Added the files from the coxeter branch

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diff --git a/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h b/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h
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+++ b/src/Coxeter_triangulation/include/gudhi/Functions/Function_Sm_in_Rd.h
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+/*    This file is part of the Gudhi Library. The Gudhi library
+ *    (Geometric Understanding in Higher Dimensions) is a generic C++
+ *    library for computational topology.
+ *
+ *    Author(s):       Siargey Kachanovich
+ *
+ *    Copyright (C) 2019 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#ifndef FUNCTIONS_FUNCTION_SM_IN_RD_H_
+#define FUNCTIONS_FUNCTION_SM_IN_RD_H_
+
+#include <gudhi/Functions/Function.h>
+#include <Eigen/Dense>
+
+namespace Gudhi {
+
+namespace coxeter_triangulation {
+
+/** 
+ * \class Function_Sm_in_Rd 
+ * \brief A class for the function that defines an m-dimensional implicit sphere embedded
+ * in the d-dimensional Euclidean space.
+ *
+ * \ingroup coxeter_triangulation
+ */
+struct Function_Sm_in_Rd: public Function {
+
+/** \brief Value of the function at a specified point.
+ * @param[in] p The input point. The dimension needs to coincide with the ambient dimension.
+ */
+  Eigen::VectorXd operator()(const Eigen::VectorXd& p) const {
+    Eigen::VectorXd x = p;
+    for (std::size_t i = 0; i < d_; ++i)
+      x(i) -= center_[i];
+    Eigen::VectorXd result = Eigen::VectorXd::Zero(k_); 
+    for (std::size_t i = 0; i < m_+1; ++i)
+      result(0) += x(i)*x(i);
+    result(0) -= r_*r_;
+    for (std::size_t j = 1; j < k_; ++j)
+      result(j) = x(m_+j);
+    return result;
+  }
+  
+  /** \brief Returns the domain dimension. Same as the ambient dimension of the sphere. */
+  std::size_t amb_d() const {return d_;};
+
+  /** \brief Returns the codomain dimension. Same as the codimension of the sphere. */
+  std::size_t cod_d() const {return k_;};
+
+  /** \brief Returns a point on the sphere. */
+  Eigen::VectorXd seed() const {
+    Eigen::VectorXd result = Eigen::VectorXd::Zero(d_);
+    result(0) += r_;
+    for (std::size_t i = 0; i < d_; ++i)
+      result(i) += center_[i];
+    return result;
+  }
+    
+  /** 
+   * \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
+   * in the d-dimensional Euclidean space.
+   *
+   * @param[in] r The radius of the sphere.
+   * @param[in] m The dimension of the sphere.
+   * @param[in] d The ambient dimension of the sphere.
+   * @param[in] center The center of the sphere.
+   */
+  Function_Sm_in_Rd(double r,
+		    std::size_t m,
+		    std::size_t d,
+		    Eigen::VectorXd center)
+    : m_(m), k_(d-m), d_(d), r_(r), center_(center) {}
+
+  /** 
+   * \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
+   * in the d-dimensional Euclidean space centered at the origin.
+   *
+   * @param[in] r The radius of the sphere.
+   * @param[in] m The dimension of the sphere.
+   * @param[in] d The ambient dimension of the sphere.
+   */
+  Function_Sm_in_Rd(double r,
+		    std::size_t m,
+		    std::size_t d)
+    : m_(m), k_(d-m), d_(d), r_(r), center_(Eigen::VectorXd::Zero(d_)) {}
+
+  
+  /** 
+   * \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
+   * in the (m+1)-dimensional Euclidean space.
+   *
+   * @param[in] r The radius of the sphere.
+   * @param[in] m The dimension of the sphere.
+   * @param[in] center The center of the sphere.
+   */
+  Function_Sm_in_Rd(double r,
+		    std::size_t m,
+		    Eigen::VectorXd center)
+    : m_(m), k_(1), d_(m_+1), r_(r), center_(center) {}
+
+  /** 
+   * \brief Constructor of the function that defines an m-dimensional implicit sphere embedded
+   * in the (m+1)-dimensional Euclidean space centered at the origin.
+   *
+   * @param[in] r The radius of the sphere.
+   * @param[in] m The dimension of the sphere.
+   */
+  Function_Sm_in_Rd(double r,
+		    std::size_t m)
+    : m_(m), k_(1), d_(m_+1), r_(r), center_(Eigen::VectorXd::Zero(d_)) {}
+
+  Function_Sm_in_Rd(const Function_Sm_in_Rd& rhs)
+    : Function_Sm_in_Rd(rhs.r_, rhs.m_, rhs.d_, rhs.center_) {}
+
+  
+protected:
+  std::size_t m_, k_, d_;
+  double r_;
+  Eigen::VectorXd center_;
+};
+
+} // namespace coxeter_triangulation
+
+} // namespace Gudhi
+
+
+#endif