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arb::relative_matrix
This commit is contained in:
Zeno Rogue
parent
6956808dea
commit
59a9605b13
@ -443,6 +443,35 @@ struct hrmap_arbi : hrmap {
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}
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}
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transmatrix relative_matrix(heptagon *h2, heptagon *h1, const hyperpoint& hint) override {
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if(gmatrix0.count(h2->c7) && gmatrix0.count(h1->c7))
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return inverse(gmatrix0[h1->c7]) * gmatrix0[h2->c7];
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transmatrix gm = Id, where = Id;
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while(h1 != h2) {
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for(int i=0; i<h1->type; i++) {
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if(h1->move(i) == h2) {
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return gm * adj(h1, i) * where;
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}
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}
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if(h1->distance > h2->distance) {
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for(int i=0; i<h1->type; i++) if(h1->move(i) && h1->move(i)->distance < h1->distance) {
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gm = gm * adj(h1, i);
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h1 = h1->move(i);
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goto again;
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}
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}
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else {
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for(int i=0; i<h2->type; i++) if(h2->move(i) && h2->move(i)->distance < h2->distance) {
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where = iadj(h2, 0) * where;
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h2 = h2->move(i);
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goto again;
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}
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}
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again: ;
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}
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return gm * where;
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}
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transmatrix adj(cell *c, int dir) override { return adj(c->master, dir); }
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ld spin_angle(cell *c, int d) override { return SPIN_NOT_AVAILABLE; }
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2
cell.cpp
2
cell.cpp
@ -983,7 +983,7 @@ EX int celldistance(cell *c1, cell *c2) {
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if(hybri) return hybrid::celldistance(c1, c2);
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#if CAP_FIELD
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if(geometry == gFieldQuotient && !GOLDBERG)
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if(geometry == gFieldQuotient && !GOLDBERG && WDIM == 2)
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return currfp.getdist(fieldpattern::fieldval(c1), fieldpattern::fieldval(c2));
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#endif
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256
fieldpattern.cpp
256
fieldpattern.cpp
@ -29,7 +29,7 @@ struct fgeomextra {
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};
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#endif
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bool isprime(int n) {
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EX bool isprime(int n) {
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for(int k=2; k<n; k++) if(n%k == 0) return false;
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return true;
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}
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@ -69,6 +69,8 @@ EX int btspin(int id, int d) {
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#if HDR
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struct fpattern {
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unsigned force_hash;
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int Prime, wsquare, Field, dual;
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// we perform our computations in the field Z_Prime[w] where w^2 equals wsquare
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@ -273,6 +275,7 @@ struct fpattern {
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}
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fpattern(int p) {
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force_hash = 0;
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if(!p) return;
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init(p);
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}
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@ -282,6 +285,17 @@ struct fpattern {
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vector<matrix> generate_isometries();
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bool check_order(matrix M, int req);
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unsigned compute_hash();
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// general 4D
