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TeX is a software system written by Donald Knuth to typeset text, especially text containing mathematics. LaTeX is a set of macros written in TeX, designed to simplify the typesetting of a document by allowing the user to concentrate on the content and structure of the document rather than the exact appearance of the finished product.LaTeX is free, and can be run on virtually any platform. It works very nicely on PCs running Linux or FreeBSD.
There is a very good help page for LaTeX on the web.
The important output of and LaTeX is a file called filename.dvi. DVI files can be viewed in X by typing xdvi filename or printed by typing dvips filename.dvi | lpr.
LaTeX is installed on UVa CS dept machines, and should work by default. LaTeX2e is installed in /usr/cs/contrib/bin, so you should have that directory early in your path.
There are (of course) emacs modes which make editing TeX and LaTeX files easier. If you're lucky, emacs will automatically go into one of those modes when you load a file with the .tex extension. Otherwise, ask somebody who knows a lot about emacs to help you make this happen.
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