Mathematics For Computer Algebra
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Author |
: Maurice Mignotte |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 357 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461391715 |
ISBN-13 |
: 1461391717 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Mathematics for Computer Algebra by : Maurice Mignotte
This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementary facts in Combinatorics (maybe only Newton's binomial formula), some theorems of Analysis at the level of high schools, and some elementary Algebra (basic results about groups, rings, fields and linear algebra). An important place is given to exercises. These exercises are only rarely direct applications of the course. More often, they constitute complements to the text. Mostly, hints or references are given so that the reader should be able to find solutions. Chapters one and two deal with elementary results of Number Theory, for example : the euclidean algorithm, the Chinese remainder theorem and Fermat's little theorem. These results are useful by themselves, but they also constitute a concrete introduction to some notions in abstract algebra (for example, euclidean rings, principal rings ... ). Algorithms are given for arithmetical operations with long integers. The rest of the book, chapters 3 through 7, deals with polynomials. We give general results on polynomials over arbitrary rings. Then polynomials with complex coefficients are studied in chapter 4, including many estimates on the complex roots of polynomials. Some of these estimates are very useful in the subsequent chapters.
Author |
: Joachim von zur Gathen |
Publisher |
: Cambridge University Press |
Total Pages |
: 811 |
Release |
: 2013-04-25 |
ISBN-10 |
: 9781107039032 |
ISBN-13 |
: 1107039037 |
Rating |
: 4/5 (32 Downloads) |
Synopsis Modern Computer Algebra by : Joachim von zur Gathen
Now in its third edition, this highly successful textbook is widely regarded as the 'bible of computer algebra'.
Author |
: Keith O. Geddes |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 594 |
Release |
: 2007-06-30 |
ISBN-10 |
: 9780585332475 |
ISBN-13 |
: 0585332479 |
Rating |
: 4/5 (75 Downloads) |
Synopsis Algorithms for Computer Algebra by : Keith O. Geddes
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.
Author |
: Joel S. Cohen |
Publisher |
: CRC Press |
Total Pages |
: 472 |
Release |
: 2003-01-03 |
ISBN-10 |
: 9781439863701 |
ISBN-13 |
: 1439863709 |
Rating |
: 4/5 (01 Downloads) |
Synopsis Computer Algebra and Symbolic Computation by : Joel S. Cohen
Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations. Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polyno
Author |
: Edmund A. Lamagna |
Publisher |
: CRC Press |
Total Pages |
: 350 |
Release |
: 2019-01-15 |
ISBN-10 |
: 9781351605830 |
ISBN-13 |
: 1351605836 |
Rating |
: 4/5 (30 Downloads) |
Synopsis Computer Algebra by : Edmund A. Lamagna
The goal of Computer Algebra: Concepts and Techniques is to demystify computer algebra systems for a wide audience including students, faculty, and professionals in scientific fields such as computer science, mathematics, engineering, and physics. Unlike previous books, the only prerequisites are knowledge of first year calculus and a little programming experience — a background that can be assumed of the intended audience. The book is written in a lean and lively style, with numerous examples to illustrate the issues and techniques discussed. It presents the principal algorithms and data structures, while also discussing the inherent and practical limitations of these systems
Author |
: Joel S. Cohen |
Publisher |
: CRC Press |
Total Pages |
: 323 |
Release |
: 2002-07-19 |
ISBN-10 |
: 9781439863695 |
ISBN-13 |
: 1439863695 |
Rating |
: 4/5 (95 Downloads) |
Synopsis Computer Algebra and Symbolic Computation by : Joel S. Cohen
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
Author |
: Eric Lehman |
Publisher |
: |
Total Pages |
: 988 |
Release |
: 2017-03-08 |
ISBN-10 |
: 9888407066 |
ISBN-13 |
: 9789888407064 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Mathematics for Computer Science by : Eric Lehman
This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions.
Author |
: James Taylor Fey |
Publisher |
: National Council of Teachers of English |
Total Pages |
: 336 |
Release |
: 2003 |
ISBN-10 |
: 0873535316 |
ISBN-13 |
: 9780873535311 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Computer Algebra Systems in Secondary School Mathematics Education by : James Taylor Fey
Author |
: Johannes Grabmeier |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 656 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9783642558269 |
ISBN-13 |
: 3642558267 |
Rating |
: 4/5 (69 Downloads) |
Synopsis Computer Algebra Handbook by : Johannes Grabmeier
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.
Author |
: J. Rafael Sendra |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 273 |
Release |
: 2007-12-10 |
ISBN-10 |
: 9783540737254 |
ISBN-13 |
: 3540737251 |
Rating |
: 4/5 (54 Downloads) |
Synopsis Rational Algebraic Curves by : J. Rafael Sendra
The central problem considered in this introduction for graduate students is the determination of rational parametrizability of an algebraic curve and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve: its complete singularity structure, computing regular points of the curve in small coordinate fields, and constructing linear systems of curves with prescribed intersection multiplicities. The book discusses various optimality criteria for rational parametrizations of algebraic curves.