This page contains the program **GalCohom** for explicitly computing the
first Galois cohomology set H^{1}(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 H^{1}(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

- Mikhail Borovoi, Willem A. de Graaf Computing Galois cohomology of a real linear algebraic group ,
arXiv:2308.04962 [math.RT].