X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=d70f0f508706f3a8600b4abb6bfb6e4782204595;hp=af54d77bbcb665ef7478c6dfd300c2d4aa4dd109;hb=f30ea8e711499ac166c4cd54357a4bc6f5e7264c;hpb=f303227c240827857e2fb0631c537f553a9845e2 diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index af54d77b..d70f0f50 100644 --- a/ginac/clifford.cpp +++ b/ginac/clifford.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */ /* - * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2010 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 @@ -20,8 +20,6 @@ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA */ -#include - #include "clifford.h" #include "ex.h" @@ -40,14 +38,14 @@ #include "archive.h" #include "utils.h" +#include + namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(clifford, indexed, print_func(&clifford::do_print_dflt). print_func(&clifford::do_print_latex)) -const tinfo_static_t clifford::return_type_tinfo_static[256] = {{}}; - GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone, tensor, print_func(&diracone::do_print). print_func(&diracone::do_print_latex)) @@ -78,7 +76,6 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracgammaR, tensor, clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1) { - tinfo_key = &clifford::tinfo_static; } DEFAULT_CTOR(diracone) @@ -97,7 +94,6 @@ DEFAULT_CTOR(diracgammaR) * @see dirac_ONE */ clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1) { - tinfo_key = &clifford::tinfo_static; } /** Construct object with one Lorentz index. This constructor is for internal @@ -107,25 +103,28 @@ clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representatio clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl, int comm_sign) : inherited(b, mu), representation_label(rl), metric(metr), commutator_sign(comm_sign) { GINAC_ASSERT(is_a(mu)); - tinfo_key = &clifford::tinfo_static; } clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = &clifford::tinfo_static; } clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, std::auto_ptr vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = &clifford::tinfo_static; +} + +return_type_t clifford::return_type_tinfo() const +{ + return make_return_type_t(representation_label); } ////////// // archiving ////////// -clifford::clifford(const archive_node & n, lst & sym_lst) : inherited(n, sym_lst) +void clifford::read_archive(const archive_node& n, lst& sym_lst) { + inherited::read_archive(n, sym_lst); unsigned rl; n.find_unsigned("label", rl); representation_label = rl; @@ -142,13 +141,12 @@ void clifford::archive(archive_node & n) const n.add_unsigned("commutator_sign+1", commutator_sign+1); } -DEFAULT_UNARCHIVE(clifford) -DEFAULT_ARCHIVING(diracone) -DEFAULT_ARCHIVING(cliffordunit) -DEFAULT_ARCHIVING(diracgamma) -DEFAULT_ARCHIVING(diracgamma5) -DEFAULT_ARCHIVING(diracgammaL) -DEFAULT_ARCHIVING(diracgammaR) +GINAC_BIND_UNARCHIVER(clifford); +GINAC_BIND_UNARCHIVER(diracone); +GINAC_BIND_UNARCHIVER(diracgamma); +GINAC_BIND_UNARCHIVER(diracgamma5); +GINAC_BIND_UNARCHIVER(diracgammaL); +GINAC_BIND_UNARCHIVER(diracgammaR); ex clifford::get_metric(const ex & i, const ex & j, bool symmetrised) const @@ -265,8 +263,21 @@ void clifford::do_print_dflt(const print_dflt & c, unsigned level) const if (is_dirac_slash(seq[0])) { seq[0].print(c, precedence()); c.s << "\\"; - } else - this->print_dispatch(c, level); + } else { // We do not print representation label if it is 0 + if (representation_label == 0) { + this->print_dispatch(c, level); + } else { // otherwise we put it before indices in square brackets; the code is borrowed from indexed.cpp + if (precedence() <= level) { + c.s << '('; + } + seq[0].print(c, precedence()); + c.s << '[' << int(representation_label) << ']'; + printindices(c, level); + if (precedence() <= level) { + c.s << ')'; + } + } + } } void clifford::do_print_latex(const print_latex & c, unsigned level) const @@ -703,28 +714,42 @@ ex dirac_ONE(unsigned char rl) return clifford(ONE, rl); } +static unsigned get_dim_uint(const ex& e) +{ + if (!is_a(e)) + throw std::invalid_argument("get_dim_uint: argument is not an index"); + ex dim = ex_to(e).get_dim(); + if (!dim.info(info_flags::posint)) + throw std::invalid_argument("get_dim_uint: dimension of index should be a positive integer"); + unsigned d = ex_to(dim).to_int(); + return d; +} + ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl) { - static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated); + //static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated); + ex unit = (new cliffordunit)->setflag(status_flags::dynallocated); if (!is_a(mu)) throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx")); exvector indices = metr.get_free_indices(); - if ((indices.size() == 2) && is_a(indices[0]) && is_a(indices[1])) { + if (indices.size() == 2) { return clifford(unit, mu, metr, rl); } else if (is_a(metr)) { matrix M = ex_to(metr); unsigned n = M.rows(); bool symmetric = true; - static varidx xi((new symbol)->setflag(status_flags::dynallocated), n), + //static idx xi((new symbol)->setflag(status_flags::dynallocated), n), + // chi((new symbol)->setflag(status_flags::dynallocated), n); + idx xi((new symbol)->setflag(status_flags::dynallocated), n), chi((new symbol)->setflag(status_flags::dynallocated), n); - if ((n == M.cols()) && (n == ex_to(mu).get_dim())) { + if ((n == M.cols()) && (n == get_dim_uint(mu))) { for (unsigned i = 0; i < n; i++) { for (unsigned j = i+1; j < n; j++) { - if (M(i, j) != M(j, i)) { + if (!M(i, j).is_equal(M(j, i))) { symmetric = false; } } @@ -734,8 +759,10 @@ ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl) throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index")); } } else if (indices.size() == 0) { // a tensor or other expression without indices - static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()), - chi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()); + //static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()), + // chi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()); + varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()), + chi((new symbol)->setflag(status_flags::dynallocated), ex_to(mu).get_dim()); return clifford(unit, mu, indexed(metr, xi, chi), rl); } else throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type tensor, matrix or an expression with two free indices")); @@ -782,19 +809,11 @@ ex dirac_slash(const ex & e, const ex & dim, unsigned char rl) return clifford(e, varidx(0, dim), indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl); } -/** Check whether a given tinfo key (as returned by return_type_tinfo() - * is that of a clifford object (with an arbitrary representation label). */ -bool is_clifford_tinfo(tinfo_t ti) -{ - p_int start_loc=(p_int)&clifford::return_type_tinfo_static; - return (p_int)ti>=start_loc && (p_int)ti(mu) ? ex_to(mu).toggle_variance() : mu; - unsigned dim = (ex_to(ex_to(mu).get_dim())).to_int(); + unsigned dim = get_dim_uint(mu); if (is_a(v)) { if (ex_to(v).cols() > ex_to(v).rows()) { @@ -1170,13 +1189,20 @@ ex lst_to_clifford(const ex & v, const ex & e) { if (min == 1) { if (dim == max) return indexed(v, mu_toggle) * e; - else + else if (max - dim == 1) { + if (ex_to(v).cols() > ex_to(v).rows()) + return v.op(0) * dirac_ONE(ex_to(e).get_representation_label()) + indexed(sub_matrix(ex_to(v), 0, 1, 1, dim), mu_toggle) * e; + else + return v.op(0) * dirac_ONE(ex_to(e).get_representation_label()) + indexed(sub_matrix(ex_to(v), 1, dim, 0, 1), mu_toggle) * e; + } else throw(std::invalid_argument("lst_to_clifford(): dimensions of vector and clifford unit mismatch")); } else throw(std::invalid_argument("lst_to_clifford(): first argument should be a vector (nx1 or 1xn matrix)")); } else if (v.info(info_flags::list)) { if (dim == ex_to(v).nops()) return indexed(matrix(dim, 1, ex_to(v)), mu_toggle) * e; + else if (ex_to(v).nops() - dim == 1) + return v.op(0) * dirac_ONE(ex_to(e).get_representation_label()) + indexed(sub_matrix(matrix(dim+1, 1, ex_to(v)), 1, dim, 0, 1), mu_toggle) * e; else throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch")); } else @@ -1198,22 +1224,27 @@ static ex