This page contains the program GalCohom for explicitly computing the first Galois cohomology set H1(R,G) of a real linear algebraic subgroup G of GL(n,C). The group is given by a list of real matrices that form a basis of the Lie algebra of G, thus defining the identity component of G, and a list of complex matrices whose elements are representatives of the elements of the component group. The main function computes an object containing a list of cocycles, whose classes exhaust H1(R,G). We also have a function for deciding equivalence of cocycles.

The program is written in the language of the computational algebra system GAP4 . For some computations in number fields we have written an interface to the system SageMath .

The program comes as a gzipped tar file. It contains a small manual (manual.pdf), which we also give here. The manual contains installation instructions (under linux).

The algorithms are described in