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Common Transversals and Tangents: The Ideal
After a suitable projective linear transformation




Using Plücker coordinates, the lines intersecting these 2 lines are given by


The quadric Q is given by the quadratic form associated to

and the condition of being tangent to it reformulates to


This leads to the formulation of the ideal as the 2-minors of the matrix

Here the cij stand for the coordinates of an 8-dimensional projective space. The Computational Aspect.

KL, 06/03 http://www.singular.uni-kl.de