QEPCAD's polynomial data structure
----------------------------------

A polynomial structure is a list of length five.  The first
element of the list is the polynomial, the second is its label,
the third its parentage, the fourth its type and the fifth its
status.  The list positions are defined in qepcad.h as
follows:

#define PO_POLY       1
#define PO_LABEL      2
#define PO_PARENT     3
#define PO_TYPE       4
#define PO_STATUS     5

The label of a polynomial is a list whose first element
is a list of characters and whose remaining elements are
integer indices.  For example, a projection factor
that appears externally as P_2,3 has the internal label
(('P'),2,3).

The parentage of a polynomial is a list containing one
element for each of its parents or parent pairs.  Each
parent or parent pair is also represented by a list.  The
first element of that list is the type of parentage, which
may be any of the following: resultant, discriminant, leading
coefficient, trailing coefficient (if the Lazard projection
was used), derivative (solution formula phase may add 
derivatives or projection factors) or factor.  The type of 
any parent of a  projection factor is 'factor' whereas the 
type of any parent of a projection polynomial is one of the 
other four types.  These five types have names that are 
defined in qepcad.h as follows:

#define PO_RES        10
#define PO_DIS        11
#define PO_LCO        12
#define PO_TCO        13
#define PO_FAC        14
#define PO_DER        15

If the parent type is PO_FAC then the parent list has
three elements, the third being the projection polynomial
(or input polynomial) of which it is a factor, and the
second is the multiplicity of the factor.

If the parent type is PO_RES then the parent list has
six elements, the fourth and sixth being the two polynomials
whose resultant is being described.  The second, third and
fifth elements relate to the subresultant projection method;
if the McCallum projection method is used these elements
are respectively 0, 1 and 1.

If the parent type is PO_DIS then the parent list has
four elements, corresponding to the first four elements of
a PO_RES parent list.

If the parent type is PO_DER then the parent list has
three elements, the third being the projection polynomial
(or input polynomial) of which it is a factor, and the
second is simply set to zero.

If the parent type is PO_LCO then the parent list has
three elements.  In this case we have the leading
coefficient of the i-th reductum of some polynomial. 
The third element is that polynomial and the second
element is i.  (i = 0 indicates no reducta.)

The type PO_TCO occurs only if the Lazard projection method
is used, which method is discouraged because it may not be
valid.