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Common Transversals and Tangents - First
computational approach
The ideal describes all quadrics Q satisfying the conditions.
In particular, it also contains three trivial cases which have to be
removed:
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• Q of rank 1:
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ideal E1 of all 2-minors of the
matrix of Q ;
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• Q = 2 planes meeting in L1:
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ideal E2=<a,b,c,d,e,f,g>
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• Q = 2 planes meeting in L2:
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ideal E3=<c,d,f,g,h,k,l>
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These excess components are removed by saturation of
I w.r.t E1, E2 and E3 in
 .
Computational Problem:
Even a standard basis of I cannot be computed in reasonable time because of
the large number of parameters (= 9)!
But saturation involves several standard basis computations.
Consequence:
Using this approach, the computation is infeasable.
A Different Approach
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