From 6e942e98f5629bc0659b9564dec4dbf29db4fb98 Mon Sep 17 00:00:00 2001
From: Zeno Rogue <zeno@attnam.com>
Date: Mon, 8 Mar 2021 13:30:55 +0100
Subject: [PATCH] fieldpattern:: now can work with triplets

---
 fieldpattern.cpp | 106 +++++++++++++++++++++++++++++++++++++++++++++++
 geom-exp.cpp     |  80 ++++++++++++++++++++++++-----------
 2 files changed, 161 insertions(+), 25 deletions(-)

diff --git a/fieldpattern.cpp b/fieldpattern.cpp
index c3ae3551..31c5b192 100644
--- a/fieldpattern.cpp
+++ b/fieldpattern.cpp
@@ -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;
diff --git a/geom-exp.cpp b/geom-exp.cpp
index 5d7c4c6a..43a25481 100644
--- a/geom-exp.cpp
+++ b/geom-exp.cpp
@@ -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;