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vector<transmatrix> fullv;
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void add1(const matrix& M);
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void add1(const matrix& M, const transmatrix& Full);
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vector<matrix> generate_isometries3();
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int solve3();
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void generate_all3();
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};
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#endif
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@ -323,6 +337,166 @@ vector<matrix> fpattern::generate_isometries() {
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return res;
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}
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vector<matrix> fpattern::generate_isometries3() {
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matrix T = Id;
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int low = wsquare ? 1-Prime : 0;
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vector<matrix> res;
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auto colprod = [&] (int a, int b) {
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return add(add(mul(T[0][a], T[0][b]), mul(T[1][a], T[1][b])), sub(mul(T[2][a], T[2][b]), mul(T[3][a], T[3][b])));
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};
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auto rowcol = [&] (int a, int b) {
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return add(add(mul(T[a][0], T[0][b]), mul(T[a][1], T[1][b])), add(mul(T[a][2], T[2][b]), mul(T[a][3], T[3][b])));
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};
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for(T[0][0]=low; T[0][0]<Prime; T[0][0]++)
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for(T[1][0]=low; T[1][0]<Prime; T[1][0]++)
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for(T[2][0]=low; T[2][0]<Prime; T[2][0]++)
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for(T[3][0]=low; T[3][0]<Prime; T[3][0]++)
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if(colprod(0, 0) == 1)
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for(T[0][1]=low; T[0][1]<Prime; T[0][1]++)
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for(T[1][1]=low; T[1][1]<Prime; T[1][1]++)
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for(T[2][1]=low; T[2][1]<Prime; T[2][1]++)
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for(T[3][1]=low; T[3][1]<Prime; T[3][1]++)
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if(colprod(1, 1) == 1)
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if(colprod(1, 0) == 0)
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for(T[0][2]=low; T[0][2]<Prime; T[0][2]++)
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for(T[0][3]=low; T[0][3]<Prime; T[0][3]++)
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if(rowcol(0, 0) == 1)
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if(rowcol(0, 1) == 0)
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for(T[1][2]=low; T[1][2]<Prime; T[1][2]++)
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for(T[1][3]=low; T[1][3]<Prime; T[1][3]++)
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if(rowcol(1, 0) == 0)
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if(rowcol(1, 1) == 1)
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for(T[2][2]=low; T[2][2]<Prime; T[2][2]++)
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for(T[3][2]=low; T[3][2]<Prime; T[3][2]++)
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if(colprod(2, 2) == 1)
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if(colprod(2, 0) == 0)
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if(colprod(2, 1) == 0)
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for(T[2][3]=low; T[2][3]<Prime; T[2][3]++)
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for(T[3][3]=low; T[3][3]<Prime; T[3][3]++)
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if(rowcol(2, 0) == 0)
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if(rowcol(2, 1) == 0)
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if(rowcol(2, 2) == 1)
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// if(colprod(3, 3) == 1)
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if(add(colprod(3, 3), 1) == 0)
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if(colprod(3, 0) == 0)
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if(colprod(3, 1) == 0)
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if(colprod(3, 2) == 0)
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if(rowcol(3, 3) == 1)
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if(rowcol(3, 0) == 0)
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if(rowcol(3, 1) == 0)
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if(rowcol(3, 2) == 0)
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res.push_back(T);
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return res;
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}
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void fpattern::add1(const matrix& M) {
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if(!matcode.count(M)) {
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int i = matrices.size();
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matcode[M] = i, matrices.push_back(M);
