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Code Issues Releases Wiki Activity

fieldpattern:: now can work with triplets

This commit is contained in:
Zeno Rogue 2021-03-08 13:30:55 +01:00
parent dd0e9ddae7
commit 6e942e98f5
2 changed files with 161 additions and 25 deletions
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106
fieldpattern.cpp
View File

@ -75,6 +75,10 @@ EX int btspin(int id, int d) {
static const int ERR = -99;
struct triplet_info {
int i, j, size;
};
struct fpattern {
unsigned force_hash;
@ -224,6 +228,13 @@ struct fpattern {
int gmul(int a, int b) { return matcode[mmul(matrices[a], matrices[b])]; }
int gpow(int a, int N) { return matcode[mpow(matrices[a], N)]; }
int gorder(int a) {
int b = a;
int q = 1;
while(b) b = gmul(b, a), q++;
return q;
}
pair<int,bool> gmul(pair<int, bool> a, int b) {
return make_pair(gmul(a.first,b), a.second);
@ -310,6 +321,8 @@ struct fpattern {
vector<matrix> generate_isometries3();
int solve3();
bool generate_all3();
vector<triplet_info> find_triplets();
#if CAP_THREAD
struct discovery *dis;
@ -671,6 +684,84 @@ int fpattern::order(const matrix& M) {
return cnt;
}
EX int triplet_id = 0;
vector<triplet_info> fpattern::find_triplets() {
int N = isize(matrices);
auto compute_transcript = [&] (int i, int j) {
vector<int> indices(N, -1);
vector<int> transcript;
vector<int> q;
int qty = 0;
auto visit = [&] (int id) {
transcript.push_back(indices[id]);
if(indices[id] == -1) {
indices[id] = isize(q);
q.push_back(id);
qty++;
}
};
visit(0);
for(int x=0; x<isize(q); x++) {
int at = q[x];
visit(gmul(at, i));
visit(gmul(at, j));
}
transcript.push_back(qty);
return transcript;
};
DEBB(DF_FIELD, ("looking for alternate solutions"));
auto orig_transcript = compute_transcript(1, S7);
set<vector<int>> transcripts_seen;
transcripts_seen.insert(orig_transcript);
set<int> conjugacy_classes;
vector<int> cc;
for(int i=0; i<N; i++) conjugacy_classes.insert(i);
for(int i=0; i<N; i++) {
if(!conjugacy_classes.count(i)) continue;
vector<int> removals;
for(int j=0; j<N; j++) {
int c = gmul(inverses[j], gmul(i, j));
if(c > i) removals.push_back(c);
}
for(auto r: removals) conjugacy_classes.erase(r);
cc.push_back(i);
}
DEBB(DF_FIELD, ("conjugacy_classes = ", cc));
vector<triplet_info> tinf;
triplet_info ti;
ti.i = 1; ti.j = S7; ti.size = orig_transcript.back();
tinf.push_back(ti);
for(int i: conjugacy_classes) if(gorder(i) == S7) {
DEBB(DF_FIELD, ("checking i=", i));
for(int j=1; j<N; j++) if(gorder(j) == 2 && gorder(gmul(i, j)) == S3) {
auto t = compute_transcript(i, j);
if(!transcripts_seen.count(t)) {
transcripts_seen.insert(t);
triplet_info ti;
ti.i = i; ti.j = j; ti.size = t.back();
tinf.push_back(ti);
}
}
}
DEBB(DF_FIELD, ("solutions found = ", isize(transcripts_seen)));
return tinf;
}
void fpattern::build() {
if(WDIM == 3) return;
@ -734,6 +825,20 @@ void fpattern::build() {
if(i%S7 == S7-1) printf("\n");
}
DEBB(DF_FIELD, ("triplet_id = ", triplet_id, " N = ", N));
if(triplet_id) {
auto triplets = find_triplets();
if(triplet_id >= 0 && triplet_id < isize(triplets)) {
auto ti = triplets[triplet_id];
R = matrices[ti.i];
P = matrices[ti.j];
dynamicval<int> t(triplet_id, 0);
build();
DEBB(DF_FIELD, ("triplet built successfully"));
return;
}
}
DEBB(DF_FIELD, ("Built.\n"));
}
@ -1229,6 +1334,7 @@ EX int current_extra = 0;
EX void nextPrime(fgeomextra& ex) {
dynamicval<eGeometry> g(geometry, ex.base);
dynamicval<int> t(triplet_id, 0);
int nextprime;
if(isize(ex.primes))
nextprime = ex.primes.back().p + 1;

