Algorithms for Computer Algebra

1992
ISBN: 978-0-7923-9259-0
Verlag: Springer US

Buch, Englisch, 586 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1068 g

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.
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.

Zielgruppe

Research

Autoren/Hrsg.

Geddes, Keith O.

Labahn, George

Czapor, Stephen R.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik EDV | Informatik EDV & Informatik Allgemein
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning

Inhaltsverzeichnis

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.