Invariant Algebras And Geometric Reasoning PDF Download
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| Author | : Hongbo Li |
| Publisher | : World Scientific |
| Total Pages | : 533 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9812770119 |
Download Invariant Algebras and Geometric Reasoning Book in PDF, ePub and Kindle
The demand for more reliable geometric computing in robotics, computer vision and graphics has revitalized many venerable algebraic subjects in mathematics OCo among them, GrassmannOCoCayley algebra and Geometric Algebra. Nowadays, they are used as powerful languages for projective, Euclidean and other classical geometries. This book contains the author and his collaborators' most recent, original development of GrassmannOCoCayley algebra and Geometric Algebra and their applications in automated reasoning of classical geometries. It includes two of the three advanced invariant algebras OCo Cayley bracket algebra, conformal geometric algebra, and null bracket algebra OCo for highly efficient geometric computing. They form the theory of advanced invariants, and capture the intrinsic beauty of geometric languages and geometric computing. Apart from their applications in discrete and computational geometry, the new languages are currently being used in computer vision, graphics and robotics by many researchers worldwide. Sample Chapter(s). Chapter 1: Introduction (252 KB). Contents: Projective Space, Bracket Algebra and GrassmannOCoCayley Algebra; Projective Incidence Geometry with Cayley Bracket Algebra; Projective Conic Geometry with Bracket Algebra and Quadratic Grassmann-Cayley Algebra; Inner-product Bracket Algebra and Clifford Algebra; Geometric Algebra; Euclidean Geometry and Conformal GrassmannOCoCayley Algebra; Conformal Clifford Algebra and Classical Geometries. Readership: Graduate students in discrete and computational geometry, and computer mathematics; mathematicians and computer scientists.
| Author | : Frank D. Grosshans |
| Publisher | : Springer |
| Total Pages | : 158 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540696172 |
Download Algebraic Homogeneous Spaces and Invariant Theory Book in PDF, ePub and Kindle
The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years. This book is an exposition of several related topics including observable subgroups, induced modules, maximal unipotent subgroups of reductive groups and the method of U-invariants, and the complexity of an action. Much of this material has not appeared previously in book form. The exposition assumes a basic knowledge of algebraic groups and then develops each topic systematically with applications to invariant theory. Exercises are included as well as many examples, some of which are related to geometry and physics.
| Author | : Igor Dolgachev |
| Publisher | : Cambridge University Press |
| Total Pages | : 244 |
| Release | : 2003-08-07 |
| Genre | : Mathematics |
| ISBN | : 9780521525480 |
Download Lectures on Invariant Theory Book in PDF, ePub and Kindle
The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
| Author | : Bernd Sturmfels |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 202 |
| Release | : 2008-06-17 |
| Genre | : Mathematics |
| ISBN | : 3211774173 |
Download Algorithms in Invariant Theory Book in PDF, ePub and Kindle
This book is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. Students will find the book an easy introduction to this "classical and new" area of mathematics. Researchers in mathematics, symbolic computation, and computer science will get access to research ideas, hints for applications, outlines and details of algorithms, examples and problems.
| Author | : Ilias S. Kotsireas |
| Publisher | : Springer |
| Total Pages | : 631 |
| Release | : 2016-04-16 |
| Genre | : Computers |
| ISBN | : 331932859X |
Download Mathematical Aspects of Computer and Information Sciences Book in PDF, ePub and Kindle
This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, held in Berlin, Germany, in November 2015. The 48 revised papers presented together with 7 invited papers were carefully reviewed and selected from numerous submissions. The papers are grouped in topical sections on curves and surfaces, applied algebraic geometry, cryptography, verified numerical computation, polynomial system solving, managing massive data, computational theory of differential and difference equations, data and knowledge exploration, algorithm engineering in geometric computing, real complexity: theory and practice, global optimization, and general session.
| Author | : Leo Dorst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 458 |
| Release | : 2011-08-28 |
| Genre | : Computers |
| ISBN | : 0857298119 |
Download Guide to Geometric Algebra in Practice Book in PDF, ePub and Kindle
This highly practical Guide to Geometric Algebra in Practice reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. Topics and features: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the description of rigid body motion, interpolation and tracking, and image processing; reviews the employment of GA in theorem proving and combinatorics; discusses the geometric algebra of lines, lower-dimensional algebras, and other alternatives to 5-dimensional CGA; proposes applications of coordinate-free methods of GA for differential geometry.
| Author | : Allen Tannenbaum |
| Publisher | : Springer |
| Total Pages | : 171 |
| Release | : 2006-11-14 |
| Genre | : Science |
| ISBN | : 3540385363 |
Download Invariance and System Theory Book in PDF, ePub and Kindle
| Author | : H.E.A. Eddy Campbell |
| Publisher | : Springer |
| Total Pages | : 234 |
| Release | : 2011-04-08 |
| Genre | : Mathematics |
| ISBN | : 9783642174056 |
Download Modular Invariant Theory Book in PDF, ePub and Kindle
This book covers the modular invariant theory of finite groups, the case when the characteristic of the field divides the order of the group, a theory that is more complicated than the study of the classical non-modular case. Largely self-contained, the book develops the theory from its origins up to modern results. It explores many examples, illustrating the theory and its contrast with the better understood non-modular setting. It details techniques for the computation of invariants for many modular representations of finite groups, especially the case of the cyclic group of prime order. It includes detailed examples of many topics as well as a quick survey of the elements of algebraic geometry and commutative algebra as they apply to invariant theory. The book is aimed at both graduate students and researchers—an introduction to many important topics in modern algebra within a concrete setting for the former, an exploration of a fascinating subfield of algebraic geometry for the latter.
| Author | : A.N. Parshin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 291 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 366203073X |
Download Algebraic Geometry IV Book in PDF, ePub and Kindle
Two contributions on closely related subjects: the theory of linear algebraic groups and invariant theory, by well-known experts in the fields. The book will be very useful as a reference and research guide to graduate students and researchers in mathematics and theoretical physics.
| Author | : Piotr Pragacz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 240 |
| Release | : 2008-03-12 |
| Genre | : Mathematics |
| ISBN | : 3764385375 |
Download Algebraic Cycles, Sheaves, Shtukas, and Moduli Book in PDF, ePub and Kindle
Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.