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}
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}
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void fpattern::add1(const matrix& M, const transmatrix& Full) {
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if(!matcode.count(M)) {
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int i = matrices.size();
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matcode[M] = i, matrices.push_back(M), fullv.push_back(Full);
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}
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}
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map<unsigned,int> hash_found;
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unsigned fpattern::compute_hash() {
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unsigned hashv = 0;
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int iR = matcode[R];
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int iP = matcode[P];
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int iX = matcode[X];
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for(int i=0; i<isize(matrices); i++) {
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hashv = 3 * hashv + gmul(i, iP) + 7 * gmul(i, iR);
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if(MWDIM == 4) hashv += 11 * gmul(i, iX);
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}
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return hashv;
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}
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void fpattern::generate_all3() {
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matrices.clear();
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matcode.clear();
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add1(Id);
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fullv = {hr::Id};
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for(int i=0; i<isize(matrices); i++) {
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add1(mmul(matrices[i], R), fullv[i] * reg3::full_R);
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add1(mmul(matrices[i], X), fullv[i] * reg3::full_X);
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}
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local_group = isize(matrices);
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for(int i=0; i<(int)matrices.size(); i++) {
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matrix E = mmul(matrices[i], P);
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if(!matcode.count(E))
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for(int j=0; j<local_group; j++) add1(mmul(E, matrices[j]));
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}
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unsigned hashv = compute_hash();
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DEBB(DF_FIELD, ("all = ", isize(matrices), "/", local_group, " = ", isize(matrices) / local_group, " hash = ", hashv, " count = ", ++hash_found[hashv]));
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}
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int fpattern::solve3() {
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if(!wsquare) return 0;
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reg3::construct_relations();
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DEBB(DF_FIELD, ("generating isometries for ", Field));
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auto iso3 = generate_isometries();
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auto iso4 = generate_isometries3();
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int cmb = 0;
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int N = isize(reg3::rels);
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vector<int> fails(N);
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vector<matrix> possible_P, possible_X, possible_R;
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for(auto& M: iso3) {
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if(check_order(M, 2))
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possible_X.push_back(M);
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if(check_order(M, reg3::r_order))
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possible_R.push_back(M);
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}
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for(auto& M: iso4)
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if(check_order(M, 2))
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possible_P.push_back(M);
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DEBB(DF_FIELD, ("field = ", Field, " #P = ", isize(possible_P), " #X = ", isize(possible_X), " #R = ", isize(possible_R), " r_order = ", reg3::r_order, " xp_order = ", reg3::xp_order));
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for(auto& xX: possible_X)
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for(auto& xP: possible_P) if(check_order(mmul(xP, xX), reg3::xp_order))
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for(auto& xR: possible_R) if(check_order(mmul(xR, xX), reg3::rx_order)) { // if(xR[0][0] == 1 && xR[0][1] == 0) {
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auto by = [&] (char ch) -> matrix& { return ch == 'X' ? xX : ch == 'R' ? xR : xP; };
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for(int i=0; i<N; i++) {
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matrix ml = Id;
