Most stability analyses for computational material dynamics schemes are difficult, tedious, and algebraically messy. This leads to the consideration of the use of algebraic manipulators. This paper gives the impression that using computer algebra software, such as REDUCE, to do stability analyses for computational material dynamics is a relatively recent research topic. However, I recall that researchers at Sandia National Laboratories in Albuquerque were using REDUCE to do computational material dynamics stability analyses at least 30 years ago. The authors compare REDUCE to Mathematica and conclude that they prefer the latter. I wonder why the algebraic manipulators selected for comparison were restricted to these two, when there are so many others with specific capabilities that are better for certain aspects of these applications, for example, Scientific Workplace, Maple, Matlab, Mathcad, and Macsyma. I have one caveat: neophytes to algebraic manipulators tend to get overexcited about their potential utility. There are several major drawbacks to using algebraic manipulators, such as the loss of “feel for the problem” and the relative insight gained by doing at least a part of the algebra “by hand.”