This proposal covers issues ranging from very theoretical to very practical. Each of the PI's would likely carry the results back to his community of colleagues. External presentation of the work on this proposal is especially important for the project's success because it is our hope that researchers outside of Cornell will be interested in connecting their software to the MathBus once the MathBus becomes viable. Therefore, we intend to present results of this research at a variety of conferences, ranging from theoretical conferences such as Logic in Computer Science (LICS) and the International Symposium on Symbolic and Algebraic Computation (ISSAC) to highly applied conferences such as Supercomputing and the SIAM annual meeting.