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By Hamilton W.R.
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Additional resources for Additional Applications of the Thepry of Algebraic Quaternions
The history of the more general problem of indefinite summation contains the names of Newton, Euler, Bernoulli and Boole, and despite the many years these distinguished mathematicians devoted to the problem, the results are surprisingly few in number. One reason for believing in the existence of an algorithm is the success achieved in solving the indefinite integral problem and the close parallels between the two conceptually. Gasper's approach involved testing many cases with MACSYMA until a pattern emerged that worked for all cases and led to the discovery of the algorithm.
This is something that might not happen if one were to attempt the problem by hand. 5 Quantum Gravity/New Frontiers Another problem that illustrates the power and interactive nature of MACSYMA occurred a couple of years ago when a colleague working in quantum gravity at Los Alamos phoned me at home one evening. He was excited believing he had found a new solution to Einstein's equations. This would indeed be exciting, and while he was on one telephone, I used my second phone to dial up MACSYMA at the MITMC machine.
Three years ago we received a call from a researcher at an aircraft company who had heard about MACSYMA. He wished to evaluate an integral arising from a turbulence and boundary layer problem. We were told that an engineer had been assigned to the task, and had spent three weeks on the problem, always obtaining a different answer. Could MACSYMA help? The deceptively simple looking integral is given by (01). It is complicated by the exponent 4 in the integrand. Numeric methods would not suffice in this case because of the two parameters in the integrand.
Additional Applications of the Thepry of Algebraic Quaternions by Hamilton W.R.