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141 lines
3.3 KiB
C++
141 lines
3.3 KiB
C++
/* explore the Janko group J1: https://en.wikipedia.org/wiki/Janko_group_J1 */
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#include "rogueviz.h"
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#if !ISWEB
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namespace hr {
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eGeometry gJanko1(eGeometry(-1));
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struct jmatrix : array<array<int, 7>, 7> {
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jmatrix operator * (const jmatrix other) {
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jmatrix res;
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for(int a=0; a<7; a++)
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for(int b=0; b<7; b++)
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res[a][b] = 0;
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for(int a=0; a<7; a++)
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for(int b=0; b<7; b++)
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for(int c=0; c<7; c++)
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res[a][c] += self[a][b] * other[b][c];
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for(int a=0; a<7; a++)
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for(int b=0; b<7; b++)
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res[a][b] %= 11;
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return res;
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}
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};
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vector<jmatrix> jms;
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std::map<jmatrix, int> ids;
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jmatrix J, Z, id;
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int get_id(const jmatrix& m) {
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if(ids.count(m)) return ids[m];
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ids[m] = isize(jms);
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jms.push_back(m);
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return isize(jms)-1;
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}
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void build_group(const jmatrix& m) {
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if(ids.count(m)) return;
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jmatrix m2 = m;
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for(int a=0; a<7; a++) { get_id(m2); m2 = m2 * J; }
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}
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void build() {
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for(int a=0; a<7; a++)
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for(int b=0; b<7; b++) J[a][b] = ((a+1-b)%7 == 0) ? 1 : 0;
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int v[49] = {
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0, 4, 0, 3, 9, 2, 1,
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4, 0, 4, 3, 7, 1, 3,
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0, 4, 10, 6, 9, 8, 1,
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3, 3, 6, 1, 7, 6, 9,
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9, 7, 9, 7, 0, 9, 10,
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2, 1, 8, 6, 9, 2, 3,
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1, 3, 1, 9, 10, 3, 8,
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/* -3,+2,-1,-1,-3,-1,-3,
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-2,+1,+1,+3,+1,+3,+3,
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-1,-1,-3,-1,-3,-3,+2,
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-1,-3,-1,-3,-3,+2,-1,
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-3,-1,-3,-3,+2,-1,-1,
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+1,+3,+3,-2,+1,+1,+3,
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+3,+3,-2,+1,+1,+3,+1*/
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};
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int a = 0;
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for(auto& row: Z) for(auto& i: row) { i = v[a++]; if(i < 0) i += 11; }
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for(int a=0; a<7; a++) for(int b=0; b<7; b++) id[a][b] = a==b ? 1 : 0;
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build_group(id);
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for(int k=0; k<isize(jms); k++) {
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build_group(jms[k] * Z);
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}
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/*
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B = Z
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J = A * B
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A = J * B * B
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*/
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println(hlog, "order = ", isize(jms));
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}
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void experiment() {
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for(int ia=1; ia<isize(jms); ia++) if(jms[ia] * jms[ia] == id)
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for(int ib=1; ib<isize(jms); ib++) if(jms[ib] * jms[ib] * jms[ib] == id) {
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jmatrix u = jms[ia] * jms[ib];
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if(u != J) continue;
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if(u == id) continue;
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jmatrix up = u, ubp = u;
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ubp = ubp * ubp; up = up * ubp;
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ubp = ubp * ubp; up = up * ubp;
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if(up != id) continue;
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println(hlog, "found: ", tie(ia, ib));
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for(auto& row: jms[ia]) {
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for(auto& i: row) print(hlog, format("%2d, ", i));
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println(hlog);
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}
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}
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exit(1);
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}
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auto h = addHook(hooks_newmap, 0, [] {
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if(geometry == gJanko1) {
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build();
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vector<int> connections;
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connections.clear();
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for(int i=0; i<isize(jms); i++) connections.push_back(get_id(jms[i] * Z));
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println(hlog, connections);
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return (hrmap*) new quotientspace::hrmap_quotient(connections);
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}
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return (hrmap*) nullptr;
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});
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void create_janko() {
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if(gJanko1 != eGeometry(-1)) return;
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ginf.push_back(ginf[gNormal]);
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gJanko1 = eGeometry(isize(ginf) - 1);
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// variation = eVariation::pure;
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auto& gi = ginf.back();
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gi.flags = qANYQ | qCLOSED | qEXPERIMENTAL;
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gi.quotient_name = "Janko";
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gi.shortname = "Janko";
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gi.menu_displayed_name = "Janko group J1";
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}
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auto shot_hooks = arg::add3("-janko1x", [] { build(); experiment(); })
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+ addHook(hooks_initialize, 100, create_janko);
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}
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#endif
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