This project investigates computer technology in of the representation and manipulation of mathematical notation by the computer. The long-term goal is to produce a consistent and constructive representation of a substantial, useful class of engineering and applied mathematics, driven the needs of significant applications. Key issues to examine include the use of multiple representations, and the encoding of geometric, algebraic, logical, algorithmic, and physical relations in symbolic mathematical computation. The specific topics to study include: (1) developing new algorithms and representations for manipulation of functions of a complex variable correctly and with some generality (In particular both correct manipulations and proofs in analysis must account for branch cuts.), (2) providing a computing framework for dealing with mathematical derivations, theorem proving, and manipulation, (3) providing a practical approach to a bounded-time version of the zero-equivalence problem for algebraic expressions, and (4) exploring of parallel algorithms for basic polynomial algorithms and pattern-directed transformations.