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for(char c: reg3::rels[i].first) { ml = mmul(ml, by(c)); if(ml == Id) { fails[i]++; goto bad; }}
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matrix mr = Id;
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for(char c: reg3::rels[i].second) { mr = mmul(mr, by(c)); if(mr == Id) { fails[i]++; goto bad; }}
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if(ml != mr) { fails[i]++; goto bad;}
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}
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P = xP; R = xR; X = xX;
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generate_all3();
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if(force_hash && compute_hash() != force_hash) continue;
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cmb++;
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goto ok;
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bad: ;
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}
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ok:
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DEBB(DF_FIELD, ("cmb = ", cmb, " for field = ", Field));
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for(int i=0; i<N; i++) if(fails[i]) DEBB(DF_FIELD, (reg3::rels[i], " fails = ", fails[i]));
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return cmb;
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}
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int fpattern::solve() {
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for(int a=0; a<MWDIM; a++) for(int b=0; b<MWDIM; b++) Id[a][b] = a==b?1:0;
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@ -347,6 +521,14 @@ int fpattern::solve() {
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}
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} else wsquare = 0;
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if(WDIM == 3) {
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if(dual == 0) {
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int s = solve3();
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if(s) return 0;
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}
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continue;
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}
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if(dual == 2) {
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if(Field <= 10) {
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vector<matrix> all_isometries = generate_isometries();
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@ -419,6 +601,8 @@ int fpattern::order(const matrix& M) {
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void fpattern::build() {
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if(WDIM == 3) return;
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for(int i=0; i<isize(qpaths); i++) {
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matrix M = strtomatrix(qpaths[i]);
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qcoords.push_back(M);
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@ -789,6 +973,7 @@ EX void info() {
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#ifndef EASY
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neasy = 0;
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#endif
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if(WDIM == 3) continue;
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fp.build();
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#ifndef EASY
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printf("Not easy: %d\n", neasy);
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@ -812,12 +997,61 @@ EX bool quotient_field_changed;
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EX struct fpattern& getcurrfp() {
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if(geometry == gFieldQuotient && quotient_field_changed)
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return current_quotient_field;
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if(WDIM == 3) {
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dynamicval<eGeometry> g(geometry, gSpace435);
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return current_quotient_field;
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if(geometry == gSpace535) {
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// 120 cells, hash = 9EF7A9C4
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static fpattern fp(5);
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return fp;
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}
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if(geometry == gSpace534) {
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// 260 cells, hash = 72414D0C (not 0C62E214)
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static fpattern fp(0);
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if(fp.Prime) return fp;
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fp.Prime = 5; fp.force_hash = 0x72414D0C; fp.solve();
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return fp;
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}
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if(geometry == gSpace435) {
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// 650 cells, hash = EB201050
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static fpattern fp(0);
