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Details of the Calendar Package

Conventions for Numbering Years

 • There are two commonly used year naming conventions in use. The first is the "Dionysian convention," or the Common Era notation system.
 • Dionysius Exiguus created the scheme for numbering using as a reference point his calculation of the year in which Jesus Christ was born (the year AD 1).
 • Since the number $0$ was not yet known at the time this system was devised in sixth century Europe, the previous year was named 1 BC. This system, while still very widely used in a slightly more modern form employing the religiously neutral "CE" ("Common Era") and "BCE" ("Before the Common Era") suffers from the lack of a year 0, which makes date arithmetic inconvenient.
 • The astronomer Jacques Cassini proposed, after the introduction of negative numbers, what is now called the "Cassini convention." The year 1 BC in the Dionysian convention is year 0 in the Cassini convention, and years prior to that are given negative numbers. Thus, for example, 47 BCE is the year -46 in the Cassini convention. In general, the year $Y$ BCE is the year $1-Y$ in the Cassini convention. The Cassini convention is universally used in scientific calculations today, while the Dionysian convention is commonly used by historians.
 • Maple's Calendar package uses the Cassini convention exclusively for numerical input and output of years.

About Historical Accuracy of Dates

 • Some calculations performed by the Calendar package are predicated on the assumption of the use of a proleptic Julian/Gregorian calendar.  In general, dates prior to the year 5 CE should not be regarded as historically accurate, as calendrical usage, such as the application of leap year rules, were applied inconsistently before this date.  (For example, the year 4 CE was, historically, not a leap year.)
 • Julian calendar rules are applied to all dates prior to October 4, 1582, the assumed date of the Gregorian calendar reform.  Gregorian calendar rules are applied to all dates after October 15, 1582.
 • Note that even the date of Gregorian calendar reform is dependent upon geography. Various countries adopted the Gregorian calendar at different times after its inception in 1582.  However, the 1582 date is used internally by the Calendar package.
 • Currently, leap seconds are ignored in computing with Date objects and their corresponding UTC Time objects.

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