Original Unnormalized QEPCAD formula data structure
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An unnormalized formula is (NOTOP F_1), (RIGHTOP F_1 F_2),
(LEFTOP F_1 F_2), (EQUIOP F_1 F_2), (ANDOP F_1 F_2 ... F_s), 
(OROP  F_1 F_2 ... F_s), or an unnormalized atomic formula, 
where NOTOP, LEFTOP, RIGHTOP, EQUIOP, ANDOP and OROP are macro 
constants defined in qepcad.h.

A unnormalized atomic formula is of the form (T,P,k,nil) where

  T : is the relational operator, one of the macro constants
      LTOP, EQOP, GTOP, GEOP, NEOP, LEOP defined in qepcad.h
  P : is an r-variate saclib polynomial
  r : a positive integer


Original Normalized QEPCAD formula data structure
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A normalized formula is (ANDOP F_1 F_2 ... F_s), 
(OROP  F_1 F_2 ... F_s), or a normalized atomic formula, where
ANDOP and OROP are macro constants defined in qepcad.h.


A normalized atomic formula is of the form (T,P,k,I) where

  T : is the relational operator, one of the macro constants
      LTOP, EQOP, GTOP, GEOP, NEOP, LEOP defined in qepcad.h
  P : is a primitive irreducible saclib polynomial in k
      variables of positive degree in it's main variable (i.e.
      a k-level polynomial in the CAD problem)
  k : the level
  I : a pair (i,j) giving the index of P in the qepcad 
      projection factor set data structure


Extensions to QEPCAD's formula data structure
---------------------------------------------
July 2002 introduced a normalized atomic formula for indexed
root expressions: (IROOT,T,j,(P_1, ..., P_s),k,(I_1, ..., I_s)) 
where

  IROOT: a macro constant defined in qepcad.h
  T    : is the relational operator, one of the macro constants
         LTOP, EQOP, GTOP, GEOP, NEOP, LEOP defined in qepcad.h
  j    : the index of the indexed root expression
  P_i  : primitive irreducible k-level polynomials
  k    : the level
  I_i  : pairs (i,j) giving the index of P_i in the qepcad
         projection factor set data structure.
  
Non-normalized - i.e. after being read-in by QFFTEV but before
going through the normalization process the format of this atomic
formula is (IROOT,T,j,P,k,NIL), where P is a k-variate saclib
polynomial of positive degree in x_k.