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InstallGlobalFunction( GroupSumBSGS, function(G, summand)
local H, n, chain, groups, m, sum, i, cosets, iso, zero, g, S, right_reps;
# stab chain computation only works on permutation groups
iso := IsomorphismPermGroup(G);
H := Image(iso, G);
chain := StabChain(H);
groups := ListStabChain(chain);
# groups[i] is the stabiliser of the first i-1 points, so
# groups[1] is H and so on. We start with the last groups[]
# element, which we have to sum naively, then move to the larger
# group and so on
m := Length(groups)-1;
groups := List([1..m], i -> GroupStabChain(groups[i]));
# summand(g) might be huge to store in memory, recall the whole
# point of this is to save memory, so only store one image at most
zero := Zero(summand(One(G)));
# We must sum G_m naively, this should be cheap (it's the
# stabiliser of a "large" set so should be "small")
sum := Sum(groups[m], g -> summand(PreImage(iso, g)));
for i in [m-1,m-2..1] do
# `sum` is the sum for G_{i+1}
right_reps := RightTransversal(groups[i], groups[i+1]);
sum := Sum(right_reps, r -> sum * summand(PreImage(iso, r)));
# now `sum` is the sum for G_i
od;
return sum;
end );
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