Shana tova umetuka! (Happy Jewish New Year!)

Question

Write the shortest program, in the language of your choice, that takes as input a year on the Hebrew calendar, and outputs the corresponding Gregorian date for Rosh Hashana, in YYYY-MM-DD format.

~$ rh 5771
2010-09-09
~$ rh 5772
2011-09-29
~$ rh 5773
2012-09-17

• The input may come from either the command line or from stdin, whichever is more convenient.
• You may assume that the year will be between 5600 (1839) and 6000 (2239), inclusive.

Answer 1

Ruby, 192 181 165 characters

require'date'
s=(-6+235*n=gets.to_i)/19*765433+73848;e=s/u=25920
$><<Date.jd(347641+e+([h=s%u/19440,84>>e%7+h&1,v=e%7*(374454>>n%19&1-h&s%u/9923),v,n-5765].count 1))

Input is given as a single number on STDIN.

Edit 1: Several arithmetic transformations saved quite a few characters.

Edit 2: There was some room for improvement.

Answer 2

C#, 212

This might seem cheap, but here I go:

using System;using System.Globalization;class P{static void Main(){int y=int.Parse(Console.ReadLine())-5771;var a=new HebrewCalendar().AddYears(new DateTime(2010,9,9),y);Console.Write(a.ToString("yyyy-MM-dd"));}}

with spacing

using System;
using System.Globalization;
class P
{
    static void Main()
    {
        int y = int.Parse(Console.ReadLine()) - 5771;
        var a = new HebrewCalendar().AddYears(new DateTime(2010, 9, 9), y);
        Console.Write(a.ToString("yyyy-MM-dd"));  
    }
}

Answer 3

CPAN 5.10, 109

This is even cheaper than the C# solution, for reasons enumerated below. Code first: (character count as a difference to perl -E'' as usual)

$ perl -E'$_="DateTime::Calendar::Hebrew";/:/;eval"require $_";say$`->from_object(object,$_->new(year,<>,month,7))->ymd'

• steals Peter Olson's idea of just outsourcing it to the library
• CPAN's current release of DateTime::Calendar::Hebrew doesn't install out of the box, you need to patch it.
• needs Perl 5.10. No earlier, no later.

At least it's short.