## A Computer Algebra Integration Web Server

(Professor Richard J. Fateman)

(NSF) CCR-9901933

This work is part of the continuing activity at Berkeley in
computer systems for symbolic mathematics (computer algebra).
This research involves the establishment and extension of TILU, our
online table-look-up symbolic integration service. This table-look-up
service currently includes only about 700 forms, although we have
data to extend it to the majority of about 13,000 forms in current
tables, including many definite integrals involving
special functions.

Why bother with table look-up, when there are alleged to be algorithms
for symbolic integration? There are several reasons. The best of the
algorithms are for indefinite integration only; even so, they somewhat
ignore special functions, and often provide a useless result: that no
answer exists in closed form *in terms of elementary
functions.* The algebraic algorithms generally ignore
the domain of validity of the answer. The results of some of the more
powerful techniques are, in many cases, woefully unsimplified. Our
table look-up can do the task in about 6.5 milliseconds CPU time
on an HP-9000/715 at *http://torte.cs.berkeley.edu:8010/tilu.*
If we can't find
it, you will know soon. By comparison, typical algorithms can be
orders of magnitude slower.

TILU serves an average of 125 requests a day, and is now tied to a button
on the new release of the "Graphing Calculator" shipped
with every Apple Macintosh computer.

In addition to studying extensions of this system to more
integrals, we are also considering applications to other domains such
as symbolic solution of ordinary differential equations.

More information (http://http.cs.berkeley.edu/~fateman) or

Send mail to the author : (fateman@cs.berkeley.edu)

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