generators included

generators/bring.cpp

@@ -0,0 +1,122 @@
+// Bring's Surface generator
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include <stdio.h>
+#include <vector>
+#include <array>
+#include <map>
+#include <algorithm>
+
+using namespace std;
+
+int isize(const auto x) { return x.size(); }
+
+int mul(int a, int b) { 
+  int p = 0;
+  for(int i=0; i<3; i++) if((a>>i)&1)
+  for(int j=0; j<3; j++) if((b>>j)&1)
+    p ^= (1<<(i+j));
+  
+  for(int z=4; z>=0; z--)
+    if(p&(8<<z)) p ^= (11<<z);
+    
+  return p;
+  }
+
+int elements = 0;
+
+vector<array<int, 5>> s5_elements;
+
+map<array<int, 5>, int> back;
+
+int multable[504][504];
+
+int mpow(int a, int n) {
+  int z = a;
+  while(n > 1) z = multable[a][z], n--;
+  return z;
+  }
+
+int inset[504];
+
+int main() {
+  array<int, 5> ar;
+  for(int i=0; i<5; i++) ar[i] = i;
+  
+  do {
+    back[ar] = isize(s5_elements);
+    s5_elements.push_back(ar);
+    }
+  while(next_permutation(ar.begin(), ar.end()));
+  
+  for(int a=0; a<120; a++)
+    for(int b=0; b<120; b++) {
+      array<int, 5> res;
+      for(int i=0; i<5; i++)
+        res[i] = s5_elements[a] [ s5_elements[b][i] ];
+      multable[a][b] = back[res];
+      }
+          
+  int id;
+  
+  for(int a=0; a<120; a++)
+    if(multable[a][a] == a) id = a;
+  
+  printf("id = %d\n", id);
+
+  int xid = 0;
+  
+  int sols = 0;
+
+  for(int R=0; R<120; R++)
+  for(int P=0; P<120; P++) {
+    if(P == 0 && mpow(R, 5) == id) printf("deg5 R\n");
+    if(multable[P][P] != id) continue;
+    if(mpow(multable[R][P], 4) != id) continue;
+    if(mpow(R, 5) != id) continue;
+    xid++;
+    vector<int> allels = {id};
+    inset[id] = xid;
+    for(int i=0; i<isize(allels); i++) {
+      for(int m: {P, R}) {
+        int im = allels[i];
+        int a = multable[im][m];
+        // printf("%d x %d = %d\n", im, m, a);
+        if(inset[a] != xid) inset[a] = xid, allels.push_back(a);
+        }
+      }
+    if(isize(allels) != 120) continue;
+    printf("R = %d P = %d count = %d\n", R, P, isize(allels));
+    for(int a: s5_elements[R]) printf("%d ", a); printf("// ");
+    for(int a: s5_elements[P]) printf("%d ", a); printf("\n");
+    sols++;
+    
+    array<int, 120> cellid;
+    array<int, 120> bycellid;
+
+    for(int a=0; a<120; a++) cellid[a] = 0;
+
+    int ncell = 0;
+    for(int a=0; a<120; a++) if(cellid[a] == 0) {
+      int b = a;
+      for(int s=0; s<5; s++) cellid[b] = ncell + s, bycellid[ncell + s] = b, b = multable[b][R];
+      ncell += 5;
+      }
+    
+    printf("ncell = %d\n", ncell);
+
+    for(int a=0; a<24; a++) {
+      printf("/* %03d */ ", a);
+      for(int b=0; b<5; b++) {
+        printf("%d, ", cellid[multable[bycellid[5*a+b]][P]]);
+        }
+      printf("\n");
+      }
+
+    return 0;
+    }
+  
+  printf("solutions = %d\n", sols);
+
+  return 0;
+  }