Fundamental Problems Of Algorithmic Algebra PDF Download
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| Author | : Chee-Keng Yap |
| Publisher | : Oxford University Press on Demand |
| Total Pages | : 511 |
| Release | : 2000 |
| Genre | : Computers |
| ISBN | : 9780195125160 |
Download Fundamental Problems of Algorithmic Algebra Book in PDF, ePub and Kindle
Popular computer algebra systems such as Maple, Macsyma, Mathematica, and REDUCE are now basic tools on most computers. Efficient algorithms for various algebraic operations underlie all these systems. Computer algebra, or algorithmic algebra, studies these algorithms and their properties and represents a rich intersection of theoretical computer science with classical mathematics. Fundamental Problems of Algorithmic Algebra provides a systematic and focused treatment of a collection of core problemsthe computational equivalents of the classical Fundamental Problem of Algebra and its derivatives. Topics covered include the GCD, subresultants, modular techniques, the fundamental theorem of algebra, roots of polynomials, Sturm theory, Gaussian lattice reduction, lattices and polynomial factorization, linear systems, elimination theory, Grobner bases, and more. Features · Presents algorithmic ideas in pseudo-code based on mathematical concepts and can be used with any computer mathematics system · Emphasizes the algorithmic aspects of problems without sacrificing mathematical rigor · Aims to be self-contained in its mathematical development · Ideal for a first course in algorithmic or computer algebra for advanced undergraduates or beginning graduate students
| Author | : Bhubaneswar Mishra |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 427 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461243440 |
Download Algorithmic Algebra Book in PDF, ePub and Kindle
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.
| Author | : B.Heinrich Matzat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 431 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 364259932X |
Download Algorithmic Algebra and Number Theory Book in PDF, ePub and Kindle
This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys tems and program packages developed with support by the research pro gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.
| Author | : Saugata Basu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 665 |
| Release | : 2007-04-21 |
| Genre | : Mathematics |
| ISBN | : 3540330992 |
Download Algorithms in Real Algebraic Geometry Book in PDF, ePub and Kindle
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.
| Author | : Gebhard Böckle |
| Publisher | : Springer |
| Total Pages | : 753 |
| Release | : 2018-03-22 |
| Genre | : Mathematics |
| ISBN | : 3319705660 |
Download Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory Book in PDF, ePub and Kindle
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
| Author | : Dario Bini |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 433 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 1461202655 |
Download Polynomial and Matrix Computations Book in PDF, ePub and Kindle
Our Subjects and Objectives. This book is about algebraic and symbolic computation and numerical computing (with matrices and polynomials). It greatly extends the study of these topics presented in the celebrated books of the seventies, [AHU] and [BM] (these topics have been under-represented in [CLR], which is a highly successful extension and updating of [AHU] otherwise). Compared to [AHU] and [BM] our volume adds extensive material on parallel com putations with general matrices and polynomials, on the bit-complexity of arithmetic computations (including some recent techniques of data compres sion and the study of numerical approximation properties of polynomial and matrix algorithms), and on computations with Toeplitz matrices and other dense structured matrices. The latter subject should attract people working in numerous areas of application (in particular, coding, signal processing, control, algebraic computing and partial differential equations). The au thors' teaching experience at the Graduate Center of the City University of New York and at the University of Pisa suggests that the book may serve as a text for advanced graduate students in mathematics and computer science who have some knowledge of algorithm design and wish to enter the exciting area of algebraic and numerical computing. The potential readership may also include algorithm and software designers and researchers specializing in the design and analysis of algorithms, computational complexity, alge braic and symbolic computing, and numerical computation.
| Author | : Wieb Bosma |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 387 |
| Release | : 2007-07-10 |
| Genre | : Computers |
| ISBN | : 3540376348 |
Download Discovering Mathematics with Magma Book in PDF, ePub and Kindle
Based on the ontology and semantics of algebra, the computer algebra system Magma enables users to rapidly formulate and perform calculations in abstract parts of mathematics. Edited by the principal designers of the program, this book explores Magma. Coverage ranges from number theory and algebraic geometry, through representation theory and group theory to discrete mathematics and graph theory. Includes case studies describing computations underpinning new theoretical results.
| Author | : Saugata Basu |
| Publisher | : Springer |
| Total Pages | : 662 |
| Release | : 2009-09-02 |
| Genre | : Mathematics |
| ISBN | : 9783540821953 |
Download Algorithms in Real Algebraic Geometry Book in PDF, ePub and Kindle
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.
| Author | : James Harold Davenport |
| Publisher | : |
| Total Pages | : 328 |
| Release | : 1993 |
| Genre | : Computers |
| ISBN | : |
Download Computer Algebra Book in PDF, ePub and Kindle
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.
| Author | : Willem Adriaan de Graaf |
| Publisher | : CRC Press |
| Total Pages | : 324 |
| Release | : 2017-08-07 |
| Genre | : Mathematics |
| ISBN | : 1498722911 |
Download Computation with Linear Algebraic Groups Book in PDF, ePub and Kindle
Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.
