## Monday, December 15, 2008

### Coloring book reject

The image below is a Groebner fan that is just too complicated to put in the coloring book, buts I think its pretty impressive:

The ideal generating this is from what I call the "super three-vortex problem", the equations for the central configurations of a 1/r^2 potential:

I am mainly interested in the nonzero solutions of this system. To get at those, we can saturate the ideal - or in practical terms we can introduce a new variable, w, and add the equation w*s12*s13*s23 - 1 = 0  to the ideal. The 3D Groebner fan of the resulting system can be seen here.