generators included

generators/macbeath.cpp

@@ -0,0 +1,132 @@
+// Fricke-Macbeath Surface generator
+// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
+
+#include <stdio.h>
+#include <vector>
+#include <array>
+#include <map>
+
+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 multable[8][8];
+
+int elements = 0;
+
+vector<array<int, 4>> psl_elements;
+
+int multable_psl[504][504];
+
+map<array<int, 4>, int> back;
+
+int mpow(int a, int n) {
+  int z = a;
+  while(n > 1) z = multable_psl[a][z], n--;
+  return z;
+  }
+
+int inset[504];
+
+int main() {
+  for(int a=0; a<8; a++) {
+    for(int b=0; b<8; b++) printf("%d ", mul(a, b));
+    printf("\n");
+    }
+
+  for(int a=0; a<8; a++)
+    for(int b=0; b<8; b++) 
+      multable[a][b] = mul(a, b);
+
+  for(int a=0; a<8; a++)
+    for(int b=0; b<8; b++) 
+      for(int c=0; c<8; c++)
+        for(int d=0; d<8; d++) 
+          if((multable[a][d] ^ multable[b][c]) == 1) {
+            array<int, 4> arr = { a, b, c, d};
+            psl_elements.emplace_back(arr);
+            }
+          
+  printf("elements = %d\n", isize(psl_elements));
+
+  for(int a=0; a<504; a++) back[psl_elements[a]] = a;
+  
+  for(int a=0; a<504; a++)
+  for(int b=0; b<504; b++) {
+    auto pa = psl_elements[a];
+    auto pb = psl_elements[b];
+    array<int, 4> pc;
+    for(int s=0; s<4; s++) {
+      int s0 = s&2;
+      int s1 = s&1;
+      pc[s] = (multable[pa[s0]][pb[s1]] ^ multable[pa[s0^1]][pb[s1^2]]);
+      }
+    multable_psl[a][b] = back[pc];
+    }
+
+  int id;
+  
+  for(int a=0; a<504; a++)
+    if(multable_psl[a][a] == a) id = a;
+  
+  printf("id = %d\n", id);
+
+  int xid = 0;
+
+  for(int R=0; R<504; R++)
+  for(int P=0; P<504; P++) {
+    if(multable_psl[P][P] != id) continue;
+    if(mpow(multable_psl[R][P], 3) != id) continue;
+    if(mpow(R, 7) != 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_psl[im][m];
+        // printf("%d x %d = %d\n", im, m, a);
+        if(inset[a] != xid) inset[a] = xid, allels.push_back(a);
+        }
+      }
+    printf("R = %d P = %d count = %d\n", R, P, isize(allels));
+
+    array<int, 504> cellid;
+    array<int, 504> bycellid;
+
+    for(int a=0; a<504; a++) cellid[a] = 0;
+
+    int ncell = 0;
+    for(int a=0; a<504; a++) if(cellid[a] == 0) {
+      int b = a;
+      for(int s=0; s<7; s++) cellid[b] = ncell + s, bycellid[ncell + s] = b, b = multable_psl[b][R];
+      ncell += 7;
+      }
+    
+    printf("ncell = %d\n", ncell);
+
+    for(int a=0; a<72; a++) {
+      printf("/* %03d */ ", a);
+      for(int b=0; b<7; b++) {
+        printf("%d, ", cellid[multable_psl[bycellid[7*a+b]][P]]);
+        }
+      printf("\n");
+      }
+
+    return 0;
+    }
+
+  return 0;
+  }