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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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