Mathematica Solutions to the ISSAC '97 Systems
Challenge
Wolfram Research, Inc.
A Systems Challenge among various computer algebra systems was
held recently
at ISSAC (International Symposium on Symbolic and Algebraic
Computations) '97. The ISSAC '97 conference, held in Maui, Hawaii, on
July 23, was sponsored by ACM SIGSAM and ACM SIGNUM and in federation
with
PASCO '97.
Below are statements of the original problems together with the
Mathematica solutions.
You
can also download the solutions in a Mathematica notebook. To do
this you need Mathematica. It is
also possible to
download MathReader
to view the
notebook. If
you would like to receive a printed version of
the solutions, please send email to ISSACSolutions@wolfram.com
and
include your fax number or postal address.
Problem 1
What is the 4significantdigit approximation to the condition number
of the 256 by 256 Hilbert matrix?
Result
See Mathematica solutions.
Problem 2
What is the value of to 7 significant digits?
Result
See Mathematica solutions.
Problem 3
What is to 14 significant digits?
Result
21.19324037771154...
See Mathematica solutions.
Problem 4
What is the coefficient of in the expansion of the
polynomial to 13 significant digits?
Result
See Mathematica solutions.
Problem 5
What is the largest zero of the 1000 Laguerre polynomial to 12
significant digits?
Result
3943.24739485...
See Mathematica solutions.
Problem 6
Find a lexicographic Gröbner basis for the following polynomial
system.
Result
See Mathematica solutions.
Problem 7
What is to 9 significant digits?
Result
See Mathematica solutions.
Problem 8
What is ?
Result
See Mathematica solutions.
Problem 9
Find the largest eigenvalue lambda to 13 significant digits for the
following integral equation.
Result
lambda = 37.5291455603353...
See Mathematica solutions.
Problem 10
Consider the following initial value problem.
,
Find the smallest positive number r such that the solution
has a derivative singularity at x = r. Calculate r
to 13 significant digits. Is y(r) infinite or finite? If
y(r)
is finite, then compute it to 13 significant digits.
Result
r = 1.6443766903388...
y(r) = 0.93193876511028...
See Mathematica solutions.
Timings and Memory
References
