Greetings, If you already know about the quaternion characteristic polynomial method for a fast closed-form solution of the least squares superposition problem, this note is mostly noise. While in the process of updating links to my project, I noticed the note at the bottom of the cctbx sourceforge page (http://cctbx.sourceforge.net/). I like the historical nature presented, and I used the historical method to numerically solve quartic polynomials in a previous project at Michigan State University that ranks relatively large datasets of protein small-molecule binding sites (with respect to a given query site). The superposition method I used has a closed form and is due to BKP Horn. Later on (after writing my dissertation), I found that using the historical method to numerically solve quartic polynomials is not numerically stable or robust. Fortunately, there is an easy solution, and if you are interested in a fast closed-form solution for the least squares superposition problem you would do well (in my opinion) to visit http://theobald.brandeis.edu/qcp/. Best regards, Jeff Van Voorst