A collection of isolated solutions
Zachary A. Griffin, Jonathan D. Hauenstein,
Chris Peterson, and
Andrew J. Sommese.
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Consider the ideal
< x12 + x2 + x3 - 1,
x1 + x22 + x3 - 1,
x1 + x2 + x32 - 1 >,
which has 5 solutions, three of multiplicity 2 and two of multiplicity 1.
The remainder of this page documents calculating the Hilbert function
for the zero-scheme corresponding to subsets of the solutions.
Directions
Before you begin, you will need to have Matlab installed. We present the computation for the second
set of points and provide the files for the others below.
- Save the files Points2, Points2dual, and HilbertFunc.m in the same directory.
- Execute the Matlab command
>> [reg, hilbertFunc, stdMon] = HilbertFunc(3, 'Points2', 'Points2dual', 1e-10, 1)
from the directory.
- Here is the output. Each row of stdMon lists the exponents of a standard monomial.
For example, the row
1 0 1
corresponds to the monomial x1 x3.
- Here is the output for all of the computations.
Additional Files
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