Are there any restrictions in php for open_basedir or some security modules that could restrict access to some files or folders? And you did not get any errors in debugging ...filter/tex/texdebug.php or ...filter/algebra/algebradebug.php ? ( set debugging first to ALL from Site administration > Development > Debugging )
You did not mention if it is moodle 2.X or 1.9.X ... and I have not used algebra filter on production sites (only tested it some years ago) but debugging or server error logs should tell the reason for this issue ( it can be some setting of php, level of error reporting, disabled functions of php, some .htaccess file, ... )
Do you have some other filters enabled in Site administration > Plugins > Filters > Manage filters ?