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Research

Our research is in computer algebra, with a particular emphasis on problems related to simplification of expressions involving elementary functions (= rational functions, algebraic functions, trigonometric and inverse trigonometric functions, logs, and exponentials) and certain special functions, on algorithms for integration in finite terms, and for solving differential equations in closed form.

Simplification and Structure of Mathematical Expressions

Simplification is a fundamental problem in symbolic mathematical computation as it is a mechanism that enables one to determine equality among expressions and to compute with them effectively. It is also fundamental in obtaining algorithmic methods for other problems such as integration in finite terms. Our interest in simplification has ranged from exploring the boundary between decidable and undecidable problems to effective simplification algorithms for elementary and special transcendental functions. We have also considered the much harder problem of simplifying elementary constants assuming that Schanuel's conjecture holds.

Integration in Finite Terms and Closed Form Solutions of Differential Equations

Our work on integration in finite terms has ranged from new methods for determining the minimal algebraic field extensions needed for expressing the logarithmic part of an elementary integral to extensions of parts of the Risch algorithm for integration in terms of certain special functions. For differential equations, we have been interested in a series of problems related to finding closed form first integrals for first order nonlinear equations.

Selected Publications


Books and Monographs


Other Publications


Editorial Boards



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Next: Teaching Up: B. F. (Bob) Previous: Addresses



B.F. (Bob) Caviness
Last updated 3/17/05