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If you know the latex code of a character which you want in unicode, just enter the its code and then press enter. The unicode character is then copied to the clipboard and then automatically pasted to last focused application (e.g. chat window).
If there is no such code found, the advanced converter turns on. The advanced converter supports the latex characters prefixed by a '' and superscripts and subscripts. Super and subscripts are supported only for digits and the +, - and = signs.
You should bind the application to a hotkey to be able to easily use. For example in Gnome you could do this in the keyboard settings:
The application currently works only on Linux. It uses python 3.2, python's tkinter library, xclip and xdotool utilities. You can start the gui on Windows/Mac though as it is cross-platform but auto-pasting isn't supported yet.
phillipberndt has created a version which works with python 2.7: https://github.com/phillipberndt/latex-to-unicode
vikhyat was kind enough to put up a similar application on his server for online use: http://vikhyat.net/stuff/latex_to_unicode/