move headers to tc directory.

include/tc/groups.h

@@ -0,0 +1,92 @@
+#pragma once
+
+#include <array>
+#include <vector>
+
+namespace tc {
+    struct Rel {
+        std::array<int, 2> gens;
+        int mult;
+    };
+
+    /**
+     * A presentation of a coxeter group. Contains a number of generators and some relations of the form (ab)^n = e
+     */
+    struct Group {
+        const int ngens;
+        std::vector<std::vector<int>> _mults;  // lookup table for multiplicities
+        std::string name;
+
+        explicit Group(int ngens, const std::vector<Rel> &rels = {}, std::string name = "G");
+
+        void setmult(Rel rel);
+
+        [[nodiscard]] std::vector<Rel> get_rels() const;
+
+        [[nodiscard]] Group product(const Group &other) const;
+
+        [[nodiscard]] Group power(int p) const;
+    };
+
+    Group operator*(const Group &g, const Group &h);
+
+    Group operator^(const Group &g, const int &p);
+
+    /**
+     * 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);
+    }
+}