Performance comparison of Maple and Mathematica

There are two major, widely available, symbolic mathematical computer systems: Maple and Mathematica. Both have recent new versions with Mathematica 5.2 and Maple 10, the latter being a major upgrade. The packages have extensive similarities in the computational work they’re intended to support. In this paper my goal is to help you decide which of them is better suited to your temperament or your current technological practice. I donot intend to try to prove, and will not assert, that one package is better than another. Rather, my methodology is intended to present a basis for each reader to create a personal metric for comparing the packages.