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if(fp.Prime) return fp;
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fp.Prime = 5; fp.force_hash = 0x72414D0C; fp.solve();
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return fp;
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}
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if(geometry == gSpace336) {
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// 672 cells in E3F6B7BC
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// 672 cells in 885F1184
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// 9408 cells in C4089F34
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static fpattern fp(0);
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if(fp.Prime) return fp;
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fp.Prime = 7; fp.force_hash = 0xE3F6B7BCu; fp.solve();
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return fp;
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}
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if(geometry == gSpace344) {
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// 600 cells in 558C8ED0
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// 2400 cells in AF042EA8
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// 2600 cells in D26948E0
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// 2600 cells in EC29DCEC
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static fpattern fp(0);
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if(fp.Prime) return fp;
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fp.Prime = 5; fp.force_hash = 0x558C8ED0u; fp.solve();
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return fp;
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// 4900 cells in CDCC7860 (7)
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}
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if(geometry == gSpace536) {
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static fpattern fp(0);
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if(fp.Prime) return fp;
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// 130 cells in 3BA5C5A4
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// 260 cells in 9FDE7B38
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fp.Prime = 7; fp.force_hash = 0x9FDE7B38u; fp.solve();
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return fp;
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}
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if(WDIM == 3) {
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static fpattern fp(0);
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if(fp.Prime) return fp;
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for(int p=2; p<8; p++) { fp.Prime = p; if(!fp.solve()) break; }
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DEBB(DF_FIELD, ("set prime = ", fp.Prime));
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return fp;
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}
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if(S7 == 8 && S3 == 3) {
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static fpattern fp(17);
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return fp;
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@ -900,6 +1134,20 @@ EX void enableFieldChange() {
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fieldpattern::current_quotient_field.init(gxcur.primes[gxcur.current_prime_id].p);
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}
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EX void field_from_current() {
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auto& go = ginf[geometry];
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dynamicval<eGeometry> g(geometry, gFieldQuotient);
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auto& gg = ginf[geometry];
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gg.sides = go.sides;
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gg.vertex = go.vertex;
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gg.distlimit = go.distlimit;
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gg.tiling_name = go.tiling_name;
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gg.flags = go.flags | qANYQ | qFIELD | qBOUNDED;
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gg.g = go.g;
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gg.default_variation = go.default_variation;
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fieldpattern::quotient_field_changed = true;
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}
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EX }
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#define currfp fieldpattern::getcurrfp()
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24
geom-exp.cpp
24
geom-exp.cpp
@ -316,6 +316,8 @@ void set_or_configure_geometry(eGeometry g) {
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bool same_tiling(eGeometry g2) {
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if(g2 == gCrystal)
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return S3 == 4;
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if(g2 == gFieldQuotient && hyperbolic && standard_tiling())
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return true;
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if(g2 == gFieldQuotient && geometry != gFieldQuotient) {
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int ce = 0;
