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FilterByRoots := function(grps, roots)
local res, i, k, j;
res := [];
for i in [1..Length(grps)] do
if Size(grps[i]) in List(roots, x -> x[1]) then
k := IdGroup(grps[i]);
if not (k in roots) then Add(res, i); fi;
fi;
od;
return grps{res};
end;
GroupsByRankWidthObliquity := function(p, d, rwo, roots, limit)
local c, grps, des, i, G;
G := ElementaryAbelianGroup(p^d);
G!.width := d;
G!.obliq := 0;
G!.rank := d;
grps := [G];
c := 0;
while c < Length(grps) do
c := c+1;
# descendants
if not IsCapable(grps[c]) then
des := [];
else
des := PqDescendants(grps[c]);
fi;
# check limit
des := Filtered(des, x -> Size(x) <= limit);
# check roots
des := FilterByRoots(des, roots);
# check width
for i in [1..Length(des)] do des[i]!.width := WidthPGroup(des[i]); od;
des := Filtered(des, x -> x!.width <= rwo[1]);
# check obliquity
for i in [1..Length(des)] do des[i]!.obliq := Obliquity(des[i]); od;
des := Filtered(des, x -> x!.obliq <= rwo[3]);
# check rank
for i in [1..Length(des)] do des[i]!.rank := SubgroupRank(des[i]); od;
des := Filtered(des, x -> x!.rank <= rwo[2]);
# info
Print("group ",c," of ",Length(grps)," has ",Length(des), " desc \n");
# add
Append(grps, des);
od;
grps := Filtered(grps, x -> x!.width = rwo[1]);
grps := Filtered(grps, x -> x!.obliq = rwo[3]);
grps := Filtered(grps, x -> x!.rank = rwo[2]);
return grps;
end;
[ Dauer der Verarbeitung: 0.29 Sekunden
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