X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.h;h=6b74a46874df441e0d4ed1f69bae94dd8bf223fd;hp=d68a18bfde1e6ac5706d936c5bc94f83ad731dda;hb=8fdf123fe6dac43ad7b8020d7bb7446c51cf75e7;hpb=b4631c1661b1945c85b3ea2e8ce1d3e58d1e6e79 diff --git a/ginac/clifford.h b/ginac/clifford.h index d68a18bf..6b74a468 100644 --- a/ginac/clifford.h +++ b/ginac/clifford.h @@ -3,7 +3,7 @@ * Interface to GiNaC's clifford algebra (Dirac gamma) objects. */ /* - * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2008 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 @@ -17,7 +17,7 @@ * * 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 + * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ #ifndef __GINAC_CLIFFORD_H__ @@ -41,43 +41,49 @@ 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); + 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, const exvector & v, bool discardable = false); - clifford(unsigned char rl, const ex & metr, std::auto_ptr vp); + 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 vp); // functions overriding virtual functions from base classes +public: + unsigned precedence() const { return 65; } 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 vp) const; unsigned return_type() const { return return_types::noncommutative; } - unsigned return_type_tinfo() const { return TINFO_clifford + representation_label; } - + 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; } - ex get_metric(const ex & i, const ex & j) const; + 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 -private: +protected: unsigned char representation_label; /**< Representation label to distinguish independent spin lines */ - ex metric; + ex metric; /**< Metric of the space, all constructors make it an indexed object */ + int commutator_sign; /**< It is the sign in the definition e~i e~j +/- e~j e~i = B(i, j) + B(j, i)*/ }; - /** This class represents the Clifford algebra unity element. */ class diracone : public tensor { @@ -95,10 +101,6 @@ class cliffordunit : public tensor { GINAC_DECLARE_REGISTERED_CLASS(cliffordunit, tensor) - // other constructors -protected: - cliffordunit(unsigned ti) : inherited(ti) {} - // functions overriding virtual functions from base classes public: bool contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const; @@ -176,10 +178,13 @@ protected: // global functions -/** Specialization of is_exactly_a(obj) for clifford objects. */ -template<> inline bool is_exactly_a(const basic & obj) +/** Check whether a given return_type_t object (as returned by return_type_tinfo() + * is that of a clifford object (with an arbitrary representation label). + * + * @param ti tinfo key */ +inline bool is_clifford_tinfo(const return_type_t& ti) { - return obj.tinfo()==TINFO_clifford; + return *(ti.tinfo) == typeid(clifford); } /** Create a Clifford unity object. @@ -191,7 +196,7 @@ ex dirac_ONE(unsigned char rl = 0); /** Create a Clifford unit object. * * @param mu Index (must be of class varidx or a derived class) - * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix) + * @param metr Metric (should be indexed, tensmetric or a derived class, or a matrix) * @param rl Representation label * @return newly constructed Clifford unit object */ ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0); @@ -275,8 +280,21 @@ inline ex clifford_bar(const ex & e) { return clifford_prime(e.conjugate()); } /** Reversion of the Clifford algebra, coincides with the conjugate(). */ inline ex clifford_star(const ex & e) { return e.conjugate(); } -/** Replaces all dirac_ONE's in e with 1 (effectively removing them). */ -ex remove_dirac_ONE(const ex & e); +/** Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1. + * For the default value rl = 0 remove all of them. Aborts if e contains any + * clifford_unit with representation_label to be removed. + * + * @param e Expression to be processed + * @param rl Value of representation label + * @param options Defines some internal use */ +ex remove_dirac_ONE(const ex & e, unsigned char rl = 0, unsigned options = 0); + +/** Returns the maximal representation label of a clifford object + * if e contains at least one, otherwise returns -1 + * + * @param e Expression to be processed + * @ignore_ONE defines if clifford_ONE should be ignored in the search*/ +char clifford_max_label(const ex & e, bool ignore_ONE = false); /** Calculation of the norm in the Clifford algebra. */ ex clifford_norm(const ex & e); @@ -288,10 +306,12 @@ ex clifford_inverse(const ex & e); * * @param v List or vector of coordinates * @param mu Index (must be of class varidx or a derived class) - * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix) + * @param metr Metric (should be indexed, tensmetric or a derived class, or a matrix) * @param rl Representation label + * @param e Clifford unit object * @return Clifford vector with given components */ 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); /** An inverse function to lst_to_clifford(). For given Clifford vector extracts * its components with respect to given Clifford unit. Obtained components may @@ -301,7 +321,8 @@ ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char * * @param e Clifford expression to be decomposed into components * @param c Clifford unit defining the metric for splitting (should have numeric dimension of indices) - * @param algebraic Use algebraic or symbolic algorithm for extractions */ + * @param algebraic Use algebraic or symbolic algorithm for extractions + * @return List of components of a Clifford vector*/ lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true); /** Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix @@ -315,8 +336,21 @@ lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true); * @param c (2,1) entry of the defining matrix * @param d (2,2) entry of the defining matrix * @param v Vector to be transformed - * @param G Metric of the surrounding space */ -ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G); + * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored + * @param rl Representation label + * @return List of components of the transformed vector*/ +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); + +/** The second form of Moebius transformations defined by a 2x2 Clifford matrix M + * This function takes the transformation matrix M as a single entity. + * + * @param M the defining matrix + * @param v Vector to be transformed + * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored + * @param rl Representation label + * @return List of components of the transformed vector*/ +ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl = 0); + } // namespace GiNaC #endif // ndef __GINAC_CLIFFORD_H__