133 lines
2.9 KiB
C++
133 lines
2.9 KiB
C++
// Fricke-Macbeath Surface generator
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// Copyright (C) 2018 Zeno Rogue, see 'hyper.cpp' for details
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#include <stdio.h>
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#include <vector>
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#include <array>
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#include <map>
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using namespace std;
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int isize(const auto x) { return x.size(); }
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int mul(int a, int b) {
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int p = 0;
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for(int i=0; i<3; i++) if((a>>i)&1)
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for(int j=0; j<3; j++) if((b>>j)&1)
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p ^= (1<<(i+j));
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for(int z=4; z>=0; z--)
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if(p&(8<<z)) p ^= (11<<z);
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return p;
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}
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int multable[8][8];
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int elements = 0;
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vector<array<int, 4>> psl_elements;
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int multable_psl[504][504];
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map<array<int, 4>, int> back;
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int mpow(int a, int n) {
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int z = a;
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while(n > 1) z = multable_psl[a][z], n--;
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return z;
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}
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int inset[504];
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int main() {
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for(int a=0; a<8; a++) {
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for(int b=0; b<8; b++) printf("%d ", mul(a, b));
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printf("\n");
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}
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for(int a=0; a<8; a++)
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for(int b=0; b<8; b++)
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multable[a][b] = mul(a, b);
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for(int a=0; a<8; a++)
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for(int b=0; b<8; b++)
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for(int c=0; c<8; c++)
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for(int d=0; d<8; d++)
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if((multable[a][d] ^ multable[b][c]) == 1) {
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array<int, 4> arr = { a, b, c, d};
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psl_elements.emplace_back(arr);
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}
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printf("elements = %d\n", isize(psl_elements));
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for(int a=0; a<504; a++) back[psl_elements[a]] = a;
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for(int a=0; a<504; a++)
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for(int b=0; b<504; b++) {
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auto pa = psl_elements[a];
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auto pb = psl_elements[b];
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array<int, 4> pc;
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for(int s=0; s<4; s++) {
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int s0 = s&2;
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int s1 = s&1;
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pc[s] = (multable[pa[s0]][pb[s1]] ^ multable[pa[s0^1]][pb[s1^2]]);
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}
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multable_psl[a][b] = back[pc];
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}
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int id;
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for(int a=0; a<504; a++)
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if(multable_psl[a][a] == a) id = a;
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printf("id = %d\n", id);
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int xid = 0;
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for(int R=0; R<504; R++)
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for(int P=0; P<504; P++) {
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if(multable_psl[P][P] != id) continue;
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if(mpow(multable_psl[R][P], 3) != id) continue;
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if(mpow(R, 7) != id) continue;
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xid++;
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vector<int> allels = {id};
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inset[id] = xid;
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for(int i=0; i<isize(allels); i++) {
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for(int m: {P, R}) {
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int im = allels[i];
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int a = multable_psl[im][m];
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// printf("%d x %d = %d\n", im, m, a);
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if(inset[a] != xid) inset[a] = xid, allels.push_back(a);
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}
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}
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printf("R = %d P = %d count = %d\n", R, P, isize(allels));
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array<int, 504> cellid;
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array<int, 504> bycellid;
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for(int a=0; a<504; a++) cellid[a] = 0;
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int ncell = 0;
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for(int a=0; a<504; a++) if(cellid[a] == 0) {
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int b = a;
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for(int s=0; s<7; s++) cellid[b] = ncell + s, bycellid[ncell + s] = b, b = multable_psl[b][R];
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ncell += 7;
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}
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printf("ncell = %d\n", ncell);
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for(int a=0; a<72; a++) {
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printf("/* %03d */ ", a);
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for(int b=0; b<7; b++) {
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printf("%d, ", cellid[multable_psl[bycellid[7*a+b]][P]]);
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}
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printf("\n");
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}
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return 0;
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}
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return 0;
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}
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