Book contents
- Frontmatter
- Contents
- Preface
- Programme Committee
- Tutorials
- Research Papers
- The Fractal Walk
- Gröbner Bases Property on Elimination Ideal in the Noncommutative Case
- 17 The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
- 18 Newton Identities in the Multivariate Case: Pham Systems
- 19 Gröbner Bases in Rings of Differential Operators
- 20 Canonical Curves and the Petri Scheme
- 21 The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
- 22 Gröbner Bases in Non-Commutative Reduction Rings
- 23 Effective Algorithms for Intrinsically Computing SAGBI-Gröbner Bases in a Polynomial Ring over a Field
- 24 De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
- 25 An application of Gröbner Bases to the Decomposition of Rational Mappings
- 26 On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
- 27 Full Factorial Designs and Distracted Fractions
- 28 Polynomial interpolation of Minimal Degree and Gröbner Bases
- 29 Inversion of Birational Maps with Gröbner Bases
- 30 Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
- 31 Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
- Appendix An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
- Index of Tutorials
24 - De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- Contents
- Preface
- Programme Committee
- Tutorials
- Research Papers
- The Fractal Walk
- Gröbner Bases Property on Elimination Ideal in the Noncommutative Case
- 17 The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
- 18 Newton Identities in the Multivariate Case: Pham Systems
- 19 Gröbner Bases in Rings of Differential Operators
- 20 Canonical Curves and the Petri Scheme
- 21 The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
- 22 Gröbner Bases in Non-Commutative Reduction Rings
- 23 Effective Algorithms for Intrinsically Computing SAGBI-Gröbner Bases in a Polynomial Ring over a Field
- 24 De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
- 25 An application of Gröbner Bases to the Decomposition of Rational Mappings
- 26 On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
- 27 Full Factorial Designs and Distracted Fractions
- 28 Polynomial interpolation of Minimal Degree and Gröbner Bases
- 29 Inversion of Birational Maps with Gröbner Bases
- 30 Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
- 31 Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
- Appendix An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
- Index of Tutorials
Summary
En el nombre del Padre que fizo toda cosa.
Et de Don Jhesucristo, fijo de la Gloriosa.
Et del Spiritu Sancto, que egual dellos prosa,
De un confesor sancto quiero fer una prosa.
Quiero fer una prosa en roman paladino,
En qual suele el pueblo fablar a su vecino,
Ga non se tan letrado por fer otro latino,
Bien valdra, como credo, un vaso de bon vino.
Gonzalo de BerceoRemembrance
It was Autumn 1983, when the researchers on Gröbner could have been counted on the fingers of two hands. Michael and me were completing our algorithm to compute resolutions (Mora, Möller 1986a, 1986b) and I was invited in Naples to give an introductory tutorial on Gröbner bases.
I had plenty of free time and, since somebody had just quoted me the Eagon-Northcott formula expressing the resolution of the ideals generated by the majors of a matrix whose entries are independent variables (Eagon, Northcott 1962)), I decided to try to see whether our tools allowed me to tackle the 5 × 3 case.
I was really surprised when not only I got the resolution but I realized that it was sufficient to give a look to the solution to devise the complete formula (Th. 1.1) and that proving it required only to generalize the computation I did: it was the first time that I realized the amazing power of Buchberger's tool.
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- Gröbner Bases and Applications , pp. 434 - 447Publisher: Cambridge University PressPrint publication year: 1998
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