Algorithms And Techniques In Computer Algebra

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Computer Algebra

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Author : James Harold Davenport
language : en
Publisher:
Release Date : 1993

Computer Algebra written by James Harold Davenport and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Computers categories.

This book still remains the best introduction to computer algebra, catering to both the interested beginner and the experienced pure mathematician and computer scientist. This updated Second Edition provides a comprehensive review, and contains excellent references to fundamental papers and worked examples. In addition to being a general text on the subject, the book includes an appendix describing the use of one particular algebra system-REDUCE.

Algorithms And Techniques In Computer Algebra

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-15

Algorithms And Techniques In Computer Algebra written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-15 with Mathematics categories.

**Algorithms and Techniques in Computer Algebra** provides a comprehensive introduction to this rapidly developing field, covering the basic concepts, core algorithms, and practical applications of computer algebra. Suitable for both undergraduate and graduate students in computer science, mathematics, and engineering, this book is an essential resource for anyone looking to master the essential concepts and techniques of computer algebra. With in-depth explanations, illustrative examples, and comprehensive exercises, this book covers a wide range of topics, from the basic concepts of field theory and ring theory to advanced topics such as Gröbner bases and analytic integration. It also includes a chapter dedicated to recent developments and open problems in computer algebra, keeping readers abreast of the latest advancements in the field. One of the key strengths of **Algorithms and Techniques in Computer Algebra** is its focus on practical applications. It demonstrates how computer algebra can be used to solve real-world problems in various fields, including cryptography, coding theory, robotics, computer graphics, and artificial intelligence. This makes the book not only a valuable resource for students but also a practical guide for professionals seeking to apply computer algebra to their work. Whether you are a seasoned professional looking to expand your knowledge or a beginner seeking to understand the fundamentals of computer algebra, **Algorithms and Techniques in Computer Algebra** is the perfect resource for you. With its clear and concise explanations, illustrative examples, and comprehensive exercises, this book will help you master the essential concepts and techniques of this exciting field. If you like this book, write a review!

Algorithmic Algebra

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Author : Bhubaneswar Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Algorithmic Algebra written by Bhubaneswar Mishra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Algorithmic Algebra studies some of the main algorithmic tools of computer algebra, covering such topics as Gröbner bases, characteristic sets, resultants and semialgebraic sets. The main purpose of the book is to acquaint advanced undergraduate and graduate students in computer science, engineering and mathematics with the algorithmic ideas in computer algebra so that they could do research in computational algebra or understand the algorithms underlying many popular symbolic computational systems: Mathematica, Maple or Axiom, for instance. Also, researchers in robotics, solid modeling, computational geometry and automated theorem proving community may find it useful as symbolic algebraic techniques have begun to play an important role in these areas. The book, while being self-contained, is written at an advanced level and deals with the subject at an appropriate depth. The book is accessible to computer science students with no previous algebraic training. Some mathematical readers, on the other hand, may find it interesting to see how algorithmic constructions have been used to provide fresh proofs for some classical theorems. The book also contains a large number of exercises with solutions to selected exercises, thus making it ideal as a textbook or for self-study.

Computer Algebra And Symbolic Computation

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Author : Joel S. Cohen
language : en
Publisher: CRC Press
Release Date : 2002-07-19

Computer Algebra And Symbolic Computation written by Joel S. Cohen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-19 with Computers categories.

This book provides a systematic approach for the algorithmic formulation and implementation of mathematical operations in computer algebra programming languages. The viewpoint is that mathematical expressions, represented by expression trees, are the data objects of computer algebra programs, and by using a few primitive operations that analyze and

Ideals Varieties And Algorithms

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Author : David Cox
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Ideals Varieties And Algorithms written by David Cox and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

