24 - De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner

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 Berceo

Remembrance

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.