical.Gregorian`, or

* `{:error, %Calendrical.InvalidSolarTermError{}}` where `index` is not
  `1` to `24`.

### Examples

    # Qingming, the fifth solar term
    iex> Calendrical.Julian.Sept1.solar_term(5, 2025)
    {:ok, ~D[2025-04-04 Calendrical.Gregorian]}

    iex> Calendrical.Julian.Sept1.solar_term(25, 2025)
    {:error, %Calendrical.InvalidSolarTermError{index: 25}}

# `traditional_leap_month`

Returns the traditional number of the month a year's leap month
follows, or `nil` (`Calendrical.Month.traditional_leap_month/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The traditional number of the month the leap month follows, or

* `nil` where the year has no leap month.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> is_nil(Calendrical.Julian.Sept1.traditional_leap_month(date.year)) ==
    ...>   is_nil(Calendrical.Julian.Sept1.leap_month(date.year))
    true

# `traditional_month`

Returns a month of a year as this calendar names it
(`Calendrical.Month.traditional_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* The month's traditional number, or `{month, :leap}` for a leap
  month, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.traditional_month(date.year, date.month) ==
    ...>   Enum.at(Calendrical.Julian.Sept1.traditional_months(date.year), date.month - 1)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.traditional_month(date.year, 99)

# `traditional_months`

Returns a year's months in order, named traditionally
(`Calendrical.Month.traditional_months/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A list of traditional months, the nth naming the year's nth month,
  with `{month, :leap}` for a leap month, and `[]` for a year the
  calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> length(Calendrical.Julian.Sept1.traditional_months(date.year)) ==
    ...>   Calendrical.Julian.Sept1.months_in_year(date.year)
    true

# `valid_date?`

Returns whether a year, month and day are a date of this calendar.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `true` if they are a date of this calendar, otherwise `false`.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.valid_date?(today.year, today.month, today.day)
    true
    iex> Calendrical.Julian.Sept1.valid_date?(today.year, today.month, 0)
    false

# `week`

Returns the seven days of a week of a year (`Calendrical.Week.week/3`).

### Arguments

* `year` is a year of this calendar.

* `week` is a week of the year.

### Returns

* A `t:Date.Range.t/0` of the week's seven days, which may begin in
  the year before or end in the year after, or

* `{:error, %Calendrical.InvalidDateError{}}` for a week the year does not have, or

* `{:error, %Calendrical.MissingFieldsError{}}` where the year or the
  week is `nil`.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week} = Calendrical.Julian.Sept1.week_of_year(date.year, date.month, date.day)
    iex> days = Calendrical.Julian.Sept1.week(week_year, week)
    iex> {Enum.count(days), date in days}
    {7, true}

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.week(date.year, 0)

# `week_date_from_date`

Returns the week-year, the week and the day of the week of a date
(`Calendrical.Week.week_date_from_date/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week, day_of_week}`, the day numbered from the day
  the calendar's weeks begin on, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week, day} = Calendrical.Julian.Sept1.week_date_from_date(date.year, date.month, date.day)
    iex> {week_year, week} == Calendrical.Julian.Sept1.week_of_year(date.year, date.month, date.day) and day in 1..7
    true

# `week_of_month`

Returns the month and the week of the month a date is in
(`Calendrical.Week.week_of_month/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{month, week}`, where the month is the one before or after where
  the date falls in that month's last or first week, or

* `{:error, exception}` for a date the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {month, week} = Calendrical.Julian.Sept1.week_of_month(date.year, date.month, date.day)
    iex> month in (date.month - 1)..(date.month + 1) and week >= 1
    true

# `week_of_year`

Returns the week-year and the week of the year a date is in
(`Calendrical.Week.week_of_year/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{week_year, week}`, where the week-year is the year before or
  after where the date falls in that year's last or first week, or

* `{:error, exception}` for a date the calendar does not have: a
  `Calendrical.MissingFieldsError` for a date missing a field, and a
  `Calendrical.InvalidDateError` otherwise.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week} = Calendrical.Julian.Sept1.week_of_year(date.year, date.month, date.day)
    iex> date in Calendrical.Julian.Sept1.week(week_year, week)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.week_of_year(date.year, date.month, 0)

# `weeks_in_week_year`

Returns the number of weeks in a week-year
(`Calendrical.Week.weeks_in_week_year/2`).

### Arguments

* `week_year` is a week-year of this calendar.

