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The vast area of Scientific Computing, which is concerned with the
computer- aided simulation of various processes in engineering,
natural, economical, or social sciences, now enjoys rapid progress
owing to the development of new efficient symbolic, numeric, and
symbolic/numeric algorithms. There has already been for a long time
a worldwide recognition of the fact that the mathematical term
algorithm takes its origin from the Latin word algo- ritmi, which
is in turn a Latin transliteration of the Arab name "AI Khoresmi"
of the Khoresmian mathematician Moukhammad Khoresmi, who lived in
the Khoresm khanate during the years 780 - 850. The Khoresm khanate
took sig- nificant parts of the territories of present-day
TUrkmenistan and Uzbekistan. Such towns of the Khoresm khanate as
Bukhara and Marakanda (the present- day Samarkand) were the centers
of mathematical science and astronomy. The great Khoresmian
mathematician M. Khoresmi introduced the Indian decimal positional
system into everyday's life; this system is based on using the
famil- iar digits 1,2,3,4,5,6,7,8,9,0. M. Khoresmi had presented
the arithmetic in the decimal positional calculus (prior to him,
the Indian positional system was the subject only for jokes and
witty disputes). Khoresmi's Book of Addition and Subtraction by
Indian Method (Arithmetic) differs little from present-day arith-
metic. This book was translated into Latin in 1150; the last
reprint was produced in Rome in 1957.
CASC 2001 continues a tradition ~ started in 1998 ~ of
international con ferences on the latest advances in the
application of computer algebra systems to the solution of various
problems in scientific computing. The three ear (CASs) lier
conferences in this sequence, CASC'98, CASC'99, and CASC 2000, were
held, Petersburg, Russia, in Munich, Germany, and in Samarkand,
respectively, in St. Uzbekistan, and proved to be very successful.
We have to thank the program committee, listed overleaf, for a
tremendous job in soliciting and providing reviews for the
submitted papers. There were more than three reviews per submission
on average. The result of this job is reflected in the present
volume, which contains revised versions of the accepted papers. The
collection of papers included in the proceedings covers various
topics of computer algebra methods, algorithms and software applied
to scientific computing. In particular, five papers are devoted to
the implementation of the analysis of involutive systems with the
aid of CASso The specific examples include new efficient algorithms
for the computation of Janet bases for monomial ideals, involutive
division, involutive reduction method, etc. A number of papers deal
with application of CASs for obtaining and vali dating new exact
solutions to initial and boundary value problems for partial
differential equations in mathematical physics. Several papers show
how CASs can be used to obtain analytic solutions of initial and
boundary value problems for ordinary differential equations and for
studying their properties.
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