clifford.h

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/*
 *  GiNaC Copyright (C) 1999-2011 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_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, bool discardable = false);
    clifford(unsigned char rl, const ex & metr, int comm_sign, std::auto_ptr<exvector> vp);

    // functions overriding virtual functions from base classes
public:
    unsigned precedence() const { return 65; }
    void archive(archive_node& n) const;
    void read_archive(const archive_node& n, lst& sym_lst);
protected:
    ex eval_ncmul(const exvector & v) const;
    bool match_same_type(const basic & other) const;
    ex thiscontainer(const exvector & v) const;
    ex thiscontainer(std::auto_ptr<exvector> vp) const;
    unsigned return_type() const { return return_types::noncommutative; }
    return_type_t return_type_tinfo() const;
    // 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 {return inherited::nops() + 1; }
    ex op(size_t i) const;
    ex & let_op(size_t i);
    ex subs(const exmap & m, unsigned options = 0) const;

protected:
    void do_print_dflt(const print_dflt & c, unsigned level) const;
    void do_print_latex(const print_latex & 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;

    // 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;
};


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;

    // 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;

    // 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;

    // 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;

    // 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);

inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); }

inline ex clifford_star(const ex & e) { return e.conjugate(); }

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