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Topics in the Representation and Manipulation
of Mathematical Knowledge

Nicholas Mitchell, Dr. J. Daniel Halpern*, 
Ben Berman, and Chien-Long Lin

(Professor R. J. Fateman)

(NSF) CCR-92-14963

We are investigating computer technology in support of the
representation and manipulation of mathematical notation by computer. Our long-term goal is to produce a consistent and constructive
representation of a substantial, useful class of engineering and
applied mathematics, driven by the needs of significant applications. Key issues we hope to examine include the use of multiple
representations, and the encoding of geometric, algebraic, logical,
algorithmic, and physical relations in symbolic mathematical
computation.

We are working toward enhancing tools for symbolic manipulation
interactive systems to increase the productivity of users of 
.I
pencil and paper
.R
mathematics\(emincluding physical scientists, programmers,
and researchers.

Some specific recent topics include:

Development of 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.

Provision, through interval-arithmetic, of "honest" plots of mathematical
functions guaranteed to be free of the defects present in usual
plotting programs that are defeated by singularities, periodicities
that match the sampling frequency of the plotting program, and
so forth.

Representation and use of large-scale tables of
indefinite and definite integration formulas to supplement algorithms.

Experimentation in optical character recognition and
two-dimensional equation parsing for the automatic input of
reference material.

Improved pattern matching and search in discrimination trees
for algebraic patterns.

Improved numerical code generation from a traditional
symbolic computing language (Lisp) to provide for more natural
treatment of symbolic-numeric algorithms.

*Post-Doctoral Researcher