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for(auto& ge: fieldpattern::fgeomextras) {
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@ -456,7 +458,15 @@ EX void select_quotient_screen() {
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"no quotient",
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g == geometry, key++);
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dialog::add_action([g] {
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if(g == gFieldQuotient)
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if(g == gFieldQuotient && WDIM == 3) {
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stop_game();
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fieldpattern::field_from_current();
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set_geometry(gFieldQuotient);
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for(int p=2;; p++) { currfp.Prime = p; currfp.force_hash = 0; if(!currfp.solve()) break; }
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println(hlog, "set prime = ", currfp.Prime);
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start_game();
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}
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else if(g == gFieldQuotient)
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pushScreen(showQuotientConfig);
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else if(g == gCrystal)
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pushScreen(crystal::show);
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@ -900,6 +910,14 @@ int read_geom_args() {
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enableFieldChange();
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set_geometry(gFieldQuotient);
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}
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else if(argis("-to-fq")) {
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shift(); unsigned hash = arghex();
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stop_game_and_switch_mode(rg::nothing);
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fieldpattern::field_from_current();
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set_geometry(gFieldQuotient);
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for(int p=2;; p++) { currfp.Prime = p; currfp.force_hash = hash; if(!currfp.solve()) break; }
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println(hlog, "set prime = ", currfp.Prime);
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}
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else if(argis("-cs")) {
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shift(); cheat();
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fieldpattern::matrix M = currfp.strtomatrix(args());
|
||||
@ -940,6 +958,10 @@ int read_geom_args() {
|
||||
fieldpattern::info();
|
||||
exit(0);
|
||||
}
|
||||
else if(argis("-fi-geo")) {
|
||||
fieldpattern::info();
|
||||
exit(0);
|
||||
}
|
||||
else if(argis("-qs")) {
|
||||
cheat();
|
||||
shift(); currfp.qpaths.push_back(args());
|
||||
|
||||
316
reg3.cpp
316
reg3.cpp
@ -32,7 +32,7 @@ EX namespace reg3 {
|
||||
EX int face;
|
||||
|
||||
EX vector<hyperpoint> cellshape;
|
||||
vector<hyperpoint> vertices_only;
|
||||
EX vector<hyperpoint> vertices_only;
|
||||
|
||||
EX transmatrix spins[12], adjmoves[12];
|
||||
|
||||
@ -237,6 +237,8 @@ EX namespace reg3 {
|
||||
|
||||
void initialize(int cell_count);
|
||||
vector<cell*>& allcells() override { return acells; }
|
||||
|
||||
vector<hyperpoint> get_vertices(cell* c) override { return vertices_only; }
|
||||
};
|
||||
#endif
|
||||
|
||||
@ -324,196 +326,37 @@ EX namespace reg3 {
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
struct hrmap_field3 : hrmap_quotient3 {
|
||||
|
||||
int mgmul(std::initializer_list<int> v) {
|
||||
int a = 0;
|
||||
for(int b: v) a = a ? currfp_gmul(a, b) : b;
|
||||
return a;
|
||||
}
|
||||
|
||||
vector<transmatrix> fullmatrices;
|
||||
|
||||
int P, R, X;
|
||||
transmatrix full_P, full_R, full_X;
|
||||
|
||||
vector<int> field_adjmoves;
|
||||
vector<int> cyclers;
|
||||
int perm_group;
|
||||
|
||||
struct hrmap_field3 : reg3::hrmap_quotient3 {
|
||||
|
||||
vector<int> cell_to_code;
|
||||
vector<int> code_to_cell;
|
||||
|
||||
void seek(set<int>& seen_matrices, set<int>& seen_codes, const transmatrix& at, int ccode, const hyperpoint checker) {
|
||||
if(hdist0(tC0(at)) > 4) return;
|
||||
int b = bucketer(tC0(at));
|
||||
if(seen_matrices.count(b)) return;
|
||||
seen_matrices.insert(b);
|
||||
for(int a=0; a<perm_group; a++) {
|
||||
transmatrix T = at * fullmatrices[a];
|
||||
if(hdist(T * checker, checker) < 1e-2) {
|
||||
int co = mgmul({ccode, a});
|
||||
seen_codes.insert(co);
|
||||
fullmatrices[co] = T;
|
||||
}
|
||||
}
|
||||
for(int a=0; a<perm_group; a++) seek(seen_matrices, seen_codes, at * fullmatrices[a] * full_P, mgmul({ccode, a, P}), checker);
|
||||
}
|
||||
|
||||
hrmap_field3() {
|
||||
eGeometry g = geometry;
|
||||
geometry = gSpace435;
|
||||
reg3::generate();
|
||||
R = currfp_get_R();
|
||||
P = currfp_get_P();
|
||||
X = currfp_get_X();
|
||||
full_P = reg3::adjmoves[0] * cspin(0, 2, M_PI) * cspin(0, 1, M_PI);
|
||||
full_R = spin(-2 * M_PI / 4);
|
||||
full_X = cspin(1, 2, M_PI / 2);
|
||||
|
||||
DEBB(DF_FIELD, ("full_P = ", full_P, " / ", R));
|
||||
DEBB(DF_FIELD, ("full_R = ", full_R, " / ", P));
|
||||
DEBB(DF_FIELD, ("full_X = ", full_X, " / ", X));
|
||||
|
||||
int N = currfp_n();
|
||||
|
||||
