// 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; }