MATLAB Examples

Complete intersection

Example 9.1 from Numerically solving polynomial systems with Bertini, by Daniel J. Bates, Jonathan D. Haunstein, Andrew J. Sommese and Charles W. Wampler (SIAM 2013).

The system

$x^2+y^2+z^2-1 = 0$

$x y = 0$

$y-z = 0$

is the intersection of the unit sphere with the yz and xz planes and also the y=z plane, yielding four points. This is an example of a complete intersection.

polysyms x y z f = x^2+y^2+z^2-1; g = x*y; h = y-z; poly_system = BertiniLab('variable_group',[x y z],'function_def',[f; g; h], ... 'config',struct('TrackType',1)); poly_system = poly_system.solve; results = poly_system.solve_summary; istart = strfind(results,'************** Decomposition'); disp(results(istart:end)) 
************** Decomposition by Degree ************** Dimension 0: 4 classified components ----------------------------------------------------- degree 1: 4 components *****************************************************