X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=b0b9c37b8112f88a0b071ea0a1191c4677add8d5;hp=610073899543b4256769bcf50d401d693e5987db;hb=HEAD;hpb=6dfb8aee92f97422e9c0e2b7aa4706ecf13cac84 diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index 61007389..2cf0facf 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) 1999-2005 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2024 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" @@ -40,11 +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)) + print_func(&clifford::do_print_latex). + print_func(&clifford::do_print_tree)) GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone, tensor, print_func(&diracone::do_print). @@ -74,15 +75,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracgammaR, tensor, // default constructors ////////// -static ex default_metric() -{ - static ex m = (new minkmetric)->setflag(status_flags::dynallocated); - return m; -} - -clifford::clifford() : representation_label(0), metric(default_metric()), anticommuting(false) +clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1) { - tinfo_key = TINFO_clifford; } DEFAULT_CTOR(diracone) @@ -99,42 +93,45 @@ DEFAULT_CTOR(diracgammaR) /** 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, bool anticommut) : inherited(b), representation_label(rl), metric(0), anticommuting(anticommut) +clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1) { - tinfo_key = TINFO_clifford; } /** Construct object with one Lorentz index. This constructor is for internal * use only. Use the clifford_unit() or dirac_gamma() functions instead. * @see clifford_unit * @see dirac_gamma */ -clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl, bool anticommut) : inherited(b, mu), representation_label(rl), metric(metr), anticommuting(anticommut) +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 = TINFO_clifford; + GINAC_ASSERT(is_a(mu)); } -clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), anticommuting(anticommut) +clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v) : inherited(not_symmetric(), v), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; } -clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, std::auto_ptr vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), anticommuting(anticommut) +clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, exvector && v) : inherited(not_symmetric(), std::move(v)), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; +} + +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; n.find_ex("metric", metric, sym_lst); - n.find_bool("anticommuting", anticommuting); + n.find_unsigned("commutator_sign+1", rl); + commutator_sign = rl - 1; } void clifford::archive(archive_node & n) const @@ -142,48 +139,96 @@ void clifford::archive(archive_node & n) const inherited::archive(n); n.add_unsigned("label", representation_label); n.add_ex("metric", metric); - n.add_bool("anticommuting", anticommuting); + 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(cliffordunit); +GINAC_BIND_UNARCHIVER(diracone); +GINAC_BIND_UNARCHIVER(diracgamma); +GINAC_BIND_UNARCHIVER(diracgamma5); +GINAC_BIND_UNARCHIVER(diracgammaL); +GINAC_BIND_UNARCHIVER(diracgammaR); -////////// -// functions overriding virtual functions from base classes -////////// ex clifford::get_metric(const ex & i, const ex & j, bool symmetrised) const { if (is_a(metric)) { if (symmetrised && !(ex_to(ex_to(metric).get_symmetry()).has_symmetry())) { if (is_a(metric.op(0))) { - return indexed((ex_to(metric.op(0)).add(ex_to(metric.op(0)).transpose())).mul(numeric(1,2)), + return indexed((ex_to(metric.op(0)).add(ex_to(metric.op(0)).transpose())).mul(numeric(1, 2)), symmetric2(), i, j); } else { return simplify_indexed(indexed(metric.op(0)*_ex1_2, i, j) + indexed(metric.op(0)*_ex1_2, j, i)); } } else { - return indexed(metric.op(0), ex_to(ex_to(metric).get_symmetry()), i, j); + return metric.subs(lst{metric.op(1) == i, metric.op(2) == j}, subs_options::no_pattern); } } else { - // should not really happen since all constructors but clifford() make the metric an indexed object - return indexed(metric, i, j); + exvector indices = metric.get_free_indices(); + if (symmetrised) + return _ex1_2*simplify_indexed(metric.subs(lst{indices[0] == i, indices[1] == j}, subs_options::no_pattern) + + metric.subs(lst{indices[0] == j, indices[1] == i}, subs_options::no_pattern)); + else + return metric.subs(lst{indices[0] == i, indices[1] == j}, subs_options::no_pattern); } } bool clifford::same_metric(const ex & other) const { - if (is_a(other)) { - return same_metric(ex_to(other).get_metric()); - } else if (is_a(other)) { - return get_metric(other.op(1), other.op(2)).is_equal(other); - } else - return false; + ex metr; + if (is_a(other)) + metr = ex_to(other).get_metric(); + else + metr = other; + + if (is_a(metr)) + return metr.op(0).is_equal(get_metric().op(0)); + else { + exvector indices = metr.get_free_indices(); + return (indices.size() == 2) + && simplify_indexed(get_metric(indices[0], indices[1])-metr).is_zero(); + } +} + +////////// +// functions overriding virtual functions from base classes +////////// + +ex clifford::op(size_t i) const +{ + GINAC_ASSERT(i(subsed)) { + ex prevmetric = ex_to(subsed).metric; + ex newmetric = prevmetric.subs(m, options); + if(!are_ex_trivially_equal(prevmetric, newmetric)) { + clifford c = ex_to(subsed); + c.metric = newmetric; + subsed = c; + } + } + return subsed; } int clifford::compare_same_type(const