Efficient Algorithms for Guessing, inequaLitiEs, Summation – EAGLES

Long ago, computer algebra was used to reproduce results that humans proved before. Nowadays, we often use computer algebra to prove new results which later somebody reproves by hand. The goal of this project is to push the efficiency of computer algebra to a level where it can prove results that are far outside the scope of paper and pencil reasoning. We focus on algorithms for automated multivariate guessing, symbolic summation/integration, and positivity proofs for large classes of functions. We will obtain significant theoretical and practical efficiency improvements, produce high-performance implementations, and apply them to highly non-trivial problems in combinatorics, number theory, or mathematical physics. Our goals are ambitious because they require combining advanced mathematical and algorithmic developments with high-performance computing. They are feasible because our consortium consists of world leading experts in computer algebra, algebraic geometry and combinatorics.