Algorithms in Invariant Theory

Algorithms in Invariant Theory
Author: Bernd Sturmfels
Publisher: Springer Science & Business Media
Total Pages: 202
Release: 2008-06-17
Genre: Mathematics
ISBN: 3211774173
GET BOOK

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.

Computational Invariant Theory

Computational Invariant Theory
Author: Harm Derksen
Publisher: Springer Science & Business Media
Total Pages: 272
Release: 2013-04-17
Genre: Mathematics
ISBN: 3662049589
GET BOOK

Download Computational Invariant Theory Book in PDF, Epub and Kindle

This book, the first volume of a subseries on "Invariant Theory and Algebraic Transformation Groups", provides a comprehensive and up-to-date overview of the algorithmic aspects of invariant theory. Numerous illustrative examples and a careful selection of proofs make the book accessible to non-specialists.

Self-Dual Codes and Invariant Theory

Self-Dual Codes and Invariant Theory
Author: Gabriele Nebe
Publisher: Springer Science & Business Media
Total Pages: 474
Release: 2006-02-09
Genre: Mathematics
ISBN: 9783540307297
GET BOOK

Download Self-Dual Codes and Invariant Theory Book in PDF, Epub and Kindle

One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.

Ideals, Varieties, and Algorithms

Ideals, Varieties, and Algorithms
Author: David Cox
Publisher: Springer Science & Business Media
Total Pages: 523
Release: 2013-04-17
Genre: Mathematics
ISBN: 1475721811
GET BOOK

Download Ideals, Varieties, and Algorithms Book in PDF, Epub and Kindle

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.

Algorithms in Invariant Theory

Algorithms in Invariant Theory
Author: Look Kwang Wong
Publisher:
Total Pages: 82
Release: 1998
Genre: Algorithms
ISBN:
GET BOOK

Download Algorithms in Invariant Theory Book in PDF, Epub and Kindle

Classical Invariant Theory

Classical Invariant Theory
Author: Peter J. Olver
Publisher: Cambridge University Press
Total Pages: 308
Release: 1999-01-13
Genre: Mathematics
ISBN: 9780521558211
GET BOOK

Download Classical Invariant Theory Book in PDF, Epub and Kindle

The book is a self-contained introduction to the results and methods in classical invariant theory.

Lectures on Invariant Theory

Lectures on Invariant Theory
Author: Igor Dolgachev
Publisher: Cambridge University Press
Total Pages: 244
Release: 2003-08-07
Genre: Mathematics
ISBN: 9780521525480
GET BOOK

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.

Invariant Theory of Finite Groups

Invariant Theory of Finite Groups
Author: Mara D. Neusel
Publisher: American Mathematical Soc.
Total Pages: 384
Release: 2010-03-08
Genre: Mathematics
ISBN: 0821849816
GET BOOK

Download Invariant Theory of Finite Groups Book in PDF, Epub and Kindle

The questions that have been at the center of invariant theory since the 19th century have revolved around the following themes: finiteness, computation, and special classes of invariants. This book begins with a survey of many concrete examples chosen from these themes in the algebraic, homological, and combinatorial context. In further chapters, the authors pick one or the other of these questions as a departure point and present the known answers, open problems, and methods and tools needed to obtain these answers. Chapter 2 deals with algebraic finiteness. Chapter 3 deals with combinatorial finiteness. Chapter 4 presents Noetherian finiteness. Chapter 5 addresses homological finiteness. Chapter 6 presents special classes of invariants, which deal with modular invariant theory and its particular problems and features. Chapter 7 collects results for special classes of invariants and coinvariants such as (pseudo) reflection groups and representations of low degree. If the ground field is finite, additional problems appear and are compensated for in part by the emergence of new tools. One of these is the Steenrod algebra, which the authors introduce in Chapter 8 to solve the inverse invariant theory problem, around which the authors have organized the last three chapters. The book contains numerous examples to illustrate the theory, often of more than passing interest, and an appendix on commutative graded algebra, which provides some of the required basic background. There is an extensive reference list to provide the reader with orientation to the vast literature.

Invariant Theory and Superalgebras

Invariant Theory and Superalgebras
Author: Frank D. Grosshans
Publisher: American Mathematical Soc.
Total Pages: 106
Release: 1987-12-31
Genre: Mathematics
ISBN: 0821807196
GET BOOK

Download Invariant Theory and Superalgebras Book in PDF, Epub and Kindle

This book brings the reader to the frontiers of research in some topics in superalgebras and symbolic method in invariant theory. Superalgebras are algebras containing positively-signed and negatively-signed variables. One of the book's major results is an extension of the standard basis theorem to superalgebras. This extension requires a rethinking of some basic concepts of linear algebra, such as matrices and coordinate systems, and may lead to an extension of the entire apparatus of linear algebra to ``signed'' modules. The authors also present the symbolic method for the invariant theory of symmetric and of skew-symmetric tensors. In both cases, the invariants are obtained from the symbolic representation by applying what the authors call the umbral operator. This operator can be used to systematically develop anticommutative analogs of concepts of algebraic geometry, and such results may ultimately turn out to be the main byproduct of this investigation. While it will be of special interest to mathematicians and physicists doing research in superalgebras, invariant theory, straightening algorithms, Young bitableaux, and Grassmann's calculus of extension, the book starts from basic principles and should therefore be accessible to those who have completed the standard graduate level courses in algebra and/or combinatorics.

Moments and Moment Invariants in Pattern Recognition

Moments and Moment Invariants in Pattern Recognition
Author: Jan Flusser
Publisher: John Wiley & Sons
Total Pages: 312
Release: 2009-11-04
Genre: Technology & Engineering
ISBN: 9780470684764
GET BOOK

Download Moments and Moment Invariants in Pattern Recognition Book in PDF, Epub and Kindle

Moments as projections of an image’s intensity onto a proper polynomial basis can be applied to many different aspects of image processing. These include invariant pattern recognition, image normalization, image registration, focus/ defocus measurement, and watermarking. This book presents a survey of both recent and traditional image analysis and pattern recognition methods, based on image moments, and offers new concepts of invariants to linear filtering and implicit invariants. In addition to the theory, attention is paid to efficient algorithms for moment computation in a discrete domain, and to computational aspects of orthogonal moments. The authors also illustrate the theory through practical examples, demonstrating moment invariants in real applications across computer vision, remote sensing and medical imaging. Key features: Presents a systematic review of the basic definitions and properties of moments covering geometric moments and complex moments. Considers invariants to traditional transforms – translation, rotation, scaling, and affine transform - from a new point of view, which offers new possibilities of designing optimal sets of invariants. Reviews and extends a recent field of invariants with respect to convolution/blurring. Introduces implicit moment invariants as a tool for recognizing elastically deformed objects. Compares various classes of orthogonal moments (Legendre, Zernike, Fourier-Mellin, Chebyshev, among others) and demonstrates their application to image reconstruction from moments. Offers comprehensive advice on the construction of various invariants illustrated with practical examples. Includes an accompanying website providing efficient numerical algorithms for moment computation and for constructing invariants of various kinds, with about 250 slides suitable for a graduate university course. Moments and Moment Invariants in Pattern Recognition is ideal for researchers and engineers involved in pattern recognition in medical imaging, remote sensing, robotics and computer vision. Post graduate students in image processing and pattern recognition will also find the book of interest.