/** @file clifford.cpp
 *
 *  Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */

/*
 *  GiNaC Copyright (C) 1999-2001 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include "clifford.h"
#include "ex.h"
#include "idx.h"
#include "ncmul.h"
#include "symbol.h"
#include "print.h"
#include "archive.h"
#include "debugmsg.h"
#include "utils.h"

#include <stdexcept>

namespace GiNaC {

GINAC_IMPLEMENT_REGISTERED_CLASS(clifford, indexed)
GINAC_IMPLEMENT_REGISTERED_CLASS(diracone, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma, tensor)
GINAC_IMPLEMENT_REGISTERED_CLASS(diracgamma5, tensor)

//////////
// default constructor, destructor, copy constructor assignment operator and helpers
//////////

clifford::clifford() : representation_label(0)
{
	debugmsg("clifford default constructor", LOGLEVEL_CONSTRUCT);
	tinfo_key = TINFO_clifford;
}

void clifford::copy(const clifford & other)
{
	inherited::copy(other);
	representation_label = other.representation_label;
}

DEFAULT_DESTROY(clifford)
DEFAULT_CTORS(diracone)
DEFAULT_CTORS(diracgamma)
DEFAULT_CTORS(diracgamma5)

//////////
// other constructors
//////////

/** Construct object without any indices. This constructor is for internal
 *  use only. Use the dirac_ONE() function instead.
 *  @see dirac_ONE */
clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
{
	debugmsg("clifford constructor from ex", LOGLEVEL_CONSTRUCT);
	tinfo_key = TINFO_clifford;
}

/** Construct object with one Lorentz index. This constructor is for internal
 *  use only. Use the dirac_gamma() function instead.
 *  @see dirac_gamma */
clifford::clifford(const ex & b, const ex & mu, unsigned char rl) : inherited(b, mu), representation_label(rl)
{
	debugmsg("clifford constructor from ex,ex", LOGLEVEL_CONSTRUCT);
	GINAC_ASSERT(is_ex_of_type(mu, varidx));
	tinfo_key = TINFO_clifford;
}

clifford::clifford(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
{
	debugmsg("clifford constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
	tinfo_key = TINFO_clifford;
}

clifford::clifford(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
{
	debugmsg("clifford constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
	tinfo_key = TINFO_clifford;
}

//////////
// archiving
//////////

clifford::clifford(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
	debugmsg("clifford constructor from archive_node", LOGLEVEL_CONSTRUCT);
	unsigned rl;
	n.find_unsigned("label", rl);
	representation_label = rl;
}

void clifford::archive(archive_node &n) const
{
	inherited::archive(n);
	n.add_unsigned("label", representation_label);
}

DEFAULT_UNARCHIVE(clifford)
DEFAULT_ARCHIVING(diracone)
DEFAULT_ARCHIVING(diracgamma)
DEFAULT_ARCHIVING(diracgamma5)

//////////
// functions overriding virtual functions from bases classes
//////////

int clifford::compare_same_type(const basic & other) const
{
	GINAC_ASSERT(other.tinfo() == TINFO_clifford);
	const clifford &o = static_cast<const clifford &>(other);

	if (representation_label != o.representation_label) {
		// different representation label
		return representation_label < o.representation_label ? -1 : 1;
	}

	return inherited::compare_same_type(other);
}

DEFAULT_COMPARE(diracone)
DEFAULT_COMPARE(diracgamma)
DEFAULT_COMPARE(diracgamma5)

DEFAULT_PRINT(diracone, "ONE")
DEFAULT_PRINT(diracgamma, "gamma")
DEFAULT_PRINT(diracgamma5, "gamma5")

/** Contraction of a gamma matrix with something else. */
bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
{
	GINAC_ASSERT(is_ex_of_type(*self, clifford));
	GINAC_ASSERT(is_ex_of_type(*other, indexed));
	GINAC_ASSERT(is_ex_of_type(self->op(0), diracgamma));
	unsigned char rl = ex_to_clifford(*self).get_representation_label();

	if (is_ex_of_type(other->op(0), diracgamma)) {

		ex dim = ex_to_idx(self->op(1)).get_dim();

		// gamma~mu*gamma.mu = dim*ONE
		if (other - self == 1) {
			*self = dim;
			*other = dirac_ONE(rl);
			return true;

		// gamma~mu*gamma~alpha*gamma.mu = (2-dim)*gamma~alpha
		} else if (other - self == 2
		        && is_ex_of_type(self[1], clifford)) {
			*self = 2 - dim;
			*other = _ex1();
			return true;

