Calculations from the paper
  `Lines tangent to 2n-2 spheres in Rn'

        by Frank Sottile and Thorsten Theobald.

Abstract We show that there are 3 x 2n-1 complex common tangent lines to 2n-2 general spheres in Rn and that there is a choice of spheres with all common tangents real.

tetrahedron.sing   Solves the case of n=3 with 4 spheres at the corners of a tetrahedron.
AffineInd.maple This file creates a Singular file to compute the Groebner basis for the example of Section 3 where we have one of the 3 factors of the ideal. This was crucial for the proof of Theorem 5.
AffineInd-Ideals Output of the Singular code from AffineInd.maple
Dependent.maple This is the maple file accompanying the proof in Section 4. It runs the computation of the proof, and prints out commentary.   Here is its output
GenQuad4.maple This maple file creates a Singular file to compute the ideal of lines in 4-space tangent to 6 general quadrics.   Here is the Singular code it creates.   Here is the output of that code.
  
Figure1.maple Draws Figure 1, the 12 lines tangent to spheres at vertices of a regular tetrahedron. The ideal as computed in tetrahedron.sing has three components, and we color the components with different colors.   Figure1.html
Figure2.maple Draws the skeleton of Figure 2, the discriminant locus of Theorem 4 in the paper.  Figure2.html


Based upon work supported by the National Science Foundation under Grant No. 0070494.
Last modified: 22 May 2001 by Frank Sottile