Section: Application Domains

Experimental mathematics with special functions

Applications in combinatorics and mathematical physics frequently involve equations of so high orders and so large sizes, that computing or even storing all their coefficients is impossible on existing computers. Making this tractable is another challenge of our project. The approach we believe in is to design algorithms of good, ideally quasi-optimal, complexity in order to extract precisely the required data from the equations, while avoiding the computationally intractable task of completely expanding them into an explicit representation.

Typical applications with expected high impact are the automatic discovery and proof of results in combinatorics and mathematical physics for which human proofs are currently unattainable.