Current computer algebra systems usually work in a shell mode: the user asks a question and the system hopefully gives an answer. To what extent would it be possible to discover additionnal mathematical structure in the user's problem in an automatic fashion? For instance, if we encounter in the output of a numerical computation, the system might suggest its replacement by . Even though guessing such addional relations was not explicitly requested by the user, it may lead to interesting insights and does not necessarily lead to a big increase of the overall computation time.

In our talk, we will address several classical guessing algorithms and present a few new ones. We will start with rational number and function recovery, the LLL-algorithm and Pade–Hermite approximation. We will next turn our attention to guessing possible asymptotic expansions for sequences and possible relations at singularities of analytic functions. If time permits it, we will also discuss some guessing techniques for symbolic expressions.

Occasions: Gecko-Tera meeting, École polytechnique, Palaiseau, November 24, 2008; Fields institute, Toronto, October 21, 2009

Documents: slideshow, TeXmacs source