source: CGBLisp/doc/order.txt@ 1

;;; LEX> (p q &optional (start 0) (end (length p)))                  [FUNCTION]
;;;    Return T if P>Q with respect to lexicographic order, otherwise NIL. 
;;;    The second returned value is T if P=Q, otherwise it is NIL.
;;;
;;; TOTAL-DEGREE (m &optional (start 0) (end (length m)))            [FUNCTION]
;;;    Return the todal degree of a monomoal M.
;;;
;;; GRLEX> (p q &optional (start 0) (end (length p)))                [FUNCTION]
;;;    Return T if P>Q with respect to graded lexicographic order, otherwise
;;;    NIL. The second returned value is T if P=Q, otherwise it is NIL.
;;;
;;; GREVLEX> (p q &optional (start 0) (end (length p)))              [FUNCTION]
;;;    Return T if P>Q with respect to graded reverse lexicographic order,
;;;    NIL otherwise. The second returned value is T if P=Q, otherwise it is
;;;    NIL. 
;;;
;;; REVLEX> (p q &optional (start 0) (end (length p)))               [FUNCTION]
;;;    Return T if P>Q with respect to reverse lexicographic order, NIL
;;;    otherwise.  The second returned value is T if P=Q, otherwise it is
;;;    NIL. This is not and admissible monomial order because some sets do
;;;    not have a minimal element. This order is useful in constructing
;;;    other orders.
;;;
;;; INVLEX> (p q &optional (start 0) (end (length p)))               [FUNCTION]
;;;    Return T if P>Q with respect to inverse lexicographic order, NIL
;;;    otherwise The second returned value is T if P=Q, otherwise it is NIL.
;;;
;;; ELIMINATION-ORDER (k &key (primary-order #'lex>)                 [FUNCTION]
;;;                    (secondary-order #'lex>))
;;;    Return a predicate which compares monomials according to the
;;;    K-th elimination order. Two optional arguments are PRIMARY-ORDER
;;;    and SECONDARY-ORDER and they should be term orders which are used
;;;    on the first K and the remaining variables.
;;;
;;; ELIMINATION-ORDER-1 (order)                                      [FUNCTION]
;;;    A special case of the ELIMINATION-ORDER when there is only
;;;    one primary variable.
;;;