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D.2.4.1 grobcov

Procedure from library grobcov.lib (see grobcov_lib).

Return:
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 (by option ("ext",1)) or in
generic representation (default option ("ext",0)). 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 representation of the segment is the P-representation.
With option ("rep",1) the representation of the segment is the C-representation.
With option ("rep",2) both representations of the segment 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.

Note:
The basering R, must be of the form Q[a][x], a=parameters, x=variables, and should be defined previously. The ideal must be defined on R.

parametric ideal.

Example:
 


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