Algebra for Symbolic Computation

by Antonio Machì

This book deals with several topics in algebra useful for computer science applications and the symbolic treatment of algebraic problems, pointing out and discussing their algorithmic nature. The topics covered range from classical results such as the Euclidean algorithm, the Chinese remainder theorem, and polynomial interpolation, to p-adic expansions of rational and algebraic numbers and rational functions, to reach the problem of the polynomial factorisation,  especially via Berlekamp’s method, and the discrete Fourier transform. Basic algebra concepts are revised in a form suited for implementation on a computer algebra system.

188 pages, Paperback

First published March 16, 2012

Reviews

[Tom Schulte · Rating 2 out of 5]

...Rather than taking the reader somewhere even like CORDIC, the presentation is the expected corollaries of classical analysis. The result is a concisely presented range of classical results including Chinese remainder theorem, polynomial interpolation, p-adic expansions of rational and algebraic numbers, discrete Fourier transform, and more. There is a light amount of examples and exercises which would benefit from implementation details for software packages such as MATLAB or Maple.

[Look for my entire review in MAA Reviews]