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1 | # run this file with |
2 | # gap -b -q < /dev/null group.gap | perl -pe 's/\\\n//s' | indent -kr |
3 | |
4 | Print("/* ----- data generated by group.gap begins ----- */\n\n"); |
5 | Print("struct group {\n unsigned long autosize;\n"); |
6 | Print(" int order, ngens;\n const char *gens;\n};\n"); |
7 | Print("struct groups {\n int ngroups;\n"); |
8 | Print(" const struct group *groups;\n};\n\n"); |
9 | Print("static const struct group groupdata[] = {\n"); |
10 | offsets := [0]; |
11 | offset := 0; |
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12 | for n in [2..26] do |
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13 | Print(" /* order ", n, " */\n"); |
14 | for G in AllSmallGroups(n) do |
15 | |
16 | # Construct a representation of the group G as a subgroup |
17 | # of a permutation group, and find its generators in that |
18 | # group. |
19 | |
20 | # GAP has the 'IsomorphismPermGroup' function, but I don't want |
21 | # to use it because it doesn't guarantee that the permutation |
22 | # representation of the group forms a Cayley table. For example, |
23 | # C_4 could be represented as a subgroup of S_4 in many ways, |
24 | # and not all of them work: the group generated by (12) and (34) |
25 | # is clearly isomorphic to C_4 but its four elements do not form |
26 | # a Cayley table. The group generated by (12)(34) and (13)(24) |
27 | # is OK, though. |
28 | # |
29 | # Hence I construct the permutation representation _as_ the |
30 | # Cayley table, and then pick generators of that. This |
31 | # guarantees that when we rebuild the full group by BFS in |
32 | # group.c, we will end up with the right thing. |
33 | |
34 | ge := Elements(G); |
35 | gi := []; |
36 | for g in ge do |
37 | gr := []; |
38 | for h in ge do |
39 | k := g*h; |
40 | for i in [1..n] do |
41 | if k = ge[i] then |
42 | Add(gr, i); |
43 | fi; |
44 | od; |
45 | od; |
46 | Add(gi, PermList(gr)); |
47 | od; |
48 | |
49 | # GAP has the 'GeneratorsOfGroup' function, but we don't want to |
50 | # use it because it's bad at picking generators - it thinks the |
51 | # generators of C_4 are [ (1,2)(3,4), (1,3,2,4) ] and that those |
52 | # of C_6 are [ (1,2,3)(4,5,6), (1,4)(2,5)(3,6) ] ! |
53 | |
54 | gl := ShallowCopy(Elements(gi)); |
55 | Sort(gl, function(v,w) return Order(v) > Order(w); end); |
56 | |
57 | gens := []; |
58 | for x in gl do |
59 | if gens = [] or not (x in gp) then |
60 | Add(gens, x); |
61 | gp := GroupWithGenerators(gens); |
62 | fi; |
63 | od; |
64 | |
65 | # Construct the C representation of the group generators. |
66 | s := []; |
67 | for x in gens do |
68 | if Size(s) > 0 then |
69 | Add(s, '"'); |
70 | Add(s, ' '); |
71 | Add(s, '"'); |
72 | fi; |
73 | sep := "\\0"; |
74 | for i in ListPerm(x) do |
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75 | chars := "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; |
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76 | Add(s, chars[i]); |
77 | od; |
78 | od; |
79 | s := JoinStringsWithSeparator([" {", String(Size(AutomorphismGroup(G))), |
80 | "L, ", String(Size(G)), |
81 | ", ", String(Size(gens)), |
82 | ", \"", s, "\"},\n"],""); |
83 | Print(s); |
84 | offset := offset + 1; |
85 | od; |
86 | Add(offsets, offset); |
87 | od; |
88 | Print("};\n\nstatic const struct groups groups[] = {\n"); |
89 | Print(" {0, NULL}, /* trivial case: 0 */\n"); |
90 | Print(" {0, NULL}, /* trivial case: 1 */\n"); |
91 | n := 2; |
92 | for i in [1..Size(offsets)-1] do |
93 | Print(" {", offsets[i+1] - offsets[i], ", groupdata+", |
94 | offsets[i], "}, /* ", i+1, " */\n"); |
95 | od; |
96 | Print("};\n\n/* ----- data generated by group.gap ends ----- */\n"); |
97 | quit; |