Algorithms for q-hypergeometric Summation in Computer Algebra HARALDBOING¨ † ANDWOLFRAMKOEPF‡ †Konrad Zuse Zentrum Berlin, Germany ‡Hochschule f¨ur Technik, Wirtschaft und Kultur Leipzig, Germany In this paper we present a short description of q-analogues of Gosper’s, Zeilberger’s. Viii Algorithms for Computer Algebra Chapter 4 Arithmetic of Polynomials, Rational Functions, and Power Series 4.1 Introduction 111 4.2 Basic Arithmetic Algorithms 112 4.3 Fast Arithmetic Algorithms: Karatsuba's Algorithm 118 4.4 Modular Representations 120 4.5 The Fast Fourier Transform 123 4.6 The Inverse Fourier Transform 128.
Publisher: Springer Science & Business Media
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Algebra 1 Book Pdf150
Algorithms For Computer Algebra Pdf
Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.