1 files changed, 116 insertions, 0 deletions
diff --git a/euclidean.hpp b/euclidean.hpp
new file mode 100644
index 0000000..b1a5e80
--- /dev/null
+++ b/euclidean.hpp
@@ -0,0 +1,116 @@
+
+#pragma once
+
+#include "matrix.hpp"
+#include "spin.hpp"
+#include "vector.hpp"
+
+template <class T, int D> class Euclidean {
+public:
+  Vector<T, D> t;
+  Matrix<T, D> r;
+
+  Euclidean(T L) {
+    for (unsigned i = 0; i < D; i++) {
+      t(i) = 0;
+      r(i, i) = 1;
+      for (unsigned j = 1; j < D; j++) {
+        r(i, (i + j) % D) = 0;
+      }
+    }
+  }
+
+  Euclidean(Vector<T, D> t0, Matrix<T, D> r0) {
+    t = t0;
+    r = r0;
+  }
+
+  template <class S> Spin<T, D, S> act(const Spin<T, D, S>& s) const {
+    Spin<T, D, S> s_new;
+
+    s_new.x = t + r * s.x;
+    s_new.s = s.s;
+
+    return s_new;
+  }
+
+  Euclidean act(const Euclidean& x) const {
+    Vector<T, D> tnew = r * x.t + t;
+    Matrix<T, D> rnew = r * x.r;
+
+    Euclidean pnew(tnew, rnew);
+
+    return pnew;
+  }
+
+  Euclidean inverse() const {
+    Vector<T, D> tnew = -r.transpose() * t;
+    Matrix<T, D> rnew = r.transpose();
+
+    Euclidean pnew(tnew, rnew);
+
+    return pnew;
+  }
+};
+
+template <class T, int D> class TorusGroup {
+private:
+  T L;
+
+public:
+  Vector<T, D> t;
+  Matrix<T, D> r;
+
+  /** brief TorusGroup - default constructor, constructs the identity
+   */
+  TorusGroup(T L) : L(L) {
+    for (unsigned i = 0; i < D; i++) {
+      t(i) = 0;
+      r(i, i) = 1;
+      for (unsigned j = 1; j < D; j++) {
+        r(i, (i + j) % D) = 0;
+      }
+    }
+  }
+
+  TorusGroup(T L, Vector<T, D> t0, Matrix<T, D> r0) : L(L) {
+    t = t0;
+    r = r0;
+  }
+
+  template <class S> Spin<T, D, S> act(const Spin<T, D, S>& s) const {
+    Spin<T, D, S> s_new;
+
+    s_new.x = t + r * s.x;
+    s_new.s = s.s;
+
+    for (unsigned i = 0; i < D; i++) {
+      s_new.x(i) = fmod(L + s_new.x(i), L);
+    }
+
+    return s_new;
+  }
+
+  TorusGroup act(const TorusGroup& x) const {
+    Vector<T, D> tnew = r * x.t + t;
+    Matrix<T, D> rnew = r * x.r;
+
+    for (unsigned i = 0; i < D; i++) {
+      tnew(i) = fmod(L + tnew(i), L);
+    }
+
+    TorusGroup pnew(this->L, tnew, rnew);
+
+    return pnew;
+  }
+
+  TorusGroup inverse() const {
+    Vector<T, D> tnew = -r.transpose() * t;
+    Matrix<T, D> rnew = r.transpose();
+
+    TorusGroup pnew(this->L, tnew, rnew);
+
+    return pnew;
+  }
+};
+