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D.2.4.2 cgsdr
Procedure from library grobcov.lib (see grobcov_lib).
- Return:
- Returns a list T describing a reduced and disjoint comprehensive
Groebner system (CGS), and whose groups of segments correspond
to constant leading power products (lpp) of the reduced Groebner
basis. The returned list is of the form:
(
(lpp, (basis,segment),...,(basis,segment)),
..,,
(lpp, (basis,segment),...,(basis,segment))
)
The bases are the reduced Groebner bases (after normalization)
for each point of the corresponding segment.
Each segment is given by a reduced representation (Ni,Wi), with
Ni radical and V(Ni)=Zariski closure of the segment Si=V(Ni)\V(hi),
where hi is the product of the polynomials w in Wi.
With option ('can',2) (the default) the lpp group of segments
when added together need not be locally closed, whereas it
does with options ('can',0) (homogenizes the given basis) and
('can',1) (homogennizes the whole given ideal). With option
('can',1) the partition into lpp groups is the canonical one
(see Wibmer's Theorem).
- Note:
- The basering R, must be of the form Q[a][x], a=parameters,
x=variables, and should be defined previously, and the ideal
defined on R.
Example:
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