Algorithmic Algebra

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Algorithmic Algebra

Bhubaneswar Mishra
Algorithmic Algebra Book PDF

Author : Bhubaneswar Mishra
Publisher : Springer Science & Business Media
Page : 427 pages
File Size : 43,9 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461243441

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Algorithmic Algebra by Bhubaneswar Mishra Pdf

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.

Fundamental Problems of Algorithmic Algebra

Chee-Keng Yap
Fundamental Problems of Algorithmic Algebra Book PDF

Author : Chee-Keng Yap
Publisher : Oxford University Press on Demand
Page : 511 pages
File Size : 54,6 Mb
Release : 2000
Category : Computers
ISBN : 0195125169

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Fundamental Problems of Algorithmic Algebra by Chee-Keng Yap Pdf

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

Algorithmic and Combinatorial Algebra

L.A. Bokut',G.P.. Kukin
Algorithmic and Combinatorial Algebra Book PDF

Author : L.A. Bokut',G.P.. Kukin
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 44,8 Mb
Release : 1994-05-31
Category : Computers
ISBN : 0792323130

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Algorithmic and Combinatorial Algebra by L.A. Bokut',G.P.. Kukin Pdf

Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Algorithmic Algebraic Number Theory

M. Pohst,H. Zassenhaus
Algorithmic Algebraic Number Theory Book PDF

Author : M. Pohst,H. Zassenhaus
Publisher : Cambridge University Press
Page : 520 pages
File Size : 43,6 Mb
Release : 1997-09-25
Category : Mathematics
ISBN : 0521596696

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Algorithmic Algebraic Number Theory by M. Pohst,H. Zassenhaus Pdf

Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.

Algorithmic Algebra and Number Theory

B.Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss
Algorithmic Algebra and Number Theory Book PDF

Author : B.Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642599323

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Algorithmic Algebra and Number Theory by B.Heinrich Matzat,Gert-Martin Greuel,Gerhard Hiss Pdf

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.

Thirty-three Miniatures

Jiří Matoušek
Thirty three Miniatures Book PDF

Author : Jiří Matoušek
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 48,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849774

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Thirty-three Miniatures by Jiří Matoušek Pdf

This volume contains a collection of clever mathematical applications of linear algebra, mainly in combinatorics, geometry, and algorithms. Each chapter covers a single main result with motivation and full proof in at most ten pages and can be read independently of all other chapters (with minor exceptions), assuming only a modest background in linear algebra. The topics include a number of well-known mathematical gems, such as Hamming codes, the matrix-tree theorem, the Lovasz bound on the Shannon capacity, and a counterexample to Borsuk's conjecture, as well as other, perhaps less popular but similarly beautiful results, e.g., fast associativity testing, a lemma of Steinitz on ordering vectors, a monotonicity result for integer partitions, or a bound for set pairs via exterior products. The simpler results in the first part of the book provide ample material to liven up an undergraduate course of linear algebra. The more advanced parts can be used for a graduate course of linear-algebraic methods or for seminar presentations. Table of Contents: Fibonacci numbers, quickly; Fibonacci numbers, the formula; The clubs of Oddtown; Same-size intersections; Error-correcting codes; Odd distances; Are these distances Euclidean?; Packing complete bipartite graphs; Equiangular lines; Where is the triangle?; Checking matrix multiplication; Tiling a rectangle by squares; Three Petersens are not enough; Petersen, Hoffman-Singleton, and maybe 57; Only two distances; Covering a cube minus one vertex; Medium-size intersection is hard to avoid; On the difficulty of reducing the diameter; The end of the small coins; Walking in the yard; Counting spanning trees; In how many ways can a man tile a board?; More bricks--more walls?; Perfect matchings and determinants; Turning a ladder over a finite field; Counting compositions; Is it associative?; The secret agent and umbrella; Shannon capacity of the union: a tale of two fields; Equilateral sets; Cutting cheaply using eigenvectors; Rotating the cube; Set pairs and exterior products; Index. (STML/53)

Algorithmic Methods in Non-Commutative Algebra

J.L. Bueso,José Gómez-Torrecillas,A. Verschoren
Algorithmic Methods in Non Commutative Algebra Book PDF

Author : J.L. Bueso,José Gómez-Torrecillas,A. Verschoren
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 55,8 Mb
Release : 2013-03-09
Category : Computers
ISBN : 9789401702850

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Algorithmic Methods in Non-Commutative Algebra by J.L. Bueso,José Gómez-Torrecillas,A. Verschoren Pdf

The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity, the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis, which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way, concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups), the so-called Poincaré-Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules, the calculation of homological dimension and of the Gelfand-Kirillov dimension, the Hilbert-Samuel polynomial, primality tests for prime ideals, etc.

