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

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