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Effective Polynomial Computation
Richard Zippel
出版Springer Science & Business Media, 1993-07-31
主題Computers / Data ProcessingComputers / Programming / AlgorithmsMathematics / Algebra / GeneralMathematics / Number TheoryMathematics / Discrete MathematicsComputers / Information Technology
ISBN07923937599780792393757
URLhttp://books.google.com.hk/books?id=--Ih9bv0m_AC&hl=&source=gbs_api
EBookSAMPLE
註釋Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained.
Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth.
Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers).
Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.