Algorithmic and Combinatorial Algebra

L.A. Bokut',G.P.. Kukin
Algorithmic and Combinatorial Algebra Book PDF

Author : L.A. Bokut',G.P.. Kukin
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120029

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Algorithmic and Combinatorial Algebra by L.A. Bokut',G.P.. Kukin Pdf

Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Ideals, Varieties, and Algorithms

David Cox,John Little,DONAL OSHEA
Ideals Varieties and Algorithms Book PDF

Author : David Cox,John Little,DONAL OSHEA
Publisher : Springer Science & Business Media
Page : 523 pages
File Size : 51,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475721812

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Ideals, Varieties, and Algorithms by David Cox,John Little,DONAL OSHEA Pdf

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.

Algorithmic Algebraic Combinatorics and Gröbner Bases

Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko
Algorithmic Algebraic Combinatorics and Gr bner Bases Book PDF

Author : Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 42,8 Mb
Release : 2009-12-24
Category : Mathematics
ISBN : 9783642019609

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Algorithmic Algebraic Combinatorics and Gröbner Bases by Mikhail Klin,Gareth A. Jones,Aleksandar Jurisic,Mikhail Muzychuk,Ilia Ponomarenko Pdf

This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries. There is special emphasis on algorithmic aspects and the use of the theory of Gröbner bases.

Algorithms for Computer Algebra

Keith O. Geddes,Stephen R. Czapor,George Labahn
Algorithms for Computer Algebra Book PDF

Author : Keith O. Geddes,Stephen R. Czapor,George Labahn
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 43,9 Mb
Release : 2007-06-30
Category : Computers
ISBN : 9780585332475

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Algorithms for Computer Algebra by Keith O. Geddes,Stephen R. Czapor,George Labahn Pdf

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.

Algorithmic Mathematics

Stefan Hougardy,Jens Vygen
Algorithmic Mathematics Book PDF

Author : Stefan Hougardy,Jens Vygen
Publisher : Springer
Page : 163 pages
File Size : 45,6 Mb
Release : 2016-10-14
Category : Computers
ISBN : 9783319395586

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Algorithmic Mathematics by Stefan Hougardy,Jens Vygen Pdf

Algorithms play an increasingly important role in nearly all fields of mathematics. This book allows readers to develop basic mathematical abilities, in particular those concerning the design and analysis of algorithms as well as their implementation. It presents not only fundamental algorithms like the sieve of Eratosthenes, the Euclidean algorithm, sorting algorithms, algorithms on graphs, and Gaussian elimination, but also discusses elementary data structures, basic graph theory, and numerical questions. In addition, it provides an introduction to programming and demonstrates in detail how to implement algorithms in C++. This textbook is suitable for students who are new to the subject and covers a basic mathematical lecture course, complementing traditional courses on analysis and linear algebra. Both authors have given this "Algorithmic Mathematics" course at the University of Bonn several times in recent years.

Algorithms in Real Algebraic Geometry

Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy
Algorithms in Real Algebraic Geometry Book PDF

Author : Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 44,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662053553

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Algorithms in Real Algebraic Geometry by Saugata Basu,Richard Pollack,Marie-Françoise Coste-Roy Pdf

In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.

A Course in Computational Algebraic Number Theory

Henri Cohen
A Course in Computational Algebraic Number Theory Book PDF

Author : Henri Cohen
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 40,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662029459

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A Course in Computational Algebraic Number Theory by Henri Cohen Pdf

A description of 148 algorithms fundamental to number-theoretic computations, in particular for computations related to algebraic number theory, elliptic curves, primality testing and factoring. The first seven chapters guide readers to the heart of current research in computational algebraic number theory, including recent algorithms for computing class groups and units, as well as elliptic curve computations, while the last three chapters survey factoring and primality testing methods, including a detailed description of the number field sieve algorithm. The whole is rounded off with a description of available computer packages and some useful tables, backed by numerous exercises. Written by an authority in the field, and one with great practical and teaching experience, this is certain to become the standard and indispensable reference on the subject.

Algebraic Operads

Murray R. Bremner,Vladimir Dotsenko
Algebraic Operads Book PDF

Author : Murray R. Bremner,Vladimir Dotsenko
Publisher : CRC Press
Page : 382 pages
File Size : 50,7 Mb
Release : 2016-04-06
Category : Mathematics
ISBN : 9781482248579

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Algebraic Operads by Murray R. Bremner,Vladimir Dotsenko Pdf

Algebraic Operads: An Algorithmic Companion presents a systematic treatment of Grobner bases in several contexts. The book builds up to the theory of Grobner bases for operads due to the second author and Khoroshkin as well as various applications of the corresponding diamond lemmas in algebra. The authors present a variety of topics including: non