MATLAB Examples

Incomplete intersection

Example 9.2 from Numerically solving polynomial systems with Bertini, by Daniel J. Bates, Jonathan D. Haunstein, Andrew J. Sommese and Charles W. Wampler (SIAM 2013).

The square system

$$ y-x^2 = 0 $$

$$ x y - z = 0 $$

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

has as its intersection the twisted cubic curve instead of isolated points.

polysyms x y z
f = y-x^2;
g = x*y-z;
h = x*z-y^2;
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 1: 1 classified component
-----------------------------------------------------
   degree 3: 1 component

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