perm_group = 24;
|
||||
fullmatrices.resize(N);
|
||||
fullmatrices[0] = Id;
|
||||
vector<bool> known(perm_group, false);
|
||||
known[0] = true;
|
||||
for(int a=0; a<perm_group; a++)
|
||||
for(int i=0; i<perm_group; i++) if(known[i]) {
|
||||
int iR = currfp_gmul(i, R);
|
||||
fullmatrices[iR] = fullmatrices[i] * full_R;
|
||||
known[iR] = true;
|
||||
int iX = currfp_gmul(i, X);
|
||||
fullmatrices[iX] = fullmatrices[i] * full_X;
|
||||
known[iX] = true;
|
||||
}
|
||||
for(int i=0; i<perm_group; i++) if(known[i]) {
|
||||
DEBB(DF_FIELD, (i, ". ", fullmatrices[i]));
|
||||
}
|
||||
|
||||
auto& f = currfp;
|
||||
auto lgr = f.local_group;
|
||||
|
||||
// find cav such that:
|
||||
// cav * Id * C0 = corner0
|
||||
// cav * adjmoves[0] * C0 = corner1
|
||||
// cav * adjmoves[1] * C0 = corner3
|
||||
// cav * adjmoves[2] * C0 = cornerx
|
||||
int N = isize(f.matrices) / lgr;
|
||||
initialize(N);
|
||||
|
||||
hyperpoint corner0 = reg3::cellshape[0];
|
||||
hyperpoint corner1 = reg3::cellshape[1];
|
||||
hyperpoint corner3 = reg3::cellshape[3];
|
||||
hyperpoint cornerx;
|
||||
vector<int> moveid(S7), movedir(lgr);
|
||||
for(int s=0; s<lgr; s++)
|
||||
for(int i=0; i<S7; i++) if(eqmatrix(f.fullv[s] * reg3::adjmoves[0], reg3::adjmoves[i]))
|
||||
moveid[i] = s;
|
||||
|
||||
for(hyperpoint h: reg3::cellshape) DEBB(DF_FIELD, ("some corner ", h));
|
||||
for(int s=0; s<lgr; s++)
|
||||
for(int i=0; i<S7; i++) if(hdist(tC0(inverse(f.fullv[s]) * reg3::adjmoves[0]), tC0(reg3::adjmoves[i])) < 1e-4)
|
||||
movedir[s] = i;
|
||||
|
||||
for(hyperpoint h: reg3::cellshape)
|
||||
if(hdist(h, corner1) > .1 && hdist(h, corner3) > .1 && abs(hdist(h, corner0)-hdist(corner0, corner1)) < .1)
|
||||
cornerx = h;
|
||||
DEBB(DF_FIELD, ("corner0 = ", corner0));
|
||||
DEBB(DF_FIELD, ("corner1 = ", corner1));
|
||||
DEBB(DF_FIELD, ("corner3 = ", corner3));
|
||||
DEBB(DF_FIELD, ("cornerx = ", cornerx));
|
||||
|
||||
transmatrix adj = Id, iadj = Id;
|
||||
|
||||
geometry = g;
|
||||
reg3::generate();
|
||||
|
||||
cyclers.clear();
|
||||
DEBB(DF_FIELD, ("S7 = ", S7));
|
||||
if(S7 == 12) {
|
||||
|
||||
transmatrix resmatrix;
|
||||
set_column(resmatrix, 0, corner0);
|
||||
set_column(resmatrix, 1, corner1);
|
||||
set_column(resmatrix, 2, corner3);
|
||||
set_column(resmatrix, 3, cornerx);
|
||||
|
||||
transmatrix transformer;
|
||||
set_column(transformer, 0, C0);
|
||||
set_column(transformer, 1, tC0(reg3::adjmoves[0]));
|
||||
set_column(transformer, 2, tC0(reg3::adjmoves[1]));
|
||||
set_column(transformer, 3, tC0(reg3::adjmoves[2]));
|
||||
|
||||
transmatrix cav = resmatrix * inverse(transformer);
|
||||
DEBB(DF_FIELD, ("cav = ", cav));
|
||||
DEBB(DF_FIELD, ("cav * C0 = ", cav * C0));
|
||||
|
||||
set<int> seen_matrices;
|
||||
set<int> seen_codes;
|
||||
seek(seen_matrices, seen_codes, Id, 0, corner0);
|
||||
|
||||
for(int x: seen_codes) cyclers.push_back(x);
|
||||
perm_group = isize(cyclers);
|
||||
adj = cav;
|
||||
iadj = inverse(cav);
|
||||
}
|
||||
else {
|
||||
for(int i=0; i<perm_group; i++) cyclers.push_back(i);
|
||||
}
|
||||
|
||||
field_adjmoves.resize(S7);
|
||||
for(int i=0; i<S7; i++) field_adjmoves[i] = -1;
|
||||
|
||||
for(int i=0; i<S7; i++)
|
||||
for(int a: cyclers)
|
||||
for(int b: cyclers) {
|
||||
transmatrix T = iadj * fullmatrices[a] * full_P * fullmatrices[b] * adj;
|
||||
if(eqmatrix(T, reg3::adjmoves[i])) {
|
||||
int code = mgmul({a,P,b});
|
||||
field_adjmoves[i] = code;
|
||||
DEBB(DF_FIELD, (i, " = ", make_tuple(a,P,b), " = ", code, " T = ", T));
|
||||
for(int a=0; a<N; a++) {
|
||||
tmatrices[a].resize(S7);
|
||||
for(int b=0; b<S7; b++) {
|
||||
int k = lgr*a;
|
||||
k = f.gmul(f.gmul(k, moveid[b]), lgr);
|
||||
for(int l=0; l<lgr; l++) if(f.gmul(k, l) % lgr == 0) {
|
||||
tmatrices[a][b] = reg3::adjmoves[b] * f.fullv[l];
|
||||
allh[a]->c.connect(b, allh[k/lgr], movedir[l], false);
|
||||
}
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("field_adjmoves = ", field_adjmoves));
|
||||
|
||||
DEBB(DF_FIELD, ("finding code_to_cell/cell_to_code..."));
|
||||
|
||||
cell_to_code.clear();
|
||||
code_to_cell.resize(N);
|
||||
for(int i=0; i<N; i++) code_to_cell[i] = -1;
|
||||
for(int i=0; i<N; i++) if(code_to_cell[i] == -1) {
|
||||
for(int j: cyclers) code_to_cell[currfp_gmul(i, j)] = isize(cell_to_code);
|
||||
cell_to_code.push_back(i);
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("building allh..."));
|
||||
int cells = N / perm_group;
|
||||
initialize(cells);
|
||||
|
||||
DEBB(DF_FIELD, ("finding tmatrices..."));
|
||||
for(int i=0; i<cells; i++) {
|
||||
for(int d=0; d<S7; d++) {
|
||||
int found = 0;
|
||||
int tmul = currfp_gmul(cell_to_code[i], field_adjmoves[d]);
|
||||
for(int s: cyclers) {
|
||||
int tmul2 = currfp_gmul(tmul, s);
|
||||
if(cell_to_code[code_to_cell[tmul2]] == tmul2) {
|
||||
allh[i]->move(d) = allh[code_to_cell[tmul2]];
|
||||
allh[i]->c7->move(d) = allh[i]->move(d)->c7;
|
||||
tmatrices[i].push_back(reg3::adjmoves[d] * iadj * fullmatrices[s] * adj);
|
||||
found++;
|
||||
}
|
||||
}
|
||||
if(found != 1) DEBB(DF_FIELD, ("bad found: ", i, "/", d, "/", found));
|
||||
// println(hlog, "tmatrix(",i,",",d,") = ", tmatrices[i][d]);
|
||||
}
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("setting spin..."));
|
||||
for(int i=0; i<cells; i++)
|
||||
for(int d=0; d<S7; d++)
|
||||
for(int e=0; e<S7; e++)
|
||||
if(allh[i]->move(d)->move(e) == allh[i]) {
|
||||
allh[i]->c.setspin(d, e, false);
|
||||
allh[i]->c7->c.setspin(d, e, false);
|
