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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.

68W30Symbolic computation and algebraic computation
00A05General mathematics
11Y99Computational number theory
OEIS; Maple
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