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D.2.4.4 multigrobcov
Procedure from library grobcov.lib (see grobcov_lib).
- Usage:
- multigrobcov(F); This routine is to be used instead of grobcov
when grobcov does not finish, and the generic case is expected
to have basis 1. It can be useful for automating discovery of
geometric theorems.
The ideal F must be defined on a parametric ring Q[a][x].
If the generic basis is not 1, then it returns the empty list,
but if the generic basis is one then it computes the
grobcov over each irreducible component of the complement of
the generic segment and returns the generic segment and the
different grobcov on each segment. From the result, the global
grobcov can be deduced eliminating convenablement the inter-
sections of the different grobcov computed over the components.
Options: A list of options of the form
('comment',0-1,'can',0-1 can,'cgs',0-1,'ext',0-1), can be given.
One can give none till 4 of these options by giving the
name of the option and the value. Options 'null' and 'nonnull' are
avoided.
When option ('comment',1) is set, the routine provides information
about the development of the computation. The default option
is ('comment',0).
When option ('can',0) is given, then the computation is
done homogenizing the given basis but not computing the
whole homogenized ideal. Thus in this case the result is not
completely canonical but it is also useful. This option
usually facilitates the computation. The default option is ('can',1).
When option ('cgs',0) is set, then instead of using cgsdr
for computing the initial reduced disjoint CGS, then
buildtree is used. Option ('cgs'0) can be tested when ('cgs',1)
(the default option) fails. When option ('ext',0) is set, only the
generic representation of the bases are computed instead of the
full representation (the default option is ('ext',1)).
- Return:
- The list whose first element is the generic case, and the
remaining elements are the grobcov over the different irreducible
components in the complementary of the generic segment.
The empty list if the generic case does not have basis 1.
- 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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