added the Janko group

rogueviz/janko.cpp

@@ -0,0 +1,144 @@
+/* explore the Janko group J1: https://en.wikipedia.org/wiki/Janko_group_J1 */
+
+#include "../hyper.h"
+
+namespace hr {
+
+eGeometry gJanko1(eGeometry(-1));
+
+struct jmatrix : array<array<int, 7>, 7> {
+  jmatrix operator * (const jmatrix other) {
+    jmatrix res;
+    for(int a=0; a<7; a++)
+    for(int b=0; b<7; b++)
+      res[a][b] = 0;
+
+    for(int a=0; a<7; a++)
+    for(int b=0; b<7; b++)
+    for(int c=0; c<7; c++)
+      res[a][c] += self[a][b] * other[b][c];
+
+    for(int a=0; a<7; a++)
+    for(int b=0; b<7; b++)
+      res[a][b] %= 11;
+
+    return res;
+    }
+  };
+
+vector<jmatrix> jms;
+unordered_map<jmatrix, int> ids;
+
+jmatrix J, Z, id;
+
+int get_id(const jmatrix& m) {
+  if(ids.count(m)) return ids[m];
+  ids[m] = isize(jms);
+  jms.push_back(m);
+  return isize(jms)-1;
+  }
+
+void build_group(const jmatrix& m) {
+  if(ids.count(m)) return;
+  jmatrix m2 = m;
+  for(int a=0; a<7; a++) { get_id(m2); m2 = m2 * J; }
+  }
+
+void build() {
+  for(int a=0; a<7; a++)
+  for(int b=0; b<7; b++) J[a][b] = ((a+1-b)%7 == 0) ? 1 : 0;
+  
+  int v[49] = {
+    0,  4,  0,  3,  9,  2,  1, 
+    4,  0,  4,  3,  7,  1,  3, 
+    0,  4, 10,  6,  9,  8,  1, 
+    3,  3,  6,  1,  7,  6,  9, 
+    9,  7,  9,  7,  0,  9, 10, 
+    2,  1,  8,  6,  9,  2,  3, 
+    1,  3,  1,  9, 10,  3,  8, 
+/*    -3,+2,-1,-1,-3,-1,-3,
+    -2,+1,+1,+3,+1,+3,+3,
+    -1,-1,-3,-1,-3,-3,+2,
+    -1,-3,-1,-3,-3,+2,-1,
+    -3,-1,-3,-3,+2,-1,-1,
+    +1,+3,+3,-2,+1,+1,+3,
+    +3,+3,-2,+1,+1,+3,+1*/
+    };
+  
+  int a = 0;
+
+  for(auto& row: Z) for(auto& i: row) { i = v[a++]; if(i < 0) i += 11; }
+  
+  for(int a=0; a<7; a++) for(int b=0; b<7; b++) id[a][b] = a==b ? 1 : 0;
+  
+  build_group(id);
+  for(int k=0; k<isize(jms); k++) {
+    build_group(jms[k] * Z);
+    }
+  
+  /*
+  B = Z
+  J = A * B
+  A = J * B * B
+  */
+
+  println(hlog, "order = ", isize(jms));
+  }
+
+void experiment() {
+  for(int ia=1; ia<isize(jms); ia++) if(jms[ia] * jms[ia] == id)
+  for(int ib=1; ib<isize(jms); ib++) if(jms[ib] * jms[ib] * jms[ib] == id) {
+    jmatrix u = jms[ia] * jms[ib];
+    if(u != J) continue;
+    if(u == id) continue;
+    jmatrix up = u, ubp = u;
+    ubp = ubp * ubp; up = up * ubp;
+    ubp = ubp * ubp; up = up * ubp;
+    if(up != id) continue;
+    println(hlog, "found: ", tie(ia, ib));
+
+    for(auto& row: jms[ia]) {
+      for(auto& i: row) print(hlog, format("%2d, ", i));
+      println(hlog);
+      }
+    }
+
+  exit(1);
+  }
+
+auto h = addHook(hooks_newmap, 0, [] {
+  if(geometry == gJanko1) {
+    build();
+    vector<int> connections;
+    connections.clear();
+    for(int i=0; i<isize(jms); i++) connections.push_back(get_id(jms[i] * Z));
+    println(hlog, connections);
+    return (hrmap*) new quotientspace::hrmap_quotient(connections);
+    }
+  return (hrmap*) nullptr;
+  });
+
+void create_janko() {
+  if(gJanko1 != eGeometry(-1)) return;
+  ginf.push_back(ginf[gNormal]);
+  gJanko1 = eGeometry(isize(ginf) - 1);
+  variation = eVariation::pure;
+  auto& gi = ginf.back();
+  gi.flags = qANYQ | qBOUNDED | qEXPERIMENTAL;
+  gi.quotient_name = "Janko";
+  gi.shortname = "Janko";
+  gi.xcode = 0x31400;
+  gi.menu_displayed_name = "Janko group J1";
+  }
+  
+auto shot_hooks = addHook(hooks_args, 100, [] {
+  if(arg::argis("-janko1x")) {
+    build();
+    experiment();
+    }
+  else return true;
+  return false;
+  }) + addHook(hooks_initialize, 100, create_janko);
+
+}
+

rogueviz/rogueviz-all.cpp

@@ -13,6 +13,7 @@
 #include "cvl.cpp"
 #include "newconf.cpp"
 #include "grigorchuk.cpp"
+#include "janko.cpp"
 #include "qtm.cpp"
 #include "rewriting.cpp"
 #include "sag.cpp"