Fast Parallel Gcd Algorithms for Several Polynomials Over Integral Domain
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.17
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Add to basketItem description from seller
Print on Demand. This book presents a new parallel algorithm for computing the GCD of many polynomials over integral domains. It provides a fast and efficient way to solve this problem, which has applications in computer algebra, coding theory, and other areas of mathematics and computer science. The author extends the theory of subresultants from two polynomials to several polynomials, allowing for the efficient computation of the GCD of multiple polynomials simultaneously. This approach provides a deeper understanding of the relationship between the GCD and the subresultant chain, and it leads to a more efficient algorithm for computing the GCD. The book also discusses the practical implementation of the algorithm, including details on how to parallelize the computation and how to handle special cases. It provides a valuable resource for researchers and practitioners working in the area of polynomial GCD computation and related topics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781332127184_0
- Title
- Fast Parallel Gcd Algorithms for Several Polynomials Over Integral Domain
- Author
- Chung-Jen Ho
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332127185
- ISBN 13
- 9781332127184
- Seller catalogs
- Algebra
Discover how to compute the greatest common divisor of many polynomials in parallel, using subresultants and the PRAM model.
This work extends the subresultant framework from two polynomials to several, delivering a practical parallel approach to GCD computation over an integral domain. It presents how to build a parallel pipeline that matches the time and processor bounds of established methods while handling larger polynomial sets.
This book grounds its methods in the theory of subresultants and Sylvester-type matrices, then shows how to translate that theory into a concrete algorithm. It discusses constructing matrices, analyzing ranks, and using parallel primitives to obtain the GCD efficiently. The study also connects classical results with contemporary parallel computation techniques, offering a clear path from theory to implementation.- Learn how to extend subresultants to multiple polynomials
- See how the Sylvester matrix and rank analysis drive parallel GCD methods
- Explore a PRAM-based model of computation and its implications for efficiency
- Understand the process from matrix construction to det(polynomial) computations and GCD extraction
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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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