Let D be a CAD and P be its projection factor set:

- (TRUE) and (FALSE) are both formulas.
- ((i,j),op) is a formula, where 0 < i <= |P| and 0 < j <=
|P_i|, and op is in {LTOP,EQOP,GTOP,GEOP,NEOP,LEOP}.
- (ANDOP,F_1,...,F_i) is a formula, where i > 1 and
F_1,...,F_i are formulas.
- (OROP,F_1,...,F_i) is a formula, where i > 1 and F_1,...,F_i
are formulas.
- ((i,j),(op,k)) is a formula,where 0 < i <= |P| and 0 < j < |P_i|, and op is in {LTOP,EQOP,GTOP,GEOP,NEOP,LEOP} and k is a non-zero int.

- if k > 0
**x_i op "the kth root of q(x_1, ..., x_{i-1}, X)"**, where**X**is a purely symbolic variable. This atomic formula is true if and only if q(x_1, ..., x_{i-1}, X) has at least k roots, and x_i bears relation op to the kth of these, ordered smallest to largest.- if 0 > k
- x_i op "the |k|th root of
q(x_1, ..., x_{i-1}, X)", where
**X**is a purely symbolic variable. This atomic formula is true if and only if q(x_1, ..., x_{i-1}, X) has at least |k| roots, and x_i bears relation op to the |k|th of these, ordered largest to smallest.

Last modified: Tue Jul 30 15:25:05 EDT 2002