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TeX is a powerful text formatter written by Donald Knuth; it is also free, like GNU Emacs. LaTeX is a simplified input format for TeX, implemented by TeX macros; it comes with TeX. SliTeX is a special form of LaTeX.1 DocTeX (.dtx) is a special file format in which the LaTeX sources are written, combining sources with documentation.
Emacs has a special TeX mode for editing TeX input files. It provides facilities for checking the balance of delimiters and for invoking TeX on all or part of the file.
TeX mode has four variants: Plain TeX mode, LaTeX mode,
SliTeX mode, and DocTeX mode (these distinct major modes differ
only slightly). They are designed for editing the four different
formats. The command M-x tex-mode looks at the contents of the
buffer to determine whether the contents appear to be either LaTeX
input, SliTeX, or DocTeX input; if so, it selects the
appropriate mode. If the file contents do not appear to be LaTeX,
SliTeX or DocTeX, it selects Plain TeX mode. If the contents
are insufficient to determine this, the variable
tex-default-mode
controls which mode is used.
When M-x tex-mode does not guess right, you can use the commands M-x plain-tex-mode, M-x latex-mode, M-x slitex-mode, and doctex-mode to select explicitly the particular variants of TeX mode.