Algorithms for Computer Algebra

Couverture
Springer Science & Business Media, 30 sept. 1992 - 586 pages
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.
 

Table des matières

Algebra of Polynomials Rational Functions and Power Series
23
Normal Forms and Algebraic Representations
79
Arithmetic of Polynomials Rational Functions and Power Series
110
Homomorphisms and Chinese Remainder Algorithms
151
Newtons Iteration and the Hensel Construction
204
Polynomial GCD Computation
279
Polynomial Factorization
336
Solving Systems of Equations
389
Gröbner Bases for Polynomial Ideals
429
Integration of Rational Functions
473
Droits d'auteur

Autres éditions - Tout afficher

Expressions et termes fréquents

Informations bibliographiques