Dima Pasechnik’s visit to Birmingham to collaborate with Sergey Shpectorov took place from 22/07/2015 to 24/07/2015. This is a quote from their report on this visit: “The focus of this collaboration is on the improvements to Sergey’s GAP package for computation of axial algebras. These are commutative non-associative algebras generated by idempotents satisfying certain fusion rules. The motivating example is the Griess-Norton algebra for the Monster sporadic simple group. The available programs for computations with axial algebras rely on the linear algebra functions available in GAP. This means that the program cannot handle partial algebras (intermediate stages) over the rationals whose dimension exceeds two-three thousand. At the same time, the algebras that we construct have significant groups of symmetries and, in particular, every partial algebra is a G-module for a certain group G. It is hoped that an efficient implementation of the basic module operations using the known character table of G will allow to increase the limit on the dimension by several orders. It is also hoped that, due to the fundamental nature of the module operations, the new routines will also find applications in many other places.”