Skip to main content Accessibility help
×
Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-23T14:31:19.893Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  05 July 2011

Ferdinando Mora
Affiliation:
Univ. Genova, Genova, Italy
Bruno Buchberger
Affiliation:
Johannes Kepler Universität Linz
Franz Winkler
Affiliation:
Johannes Kepler Universität Linz
Get access

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.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×