Small algorithms for small systems

Abstract

Knuth is said to have described Computer Science as "that part of mathematics in which log log n = 3". This paper only considers some parts of Computer Algebra, and the even more special case when log n ≈ 3, or even less, and where compactness of the algorithm itself, as well as the data structures, is important. We begin with a few remarks on integration, which, while in some sense the culmination of computer algebra for the "compact computer algebra" market, also inspired many of our other suggestions. Acknowledgements. This paper was prepared when the author was visiting the Symbolic Com putation Group in the David R. Cheriton School of Computer Science, University of Waterloo, and the author is grateful to Prof. Giesbrecht and colleagues for their hospitality. Its preparation was inspired by an invitation to talk at the Compact Computer Algebra workshop at CICM 2009, and the author is grateful to Dr Smirnova for the invitation. At that workshop Prof. Geddes remarked that the subresultant algorithm did not work well for multivariates, which inspired section 5.