From Oil Fields to Hilbert Schemes
DOI10.1007/978-3-211-99314-9_1zbMath1191.13034OpenAlexW2115350669MaRDI QIDQ3576570
Hennie Poulisse, Lorenzo Robbiano, Martin Kreuzer
Publication date: 30 July 2010
Published in: Texts and Monographs in Symbolic Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/978-3-211-99314-9_1
Hilbert schemeeigenvalue methodpolynomial system solvingborder basisapproximate algorithmborder basis schemeBuchberger-Möller algorithm\texttt{CoCoA}oil fieldGröbner basis scheme
Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Parametrization (Chow and Hilbert schemes) (14C05) Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.) (13P25) Solving polynomial systems; resultants (13P15)
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Cites Work
- A description of certain affine open subschemes that form an open covering of \(\text{Hilb}^n_{\mathbb{A}^2_k}\).
- Approximate computation of zero-dimensional polynomial ideals
- Computing border bases
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- Characterizations of border bases
- Thinning out redundant empirical data
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- Subideal border bases
- Numerical Polynomial Algebra
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