Titlebook: Computer Algebra; Symbolic and Algebra Bruno Buchberger,George Edwin Collins,Rüdiger Loos Book 19821st edition Springer-Verlag Wien 1982 al

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Systems Collaboration and IntegrationIn this survey an attempt is made to give some impression of the capabilities of currently available programs for computations with finitely generated groups and their representations.

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https://doi.org/10.1007/978-3-031-44373-2This article provides a brief summary of the most important publications relating to quantifier elimination algorithms for the elementary theory of real closed fields. Especially mentioned is the cylindrical algebraic decomposition method and its relation to the facilities of computer algebra facilities.

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https://doi.org/10.1007/978-3-662-64517-8Some fundamental inequalities for the following values are listed: the determinant of a matrix, the absolute value of the roots of a polynomial, the coefficients of divisors of polynomials, and the minimal distance between the roots of a polynomial. These inequalities are useful for the analysis of algorithms in various areas of computer algebra.

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Introduction,In this introduction we first give a working definition of computer algebra. We then describe the organization of research activities in this field. Finally the overall structure and the intention of the present volume on computer algebra is explained. Some technical information (basic references, notation etc.) about the volume is given.

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Computing with Groups and Their Character Tables,In this survey an attempt is made to give some impression of the capabilities of currently available programs for computations with finitely generated groups and their representations.

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Some Useful Bounds,Some fundamental inequalities for the following values are listed: the determinant of a matrix, the absolute value of the roots of a polynomial, the coefficients of divisors of polynomials, and the minimal distance between the roots of a polynomial. These inequalities are useful for the analysis of algorithms in various areas of computer algebra.

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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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Integration in Finite Terms, 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.