clifford.cpp File Reference

Implementation of GiNaC's clifford algebra (Dirac gamma) objects. More...

#include "clifford.h"
#include "ex.h"
#include "idx.h"
#include "ncmul.h"
#include "symbol.h"
#include "numeric.h"
#include "symmetry.h"
#include "lst.h"
#include "relational.h"
#include "operators.h"
#include "add.h"
#include "mul.h"
#include "power.h"
#include "matrix.h"
#include "archive.h"
#include "utils.h"
#include <stdexcept>

Go to the source code of this file.

Classes
struct	GiNaC::is_not_a_clifford
	Predicate for finding non-clifford objects. More...

Namespaces
namespace	GiNaC

Functions
	GiNaC::GINAC_IMPLEMENT_REGISTERED_CLASS_OPT (clifford, indexed, print_func< print_dflt >(&clifford::do_print_dflt). print_func< print_latex >(&clifford::do_print_latex). print_func< print_tree >(&clifford::do_print_tree)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone
	GiNaC::print_func< print_dflt > (&diracone::do_print). print_func< print_latex >(&diracone
	GiNaC::GINAC_BIND_UNARCHIVER (clifford)
	GiNaC::GINAC_BIND_UNARCHIVER (cliffordunit)
	GiNaC::GINAC_BIND_UNARCHIVER (diracone)
	GiNaC::GINAC_BIND_UNARCHIVER (diracgamma)
	GiNaC::GINAC_BIND_UNARCHIVER (diracgamma5)
	GiNaC::GINAC_BIND_UNARCHIVER (diracgammaL)
	GiNaC::GINAC_BIND_UNARCHIVER (diracgammaR)
static bool	GiNaC::is_dirac_slash (const ex &seq0)
static void	GiNaC::base_and_index (const ex &c, ex &b, ex &i)
	This function decomposes gamma~mu -> (1, mu) and a\ -> (a.ix, ix) More...
ex	GiNaC::dirac_ONE (unsigned char rl=0)
	Create a Clifford unity object. More...
static unsigned	GiNaC::get_dim_uint (const ex &e)
ex	GiNaC::clifford_unit (const ex &mu, const ex &metr, unsigned char rl=0)
	Create a Clifford unit object. More...
ex	GiNaC::dirac_gamma (const ex &mu, unsigned char rl=0)
	Create a Dirac gamma object. More...
ex	GiNaC::dirac_gamma5 (unsigned char rl=0)
	Create a Dirac gamma5 object. More...
ex	GiNaC::dirac_gammaL (unsigned char rl=0)
	Create a Dirac gammaL object. More...
ex	GiNaC::dirac_gammaR (unsigned char rl=0)
	Create a Dirac gammaR object. More...
ex	GiNaC::dirac_slash (const ex &e, const ex &dim, unsigned char rl=0)
	Create a term of the form e_mu * gamma~mu with a unique index mu. More...
static unsigned char	GiNaC::get_representation_label (const return_type_t &ti)
	Extract representation label from tinfo key (as returned by return_type_tinfo()). More...
static ex	GiNaC::trace_string (exvector::const_iterator ix, size_t num)
	Take trace of a string of an even number of Dirac gammas given a vector of indices. More...
ex	GiNaC::dirac_trace (const ex &e, const std::set< unsigned char > &rls, const ex &trONE=4)
	Calculate dirac traces over the specified set of representation labels. More...
ex	GiNaC::dirac_trace (const ex &e, const lst &rll, const ex &trONE=4)
	Calculate dirac traces over the specified list of representation labels. More...
ex	GiNaC::dirac_trace (const ex &e, unsigned char rl=0, const ex &trONE=4)
	Calculate the trace of an expression containing gamma objects with a specified representation label. More...
ex	GiNaC::canonicalize_clifford (const ex &e)
	Bring all products of clifford objects in an expression into a canonical order. More...
ex	GiNaC::clifford_star_bar (const ex &e, bool do_bar, unsigned options)
	An auxillary function performing clifford_star() and clifford_bar(). More...
ex	GiNaC::clifford_prime (const ex &e)
	Automorphism of the Clifford algebra, simply changes signs of all clifford units. More...
ex	GiNaC::remove_dirac_ONE (const ex &e, unsigned char rl=0, unsigned options=0)
	Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1. More...
int	GiNaC::clifford_max_label (const ex &e, bool ignore_ONE=false)
	Returns the maximal representation label of a clifford object if e contains at least one, otherwise returns -1. More...
ex	GiNaC::clifford_norm (const ex &e)
	Calculation of the norm in the Clifford algebra. More...
ex	GiNaC::clifford_inverse (const ex &e)
	Calculation of the inverse in the Clifford algebra. More...
ex	GiNaC::lst_to_clifford (const ex &v, const ex &mu, const ex &metr, unsigned char rl=0)
	List or vector conversion into the Clifford vector. More...
ex	GiNaC::lst_to_clifford (const ex &v, const ex &e)
	List or vector conversion into the Clifford vector. More...
static ex	GiNaC::get_clifford_comp (const ex &e, const ex &c, bool root=true)
	Auxiliary structure to define a function for striping one Clifford unit from vectors. More...
lst	GiNaC::clifford_to_lst (const ex &e, const ex &c, bool algebraic=true)
	An inverse function to lst_to_clifford(). More...
ex	GiNaC::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)
	Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix (a b\c d) in linear spaces with arbitrary signature. More...
ex	GiNaC::clifford_moebius_map (const ex &M, const ex &v, const ex &G, unsigned char rl=0)
	The second form of Moebius transformations defined by a 2x2 Clifford matrix M This function takes the transformation matrix M as a single entity. More...

Variables
	GiNaC::tensor

Detailed Description

Implementation of GiNaC's clifford algebra (Dirac gamma) objects.

Definition in file clifford.cpp.