Search results for: some-tapas-of-computer-algebra

Some Tapas of Computer Algebra

Author : Arjeh M. Cohen
File Size : 56.43 MB
Format : PDF, ePub, Docs
Download : 378
Read : 159
Download »
This book presents the basic concepts and algorithms of computer algebra using practical examples that illustrate their actual use in symbolic computation. A wide range of topics are presented, including: Groebner bases, real algebraic geometry, lie algebras, factorization of polynomials, integer programming, permutation groups, differential equations, coding theory, automatic theorem proving, and polyhedral geometry. This book is a must read for anyone working in the area of computer algebra, symbolic computation, and computer science.

Some Tapas of Computer Algebra

Author : Arjeh M. Cohen
File Size : 21.16 MB
Format : PDF, Docs
Download : 353
Read : 792
Download »

Computer Algebra Handbook

Author : Johannes Grabmeier
File Size : 37.70 MB
Format : PDF, Docs
Download : 289
Read : 1030
Download »
This Handbook gives a comprehensive snapshot of a field at the intersection of mathematics and computer science with applications in physics, engineering and education. Reviews 67 software systems and offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education.

Codes Cryptology and Curves with Computer Algebra

Author : Ruud Pellikaan
File Size : 39.90 MB
Format : PDF
Download : 264
Read : 479
Download »
Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

Algorithms in Real Algebraic Geometry

Author : Saugata Basu
File Size : 22.19 MB
Format : PDF, ePub, Mobi
Download : 403
Read : 697
Download »
This is the first graduate textbook on the algorithmic aspects of real algebraic geometry. The main ideas and techniques presented form a coherent and rich body of knowledge. Mathematicians will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. Being self-contained the book is accessible to graduate students and even, for invaluable parts of it, to undergraduate students. This second edition contains several recent results on discriminants of symmetric matrices and other relevant topics.

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
File Size : 72.32 MB
Format : PDF, ePub, Docs
Download : 389
Read : 1240
Download »
The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Algebra Geometry and Software Systems

Author : Michael Joswig
File Size : 89.70 MB
Format : PDF, ePub, Mobi
Download : 954
Read : 1075
Download »
A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Graphs Networks and Algorithms

Author : Dieter Jungnickel
File Size : 26.70 MB
Format : PDF
Download : 394
Read : 560
Download »
Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed

Introduction to Maple

Author : Andre HECK
File Size : 36.22 MB
Format : PDF, Kindle
Download : 576
Read : 1331
Download »
The fully revised edition of this best-selling title presents the modern computer algebra system Maple. It teaches the reader not only what can be done by Maple but also how and why it can be done. It provides the necessary background for those who want the most of Maple or want to extend its built-in knowledge, and it includes both elementary and more sophisticated examples as well as many exercises.

A Singular Introduction to Commutative Algebra

Author : Gert-Martin Greuel
File Size : 63.32 MB
Format : PDF, ePub
Download : 503
Read : 1078
Download »
This book can be understood as a model for teaching commutative algebra, and takes into account modern developments such as algorithmic and computational aspects. As soon as a new concept is introduced, the authors show how the concept can be worked on using a computer. The computations are exemplified with the computer algebra system Singular, developed by the authors. Singular is a special system for polynomial computation with many features for global as well as for local commutative algebra and algebraic geometry. The book includes a CD containing Singular as well as the examples and procedures explained in the book.

Formal Techniques in Real Time and Fault Tolerant Systems

Author : Mathai Joseph
File Size : 55.71 MB
Format : PDF, ePub
Download : 344
Read : 1251
Download »
This book constitutes the refereed proceedings of the 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems, FTRTFT 2000, held in Pune, India in September 2000. The 21 revised full papers presented together with three invited contributions were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on model checking, fault tolerance, scheduling, validation, verification, logic and automata.

Computational Commutative Algebra 2

Author : Martin Kreuzer
File Size : 80.75 MB
Format : PDF
Download : 512
Read : 248
Download »
"The second volume of the authors’ ‘Computational commutative algebra’...covers on its 586 pages a wealth of interesting material with several unexpected applications. ... an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH

Algebraic Methodology and Software Technology

Author : Helene Kirchner
File Size : 60.61 MB
Format : PDF
Download : 863
Read : 449
Download »
This volume contains the proceedings of AMAST 2002, the 9th International Conference on Algebraic Methodology and Software Technology, held during September 9–13, 2002, in Saint-Gilles-les-Bains, R ́eunion Island, France. The major goal of the AMAST conferences is to promote research that may lead to setting software technology on a ?rm mathematical basis. This goal is achieved through a large international cooperation with contributions from both academia and industry. Developing a software technology on a mathematical basis p- duces software that is: (a) correct, and the correctness can be proved mathem- ically, (b) safe, so that it can be used in the implementation of critical systems, (c) portable, i. e. , independent of computing platforms and language generations, (d) evolutionary, i. e. , it is self-adaptable and evolves with the problem domain. All previous AMAST conferences, which were held in Iowa City (1989, 1991), Twente (1993), Montreal (1995), Munich (1996), Sydney (1997), Manaus (1999), and Iowa City (2000), made contributions to the AMAST goals by reporting and disseminating academic and industrial achievements within the AMAST area of interest. During these meetings, AMAST attracted an international following among researchers and practitioners interested in software technology, progr- ming methodology, and their algebraic, and logical foundations.

