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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.

Problem 1

What is the 4-significant-digit approximation to the condition number of the 256 by 256 Hilbert matrix?

Result

Problem 2

What is the value of to 7 significant digits?

Result

Problem 3

What is to 14 significant digits?

Result
21.19324037771154...

Problem 4

What is the coefficient of in the expansion of the polynomial to 13 significant digits?

Result

Problem 5

What is the largest zero of the 1000 Laguerre polynomial to 12 significant digits?

Result
3943.24739485...

Problem 6

Find a lexicographic Gröbner basis for the following polynomial system.

Result

Problem 7

What is to 9 significant digits?

Result

Problem 8

What is ?

Result

Problem 9

Find the largest eigenvalue lambda to 13 significant digits for the following integral equation.

Result
lambda = 37.5291455603353...

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...