real_polyhedral_homotopy_continuation/reference/include/function_tree/symbols/differential.hpp

// This file is part of Bertini 2.
//
// differential.hpp is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
//(at your option) any later version.
//
// differential.hpp is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with differential.hpp.  If not, see <http://www.gnu.org/licenses/>.
//
//  Copyright(C) 2015 - 2021 by Bertini2 Development Team
//
//  See <http://www.gnu.org/licenses/> for a copy of the license,
//  as well as COPYING.  Bertini2 is provided with permitted
//  additional terms in the b2/licenses/ directory.

// individual authors of this file include:
//  James Collins
//  West Texas A&M University
//  Spring, Summer 2015
//
// silviana amethyst, university of wisconsin-eau claire
//
//  Created by Collins, James B. on 4/30/15.
//
//
// differential.hpp:  Declares the class SpecialNumber.

/**
\file differential.hpp

\brief Provides the differential Node class.

*/

#ifndef BERTINI_NODE_DIFFERENTIAL_HPP
#define BERTINI_NODE_DIFFERENTIAL_HPP

#include <memory>

#include "function_tree/node.hpp"
#include "function_tree/symbols/number.hpp"
#include "function_tree/symbols/symbol.hpp"

namespace bertini {
namespace node {
class Variable;

/**
\brief Provides the differential type for differentiation of expression trees.

This class represents differentials.  These are produced in the course of
differentiation of a non-constant expression tree.
*/
class Differential : public virtual NamedSymbol,
                     public virtual EnableSharedFromThisVirtual<Differential> {
 public:
  BERTINI_DEFAULT_VISITABLE()

  template <typename... Ts>
  static std::shared_ptr<Differential> Make(Ts&&... ts) {
    return std::shared_ptr<Differential>(new Differential(ts...));
  }

 private:
  /**
   Input shared_ptr to a Variable.
   */
  Differential(std::shared_ptr<const Variable> diff_variable,
               std::string var_name);

 public:
  void Reset() const override;

  const std::shared_ptr<const Variable>& GetVariable() const;

  void print(std::ostream& target) const override;

  /**
   Differentiates a number.
   */
  std::shared_ptr<Node> Differentiate(
      std::shared_ptr<Variable> const& v = nullptr) const override;

  virtual ~Differential() = default;

  /**
  Compute the degree with respect to a single variable.   For differentials, the
  degree is 0.
  */
  int Degree(std::shared_ptr<Variable> const& v = nullptr) const override;

  int Degree(VariableGroup const& vars) const override;

  std::vector<int> MultiDegree(VariableGroup const& vars) const override;

  void Homogenize(VariableGroup const& vars,
                  std::shared_ptr<Variable> const& homvar) override;

  bool IsHomogeneous(
      std::shared_ptr<Variable> const& v = nullptr) const override;

  /**
  Check for homogeneity, with respect to a variable group.
  */
  bool IsHomogeneous(VariableGroup const& vars) const override;

  /**
   Change the precision of this variable-precision tree node.

   \param prec the number of digits to change precision to.
   */
  void precision(unsigned int prec) const override;

 protected:
  // This should never be called for a Differential.  Only for Jacobians.
  dbl FreshEval_d(
      std::shared_ptr<Variable> const& diff_variable) const override;

  void FreshEval_d(
      dbl& evaluation_value,
      std::shared_ptr<Variable> const& diff_variable) const override;

  mpfr_complex FreshEval_mp(
      std::shared_ptr<Variable> const& diff_variable) const override;

  void FreshEval_mp(
      mpfr_complex& evaluation_value,
      std::shared_ptr<Variable> const& diff_variable) const override;

 private:
  Differential() = default;
  std::shared_ptr<const Variable> differential_variable_;

  friend class boost::serialization::access;

  template <class Archive>
  void save(Archive& ar, const unsigned int version) const {
    ar& boost::serialization::base_object<NamedSymbol>(*this);
    ar & differential_variable_;
    // ar & const_cast<std::shared_ptr<const Variable>
    // >(differential_variable_);
  }

  template <class Archive>
  void load(Archive& ar, const unsigned int version) {
    ar& boost::serialization::base_object<NamedSymbol>(*this);
    ar& std::const_pointer_cast<Variable>(differential_variable_);
  }

  // BOOST_SERIALIZATION_SPLIT_MEMBER()
};

}  // namespace node
}  // namespace bertini

#endif