Some things to do with &EXT()

Incantation	Result	Explanation
request.filename	&EXT('request.filename')	full internal path of the current resource
request.uri	&EXT('request.uri')	URI of the currently viewed resource
request.state	&EXT('request.state')	state of the resource, either: construct or published
user.name	&EXT('user.name')	username of user
user.domain	&EXT('user.domain')	Domain the user is in
user.course.sec	&EXT('user.course.sec')	Users's Course Section
environment.firstname	&EXT('environment.firstname')	User's first name
environment.middlename	&EXT('environment.middlename')	User's middle name
environment.lastname	&EXT('environment.lastname')	User's last name
environment.generation	&EXT('environment.generation')	Jr., Sr., III, etc.
environment.screenname	&EXT('environment.screenname')	User's screen name (name that appears in discussion postings)
environment.nickname	&EXT('environment.nickname')	User's nickname. (Name the user prefers to be called in person)
environment.id	&EXT('environment.id')	User's student/employee ID number
request.browser.version	&EXT('request.browser.version')	Version of the user's browser
request.browser.type	&EXT('request.browser.type')	What type of browser is the user using
course.description	&EXT('course.decription')	Descriptive name for a course
course.num	&EXT('course.num')	Internal Course Identifier
course.url	&EXT('course.url')	Current course toplevel map.
query.*		query.* allows access to ny passed-in form parameters
query.grade_target	&EXT('query.grade_target')	Ignore this. It isn't generally useful.

Other things:

Incantation	Result	Explanation
$external::target	$external::target	Whether we are printing (tex) or viewing on screen (web)
$external::part	$external::part	current Part id
$external::gradestatus	$external::gradestatus	The solved status of the current part.
$external::datestatus	\verb+$external::datestatus+	The current status of the problem CLOSED either before opendate or between duedate and answerdate CAN_ANSWER CANNOT_ANSWER still open but either exhausted tries, has the problem correct, or has been excused SHOW_ANSWER after answerdate and some rare states that if they occur the problem isn't shown (you can safely ignore these): NOT_YET_VIEWED limited view period being used and student hasn't "checked out" the problem yet INVALID_ACCESS IP restrictions in effect, and user's IP address is not allowed access UNAVAILABLE network problems are occurring
$external::randomseed	$external::randomseed	The randomseed currently in use.