		// gamma~mu*gamma~alpha*gamma~beta*gamma.mu = 4*g~alpha~beta+(dim-4)*gamam~alpha*gamma~beta
		} else if (other - self == 3
		        && is_ex_of_type(self[1], clifford)
		        && is_ex_of_type(self[2], clifford)) {
			*self = 4 * metric_tensor(self[1].op(1), self[2].op(1)) * dirac_ONE(rl) + (dim - 4) * self[1] * self[2];
			self[1] = _ex1();
			self[2] = _ex1();
			*other = _ex1();
			return true;

		// gamma~mu*gamma~alpha*gamma~beta*gamma~delta*gamma.mu = -2*gamma~delta*gamma~beta*gamma~alpha+(4-dim)*gamma~alpha*gamma~beta*gamma~delta
		} else if (other - self == 4
		        && is_ex_of_type(self[1], clifford)
		        && is_ex_of_type(self[2], clifford)
		        && is_ex_of_type(self[3], clifford)) {
			*self = -2 * self[3] * self[2] * self[1] + (4 - dim) * self[1] * self[2] * self[3];
			self[1] = _ex1();
			self[2] = _ex1();
			self[3] = _ex1();
			*other = _ex1();
			return true;
		}
	}

	return false;
}

/** Perform automatic simplification on noncommutative product of clifford
 *  objects. This removes superfluous ONEs, permutes gamma5's to the front
 *  and removes squares of gamma objects. */
ex clifford::simplify_ncmul(const exvector & v) const
{
	exvector s;
	s.reserve(v.size());
	unsigned rl = ex_to_clifford(v[0]).get_representation_label();

	// Remove superfluous ONEs
	exvector::const_iterator cit = v.begin(), citend = v.end();
	while (cit != citend) {
		if (!is_ex_of_type(cit->op(0), diracone))
			s.push_back(*cit);
		cit++;
	}

	bool something_changed = false;
	int sign = 1;

	// Anticommute gamma5's to the front
	if (s.size() >= 2) {
		exvector::iterator first = s.begin(), next_to_last = s.end() - 2;
		while (true) {
			exvector::iterator it = next_to_last;
			while (true) {
				exvector::iterator it2 = it + 1;
				if (!is_ex_of_type(it->op(0), diracgamma5) && is_ex_of_type(it2->op(0), diracgamma5)) {
					it->swap(*it2);
					sign = -sign;
					something_changed = true;
				}
				if (it == first)
					break;
				it--;
			}
			if (next_to_last == first)
				break;
			next_to_last--;
		}
	}

	// Remove squares of gamma5
	while (s.size() >= 2 && is_ex_of_type(s[0].op(0), diracgamma5) && is_ex_of_type(s[1].op(0), diracgamma5)) {
		s.erase(s.begin(), s.begin() + 2);
		something_changed = true;
	}

	// Remove equal adjacent gammas
	if (s.size() >= 2) {
		exvector::iterator it = s.begin(), itend = s.end() - 1;
		while (it != itend) {
			ex & a = it[0];
			ex & b = it[1];
			if (is_ex_of_type(a.op(0), diracgamma) && is_ex_of_type(b.op(0), diracgamma)) {
				const ex & ia = a.op(1);
				const ex & ib = b.op(1);
				if (ia.is_equal(ib)) {
					a = lorentz_g(ia, ib);
					b = dirac_ONE(rl);
					something_changed = true;
				}
			}
			it++;
		}
	}

	if (s.size() == 0)
		return clifford(diracone(), rl) * sign;
	if (something_changed)
		return nonsimplified_ncmul(s) * sign;
	else
		return simplified_ncmul(s) * sign;
}

ex clifford::thisexprseq(const exvector & v) const
{
	return clifford(representation_label, v);
}

ex clifford::thisexprseq(exvector * vp) const
{
	return clifford(representation_label, vp);
}

//////////
// global functions
//////////

ex dirac_ONE(unsigned char rl)
{
	return clifford(diracone(), rl);
}

ex dirac_gamma(const ex & mu, unsigned char rl)
{
	if (!is_ex_of_type(mu, varidx))
		throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));

	return clifford(diracgamma(), mu, rl);
}

ex dirac_gamma5(unsigned char rl)
{
	return clifford(diracgamma5(), rl);
}

ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
{
	varidx mu((new symbol)->setflag(status_flags::dynallocated), dim);
	return indexed(e, mu.toggle_variance()) * dirac_gamma(mu, rl);
}