We wrote this book to introduce undergraduates to some interesting ideas in algebraic geometry and commutative algebra. Until recently, these topics involved a lot of abstract mathematics and were only taught in graduate school. But in the 1960's, Buchberger and Hironaka discovered new algorithms for manipulating systems of polynomial equations. Fueled by the development of computers fast enough to run these algorithms, the last two decades have seen a minor revolution in commutative algebra. The ability to compute efficiently with polynomial equations has made it possible to investigate complicated examples that would be impossible to do by hand, and has changed the practice of much research in algebraic geometry. This has also enhanced the importance of the subject for computer scientists and engineers, who have begun to use these techniques in a whole range of problems. It is our belief that the growing importance of these computational techniques warrants their introduction into the undergraduate (and graduate) mathematics curricu lum. Many undergraduates enjoy the concrete, almost nineteenth century, flavor that a computational emphasis brings to the subject. At the same time, one can do some substantial mathematics, including the Hilbert Basis Theorem, Elimination Theory and the Nullstellensatz. The mathematical prerequisites of the book are modest: the students should have had a course in linear algebra and a course where they learned how to do proofs. Examples of the latter sort of course include discrete math and abstract algebra.

Numerical Algorithms

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Author : Justin Solomon
language : en
Publisher: CRC Press
Release Date : 2015-06-24

Numerical Algorithms written by Justin Solomon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-24 with Computers categories.

Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Computational Algebra And Number Theory

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Author : Wieb Bosma
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Computational Algebra And Number Theory written by Wieb Bosma and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for implementing computational methods, the viewing of old techniques from a concrete algorithmic vantage point, to name but a few. Computational Algebra and Number Theory lies at the lively intersection of computer science and mathematics. It highlights the surprising width and depth of the field through examples drawn from current activity, ranging from category theory, graph theory and combinatorics, to more classical computational areas, such as group theory and number theory. Many of the papers in the book provide a survey of their topic, as well as a description of present research. Throughout the variety of mathematical and computational fields represented, the emphasis is placed on the common principles and the methods employed. Audience: Students, experts, and those performing current research in any of the topics mentioned above.

Algorithms In Real Algebraic Geometry

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Author : Saugata Basu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-21

Algorithms In Real Algebraic Geometry written by Saugata Basu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-21 with Mathematics categories.

The algorithmic problems of real algebraic geometry such as real root counting, deciding the existence of solutions of systems of polynomial equations and inequalities, finding global maxima or deciding whether two points belong in the same connected component of a semi-algebraic set appear frequently in many areas of science and engineering. In this textbook 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, real root isolation, global optimization, quantitative results on semi-algebraic sets and the first single exponential algorithm computing their first Betti number.

Computer Algebra

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Author : R. Albrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computer Algebra written by R. Albrecht and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

this gap. In sixteen survey articles the most important theoretical results, algorithms and software methods of computer algebra are covered, together with systematic references to literature. In addition, some new results are presented. Thus the volume should be a valuable source for obtaining a first impression of computer algebra, as well as for preparing a computer algebra course or for complementary reading. The preparation of some papers contained in this volume has been supported by grants from the Austrian "Fonds zur Forderung der wissenschaftlichen For schung" (Project No. 3877), the Austrian Ministry of Science and Research (Department 12, Dr. S. Hollinger), the United States National Science Foundation (Grant MCS-8009357) and the Deutsche Forschungsgemeinschaft (Lo-23 1-2). The work on the volume was greatly facilitated by the opportunity for the editors to stay as visitors at the Department of Computer and Information Sciences, University of Delaware, at the General Electric Company Research and Development Center, Schenectady, N. Y. , and at the Mathematical Sciences Department, Rensselaer Polytechnic Institute, Troy, N. Y. , respectively. Our thanks go to all these institutions. The patient and experienced guidance and collaboration of the Springer-Verlag Wien during all the stages of production are warmly appreciated. The editors of the Cooperative editor of Supplementum Computing B. Buchberger R. Albrecht G. Collins R. Loos Contents Loos, R. : Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . 1 Buchberger, B. , Loos, R. : Algebraic Simplification . . . . . . . . . . 11 Neubiiser, J. : Computing with Groups and Their Character Tables. 45 Norman, A. C. : Integration in Finite Terms. . . . . . . . . . . . . .

Probability And Computing

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Author : Michael Mitzenmacher
language : en
Publisher: Cambridge University Press
Release Date : 2005-01-31

Probability And Computing written by Michael Mitzenmacher and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-31 with Computers categories.

Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.