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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.
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 three variants, Plain TeX mode, LaTeX mode, and
SliTeX mode (these three distinct major modes differ only slightly).
They are designed for editing the three 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 or SliTeX
input; if so, it selects the appropriate mode. If the file contents do
not appear to be LaTeX or SliTeX, 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, and M-x slitex-mode to select explicitly the particular variants of TeX mode.
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