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## Integration with SmallGrps
# Get the next available "layer" id (the built-in library
# consists of 11 layers, but other packages may already have
# added further layers).
BindGlobal("SOTGRPS_LAYER", Length(SMALL_AVAILABLE_FUNCS) + 1);
# Determine where to add our new lookup functions
BindGlobal("SOTGRPS_POS", Maximum(List([
SMALL_GROUP_FUNCS,
SMALL_GROUPS_INFORMATION,
NUMBER_SMALL_GROUPS_FUNCS,
ID_GROUP_FUNCS,
SELECT_SMALL_GROUPS_FUNCS,
], Length)) + 1);
#
# hook us up on the layer level
#
# meta data on small groups data we provide
SMALL_AVAILABLE_FUNCS[SOTGRPS_LAYER] := function( size )
if IsSOTAvailable(size) then
return rec (
lib := SOTGRPS_LAYER,
func := SOTGRPS_POS,
number := NumberOfSOTGroups(size) # number of groups of this order
);
fi;
return fail;
end;
# meta data on IdGroup functionality we provide
ID_AVAILABLE_FUNCS[SOTGRPS_LAYER] := SMALL_AVAILABLE_FUNCS[SOTGRPS_LAYER];
# Method for SmallGroup(size, i):
SMALL_GROUP_FUNCS[ SOTGRPS_POS ] := function( size, i, inforec )
local g;
# Now create the actual group
g := SOTGroup(size, i);
return g;
end;
# Method which selects a subset of all those groups with
# a certain combination of properties.
# A default method can be used; but more user friendly would be
# to install something custom which e.g. takes care of filtering
# the abelian /nilpotent / solvable groups.
SELECT_SMALL_GROUPS_FUNCS[ SOTGRPS_POS ] := SELECT_SMALL_GROUPS_FUNCS[ 11 ];
#SELECT_SMALL_GROUPS_FUNCS[ pos ] := function( funcs, vals, inforec, all, id )
# Error("TODO");
#end;
# Method for IdGroup(size, i).
ID_GROUP_FUNCS[ SOTGRPS_POS ] := function( G, inforec )
return IdSOTGroup(G)[2];
end;
# Method for SmallGroupsInformation(size):
SMALL_GROUPS_INFORMATION[ SOTGRPS_POS ] := function( size, inforec, num )
local fac, ind;
fac := Collected(Factors(size));
SortBy(fac, Reversed);
ind := List(fac, x -> x[2]);
_SOTGroupsInformation(size, fac, ind);
Print("\n");
end;
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