Real Solutions to Equations from Geometry (University Lecture Series) - Tapa blanda

Sottile, Frank

 
9780821853313: Real Solutions to Equations from Geometry (University Lecture Series)
Tapa blanda
ISBN 10: 0821853317 ISBN 13: 9780821853313
Editorial: American Mathematical Society, 2011

Sinopsis

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.

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Acerca del autor

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

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
American Mathematical Society
Año de publicación
2011
Idioma
Inglés
ISBN 10 
0821853317
ISBN 13 
9780821853313
Encuadernación
Tapa blanda
Número de páginas
199
Contacto del fabricante
no disponible
Persona responsable
no disponible