Algebra for Symbolic Computation
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.
From the reviews:
“The contents of this book is classical. … Many examples illustrate the text and make the mathematical objects very concrete. There are also many practical exercises. … It is clear that a thorough comprehension of these subjects would be greatly simplified if it is accompanied by exercises at the computer. Many examples of algorithms are given in the text, others may be easily deduced from the theory. … this book will be very useful and is very pleasant to read.” (Maurice Mignotte, Zentralblatt MATH, Vol. 1238, 2012)