A system with isolated and positive-dimensional solution components
Zachary A. Griffin, Jonathan D. Hauenstein,
Chris Peterson, and
Andrew J. Sommese.
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Consider the ideal
<(x2 - x12)(x1 - 2)2,
(x1x2 - x3)(x2 - 2)2,
(x22 - x1x3)(x3 - 2)>,
which has 5 isolated solutions, four of multiplicity 2 and one of multiplicity 8, and
the twisted cubic C = {(t,t2,t3)}.
The remainder of this page documents calculating the Hilbert function
for the zero-scheme corresponding to the isolated solutions and its radical.
Directions
Before you begin, you will need to have Matlab installed.
- Save the files Points, Pointsdual, HilbertFunc.m,
HilbertFuncVeronese.m in the same directory.
- Execute the Matlab commands
>> [reg, hilbertFunc] = HilbertFunc(3, 'Points', 'Pointsdual', 1e-10, 0)
>> [reg, hilbertFunc] = HilbertFuncVeronese(3, 'Points', 1e-10, 0)
from the directory.
- Here is the output.
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