Update: This book might be split into a few volumes.

I am writing a book, Computer Algebra and Algebraic Programming, intending to be a comprehensive introduction to the methods of computer algebra, intended for both computer scientists and mathematicians. It treats the subject programmatically and mathematically, and includes motivation for topics, examples, and pseudocode. It will also contain information on the “algebraic paradigm”, seemingly unrelated, but serves as a foundation for thinking about algebra and programming.

It is a very ambitious project in that there is a lot to cover. It is only “introductory” because it can be read by someone who does not know anything about computer algebra. The text is set out to give a comprehensive treatment of both basic algorithms like the Euclidean algorithm, as well as very advanced algorithms like the Risch algorithm.

A draft can be downloaded at no charge: PDF