The GAP (4.14.0) code in this repository contains several computations that verify claims in the paper "Root graded groups of type $H_3$ and $H_4$" (https://doi.org/10.1016/j.jalgebra.2025.06.007) by Lennart Berg and Torben Wiedemann. We refer to this paper by [BW] in the code.

1. The folder Blueprint computations contains the code for the blueprint computations (see [BW, Sections 8 and 9]) and the results of these computations (in tex, pdf and txt format).
2. The folder Auxiliary computations contains all remaining computations for various claims in [BW]. In particular, it contains: (a) The realisation of the root systems $H_3$ and $H_4$ as foldings of $D_6$ and $E_8$, respectively. (b) The construction of an $H_3$-graded group from a Chevalley group of type $D_6$, of an $H_4$-graded group from a Chevalley group of type $E_8$, and computations in these groups.

Consult the readme files in the corresponding folders for more details.