||||
}
|
||||
|
||||
DEBB(DF_FIELD, ("creating patterns..."));
|
||||
}
|
||||
create_patterns();
|
||||
}
|
||||
|
||||
@ -529,8 +372,9 @@ EX namespace reg3 {
|
||||
|
||||
|
||||
void create_patterns() {
|
||||
auto& f = currfp;
|
||||
// change the geometry to make sure that the correct celldistance is used
|
||||
dynamicval<eGeometry> g(geometry, S7 == 12 ? gField534 : gField435);
|
||||
dynamicval<eGeometry> g(geometry, gFieldQuotient);
|
||||
// also, strafe needs currentmap
|
||||
dynamicval<hrmap*> c(currentmap, this);
|
||||
|
||||
@ -572,7 +416,7 @@ EX namespace reg3 {
|
||||
for(int i=0; i<currfp_n(); i++) {
|
||||
bool ok = true;
|
||||
for(auto o: plane_indices) {
|
||||
int j = code_to_cell[currfp_gmul(i, cell_to_code[o])];
|
||||
int j = currfp_gmul(i, o * f.local_group) / f.local_group;
|
||||
if(plane_indices.count(j)) ok = false;
|
||||
forCellEx(c1, allcells()[j]) if(plane_indices.count(c1->master->fieldval)) ok = false;
|
||||
}
|
||||
@ -595,17 +439,13 @@ EX namespace reg3 {
|
||||
int u = 0;
|
||||
for(int a=0; a<5; a++) {
|
||||
for(int o: plane_indices) {
|
||||
int j = code_to_cell[currfp_gmul(u, cell_to_code[o])];
|
||||
int j = currfp_gmul(u, o * f.local_group) / f.local_group;
|
||||
allcells()[j]->master->zebraval |= 2;
|
||||
}
|
||||
u = currfp_gmul(u, gpow);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
vector<hyperpoint> get_vertices(cell* c) override {
|
||||
return vertices_only;
|
||||
}
|
||||
};
|
||||
|
||||
/** homology cover of the Seifert-Weber space */
|
||||
@ -770,7 +610,7 @@ EX namespace reg3 {
|
||||
quotient_map = new seifert_weber::hrmap_seifert_cover;
|
||||
h.zebraval = quotient_map->allh[0]->zebraval;
|
||||
}
|
||||
else if(hyperbolic && !(cgflags & qIDEAL)) {
|
||||
else if(hyperbolic) {
|
||||
quotient_map = new hrmap_field3;
|
||||
h.zebraval = quotient_map->allh[0]->zebraval;
|
||||
}
|
||||
@ -1085,6 +925,7 @@ EX bool pseudohept(cell *c) {
|
||||
return hr::celldistance(c, currentmap->gamestart()) & 1;
|
||||
if(geometry == gCrystal344 || geometry == gCrystal534 || geometry == gSeifertCover)
|
||||
return false;
|
||||
if(quotient) return false; /* added */
|
||||
if(hyperbolic) {
|
||||
heptagon *h = m->reg_gmatrix[c->master].first;
|
||||
return (h->zebraval == 1) && (h->distance & 1);
|
||||
@ -1225,6 +1066,99 @@ EX cellwalker strafe(cellwalker cw, int j) {
|
||||
println(hlog, "incorrect strafe");
|
||||
exit(1);
|
||||
}
|
||||
|
||||
EX vector<pair<string, string> > rels;
|
||||
EX int xp_order, r_order, rx_order;
|
||||
|
||||
EX transmatrix full_X, full_R, full_P;
|
||||
geometry_information *for_cgi;
|
||||
|
||||
EX int matrix_order(const transmatrix A) {
|
||||
transmatrix T = A;
|
||||
int res = 1;
|
||||
while(!eqmatrix(T, Id)) {
|
||||
res++; T = T * A;
|
||||
}
|
||||
return res;
|
||||
}
|
||||
|
||||
EX void construct_relations() {
|
||||
if(for_cgi == &cgi) return;
|
||||
for_cgi = &cgi;
|
||||
rels.clear();
|
||||
|
||||
reg3::generate();
|
||||
reg3::generate_cellrotations();
|
||||
vector<transmatrix> all;
|
||||
|
||||
vector<string> formulas;
|
||||
|
||||
formulas.push_back("");
|
||||
|
||||
all.push_back(Id);
|
||||
hyperpoint v = reg3::cellshape[0];
|
||||
auto add = [&] (transmatrix T) {
|
||||
for(int i=0; i<isize(all); i++) if(eqmatrix(all[i], T)) return i;
|
||||
int S = isize(all);
|
||||
all.push_back(T);
|
||||
return S;
|
||||
};
|
||||
|
||||
auto cons = [&] (int i0, int i1, int i2) {
|
||||
using reg3::adjmoves;
|
||||
transmatrix T = build_matrix(adjmoves[ 0]*C0, adjmoves[ 1]*C0, adjmoves[ 2]*C0, C0);
|
||||
transmatrix U = build_matrix(adjmoves[i0]*C0, adjmoves[i1]*C0, adjmoves[i2]*C0, C0);
|
||||
return U * inverse(T);
|
||||
};
|
||||
|
||||
full_P = reg3::adjmoves[0];
|
||||
full_R = S7 == 8 ? cons(1, 7, 0) : cons(1, 2, 0);
|
||||
full_X = S7 == 8 ? cons(1, 0, 6) : S7 == 6 ? cons(1, 0, 5) : cons(1, 0, reg3::face);
|
||||
|
||||
println(hlog, reg3::cellshape);
|
||||
|
||||
println(hlog, "cellshape = ", isize(reg3::cellshape));
|
||||
bool ok = true;
|
||||
int last_i = -1;
|
||||
for(hyperpoint h: reg3::cellshape) {
|
||||
int i = 0, j = 0;
|
||||
for(hyperpoint u: reg3::cellshape) if(hdist(h, full_X*u) < 1e-4) i++;
|
||||
for(hyperpoint u: reg3::cellshape) if(hdist(h, full_R*u) < 1e-4) j++;
|
||||
if(last_i == -1) last_i = i;
|
||||
if(i != j || i != last_i) ok = false;
|
||||
}
|
||||
|
||||
if(!ok) { println(hlog, "something wrong"); exit(1); }
|
||||
|
||||
add(Id);
|
||||
|
||||
auto work = [&] (transmatrix T, int p, char c) {
|
||||
if(hdist0(tC0(T)) > 5) return;
|
||||
for(hyperpoint h: reg3::cellshape) if(hdist(T * h, v) < 1e-4) goto ok;
|
||||
return;
|
||||
ok:
|
||||
int id = add(T);
|
||||
// println(hlog, p, " x ", (s0+c), " = ", id);
|
||||
|
||||
if(id >= isize(formulas)) formulas.push_back(formulas[p] + c);
|
||||
else if(id == 0) println(hlog, "reached identity: ", formulas[p]+c);
|
||||
else if(formulas[p][0] != formulas[id][0])
|
||||
rels.emplace_back(formulas[p] + c, formulas[id]);
|
||||
};
|
||||
|
||||
for(int i=0; i<isize(all); i++) {
|
||||
transmatrix T = all[i];
|
||||
work(T * full_R, i, 'R');
|
||||
work(T * full_X, i, 'X');
|
||||
work(T * full_P, i, 'P');
|
||||
}
|
||||
|
||||
xp_order = matrix_order(full_X * full_P);
|
||||
r_order = matrix_order(full_R);
|
||||
rx_order = matrix_order(full_R * full_X);
|
||||
println(hlog, "orders = ", tie(rx_order, r_order, xp_order));
|
||||
}
|
||||
|
||||
EX }
|
||||
#endif
|
||||
}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user