WIP: Copy tc logic from toddcox-faster

tc/include/tc/core.hpp

@@ -0,0 +1,165 @@
+#pragma once
+
+#include <array>
+#include <functional>
+#include <vector>
+#include <string>
+
+namespace tc {
+    struct Action {
+        int from_idx = -1;
+        int gen = -1;
+
+        Action() = default;
+
+        Action(const Action &) = default;
+
+        Action(int from_idx, int gen);
+    };
+
+    struct Path {
+        std::vector<Action> path;
+
+        Path() = default;
+
+        Path(const Path &) = default;
+
+        void add_row();
+
+        [[nodiscard]] Action get(int to_idx) const;
+
+        void put(int from_idx, int gen, int to_idx);
+
+        template<class C, class T, class E>
+        void walk(
+            C& res,
+            T start,
+            std::vector<E> gens,
+            std::function<T(const T &, const E &)> op
+        ) const {
+            size_t s = size();
+            res.reserve(s);
+            res.push_back(start);
+
+            for (int i = 1; i < s; ++i) {
+                auto &action = path[i];
+                auto &from = res.get(action.from_idx);
+                auto &val = gens[action.gen];
+                res.push_back(op(from,val));
+            }
+        }
+
+        template<class T, class E>
+        [[nodiscard]] std::vector<T> walk(
+            T start,
+            std::vector<E> gens,
+            std::function<T(const T &, const E &)> op
+        ) const {
+            std::vector<T> res;
+            res.reserve(size());
+            res.push_back(start);
+
+            for (int i = 1; i < size(); ++i) {
+                auto &action = path[i];
+                auto &from = res[action.from_idx];
+                auto &val = gens[action.gen];
+                res.push_back(op(from, val));
+            }
+
+            return res;
+        }
+
+        template<class T>
+        [[nodiscard]] std::vector<T> walk(
+            T start,
+            std::function<T(const T &, const int &)> op
+        ) const {
+            std::vector<T> res;
+            res.reserve(size());
+            res.push_back(start);
+
+            for (int i = 1; i < size(); ++i) {
+                auto &action = path[i];
+                auto &from = res[action.from_idx];
+                auto &val = action.gen;
+                res[i] = op(from, val);
+            }
+
+            return res;
+        }
+
+        [[nodiscard]] size_t size() const;
+    };
+
+    struct Cosets {
+        int ngens;
+        std::vector<int> data;
+        Path path;
+
+        Cosets(const Cosets &) = default;
+
+        explicit Cosets(int ngens);
+
+        void add_row();
+
+        void put(int coset, int gen, int target);
+
+        void put(int idx, int target);
+
+        [[nodiscard]] int get(int coset, int gen) const;
+
+        [[nodiscard]] int get(int idx) const;
+
+        [[nodiscard]] size_t size() const;
+    };
+
+    struct Rel {
+        std::array<int, 2> gens;
+        int mult;
+
+        Rel() = default;
+
+        Rel(const Rel &) = default;
+
+        Rel(int a, int b, int m);
+
+        [[nodiscard]] Rel shift(int off) const;
+    };
+
+    struct SubGroup;
+
+    struct Group {
+        int ngens;
+        std::vector<std::vector<int>> _mults;
+        std::string name;
+
+        Group(const Group &) = default;
+
+        explicit Group(int ngens, const std::vector<Rel> &rels = {}, std::string name = "G");
+
+        void set(const Rel &r);
+
+        [[nodiscard]] int get(int a, int b) const;
+
+        [[nodiscard]] std::vector<Rel> rels() const;
+
+        [[nodiscard]] SubGroup subgroup(const std::vector<int> &gens) const;
+
+        [[nodiscard]] Group product(const Group &other) const;
+
+        [[nodiscard]] Group power(int p) const;
+
+        [[nodiscard]] Cosets solve(const std::vector<int> &sub_gens = {}) const;
+    };
+
+    struct SubGroup : public Group {
+        std::vector<int> gen_map;
+        const Group &parent;
+
+        SubGroup(const Group &parent, std::vector<int> gen_map);
+    };
+
+    Group operator*(const Group &g, const Group &h);
+
+    Group operator^(const Group &g, int p);
+}

tc/include/tc/groups.hpp

@@ -0,0 +1,70 @@
+#pragma once
+
+#include "core.hpp"
+
+
+namespace tc {
+    /**
+     * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
+     * @param mults: The sequence of multiplicites between adjacent generators.
+     */
+    Group schlafli(const std::vector<int> &mults, const std::string &name);
+
+    /**
+     * Construct a group from a (simplified) Schlafli Symbol of the form [a, b, ..., c]
+     * @param mults: The sequence of multiplicites between adjacent generators.
+     */
+    Group schlafli(const std::vector<int> &mults);
+
+    namespace group {
+        /**
+         * Simplex
+         */
+        Group A(int dim);
+
+        /**
+         * Cube, Orthoplex
+         */
+        Group B(int dim);
+
+        /**
+         * Demicube, Orthoplex
+         */
+        Group D(int dim);
+
+        /**
+         * E groups
+         */
+        Group E(int dim);
+
+        /**
+         * 24 Cell
+         */
+        Group F4();
+
+        /**
+         * Hexagon
+         */
+        Group G2();
+
+        /**
+         * Icosahedron
+         */
+        Group H(int dim);
+
+        /**
+         * Polygonal
+         */
+        Group I2(int n);
+
+        /**
+         * Toroidal. I2(n) * I2(m)
+         */
+        Group T(int n, int m);
+
+        /**
+         * Toroidal. T(n, n)
+         */
+        Group T(int n);
+    }
+}