Real Solutions to Equations from Geometry

摘要: Understanding, finding, or even deciding on the existence of real solutions to a system equations is difficult problem with many applications outside mathematics. While it hopeless expect much in general, we know surprising amount about these questions for systems which possess additional structure often coming from geometry. This book focuses toric varieties and Grassmannians. Not only known these, but such are common applications. There three main themes: upper bounds number solutions, lower geometric problems that can have all be real. The begins an overview, giving background univariate polynomials geometry sparse polynomial systems. first half concludes fewnomial second by sampling some real, before devoting last five chapters Shapiro Conjecture, relevant solutions.