Real Solutions to Equations from Geometry - Couverture souple

Sottile, Frank

 
9780821853313: Real Solutions to Equations from Geometry
Couverture souple
ISBN 10 : 0821853317 ISBN 13 : 9780821853313
Editeur : American Mathematical Society, 2011

Synopsis

Understanding, finding, or even deciding on the existence of real solutions to a system of equations is a difficult problem with many applications outside of mathematics. While it is hopeless to expect much in general, we know a surprising amount about these questions for systems which possess additional structure often coming from geometry.

This book focuses on equations from toric varieties and Grassmannians. Not only is much known about these, but such equations are common in applications. There are three main themes: upper bounds on the number of real solutions, lower bounds on the number of real solutions, and geometric problems that can have all solutions be real. The book begins with an overview, giving background on real solutions to univariate polynomials and the geometry of sparse polynomial systems. The first half of the book concludes with fewnomial upper bounds and with lower bounds to sparse polynomial systems. The second half of the book begins by sampling some geometric problems for which all solutions can be real, before devoting the last five chapters to the Shapiro Conjecture, in which the relevant polynomial systems have only real solutions.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

Frank Sottile is at Texas A&M University, College Station, TX

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
American Mathematical Society
Date d'édition
2011
Langue
anglais
ISBN 10 
0821853317
ISBN 13 
9780821853313
Reliure
Broché
Nombre de pages
199
Coordonnées du fabricant
non disponible
Personne responsable
non disponible