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＜電子ブック＞
Algorithms for Computer Algebra / by Keith O. Geddes, Stephen R. Czapor, George Labahn

版	1st ed. 1992.
出版者	(New York, NY : Springer US : Imprint: Springer)
出版年	1992
本文言語	英語
大きさ	XXII, 586 p : online resource
著者標目	*Geddes, Keith O author Czapor, Stephen R author Labahn, George author SpringerLink (Online service)
件　名	LCSH:Computer software LCSH:Computer vision LCSH:Algebra LCSH:Computer science -- Mathematics  全ての件名で検索 LCSH:Numerical analysis LCSH:Computer science FREE:Mathematical Software FREE:Computer Vision FREE:Algebra FREE:Symbolic and Algebraic Manipulation FREE:Numerical Analysis FREE:Computer Science
一般注記	to Computer Algebra -- Algebra of Polynomials, Rational Functions, and Power Series -- Normal Forms and Algebraic Representations -- Arithmetic of Polynomials, Rational Functions, and Power Series -- Homomorphisms and Chinese Remainder Algorithms -- Newton’s Iteration and the Hensel Construction -- Polynomial GCD Computation -- Polynomial Factorization -- Solving Systems of Equations -- Gröbner Bases for Polynomial Ideals -- Integration of Rational Functions -- The Risch Integration Algorithm 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 HTTP:URL=https://doi.org/10.1007/b102438

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