80
geom-exp.cpp
View File

@ -46,6 +46,7 @@ void showQuotientConfig() {
for(int i=0; i<isize(fgeomextras); i++) {
auto& g = fgeomextras[i];
dialog::addBoolItem(ginf[g.base].tiling_name, g.base == gxcur.base, 'a'+i);
dialog::add_action([i] { current_extra = i; });
}
dialog::addBreak(100);
@ -64,6 +65,7 @@ void showQuotientConfig() {
s += stars[gxcur.dualval[i]];
dialog::addBoolItem(s, i == gxcur.current_prime_id, 'A'+i);
dialog::add_action([&gxcur, i] { gxcur.current_prime_id = i; });
}
if(isize(gxcur.primes) <= 6) {
@ -79,34 +81,57 @@ void showQuotientConfig() {
}
dialog::addItem("find the next prime", 'p');
dialog::add_action([&gxcur] { nextPrime(gxcur); });
dialog::addItem("activate", 'x');
dialog::addItem("default", 'c');
dialog::add_action_confirmed([&gxcur] {
set_geometry(gxcur.base);
enableFieldChange();
set_geometry(gFieldQuotient);
start_game();
});
dialog::addItem("find alternate manifolds", 'y');
dialog::add_action_confirmed([&gxcur] {
set_geometry(gxcur.base);
triplet_id = 0;
enableFieldChange();
set_geometry(gFieldQuotient);
start_game();
auto& cfp = currfp;
auto triplets = cfp.find_triplets();
pushScreen([triplets] {
gamescreen(2);
dialog::init(XLAT("alternate manifolds"));
int id = 0;
for(auto t: triplets) {
dialog::addItem(XLAT("generators (%1,%2), size %3", its(t.i), its(t.j), its(t.size/S7)), 'a'+id);
dialog::add_action([id] {
stop_game();
triplet_id = id;
fieldpattern::enableFieldChange();
start_game();
});
id++;
}
dialog::addBreak(100);
dialog::addHelp(XLAT(
"This option finds alternate solutions. For example, there are three {7,3} manifolds with 156 heptagons each (\"first Hurwitz triplet\").")
);
dialog::display();
});
});
dialog::addItem("default", 'z');
dialog::add_action_confirmed([] {
set_geometry(gEuclid);
fieldpattern::quotient_field_changed = false;
set_geometry(gFieldQuotient);
start_game();
});
dialog::addBack();
keyhandler = [&gxcur] (int sym, int uni) {
if(uni >= 'a' && uni < 'a' + isize(fgeomextras))
current_extra = uni - 'a';
else if(uni >= 'A' && uni < 'A' + isize(gxcur.primes))
gxcur.current_prime_id = uni - 'A';
else if(uni == 'p')
nextPrime(gxcur);
else if(uni == 'x' || uni == '\n') dialog::do_if_confirmed([&gxcur] {
set_geometry(gxcur.base);
enableFieldChange();
set_geometry(gFieldQuotient);
start_game();
});
else if(uni == 'c') dialog::do_if_confirmed([] {
set_geometry(gEuclid);
fieldpattern::quotient_field_changed = false;
set_geometry(gFieldQuotient);
start_game();
});
else if(doexiton(sym, uni))
popScreen();
};
dialog::display();
}
#endif
@ -1111,6 +1136,11 @@ int read_geom_args() {
enableFieldChange();
set_geometry(gFieldQuotient);
}
else if(argis("-triplet")) {
stop_game();
shift(); fieldpattern::triplet_id = argi();
fieldpattern::enableFieldChange();
}
else if(argis("-to-fq")) {
cgi.require_basics();
int p = 2;