tensor.h

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/*
 *  GiNaC Copyright (C) 1999-2023 Johannes Gutenberg University Mainz, Germany
 *
 *  This program 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 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program 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 this program; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#ifndef GINAC_TENSOR_H
#define GINAC_TENSOR_H
 
#include "ex.h"
#include "archive.h"
 
namespace GiNaC {
 
class tensor : public basic
{
    GINAC_DECLARE_REGISTERED_CLASS(tensor, basic)
 
    // functions overriding virtual functions from base classes
protected:
    unsigned return_type() const override { return return_types::noncommutative_composite; }
 
    // non-virtual functions in this class
public:
    bool replace_contr_index(exvector::iterator self, exvector::iterator other) const;
};
 
 
class tensdelta : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(tensdelta, tensor)
 
    // functions overriding virtual functions from base classes
public:
    bool info(unsigned inf) const override;
    ex eval_indexed(const basic & i) const override;
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
protected:
    unsigned return_type() const override { return return_types::commutative; }
 
    // non-virtual functions in this class
protected:
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
};
GINAC_DECLARE_UNARCHIVER(tensdelta);
 
 
class tensmetric : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(tensmetric, tensor)
 
    // functions overriding virtual functions from base classes
public:
    bool info(unsigned inf) const override;
    ex eval_indexed(const basic & i) const override;
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
protected:
    unsigned return_type() const override { return return_types::commutative; }
 
    // non-virtual functions in this class
protected:
    void do_print(const print_context & c, unsigned level) const;
};
GINAC_DECLARE_UNARCHIVER(tensmetric);
 
 
class minkmetric : public tensmetric
{
    GINAC_DECLARE_REGISTERED_CLASS(minkmetric, tensmetric)
 
    // other constructors
public:
    minkmetric(bool pos_sig);
 
    // functions overriding virtual functions from base classes
public:
    bool info(unsigned inf) const override;
    ex eval_indexed(const basic & i) const override;
 
    void archive(archive_node& n) const override;
    void read_archive(const archive_node& n, lst& syms) override;
protected:
    unsigned return_type() const override { return return_types::commutative; }
 
    // non-virtual functions in this class
protected:
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
 
    // member variables
private:
    bool pos_sig; 
};
GINAC_DECLARE_UNARCHIVER(minkmetric); 
 
 
class spinmetric : public tensmetric
{
    GINAC_DECLARE_REGISTERED_CLASS(spinmetric, tensmetric)
 
    // functions overriding virtual functions from base classes
public:
    bool info(unsigned inf) const override;
    ex eval_indexed(const basic & i) const override;
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
 
protected:
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
};
GINAC_DECLARE_UNARCHIVER(spinmetric);
 
 
class tensepsilon : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(tensepsilon, tensor)
 
    // other constructors
public:
    tensepsilon(bool minkowski, bool pos_sig);
 
    // functions overriding virtual functions from base classes
public:
    bool info(unsigned inf) const override;
    ex eval_indexed(const basic & i) const override;
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
 
    void archive(archive_node& n) const override;
    void read_archive(const archive_node& n, lst& syms) override;
protected:
    unsigned return_type() const override { return return_types::commutative; }
 
    // non-virtual functions in this class
protected:
    void do_print(const print_context & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
 
    // member variables
private:
    bool minkowski; 
    bool pos_sig;   
};
GINAC_DECLARE_UNARCHIVER(tensepsilon); 
 
 
// utility functions
 
ex delta_tensor(const ex & i1, const ex & i2);
 
ex metric_tensor(const ex & i1, const ex & i2);
 
ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig = false);
 
ex spinor_metric(const ex & i1, const ex & i2);
 
ex epsilon_tensor(const ex & i1, const ex & i2);
 
ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3);
 
ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig = false);
 
} // namespace GiNaC
 
#endif // ndef GINAC_TENSOR_H