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Emerging tools for experimental mathematics. (English) Zbl 0980.68146

Summary: Using mostly elementary examples, we discuss the use of some recent and emerging tools for experimental mathematics. The tools discussed include so-called “inverse symbolic computation”, using lattice reduction algorithms such as “LLL” and “PSLQ”, and Sloane and Plouffe’s integer sequence lookup program. We concentrate on computer-assisted discovery of mathematical results, but a little computer-assisted proof creeps in as well. We use MAPLE throughout the paper, but any other good computer algebra system would be as effective.

This paper is not a tutorial on how lattice basis reduction algorithms such as LLL or PSLQ actually work; rather, we discuss some of the ways these tools can be used to generate conjectures, and for that, a detailed understanding of the underlying algorithms is not necessary. We do hope, however, to convey some appreciation of their power.

MSC:
68W30Symbolic computation and algebraic computation
00A05General mathematics
11Y99Computational number theory
Software:
Maple