The list
(
(lpp_1,basis_1,segment_1,lpph_1),
...
(lpp_s,basis_s,segment_s,lpph_s)
)
The lpp are constant over a segment and correspond to the
set of lpp of the reduced Groebner basis for each point
of the segment.
The lpph corresponds to the lpp of the homogenized ideal
and is different for each segment. It is given as a string.
Basis: to each element of lpp corresponds an I-regular function given
in full representation. The
I-regular function is the corresponding element of the reduced
Groebner basis for each point of the segment with the given lpp.
For each point in the segment, the polynomial or the set of
polynomials representing it, if they do not specialize to 0,
then after normalization, specializes to the corresponding
element of the reduced Groebner basis. In the full representation
at least one of the polynomials representing the I-regular
function specializes to non-zero.
With the default option ("rep",0) the segments are given
in P-representation.
With option ("rep",1) the segments are given
in C-representation.
With option ("rep",2) both representations of the segments are
given.
The P-representation of a segment is of the form
((p_1,(p_11,..,p_1k1)),..,(p_r,(p_r1,..,p_rkr))
representing the segment U_i (V(p_i) \ U_j (V(p_ij))),
where the p's are prime ideals.
The C-representation of a segment is of the form
(E,N) representing V(E)\V(N), and the ideals E and N are
radical and N contains E.