### Returns

* The number of weeks, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week, _day} = Calendrical.Julian.Sept1.week_date_from_date(date.year, date.month, date.day)
    iex> week <= Calendrical.Julian.Sept1.weeks_in_week_year(week_year)
    true

# `weeks_in_year`

Returns the number of weeks in a year (`Calendrical.Week.weeks_in_year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* The number of weeks, or

* `{:error, exception}` for a year the calendar does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {week_year, week} = Calendrical.Julian.Sept1.week_of_year(date.year, date.month, date.day)
    iex> week <= Calendrical.Julian.Sept1.weeks_in_year(week_year)
    true

# `weeks_of_month`

Returns the weeks of a month of a year in order
(`Calendrical.Week.weeks_of_month/3`).

### Arguments

* `year` and `month` are a month of this calendar.

### Returns

* A list of `t:Date.Range.t/0`, one for each week `week_of_month/3`
  names for the month, the first of which may begin in the month
  before and the last run into the month after, or

* `{:error, exception}` for a month the year does not have.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.weeks_of_month(date.year, date.month) |> Enum.all?(&(Enum.count(&1) == 7))
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidMonthError{}} = Calendrical.Julian.Sept1.weeks_of_month(date.year, 99)

# `written_date`

Returns the figures a date is written with: the base month and day
that name it, with the base year or this calendar's own year as
`:written_year` says.

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{year, month, day}` as the date is written.

### Examples

    iex> {:ok, today} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year, month, day} = Calendrical.Julian.Sept1.written_date(today.year, today.month, today.day)
    iex> Calendrical.Julian.Sept1.date_from_written_date(year, month, day)
    {:ok, {today.year, today.month, today.day}}

# `written_month_from_cldr_month`

Returns the month a CLDR month is written with in a year
(`Calendrical.Month.written_month_from_cldr_month/3`).

### Arguments

* `year` is a year of this calendar.

* `cldr_month` is a CLDR month number, or `{month, :leap}`.

### Returns

* The month as `written_date/3` writes it, or

* `{:error, :invalid_month}` where the year has no month of that
  name. The reason is an atom, not an exception: Localize's date parser
  reads it, where `Calendrical.Month.written_month_from_cldr_month/3`
  answers with an exception.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {_year, written_month, _day} = Calendrical.Julian.Sept1.written_date(date.year, date.month, date.day)
    iex> cldr_month = Calendrical.Julian.Sept1.cldr_month(date.year, date.month)
    iex> Calendrical.Julian.Sept1.written_month_from_cldr_month(date.year, cldr_month) == written_month
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.written_month_from_cldr_month(date.year, 99)
    {:error, :invalid_month}

# `year`

Returns the days of a year (`Calendrical.Period.year/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* A `t:Date.Range.t/0`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for
  no year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> date in Calendrical.Julian.Sept1.year(date.year)
    true

    iex> {:error, %Calendrical.MissingFieldsError{}} = Calendrical.Julian.Sept1.year(nil)

# `year_of_era`

Returns the year of era and era of a year (`Calendrical.Era.year_of_era/2`).

### Arguments

* `year` is a year of this calendar.

### Returns

* `{year_of_era, era}`, the era in effect on the year's first day,
  or

* `{:error, %Calendrical.InvalidDateError{}}` for a year the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> Calendrical.Julian.Sept1.year_of_era(date.year) ==
    ...>   Calendrical.Julian.Sept1.year_of_era(date.year, date.month, date.day)
    true

# `year_of_era`

Returns the year of era and era of a date (`Calendrical.Era.year_of_era/4`).

### Arguments

* `year`, `month` and `day` are a date of this calendar.

### Returns

* `{year_of_era, era}`, or

* `{:error, %Calendrical.InvalidDateError{}}` for a date the calendar does not have,
  or

* `{:error, exception}`, a `Calendrical.MissingFieldsError`, for no
  year.

### Examples

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {year_of_era, era} = Calendrical.Julian.Sept1.year_of_era(date.year, date.month, date.day)
    iex> year_of_era >= 1 and is_integer(era)
    true

    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> {:error, %Calendrical.InvalidDateError{}} = Calendrical.Julian.Sept1.year_of_era(date.year, 99, 1)

# `years_in_cycle`

Returns the number of years after which this calendar's years
repeat, as its `info/0` states, or `{:error, %Calendrical.NotDefinedError{}}`.

### Returns

* The number of years in the cycle, or

* `{:error, %Calendrical.NotDefinedError{}}` where the calendar states none.

### Examples

    # A year has as many days as the year one cycle later
    iex> {:ok, date} = Date.convert(~D[2024-06-01], Calendrical.Julian.Sept1)
    iex> case Calendrical.Julian.Sept1.years_in_cycle() do
    ...>   {:error, %Calendrical.NotDefinedError{}} -> true
    ...>   years -> Calendrical.Julian.Sept1.days_in_year(date.year) == Calendrical.Julian.Sept1.days_in_year(date.year + years)
    ...> end
    true

---

*Consult [api-reference.md](api-reference.md) for complete listing*