New Material

On this page we publish new material that would be included in the second edition of the book.

New blade factorization algorithm, new Join algorithm.

We have found a new way to factor blades that also helps to speed up computing the join of blades. Computing the join of blades is now 10x faster than the algorithms presented in the book (as benchmarked in Section 5.11.2).

A rewritten version of this paper would replace Sections 21.6 and 21.7 in a second edition of the book. The paper is rather dense because of the 10-page limit set by the AGACSE 2008 conference, so be sure to read those sections first!

Extended Treatment of Meet and Join.

One of our readers, Greg Grunberg, found our treatment of the Meet and Join operators in Chapter 5 interesting, but terse. He has written a more extended discussion of some of the basic properties, including explicit proofs and derivations. We are grateful that he has allowed us to post this on our book website.