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(kpathsea.info)Tilde expansion

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Tilde expansion
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  A leading `~' in a path element is replaced by the value of the
environment variable `HOME', or `.' if `HOME' is not set.

  A leading `~USER' in a path element is replaced by USER's home
directory from the system `passwd' database.

  For example,
     setenv TEXINPUTS ~/mymacros:

will prepend a directory `mymacros' in your home directory to the
default path.

  As a special case, if a home directory ends in `/', the trailing
slash is dropped, to avoid inadvertently creating a `//' construct in
the path.  For example, if the home directory of the user `root' is
`/', the path element `~root/mymacros' expands to just `/mymacros', not
`//mymacros'.

  Tilde expansion is implemented in the source file `kpathsea/tilde.c'.