I am working on a GAP package with functions to study the topology, dynamics and spectrum of spaces of aperiodic tilings, mostly tilings generated by primitive substitutions or inflations. This is work in progress. Much of the software is already written, but it still needs to be documented and integrated with a user-friendly interface.
At this point, I am providing here some stand-alone functions for reference, which have been essential for obtaining the results of some publications.
The first two functions were used in the paper Determining pure discrete spectrum for some self-affine tilings, by S. Akiyama, F. Gähler, and J.-Y. Lee, Discr. Math. Th. Comp. Sci. (DMTCS) 16:3, 305-316 (2014). The first one determines whether a primitive Pisot substitution tiling in one dimenstion admits an overlap coincidence, which is equivalent to the substitution having pure discrete dynamical spectrum. The second function determines whether the substitution admits a balanced pair coincidence, which also implies that the substitution has pure discrete spectrum. The two algorithms are explained in V.F. Sirvent and B. Solomyak, Canad. Math. Bull. Vol. 45 (2002), pp.697-710. The two functions, along with some explanations, are contained in file olap.g.
A third function plays an essential role in the paper Cohomology groups for spaces of 12-fold tilings, by N. Bédaride, F. Gähler, and A.G. Lecuona. It computes the cohomology of 12-fold projection method tilings, as discussed in that paper. This function, along with some explanations, is contained in file coh12.g.