Synopsis
Sottile (Texas A&M) explores real solutions to systems of multivariate polynomial equations, and applies them to the art of counting geometric figures satisfying conditions imposed by fixed geometric figures. The graduate text develops the theories of upper bounds and lower bounds for sparse polynomial systems, and introduces the Shapiro Conjecture and its generalizations, where the upper bound is also the lower bound. Color figures are provided. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
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About the Author
Frank Sottile is at Texas A&M University, College Station, TX
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Real Solutions to Equations from Geometry (University Lecture Series, 57)
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Amer Mathematical Society, 2011
ISBN 10: 0821853317
ISBN 13: 9780821853313
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Real Solutions to Equations from Geometry
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American Mathematical Society, US, 2011
ISBN 10: 0821853317
ISBN 13: 9780821853313
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Paperback. Condition: New. 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. Seller Inventory # LU-9780821853313
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Real Solutions to Equations from Geometry (University Lecture Series)
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ISBN 10: 0821853317
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Condition: New. 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. Series: University Lecture Series. Num Pages: 199 pages, Illustrations (some col.). BIC Classification: PBMW. Category: (G) General (US: Trade). Dimension: 254 x 178. Weight in Grams: 394. . 2011. Paperback. . . . . Seller Inventory # V9780821853313
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Real Solutions to Equations from Geometry
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Real Solutions to Equations from Geometry (University Lecture Series)
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Condition: New. 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. Series: University Lecture Series. Num Pages: 199 pages, Illustrations (some col.). BIC Classification: PBMW. Category: (G) General (US: Trade). Dimension: 254 x 178. Weight in Grams: 394. . 2011. Paperback. . . . . Books ship from the US and Ireland. Seller Inventory # V9780821853313
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Real Solutions to Equations from Geometry
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Real solutions to equations from geometry. University lecture series; v. 57.
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Real Solutions to Equations from Geometry
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American Mathematical Society, US, 2011
ISBN 10: 0821853317
ISBN 13: 9780821853313
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Paperback. Condition: New. 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. Seller Inventory # LU-9780821853313
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