/** Check whether a given tinfo key (as returned by return_type_tinfo()
 *  is that of a clifford object with the specified representation label. */
static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
{
	return ti == (TINFO_clifford + rl);
}

ex dirac_trace(const ex & e, unsigned char rl)
{
	if (is_ex_of_type(e, clifford)) {

		if (ex_to_clifford(e).get_representation_label() == rl
		 && is_ex_of_type(e.op(0), diracone))
			return _ex4();
		else
			return _ex0();

	} else if (is_ex_exactly_of_type(e, add)) {

		// Trace of sum = sum of traces
		ex sum = _ex0();
		for (unsigned i=0; i<e.nops(); i++)
			sum += dirac_trace(e.op(i), rl);
		return sum;

	} else if (is_ex_exactly_of_type(e, mul)) {

		// Trace of product: pull out non-clifford factors
		ex prod = _ex1();
		for (unsigned i=0; i<e.nops(); i++) {
			const ex &o = e.op(i);
			unsigned ti = o.return_type_tinfo();
			if (is_clifford_tinfo(o.return_type_tinfo(), rl))
				prod *= dirac_trace(o, rl);
			else
				prod *= o;
		}
		return prod;

	} else if (is_ex_exactly_of_type(e, ncmul)) {

		if (!is_clifford_tinfo(e.return_type_tinfo(), rl))
			return _ex0();

		// Expand product, if necessary
		ex e_expanded = e.expand();
		if (!is_ex_of_type(e_expanded, ncmul))
			return dirac_trace(e_expanded, rl);

		// gamma5 gets moved to the front so this check is enough
		bool has_gamma5 = is_ex_of_type(e.op(0).op(0), diracgamma5);
		unsigned num = e.nops();

		if (has_gamma5) {

			// Trace of gamma5 * odd number of gammas and trace of
			// gamma5 * gamma_mu * gamma_nu are zero
			if ((num & 1) == 0 || num == 3)
				return _ex0();

			// Tr gamma5 S_2k =
			//   epsilon0123_mu1_mu2_mu3_mu4 * Tr gamma_mu1 gamma_mu2 gamma_mu3 gamma_mu4 S_2k
			ex dim = ex_to_idx(e.op(1).op(1)).get_dim();
			varidx mu1((new symbol)->setflag(status_flags::dynallocated), dim),
			       mu2((new symbol)->setflag(status_flags::dynallocated), dim),
			       mu3((new symbol)->setflag(status_flags::dynallocated), dim),
			       mu4((new symbol)->setflag(status_flags::dynallocated), dim);
			exvector v;
			v.reserve(num + 3);
			v.push_back(dirac_gamma(mu1, rl));
			v.push_back(dirac_gamma(mu2, rl));
			v.push_back(dirac_gamma(mu3, rl));
			v.push_back(dirac_gamma(mu4, rl));
			for (int i=1; i<num; i++)
				v.push_back(e.op(i));

			return (eps0123(mu1.toggle_variance(), mu2.toggle_variance(), mu3.toggle_variance(), mu4.toggle_variance()) *
			        dirac_trace(ncmul(v), rl)).simplify_indexed() / 24;

		} else { // no gamma5

			// Trace of odd number of gammas is zero
			if ((num & 1) == 1)
				return _ex0();

			// Tr gamma_mu gamma_nu = 4 g_mu_nu
			if (num == 2)
				return 4 * lorentz_g(e.op(0).op(1), e.op(1).op(1));

			// Traces of 4 or more gammas are computed recursively:
			// Tr gamma_mu1 gamma_mu2 ... gamma_mun =
			//   + eta_mu1_mu2 * Tr gamma_mu3 ... gamma_mun
			//   - eta_mu1_mu3 * Tr gamma_mu2 gamma_mu4 ... gamma_mun
			//   + eta_mu1_mu4 * Tr gamma_mu3 gamma_mu3 gamma_mu5 ... gamma_mun
			//   - ...
			//   + eta_mu1_mun * Tr gamma_mu2 ... gamma_mu(n-1)
			exvector v(num - 2);
			int sign = 1;
			const ex &ix1 = e.op(0).op(1);
			ex result;
			for (int i=1; i<num; i++) {
				for (int n=1, j=0; n<num; n++) {
					if (n == i)
						continue;
					v[j++] = e.op(n);
				}
				result += sign * lorentz_g(ix1, e.op(i).op(1)) * dirac_trace(ncmul(v), rl);
				sign = -sign;
			}
			return result;
		}
	}

	return _ex0();
}

} // namespace GiNaC