I would like to know how this person is able to switch between search forms by simply clicking the links "dictionary | site wide". What is this code called? I checked the source code, but it doesn't provide me with much information. Any opinions? Ideas? It's not so much important to know how the search form switches, I think just by knowing the code generally, I will be able to deduce how the form switches.
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Clicking on dictionary/site wide calls a function called switch_menu() which is about 10 lines of code (looks like a self-written script, with no copyright info) which sets display style on the search boxes to display the correct one.
Googling getElementById will give you the code you need to change the display.
Their google(sitewide) searchbox is the standard google search box that any site admin can get from google. Their own search box will be a custom search written into the wiki.
Changing the layer to display (switch_menu) is a very easy function to write (so easy that using it would be very unlikely to cause a problem). The div containing the google search is easy to obtain from google and their own custom search will be part of their wiki.