clifford.h

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/*
 *  GiNaC Copyright (C) 1999-2026 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, see <https://www.gnu.org/licenses/>.
 */
 
#ifndef GINAC_CLIFFORD_H
#define GINAC_CLIFFORD_H
 
#include "indexed.h"
#include "tensor.h"
#include "symbol.h"
#include "idx.h"
 
#include <set>
 
namespace GiNaC {
 
class clifford : public indexed
{
    GINAC_DECLARE_REGISTERED_CLASS(clifford, indexed)
    // other constructors
public:
    clifford(const ex & b, unsigned char rl = 0);
    clifford(const ex & b, const ex & mu,  const ex & metr, unsigned char rl = 0, int comm_sign = -1);
 
    // internal constructors
    clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v);
    clifford(unsigned char rl, const ex & metr, int comm_sign, exvector && v);
 
    // functions overriding virtual functions from base classes
public:
    unsigned precedence() const override { return 65; }
    void archive(archive_node& n) const override;
    void read_archive(const archive_node& n, lst& sym_lst) override;
protected:
    ex eval_ncmul(const exvector & v) const override;
    bool match_same_type(const basic & other) const override;
    ex thiscontainer(const exvector & v) const override;
    ex thiscontainer(exvector && v) const override;
    unsigned return_type() const override { return return_types::noncommutative; }
    return_type_t return_type_tinfo() const override;
    // non-virtual functions in this class
public:
    unsigned char get_representation_label() const { return representation_label; }
    ex get_metric() const { return metric; }
    virtual ex get_metric(const ex & i, const ex & j, bool symmetrised = false) const;
    bool same_metric(const ex & other) const;
    int get_commutator_sign() const { return commutator_sign; } //**< See the member variable commutator_sign */
 
    inline size_t nops() const override {return inherited::nops() + 1; }
    ex op(size_t i) const override;
    ex & let_op(size_t i) override;
    ex subs(const exmap & m, unsigned options = 0) const override;
 
protected:
    void do_print_dflt(const print_dflt & c, unsigned level) const;
    void do_print_latex(const print_latex & c, unsigned level) const;
    void do_print_tree(const print_tree & c, unsigned level) const;
 
    // member variables
protected:
    unsigned char representation_label; 
    ex metric; 
    int commutator_sign; 
};
GINAC_DECLARE_UNARCHIVER(clifford); 
 
class diracone : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(diracone, tensor)
 
    // 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(diracone);
 
 
class cliffordunit : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor)
 
    // functions overriding virtual functions from base classes
public:
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
 
    // 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(cliffordunit);
 
 
class diracgamma : public cliffordunit
{
    GINAC_DECLARE_REGISTERED_CLASS(diracgamma, cliffordunit)
 
    // functions overriding virtual functions from base classes
public:
    bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const override;
 
    // 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(diracgamma);
 
 
class diracgamma5 : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(diracgamma5, tensor)
 
    // functions overriding virtual functions from base classes
    ex conjugate() const override;
 
    // 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(diracgamma5);
 
 
class diracgammaL : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(diracgammaL, tensor)
 
    // functions overriding virtual functions from base classes
    ex conjugate() const override;
 
    // 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(diracgammaL);
 
 
class diracgammaR : public tensor
{
    GINAC_DECLARE_REGISTERED_CLASS(diracgammaR, tensor)
 
    // functions overriding virtual functions from base classes
    ex conjugate() const override;
 
    // 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(diracgammaR);
 
 
// global functions
 
inline bool is_clifford_tinfo(const return_type_t& ti)
{
    return *(ti.tinfo) == typeid(clifford);
}
 
ex dirac_ONE(unsigned char rl = 0);
 
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);
 
ex dirac_gamma(const ex & mu, unsigned char rl = 0);
 
ex dirac_gamma5(unsigned char rl = 0);
 
ex dirac_gammaL(unsigned char rl = 0);
 
ex dirac_gammaR(unsigned char rl = 0);
 
ex dirac_slash(const ex & e, const ex & dim, unsigned char rl = 0);
 
ex dirac_trace(const ex & e, const std::set<unsigned char> & rls, const ex & trONE = 4);
 
ex dirac_trace(const ex & e, const lst & rll, const ex & trONE = 4);
 
ex dirac_trace(const ex & e, unsigned char rl = 0, const ex & trONE = 4);
 
ex canonicalize_clifford(const ex & e);
 
ex clifford_prime(const ex & e);
 
ex clifford_star_bar(const ex & e, bool do_bar, unsigned options);
 
inline ex clifford_bar(const ex & e) { return clifford_star_bar(e, true, 0); }
 
inline ex clifford_star(const ex & e) { return clifford_star_bar(e, false, 0); }
 
ex remove_dirac_ONE(const ex & e, unsigned char rl = 0, unsigned options = 0);
 
int clifford_max_label(const ex & e, bool ignore_ONE = false);
 
ex clifford_norm(const ex & e);
 
ex clifford_inverse(const ex & e);
 
ex lst_to_clifford(const ex & v, const ex & mu,  const ex & metr, unsigned char rl = 0);
 
ex lst_to_clifford(const ex & v, const ex & e);
 
lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true);
 
ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl = 0);
 
ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0);
 
} // namespace GiNaC
 
#endif // ndef GINAC_CLIFFORD_H