The long-term objectives of this research program are to contribute to the development of algorithms for the mechanization of mathematics and to implement the algorithms in a computer algebra system. To focus such a broadly-stated goal, the types of mathematics being considered are the computational aspects of algebra and analysis, including the solution of problems in integral and differential calculus, and closed-form summation.
The short-term objectives are to design and implement algorithms which enhance our mathematical problem-solving capabilities by exploiting an appropriate combination of the symbolic and numeric paradigms in scientific computation. To this end, the short-term focus is on the design of symbolic and hybrid symbolic-numeric algorithms for multidimensional integration, integral equations, automated generation of numerical evaluation subroutines, and summation problems.
The overall objective of this research program is to develop algorithms which can be incorporated into the Maple computer algebra system. Maple and its algorithms have proven to be a useful tool for engineers, scientists, mathematicians, and researchers in various disciplines, and it has achieved a worldwide impact.
The system allows users to perform sophisticated mathematical operations in their natural symbolic form, as well as providing numerical facilities, graphical displays, and mathematical document-preparation capabilities. Symbolic closed-form solutions to problems generally yield much greater insight than purely numerical solutions, and the Maple system expands the applications of computers to include this non-numeric mode of mathematical analysis.
Sales and Marketing for the Maple software product, as well as ongoing Research and Development, is the responsibility of Maplesoft, a company based in Waterloo, Ontario, Canada.
