Modular Algorithms In Symbolic Summation And Symbolic Integration
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Modular Algorithms In Symbolic Summation And Symbolic Integration
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Author : Jürgen Gerhard
language : en
Publisher: Springer
Release Date : 2004-11-12
Modular Algorithms In Symbolic Summation And Symbolic Integration written by Jürgen Gerhard and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-11-12 with Computers categories.
This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.
Hypergeometric Summation
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Author : Wolfram Koepf
language : en
Publisher: Springer
Release Date : 2014-06-10
Hypergeometric Summation written by Wolfram Koepf and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-10 with Computers categories.
Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system MapleTM. The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hypergeometric summation and recurrence equations, efficient multivariate summation as well as q-analogues of the above algorithms are covered. Similar algorithms concerning differential equations are considered. An equivalent theory of hyperexponential integration due to Almkvist and Zeilberger completes the book. The combination of these results gives orthogonal polynomials and (hypergeometric and q-hypergeometric) special functions a solid algorithmic foundation. Hence, many examples from this very active field are given. The materials covered are suitable for an introductory course on algorithmic summation and will appeal to students and researchers alike.
Modern Computer Algebra
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Author : Joachim von zur Gathen
language : en
Publisher: Cambridge University Press
Release Date : 2013-04-25
Modern Computer Algebra written by Joachim von zur Gathen 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 2013-04-25 with Computers categories.
Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.
Computer Mathematics
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Author : Ruyong Feng
language : en
Publisher: Springer
Release Date : 2014-09-30
Computer Mathematics written by Ruyong Feng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-30 with Mathematics categories.
This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers.
D Finite Functions
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Author : Manuel Kauers
language : en
Publisher: Springer Nature
Release Date : 2023-11-08
D Finite Functions written by Manuel Kauers and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-08 with Mathematics categories.
Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of “explicit” expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are explained in detail. The book comes “with batteries included” in the sense that it requires no background in computer algebra as the relevant facts from this area are summarized in the beginning. This makes the book accessible to a wide range of readers, from mathematics students who plan to work themselves on D-finite functions to researchers who want to apply the theory to their own work. Hundreds of exercises invite the reader to apply the techniques in the book and explore further aspects of the theory on their own. Solutions to all exercises are given in the appendix. When algorithms for D-finite functions came up in the early 1990s, computer proofs were met with a certain skepticism. Fortunately, these times are over and computer algebra has become a standard tool for many mathematicians. Yet, this powerful machinery is still not as widely known as it deserves. This book helps to spread the word that certain tasks can be safely delegated to a computer algebra system, and also what the limitations of these techniques are.
Computer Algebra In Scientific Computing
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Author : Vladimir P. Gerdt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-18
Computer Algebra In Scientific Computing written by Vladimir P. Gerdt 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 2010-08-18 with Computers categories.
This book constitutes the refereed proceedings of the 12th International Workshop on Computer Algebra in Scientific Computing, CASC 2010, held in Tsakhadzor, Armenia, in September 2010. The book includes two invited talks and an abstract in addition to 23 full papers.
Maple Techniques And Applications
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Author : Richard Johnson
language : en
Publisher: HiTeX Press
Release Date : 2025-06-12
Maple Techniques And Applications written by Richard Johnson and has been published by HiTeX Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-12 with Computers categories.
"Maple Techniques and Applications" "Maple Techniques and Applications" is an authoritative guide that illuminates both the foundations and advanced capabilities of the Maple computational system. Beginning with the system's core architecture, the book explains Maple’s kernel and front-end design, dives into expression trees and memory management, and addresses critical topics such as session persistence, interoperability with external code, and robust security measures. These insights enable readers to master Maple’s infrastructure, equipping them for both everyday tasks and large-scale symbolic computation. The book proceeds to explore advanced programming paradigms, including encapsulation with modules and packages, functional and rule-based programming, meta-programming, and modern software development practices such as profiling and parallel computation. Through lucid explanations and detailed examples, readers gain proficiency in leveraging Maple’s symbolic and numeric engines across diverse mathematical domains—spanning sophisticated algebraic manipulation, differential equations, integration techniques, and complex linear algebra operations. Chapters devoted to scientific visualization reveal methods for high-volume data rendering, interactive animation, and publication-ready graphical output, all integrated seamlessly within the Maple environment. Transitioning from computational methods to practical automation, the text guides readers through scripting, workflow orchestration, cloud deployment, and collaborative development. Extensive domain-specific case studies showcase how Maple empowers researchers and practitioners in physics, engineering, finance, biology, and machine learning to achieve reproducible results and innovative solutions. Rich with best practices and real-world examples, "Maple Techniques and Applications" is an indispensable resource for advanced users, researchers, and developers seeking to unlock the full potential of Maple for modern scientific and engineering challenges.
Scientific And Technical Aerospace Reports
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Author :
language : en
Publisher:
Release Date : 1994
Scientific And Technical Aerospace Reports written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Aeronautics categories.
Algorithmic Combinatorics Enumerative Combinatorics Special Functions And Computer Algebra
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Author : Veronika Pillwein
language : en
Publisher: Springer Nature
Release Date : 2020-09-28
Algorithmic Combinatorics Enumerative Combinatorics Special Functions And Computer Algebra written by Veronika Pillwein and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Computers categories.
The book is centered around the research areas of combinatorics, special functions, and computer algebra. What these research fields share is that many of their outstanding results do not only have applications in Mathematics, but also other disciplines, such as computer science, physics, chemistry, etc. A particular charm of these areas is how they interact and influence one another. For instance, combinatorial or special functions' techniques have motivated the development of new symbolic algorithms. In particular, first proofs of challenging problems in combinatorics and special functions were derived by making essential use of computer algebra. This book addresses these interdisciplinary aspects. Algorithmic aspects are emphasized and the corresponding software packages for concrete problem solving are introduced. Readers will range from graduate students, researchers to practitioners who are interested in solving concrete problems within mathematics and other research disciplines.
Q
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Author : Сергей Абрамов
language : ru
Publisher: Litres
Release Date : 2015-02-23
Q written by Сергей Абрамов and has been published by Litres this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-23 with Mathematics categories.
Рассматривается ряд алгоритмов, связанных с линейными обыкновенными дифференциальными, разностными и q-разностными операторами (и уравнениями) с полиномиальными коэффициентами. Эти алгоритмы не только представляют известный самостоятельный интерес для компьютерной алгебры, но являются еще и основой других, более универсальных и сложных алгоритмов. Обсуждаются некоторые неразрешимые алгоритмические проблемы, возникающие при изучении уравнений с параметрами. Подробно разобран один из компьютерно-алгебраических подходов в теоретических математических исследованиях.Для студентов и аспирантов, специализирующихся в области математики и информатики, и всех тех, кто в своей работе так или иначе соприкасается с компьютерной алгеброй.