Nine-point path synthesis problem

Zachary A. Griffin, Jonathan D. Hauenstein, Chris Peterson, and Andrew J. Sommese.

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    Consider computing the Hilbert function for the zero-scheme defined by the 8652 isolated nonsingular solutions of the nine-point path synthesis problem described in Problem 3 of [WMS]. This problem computes the four-bar linkages through the following 9 real points
(0.25, 0.00),  (0.52, 0.10),  (0.80, 0.70), 
(1.20, 1.00),  (1.40, 1.30),  (1.10, 1.48), 
(0.70, 1.40),  (0.20, 1.00),  (0.02, 0.40). 
See Four-bar linkages using alphaCertified for more details.
The remainder of this page documents calculating the Hilbert function for the zero-scheme corresponding to the 8652 isolated nonsingular solutions which is
1, 13, 87, 403, 1454, 4342, 8652, 8652, ...
Directions
Before you begin, you will need to have Matlab installed.
[WMS]  C.W Wampler, A.P. Morgan, and A.J. Sommese, Complete solution of the nine-point path synthesis problem for four-bar linkages, ASME J. Mech. Des., 114 (1992), 153–159.
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