Chapter 7

Too Large to Be Easy,
Too Small to Be Hard

Folkmar Bornemann

Problem 7

7.1 A First Look · 7.2 Solving It Directly · 7.3 Solving It Iteratively · 7.4 How Many Digits Are Correct? · 7.5 Solving It Exactly

Exact rational solution is known: 97,389-digits numerator, 97,389-digits denominator (courtesy of Jean-Guillaume Dumas).

The first 10,002 digits.

Code

• Mathematica (supporting code is included as initialization cells)
   
  • Sessions: pp. 149, 153/154 (as alternative to MATLAB), 158, 161
  • Proof of Lemma 7.1 (interval calculations)
  • Congruential approach (bare-bones implementation)
  • p-adic approach (bare-bones implementation)
     
• MATLAB
   
  • Sessions: pp. 148, 150, 151, 156, 157
  • Snippets: pp. 153/154, 160
  • Tables: 7.1, 7.2, 7.3, 7.4
  • Figures: 7.1, 7.2, 7.3, 7.4 (left), 7.4 (right)
     
• MATLAB/INTLAB (download INTLAB)
   
  • Session: p. 161
  • Table: 7.5
  • Proof of Lemma 7.1 (interval calculations)

Links

• Project LinBox

Updates

• Zhendong Wan has a breakthrough in speed for the rational solution
   
  • Wan's e-mail announcement of June 25, 2004
  • Wan's paper of January 28, 2005 (Submitted to Journal of Symbolic Computation)
  • Mathematica code that allows to calculate the exact solution to Problem 7 in about 6 hours

This is a web page for the book:

Folkmar Bornemann, Dirk Laurie, Stan Wagon, Jörg Waldvogel: The SIAM 100-Digit Challenge, A Study in High-Accuracy Numerical Computing. Society of Industrial and Applied Mathematics (SIAM), Philadelphia, 2004.

last modified: 01/31/05 16:50 +0100 (FB)