Effective computations of the Atiyah-Bott formula

We present an implementation of the Atiyah-Bott residue formula for ${\bar{M}}_{0,m}({\mathbb{P}}^n,d)$. We use this implementation to compute a large number of Gromov-Witten invariants of genus $0$, including intersection numbers of rational curves on general complete intersections. We also compute some numbers of rational contact curves satisfying suitable Schubert conditions. Our computations confirm known predictions made by Mirror Symmetry. The code we developed for these problems is publicly available and can also be used for other types of computations.