Convert between world time zones with daylight saving times

This is a very simple yet powerful function to convert a datenum from one timezone to another.

Update (2014-12-16): I now greatly recommend to use the Joda Time library instead of this function:
http://joda-time.sourceforge.net/
I have been using the C# port Noda Time lately and it is perfectly suited for this kind of tasks.
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As I could find no built-in function nor reliable contribution to achieve that, I had no choice but to write my own, leveraging the GregorianCalendar Java class.
Usage is quite simple:
targetDST = TimezoneConvert( dn, fromTimezone, toTimezone )
The datenum dn corresponds to the datetime you want to convert. Just specify from which timezone it comes and the target timezone, and you should get the expected result, that takes into account daylight saving time.

Feel free to let me know if I can extend it to support more situations (like Julian Calendar, obviously ;-).

You can get the name of the available timezones using this command:
TimeZone.getAvailableIDs
after importing the relevant java packages.
import java.lang.String
import java.util.* java.awt.*
import java.util.Enumeration