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D.2.4.3 gencase1

Procedure from library grobcov.lib (see grobcov_lib).

Usage:
gencase1(F); This routine determines the generic segment when the generic case has basis 1, and returns the empty list if not. It is useful, for example in automatic discovery of geometric theorems, to determine the prime varieties over which solutions exist. It can work, even if the complete grobcov does not finish. It serves to obtain a partial result that can be sometimes very useful. It is also used internally in the canonical computation grobcov, but can be called by the user. Only the basering Q[a][x] needs to be defined and the ideal given in this ring.
Options: It allows an option ('compbas,0-1),
If the routine is called with option
('compbas',0), then the given ideal must be the reduced Groebner basis of the ideal in the ring Q[x,a].
If the routine is called by the user this option not to be used, and the algorithm will compute internally the reduced Groebner basis of the ideal in the ring Q[x,a].

Return:
The list of the generic case, when its basis is 1, or the empty list if not.
The output is of the form
(lpp=1,basis=1,(null ideal=0,(p1,..ps)),N)
where (0,(p1,..,ps)) is the P-representation of the generic segment (the pi's are the prime components) and N is its intersection

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.

Example:
 


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