ref: f967bfa87b6ea08434501558e0c41184fdce333d
dir: /unfinished/group.gap/
# run this file with # gap -b -q < /dev/null group.gap | perl -pe 's/\\\n//s' | indent -kr Print("/* ----- data generated by group.gap begins ----- */\n\n"); Print("struct group {\n unsigned long autosize;\n"); Print(" int order, ngens;\n const char *gens;\n};\n"); Print("struct groups {\n int ngroups;\n"); Print(" const struct group *groups;\n};\n\n"); Print("static const struct group groupdata[] = {\n"); offsets := [0]; offset := 0; for n in [2..26] do Print(" /* order ", n, " */\n"); for G in AllSmallGroups(n) do # Construct a representation of the group G as a subgroup # of a permutation group, and find its generators in that # group. # GAP has the 'IsomorphismPermGroup' function, but I don't want # to use it because it doesn't guarantee that the permutation # representation of the group forms a Cayley table. For example, # C_4 could be represented as a subgroup of S_4 in many ways, # and not all of them work: the group generated by (12) and (34) # is clearly isomorphic to C_4 but its four elements do not form # a Cayley table. The group generated by (12)(34) and (13)(24) # is OK, though. # # Hence I construct the permutation representation _as_ the # Cayley table, and then pick generators of that. This # guarantees that when we rebuild the full group by BFS in # group.c, we will end up with the right thing. ge := Elements(G); gi := []; for g in ge do gr := []; for h in ge do k := g*h; for i in [1..n] do if k = ge[i] then Add(gr, i); fi; od; od; Add(gi, PermList(gr)); od; # GAP has the 'GeneratorsOfGroup' function, but we don't want to # use it because it's bad at picking generators - it thinks the # generators of C_4 are [ (1,2)(3,4), (1,3,2,4) ] and that those # of C_6 are [ (1,2,3)(4,5,6), (1,4)(2,5)(3,6) ] ! gl := ShallowCopy(Elements(gi)); Sort(gl, function(v,w) return Order(v) > Order(w); end); gens := []; for x in gl do if gens = [] or not (x in gp) then Add(gens, x); gp := GroupWithGenerators(gens); fi; od; # Construct the C representation of the group generators. s := []; for x in gens do if Size(s) > 0 then Add(s, '"'); Add(s, ' '); Add(s, '"'); fi; sep := "\\0"; for i in ListPerm(x) do chars := "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; Add(s, chars[i]); od; od; s := JoinStringsWithSeparator([" {", String(Size(AutomorphismGroup(G))), "L, ", String(Size(G)), ", ", String(Size(gens)), ", \"", s, "\"},\n"],""); Print(s); offset := offset + 1; od; Add(offsets, offset); od; Print("};\n\nstatic const struct groups groups[] = {\n"); Print(" {0, NULL}, /* trivial case: 0 */\n"); Print(" {0, NULL}, /* trivial case: 1 */\n"); n := 2; for i in [1..Size(offsets)-1] do Print(" {", offsets[i+1] - offsets[i], ", groupdata+", offsets[i], "}, /* ", i+1, " */\n"); od; Print("};\n\n/* ----- data generated by group.gap ends ----- */\n"); quit;