Ideals Varieties and Algorithms

Author : David A. Cox
File Size : 32.43 MB
Format : PDF, ePub, Docs
Download : 442
Read : 190
Download »
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly

Mathematics Unlimited 2001 and Beyond

Author : Björn Engquist
File Size : 36.61 MB
Format : PDF, Mobi
Download : 656
Read : 820
Download »
This is a book guaranteed to delight the reader. It not only depicts the state of mathematics at the end of the century, but is also full of remarkable insights into its future de- velopment as we enter a new millennium. True to its title, the book extends beyond the spectrum of mathematics to in- clude contributions from other related sciences. You will enjoy reading the many stimulating contributions and gain insights into the astounding progress of mathematics and the perspectives for its future. One of the editors, Björn Eng- quist, is a world-renowned researcher in computational sci- ence and engineering. The second editor, Wilfried Schmid, is a distinguished mathematician at Harvard University. Likewi- se the authors are all foremost mathematicians and scien- tists, and their biographies and photographs appear at the end of the book. Unique in both form and content, this is a "must-read" for every mathematician and scientist and, in particular, for graduates still choosing their specialty. Limited collector's edition - an exclusive and timeless work. This special, numbered edition will be available until June 1, 2000. Firm orders only.

Selected Topics in Geometry with Classical vs Computer Proving

Author : Pavel Pech
File Size : 40.77 MB
Format : PDF, ePub, Docs
Download : 926
Read : 748
Download »
This textbook presents various automatic techniques based on Gröbner bases elimination to prove well-known geometrical theorems and formulas. Besides proving theorems, these methods are used to discover new formulas, solve geometric inequalities, and construct objects — which cannot be easily done with a ruler and compass. Each problem is firstly solved by an automatic theorem proving method. Secondly, problems are solved classically — without using computer where possible — so that readers can compare the strengths and weaknesses of both approaches.

Geometric Computation

Author : Falai Chen
File Size : 76.71 MB
Format : PDF, ePub, Mobi
Download : 155
Read : 990
Download »
This book contains tutorial surveys and original research contributions in geometric computing, modeling, and reasoning. Highlighting the role of algebraic computation, it covers: surface blending, implicitization, and parametrization; automated deduction with Clifford algebra and in real geometry; and exact geometric computation. Basic techniques, advanced methods, and new findings are presented coherently, with many examples and illustrations. Using this book the reader will easily cross the frontiers of symbolic computation, computer aided geometric design, and automated reasoning. The book is also a valuable reference for people working in other relevant areas, such as scientific computing, computer graphics, and artificial intelligence. Contents: Algebraic Methods in Computer Aided Geometric Design: Theoretical and Practical Applications (L Gonzilez-Vega et al.); Constructing Piecewise Algebraic Blending Surfaces (Y Feng et al.); Rational Curves and Surfaces: Algorithms and Some Applications (J R Sendra); Panorama of Methods for Exact Implicitization of Algebraic Curves and Surfaces (I S Kotsireas); Implicitization and Offsetting via Regular Systems (D Wang); Determining the Intersection Curve of Two 3D Implicit Surfaces by Using Differential Geometry and Algebraic Techniques (L Gonzilez-Vega et al.); Analytical Properties of Semi-Stationary Subdivision Schemes (H Zhang & G Wang); Meshless Method for Numerical Solution of PDE Using Hermitian Interpolation with Radial Basis (Z Wu & J Liu); Clifford Algebras in Geometric Computation (H Li); Automated Deduction in Real Geometry (L Yang & B Xia); Automated Derivation of Unknown Relations and Determination of Geometric Loci (Y Li); On Guaranteed Accuracy Computation (C K Yap); Dixon A-Resultant Quotients for 6-Point Isosceles Triangular Corner Cutting (M-C Foo & E-W Chionh); Face Recognition Using Hidden Markov Models and Artificial Neural Network Techniques (Z Ou & B Xue). Readership: Upper-level undergraduates, graduate students, researchers and engineers in geometric modeling."

Geometric and Algorithmic Aspects of Computer aided Design and Manufacturing

Author : Ravi Janardan
File Size : 61.88 MB
Format : PDF
Download : 983
Read : 1090
Download »
Computer-Aided Design and Manufacturing (CAD/CAM) is concerned with all aspects of the process of designing, prototyping, manufacturing, inspecting, and maintaining complex geometric objects under computer control. As such, there is a natural synergy between this field and Computational Geometry (CG), which involves the design, analysis, implementation, and testing of efficient algorithms and data representation techniques for geometric entities such as points, polygons, polyhedra, curves, and surfaces. The DIMACS Center (Piscataway, NJ) sponsored a workshop to further promote the interaction between these two fields. Attendees from academia, research laboratories, and industry took part in the invited talks, contributed presentations, and informal discussions. This volume is an outgrowth of that meeting. Topics covered in this volume include geometric modeling, computational topology, computational metrology, geometric constraint solving, part immobilization, geometric aspects of machining, layered manufacturing, and algebraic methods. The book is suitable for graduate students and researchers interested in geometric and algorithmic aspects of computer-aided design and manufacturing.

Bifurcations in Hamiltonian Systems

Author : Henk Broer
File Size : 32.8 MB
Format : PDF, ePub, Docs
Download : 999
Read : 426
Download »
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.

Algebraic Theory of Differential Equations

Author :
File Size : 53.71 MB
Format : PDF, ePub
Download : 764
Read : 772
Download »