Applications Of Computational Algebraic Geometry

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Emerging Applications of Algebraic Geometry

Author : Mihai Putinar
Publisher : Springer Science & Business Media
ISBN 13 : 0387096868
Total Pages : 382 pages
Book Rating : 4.3/5 (87 download)

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Book Synopsis Emerging Applications of Algebraic Geometry by : Mihai Putinar

Download or read book Emerging Applications of Algebraic Geometry written by Mihai Putinar and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Applications of Computational Algebraic Geometry

Author : David A. Cox Dinesh N. Manocha Bernd Sturmfels
Publisher : American Mathematical Soc.
ISBN 13 : 9780821867587
Total Pages : 194 pages
Book Rating : 4.8/5 (675 download)

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Book Synopsis Applications of Computational Algebraic Geometry by : David A. Cox Dinesh N. Manocha Bernd Sturmfels

Download or read book Applications of Computational Algebraic Geometry written by David A. Cox Dinesh N. Manocha Bernd Sturmfels and published by American Mathematical Soc.. This book was released on with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Ideals, Varieties, and Algorithms

Author : David Cox
Publisher : Springer Science & Business Media
ISBN 13 : 1475721811
Total Pages : 523 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Ideals, Varieties, and Algorithms by : David Cox

Download or read book Ideals, Varieties, and Algorithms written by David Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.

A Primer of Algebraic Geometry

Author : Huishi Li
Publisher : CRC Press
ISBN 13 : 1482270331
Total Pages : 393 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis A Primer of Algebraic Geometry by : Huishi Li

Download or read book A Primer of Algebraic Geometry written by Huishi Li and published by CRC Press. This book was released on 2017-12-19 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Presents the structure of algebras appearing in representation theory of groups and algebras with general ring theoretic methods related to representation theory. Covers affine algebraic sets and the nullstellensatz, polynomial and rational functions, projective algebraic sets. Groebner basis, dimension of algebraic sets, local theory, curves and elliptic curves, and more."

Applications of Computational Algebraic Geometry

Author : David A. Cox
Publisher : American Mathematical Soc.
ISBN 13 : 0821807501
Total Pages : 188 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Applications of Computational Algebraic Geometry by : David A. Cox

Download or read book Applications of Computational Algebraic Geometry written by David A. Cox and published by American Mathematical Soc.. This book was released on 1998 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that "crunching equations" is now as easy as "crunching numbers" has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in this book assume no previous acquaintance with the material.

Polyhedral and Algebraic Methods in Computational Geometry

Author : Michael Joswig
Publisher : Springer Science & Business Media
ISBN 13 : 1447148177
Total Pages : 251 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Polyhedral and Algebraic Methods in Computational Geometry by : Michael Joswig

Download or read book Polyhedral and Algebraic Methods in Computational Geometry written by Michael Joswig and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Computational Algebraic Geometry

Author : Frederic Eyssette
Publisher : Springer Science & Business Media
ISBN 13 : 1461227526
Total Pages : 334 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Computational Algebraic Geometry by : Frederic Eyssette

Download or read book Computational Algebraic Geometry written by Frederic Eyssette and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and practice of computation in algebraic geometry and related domains, from a mathematical point of view, has generated an increasing interest both for its rich theoretical possibilities and its usefulness in applications in science and engineering. In fact, it is one of the master keys for future significant improvement of the computer algebra systems (e.g., Reduce, Macsyma, Maple, Mathematica, Axiom, Macaulay, etc.) that have become such useful tools for many scientists in a variety of disciplines. The major themes covered in this volume, arising from papers p- sented at the conference MEGA-92 were: - Effective methods and complexity issues in commutative algebra, projective geometry, real geometry, and algebraic number theory - Algebra-geometric methods in algebraic computing and applica tions. MEGA-92 was the second of a new series of European conferences on the general theme of Effective Methods in Algebraic Geometry. It was held in Nice, France, on April 21-25, 1992 and built on the themes presented at MEGA-90 (Livomo, Italy, April 17-21, 1990). The next conference - MEGA-94 - will be held in Santander, Spain in the spring of 1994. The Organizing committee that initiatiod and supervises this bi enniel conference consists of A. Conte (Torino), J.H. Davenport (Bath), A. Galligo (Nice), D. Yu. Grigoriev (Petersburg), J. Heintz (Buenos Aires), W. Lassner (Leipzig), D. Lazard (paris), H.M. MOller (Hagen), T. Mora (Genova), M. Pohst (DUsseldort), T. Recio (Santander), J.J.

