I'm currently working on a paper on the Indian calendar, with an emphasis on computing the date of Deepavali and regional varieties. In the meantime you can look at these papers.
The Indian calendars are very interesting, but very complicated. Indians use both solar and lunisolar calendars. The solar calendars follow the sidereal year. The lunisolar calendars are of two types; some have months that run from new Moon to new Moon, while some have months that run from full Moon to full Moon. In addition to leap months, the lunisolar calendars sometimes skip months. They also follow the Moon for the days, so sometimes they skip or add days. They are probably the most complicated calendars currently used in the world. There are also several regional variations.
A basic reference is the book Calendrical Calculations by Nachum Dershowitz and Edward M. Reingold. Unfortunately, the first edition had some weaknesses in the chapters on the Indian calendar, but this has been corrected in the second edition. However, their main emphasis is to code the Surya Siddhanta algorithms, and they are not interested in regional varieties. For more details, you may want to try to get hold of the book Indian Calendric System by Commodore S.K. Chatterjee (Retd.).
One of my honours students, LEOW Choon Lian, has written a project on Indian Calendars. She has also written a Mathematica package, IndianCalendar.m. It uses the code of Nachum Dershowitz and Edward M. Reingold from their book Calendrical Calculations. Their Lisp functions were translated into the Mathematica package Calendrica by Robert C. McNally. Please note that this is the code from the first edition, which is freely available. The code from the new edition will only be available with the book.
The Mathematica notebook IndianCalendar.nb demonstrates the commands. (If you don't have Mathematica, you can download a copy of the MathReader.)
I have also supervised a number of undergraduate research projects on the Indian calendars.
If you know much about the different regional variations of the Indian calendar, I would love to hear from you.
Back to Helmer Aslaksen's page on Calendars in Singapore.
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