Titlebook: Computer Algebra; Symbolic and Algebra Bruno Buchberger,George Edwin Collins,Rudolf Albre Book 1983Latest edition Springer-Verlag Wien 1983

易于

Algebraic Simplification,sions, radical expressions and transcendental expressions are treated (Sections 3–7). As examples for completion algorithms the Knuth-Bendix algorithm for rewrite rules and an algorithm for completing bases of polynomial ideals are described (Sections 8–11).

Meander

Miguel A. Aon,Valdur Saks,Uwe Schlattnerr introducing Zassenhaus’ quadratic lifting construction, again, the case of Z and .[..,…,..]is considered. For both techniques, Chinese remaindering as well as the lifting algorithms, a complete computational example is presented and the most frequent applications are discussed.

兵團(tuán)

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Algebraic Simplification,formally stated and some elementary facts are derived that explain the fundamental role of simplification in Computer algebra. In the subsequent sections two major groups of simplification techniques are presented: special techniques for simplifying terms over numerical domains and completion algori

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群島

Real Zeros of Polynomials,oints, each containing exactly one real zero of . and together containing all real zeros of .. We describe an algorithm due to Kronecker based on the minimum root Separation, Sturm’s algorithm, an algorithm based on Rolle’s theorem due to Collins and Loos and the modified Uspensky algorithm due to C

危機(jī)

Factorization of Polynomials,ds, the integers, or algebraic extensions of the rationals, and to multivariate polynomials with integral coefficients. In particular, various squarefree decomposition algorithms and Hensel lifting techniques are analyzed. An attempt is made to establish a complete historic trace for today’s methods

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