A First Course in Computational Algebraic Geometry

Author : Wolfram Decker
Publisher : Cambridge University Press
ISBN 13 : 1107612535
Total Pages : 127 pages
Book Rating : 4.1/5 (76 download)

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Book Synopsis A First Course in Computational Algebraic Geometry by : Wolfram Decker

Download or read book A First Course in Computational Algebraic Geometry written by Wolfram Decker and published by Cambridge University Press. This book was released on 2013-02-07 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

Using Algebraic Geometry

Author : David A. Cox
Publisher : Springer Science & Business Media
ISBN 13 : 1475769113
Total Pages : 513 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Using Algebraic Geometry by : David A. Cox

Download or read book Using Algebraic Geometry written by David A. Cox and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

Algebraic Geometry and Statistical Learning Theory

Author : Sumio Watanabe
Publisher : Cambridge University Press
ISBN 13 : 0521864674
Total Pages : 295 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Algebraic Geometry and Statistical Learning Theory by : Sumio Watanabe

Download or read book Algebraic Geometry and Statistical Learning Theory written by Sumio Watanabe and published by Cambridge University Press. This book was released on 2009-08-13 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sure to be influential, Watanabe's book lays the foundations for the use of algebraic geometry in statistical learning theory. Many models/machines are singular: mixture models, neural networks, HMMs, Bayesian networks, stochastic context-free grammars are major examples. The theory achieved here underpins accurate estimation techniques in the presence of singularities.

Computational Algebraic Geometry

Author : Hal Schenck
Publisher : Cambridge University Press
ISBN 13 : 9780521536509
Total Pages : 212 pages
Book Rating : 4.5/5 (365 download)

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Book Synopsis Computational Algebraic Geometry by : Hal Schenck

Download or read book Computational Algebraic Geometry written by Hal Schenck and published by Cambridge University Press. This book was released on 2003-10-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. This opens wonderful new vistas and allows us to pose, study and solve problems that were previously out of reach. Suitable for graduate students, the objective of this 2003 book is to bring advanced algebra to life with lots of examples. The first chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book focuses on three active areas of contemporary algebra: Homological Algebra (the snake lemma, long exact sequence inhomology, functors and derived functors (Tor and Ext), and double complexes); Algebraic Combinatorics and Algebraic Topology (simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes); and Algebraic Geometry (points and curves in projective space, Riemann-Roch, Cech cohomology, regularity).

Applications of Algebraic Geometry to Coding Theory, Physics and Computation

Author : Ciro Ciliberto
Publisher : Springer Science & Business Media
ISBN 13 : 9401010110
Total Pages : 343 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Applications of Algebraic Geometry to Coding Theory, Physics and Computation by : Ciro Ciliberto

Download or read book Applications of Algebraic Geometry to Coding Theory, Physics and Computation written by Ciro Ciliberto and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.

Applications of Geometric Algebra in Computer Science and Engineering

Author : Leo Dorst
Publisher : Springer Science & Business Media
ISBN 13 : 146120089X
Total Pages : 479 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Applications of Geometric Algebra in Computer Science and Engineering by : Leo Dorst

Download or read book Applications of Geometric Algebra in Computer Science and Engineering written by Leo Dorst and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Computing in Algebraic Geometry

Author : Wolfram Decker
Publisher : Springer Science & Business Media
ISBN 13 : 3540289925
Total Pages : 331 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Computing in Algebraic Geometry by : Wolfram Decker

Download or read book Computing in Algebraic Geometry written by Wolfram Decker and published by Springer Science & Business Media. This book was released on 2006-03-02 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a quick access to computational tools for algebraic geometry, the mathematical discipline which handles solution sets of polynomial equations. Originating from a number of intense one week schools taught by the authors, the text is designed so as to provide a step by step introduction which enables the reader to get started with his own computational experiments right away. The authors present the basic concepts and ideas in a compact way.

Applications of Computational Algebraic Geometry

Author : Dinesh Manocha
Publisher : American Mathematical Society(RI)
ISBN 13 : 9780821892688
Total Pages : 186 pages
Book Rating : 4.8/5 (926 download)

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Book Synopsis Applications of Computational Algebraic Geometry by : Dinesh Manocha

Download or read book Applications of Computational Algebraic Geometry written by Dinesh Manocha and published by American Mathematical Society(RI). This book was released on 2014-05-10 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gr obner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that crunching equations is now as easy as crunching numbers has had a impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusual and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gr obner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in this book assume no previous acquaintance with the material.

Computational Algebra: Course And Exercises With Solutions

Author : Ihsen Yengui
Publisher : World Scientific
ISBN 13 : 981123826X
Total Pages : 283 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Computational Algebra: Course And Exercises With Solutions by : Ihsen Yengui

Download or read book Computational Algebra: Course And Exercises With Solutions written by Ihsen Yengui and published by World Scientific. This book was released on 2021-05-17 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

Algorithms in Real Algebraic Geometry

Author : Saugata Basu
Publisher : Springer Science & Business Media
ISBN 13 : 3662053551
Total Pages : 602 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Algorithms in Real Algebraic Geometry by : Saugata Basu

Download or read book Algorithms in Real Algebraic Geometry written by Saugata Basu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.