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

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The Control Analysis of Signal Transductionds, 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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https://doi.org/10.1007/978-3-642-38505-6Habicht, we show how certain powers of leading coefficients enter systematically all following remainders. The key tool is the subresultant chain of two polynomials. We study the primitive, the reduced and the improved subresultant p.r.s. algorithm of Brown and Collins as basis for Computing polynom

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Miguel A. Aon,Valdur Saks,Uwe Schlattnerated extensively. Chinese remaindering is first presented in an abstract setting. Then the specialization to Euclidean domains, in particular Z, K[.] and Z[..,…,..] is treated. The lifting construction is first also presented in an abstract form from which Henss Lemma derives by specialization. Afte

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The Control Analysis of Signal Transductionctions over the field. The computational difficulty associated with such extensions is in verifying that proposed extensions are transcendental. When the extensions being considered are functions, and where a differentiation operator can be defined for them, strueture theorems can be used to determi

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Miguel A. Aon,Valdur Saks,Uwe Schlattnerlk about arithmetic in Q(.) and GF(..) in Section 1 and some polynomial algorithms with coefficients from these domains in Section 2. Then, we will consider the field . of all algebraic numbers over . and show constructively that K indeed is a field, that multiple extensions can be replaced by singl

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Miguel A. Aon,Valdur Saks,Uwe Schlattneron the basic algebraic domains. The algorithms for these basic domains are those most frequently used in any Computer algebra system. Therefore the best known algorithms, from a computational point of view, are presented. The basic domains considered here are the rational integers, the rational numb

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Deepa R. Varkey,Martina A. Doblin and elementary transcendental integrands are reviewed. Heuristic techniques for indefinite integration, and techniques for definite integration and ordinary differential equations are touched on only briefly.