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Synopsis
The book gives a thorough introduction to the mathematical underpinnings of computer algebra. The subjects treated range from arithmetic of integers and polynomials to fast factorization methods, Gröbner bases, and algorithms in algebraic geometry. The algebraic background for all the algorithms presented in the book is fully described, and most of the algorithms are investigated with respect to their computational complexity. Each chapter closes with a brief survey of the related literature.
The book is designed as a textbook for a course in computer algebra for advanced undergraduate or beginning graduate students. Every chapter contains a considerable number of exercises, some of which are solved in the appendix. In bridging the gap between the algebraic theory and computer algebra software, the book should be of interest to both mathematics and computer science students.