get_clifford_comp(const ex & e, const ex & c) else if (is_a(e) || is_a(e)) { // find a Clifford unit with the same metric, delete it and substitute its index size_t ind = e.nops() + 1; - for (size_t j = 0; j < e.nops(); j++) - if (is_a(e.op(j)) && ex_to(c).same_metric(e.op(j))) - if (ind > e.nops()) + for (size_t j = 0; j < e.nops(); j++) { + if (is_a(e.op(j)) && ex_to(c).same_metric(e.op(j))) { + if (ind > e.nops()) { ind = j; - else + } + else { throw(std::invalid_argument("get_clifford_comp(): expression is a Clifford multi-vector")); + } + } + } if (ind < e.nops()) { ex S = 1; bool same_value_index, found_dummy; same_value_index = ( ex_to(e.op(ind).op(1)).is_numeric() && (ival == ex_to(ex_to(e.op(ind).op(1)).get_value()).to_int()) ); found_dummy = same_value_index; - for(size_t j=0; j < e.nops(); j++) - if (j != ind) - if (same_value_index) + for (size_t j=0; j < e.nops(); j++) { + if (j != ind) { + if (same_value_index) { S = S * e.op(j); + } else { exvector ind_vec = ex_to(e.op(j)).get_dummy_indices(ex_to(e.op(ind))); if (ind_vec.size() > 0) { @@ -1231,6 +1262,8 @@ static ex get_clifford_comp(const ex & e, const ex & c) } else S = S * e.op(j); } + } + } return (found_dummy ? S : 0); } else throw(std::invalid_argument("get_clifford_comp(): expression is not a Clifford vector to the given units")); @@ -1261,19 +1294,28 @@ lst clifford_to_lst(const ex & e, const ex & c, bool algebraic) or (not is_a(pow(c.subs(mu == i, subs_options::no_pattern), 2)))) algebraic = false; lst V; + ex v0 = remove_dirac_ONE(canonicalize_clifford(e+clifford_prime(e)).normal())/2; + if (not v0.is_zero()) + V.append(v0); + ex e1 = canonicalize_clifford(e - v0 * dirac_ONE(ex_to(c).get_representation_label())); if (algebraic) { for (unsigned int i = 0; i < D; i++) V.append(remove_dirac_ONE( - simplify_indexed(canonicalize_clifford(e * c.subs(mu == i, subs_options::no_pattern) + c.subs(mu == i, subs_options::no_pattern) * e)) + simplify_indexed(canonicalize_clifford(e1 * c.subs(mu == i, subs_options::no_pattern) + c.subs(mu == i, subs_options::no_pattern) * e1)) / (2*pow(c.subs(mu == i, subs_options::no_pattern), 2)))); } else { - ex e1 = canonicalize_clifford(e); try { for (unsigned int i = 0; i < D; i++) V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern))); } catch (std::exception &p) { /* Try to expand dummy summations to simplify the expression*/ - e1 = canonicalize_clifford(expand_dummy_sum(e1, true)); + e1 = canonicalize_clifford(expand_dummy_sum(e, true)); + V.remove_all(); + v0 = remove_dirac_ONE(canonicalize_clifford(e1+clifford_prime(e1)).normal())/2; + if (not v0.is_zero()) { + V.append(v0); + e1 = canonicalize_clifford(e1 - v0 * dirac_ONE(ex_to(c).get_representation_label())); + } for (unsigned int i = 0; i < D; i++) V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern))); } @@ -1292,14 +1334,16 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, if (is_a(G)) { cu = G; } else { - if (is_a(G)) - D = ex_to(G.op(1)).get_dim(); - else if (is_a(G)) + if (is_a(G)) { + D = ex_to(G.op(1)).get_dim(); + varidx mu((new symbol)->setflag(status_flags::dynallocated), D); + cu = clifford_unit(mu, G, rl); + } else if (is_a(G)) { D = ex_to(G).rows(); - else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit")); + idx mu((new symbol)->setflag(status_flags::dynallocated), D); + cu = clifford_unit(mu, G, rl); + } else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit")); - varidx mu((new symbol)->setflag(status_flags::dynallocated), D); - cu = clifford_unit(mu, G, rl); } x = lst_to_clifford(v, cu); @@ -1309,11 +1353,10 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl) { - if (is_a(M)) - return clifford_moebius_map(ex_to(M)(0,0), ex_to(M)(0,1), - ex_to(M)(1,0), ex_to(M)(1,1), v, G, rl); + if (is_a(M) && (ex_to(M).rows() == 2) && (ex_to(M).cols() == 2)) + return clifford_moebius_map(M.op(0), M.op(1), M.op(2), M.op(3), v, G, rl); else - throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a matrix")); + throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a 2x2 matrix")); } } // namespace GiNaC