add bound to support for infinite groups and free relations

special values tc::UNBOUND and tc::FREE used for this.

tc/bench/benchmark.cpp

@@ -10,19 +10,26 @@
 
 #define NAMED(x) #x, x
 
-void bench(std::string group_expr, tc::Group group, const std::vector<tc::Gen> &gens) {
+void bench(
+    std::string group_expr,
+    const tc::Group &group,
+    const std::vector<tc::Gen> &gens,
+    const tc::Coset bound = tc::UNBOUNDED
+) {
     std::clock_t s = std::clock();
-    tc::Cosets cosets = tc::solve(group, gens);
+    tc::Cosets cosets = tc::solve(group, gens, bound);
     std::clock_t e = std::clock();
 
-    double time = (double) (e - s) / CLOCKS_PER_SEC;
+    auto time = (double) (e - s) / CLOCKS_PER_SEC;
     tc::Coset order = cosets.size();
-    size_t cos_s = (size_t) (order / time);
+    auto cos_s = (size_t) (order / time);
+
+    bool complete = cosets.complete;
 
     std::string name = fmt::format("{}/{}", group_expr, gens);
     std::string row = fmt::format(
-        "{:>24},{:>10},{:>8.3f}s,{:>10L}",
-        name, order, time, cos_s
+        "{:>24},{:>10},{:>6},{:>8.3f}s,{:>10L}",
+        name, order, complete, time, cos_s
     );
     fmt::print("{}\n", row);
 }
@@ -40,6 +47,11 @@ int main(int argc, char *argv[]) {
 
     fmt::print("{:>24},{:>10},{:>9},{:>10}\n", "NAME", "ORDER", "TIME", "COS/S");
 
+    auto g = tc::group::A(4);
+    g.set(tc::Rel{0, 3, 3});
+    bench("~A(3)", g, {}, 4385964);
+    bench("~I(1)", sch(tc::FREE), {}, 4385964);
+
     bench(NAMED(H(2)), {});
     bench(NAMED(H(3)), {});
     bench(NAMED(H(4)), {});

tc/include/tc/core.hpp

@@ -10,5 +10,7 @@
 #include "group.hpp"
 
 namespace tc {
-    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens);
+    constexpr Coset UNBOUNDED = (Coset) (-1);
+
+    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens, const Coset &bound = UNBOUNDED);
 }

tc/include/tc/cosets.hpp

@@ -8,15 +8,16 @@ namespace tc {
     using Coset = uint32_t;
     using Gen = uint8_t;
     using Mult = uint16_t;
+    constexpr Mult FREE = Mult(-1);
+    constexpr Coset UNSET = Coset(-1);
 
     using Rel = std::tuple<Gen, Gen, Mult>;
 
     struct Cosets {
-        const Coset UNSET = Coset(-1);
-
         Gen ngens;
         std::vector<int> data;
         Path path;
+        bool complete = false;
 
         Cosets(const Cosets &) = default;
 

tc/include/tc/group.hpp

@@ -8,6 +8,23 @@ namespace tc {
     struct Group;
     struct SubGroup;
 
+    /** 
+     * @brief Manage the presentation of a Coxeter group and enforce constraints
+     * on the multiplicities of its relations.
+     * <ul>
+     *   <li>
+     *     <code>m_ij = 1</code> iff <code>i != j</code>
+     *   </li>
+     *   <li>
+     *     <code>m_ij = m_ji</code>
+     *   </li>
+     *   <li>
+     *     If <code>m_ij == inf</code> (<code>tc::FREE</code>) then no relation is imposed.
+     *   </li>
+     * </ul>
+     * @see
+     * <a href="https://en.wikipedia.org/wiki/Coxeter_group#Definition">Coxeter Group (Wikipedia)</a>
+     */
     struct Group {
         int ngens;
         tc::pair_map<int> _mults;
@@ -17,6 +34,10 @@ namespace tc {
         explicit Group(int ngens, const std::vector<Rel> &rels = {})
             : ngens(ngens), _mults(ngens, 2) {
 
+            for (int i = 0; i < ngens; ++i) {
+                set(Rel{i, i, 1});
+            }
+            
             for (const auto &rel: rels) {
                 set(rel);
             }
@@ -24,6 +45,9 @@ namespace tc {
 
         void set(const Rel &r) {
             auto &[i, j, m] = r;
+            if (i == j && m != 1) {
+                throw std::runtime_error("Coxeter groups must satisfy m_ii=1.");
+            }
             _mults(i, j) = m;
         }
 
@@ -31,16 +55,6 @@ namespace tc {
             return _mults(i, j);
         }
 
-        [[nodiscard]] std::vector<Rel> rels() const {
-            std::vector<Rel> res;
-            for (int i = 0; i < ngens - 1; ++i) {
-                for (int j = i + 1; j < ngens; ++j) {
-                    res.emplace_back(i, j, get(i, j));
-                }
-            }
-            return res;
-        }
-
         [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
     };
 

tc/src/core.cpp

@@ -40,7 +40,7 @@ namespace tc {
         }
     };
 
-    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens) {
+    Cosets solve(const Group &group, const std::vector<Gen> &sub_gens, const Coset &bound) {
         auto ngens = group.ngens;
 
         // region Initialize Cosets Table
@@ -48,6 +48,7 @@ namespace tc {
         cosets.add_row();
 
         if (ngens == 0) {
+            cosets.complete = true;
             return cosets;
         }
 
@@ -57,9 +58,22 @@ namespace tc {
         }
         // endregion
 
-        auto rels = group.rels();
-
         // region Initialize Relation Tables
+        std::vector<std::tuple<Gen, Gen, Mult>> rels;
+        for (const auto &[i, j, m]: group._mults) {
+            // The algorithm only works for Coxeter groups; multiplicities m_ii=1 are assumed. Relation tables
+            // _may_ be added for them, but they are redundant and hurt performance so are skipped.
+            if (i == j) continue;
+
+            // Coxeter groups admit infinite multiplicities, represented by contexpr tc::FREE. Relation tables
+            // for these should be skipped.
+            if (m == FREE) {
+                continue;
+            }
+
+            rels.emplace_back(i, j, m);
+        }
+
         Tables rel_tables(rels);
         std::vector<std::vector<size_t>> tables_for(ngens);
         int rel_idx = 0;
@@ -97,6 +111,10 @@ namespace tc {
             while (idx < cosets.data.size() and cosets.isset(idx))
                 idx++;
 
+            if (cosets.size() >= bound) {
+                return cosets;
+            }
+
             // if there are none, then return
             if (idx == cosets.data.size()) {
                 // todo unrolled linked list interval
@@ -191,6 +209,7 @@ namespace tc {
             }
         }
 
+        cosets.complete = true;
         return cosets;
     }
 }