basic & other) const @@ -204,7 +249,7 @@ bool clifford::match_same_type(const basic & other) const GINAC_ASSERT(is_a(other)); const clifford &o = static_cast(other); - return (representation_label == o.representation_label) && same_metric(o); + return ((representation_label == o.representation_label) && (commutator_sign == o.get_commutator_sign()) && same_metric(o)); } static bool is_dirac_slash(const ex & seq0) @@ -220,8 +265,21 @@ 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 @@ -237,6 +295,17 @@ void clifford::do_print_latex(const print_latex & c, unsigned level) const } } +void clifford::do_print_tree(const print_tree & c, unsigned level) const +{ + c.s << std::string(level, ' ') << class_name() << " @" << this + << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec + << ", " << seq.size()-1 << " indices" + << ", symmetry=" << symtree << std::endl; + metric.print(c, level + c.delta_indent); + seq[0].print(c, level + c.delta_indent); + printindices(c, level + c.delta_indent); +} + DEFAULT_COMPARE(diracone) DEFAULT_COMPARE(cliffordunit) DEFAULT_COMPARE(diracgamma) @@ -255,7 +324,7 @@ DEFAULT_PRINT_LATEX(diracgammaR, "gammaR", "{\\gamma_R}") static void base_and_index(const ex & c, ex & b, ex & i) { GINAC_ASSERT(is_a(c)); - GINAC_ASSERT(c.nops() == 2); + GINAC_ASSERT(c.nops() == 2+1); if (is_a(c.op(0))) { // proper dirac gamma object or clifford unit i = c.op(1); @@ -264,14 +333,14 @@ static void base_and_index(const ex & c, ex & b, ex & i) i = _ex0; b = _ex1; } else { // slash object, generate new dummy index - varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(c.op(1)).get_dim()); + varidx ix(dynallocate(), ex_to(c.op(1)).get_dim()); b = indexed(c.op(0), ix.toggle_variance()); i = ix; } } /** Predicate for finding non-clifford objects. */ -struct is_not_a_clifford : public std::unary_function { +struct is_not_a_clifford { bool operator()(const ex & e) { return !is_a(e); @@ -292,7 +361,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other if (is_a(*other)) { - // Contraction only makes sense if the represenation labels are equal + // Contraction only makes sense if the representation labels are equal if (ex_to(*other).get_representation_label() != rl) return false; @@ -342,7 +411,7 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other if (std::find_if(self + 1, other, is_not_a_clifford()) != other) return false; - *self = ncmul(exvector(std::reverse_iterator(other), std::reverse_iterator(self + 1)), true); + *self = ncmul(exvector(std::reverse_iterator(other), std::reverse_iterator(self + 1))); std::fill(self + 1, other, _ex1); *other = _ex_2; return true; @@ -354,9 +423,9 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other if (std::find_if(self + 1, other, is_not_a_clifford()) != other) return false; - exvector::iterator next_to_last = other - 1; - ex S = ncmul(exvector(self + 1, next_to_last), true); - ex SR = ncmul(exvector(std::reverse_iterator(next_to_last), std::reverse_iterator(self + 1)), true); + auto next_to_last = other - 1; + ex S = ncmul(exvector(self + 1, next_to_last)); + ex SR = ncmul(exvector(std::reverse_iterator(next_to_last), std::reverse_iterator(self + 1))); *self = (*next_to_last) * S + SR * (*next_to_last); std::fill(self + 1, other, _ex1); @@ -370,8 +439,8 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other if (std::find_if(self + 1, other, is_not_a_clifford()) != other) return false; - exvector::iterator next_to_last = other - 1; - ex S = ncmul(exvector(self + 1, next_to_last), true); + auto next_to_last = other - 1; + ex S = ncmul(exvector(self + 1, next_to_last)); *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last); std::fill(self + 1, other + 1, _ex1); @@ -389,22 +458,6 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other return false; } -/** An utility function looking for a given metric within an exvector, - * used in cliffordunit::contract_with(). */ -static int find_same_metric(exvector & v, ex & c) -{ - for (size_t i=0; i(v[i]) && !is_a(v[i]) - && ((ex_to(c.op(1)) == ex_to(v[i]).get_indices()[0] - && ex_to(c.op(1)) == ex_to(v[i]).get_indices()[1]) - || (ex_to(c.op(1)).toggle_variance() == ex_to(v[i]).get_indices()[0] - && ex_to(c.op(1)).toggle_variance() == ex_to(v[i]).get_indices()[1]))) { - return i; // the index of the found - } - } - return -1; //nothing found -} - /** Contraction of a Clifford unit with something else. */ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const { @@ -415,59 +468,31 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth unsigned char rl = unit.get_representation_label(); if (is_a(*other)) { - // Contraction only makes sense if the represenation labels are equal + // Contraction only makes sense if the representation labels are equal // and the metrics are the same if ((ex_to(*other).get_representation_label() != rl) && unit.same_metric(*other)) return false; - // Find if a previous contraction produces the square of self - int prev_square = find_same_metric(v, *self); - const varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to(self->op(1)).get_dim()), - in1((new symbol)->setflag(status_flags::dynallocated), ex_to(self->op(1)).get_dim()), - in2((new symbol)->setflag(status_flags::dynallocated), ex_to(self->op(1)).get_dim()); - ex squared_metric; - if (prev_square > -1) - squared_metric = simplify_indexed(indexed(v[prev_square].op(0), in1, d) - * unit.get_metric(d.toggle_variance(), in2, true)).op(0); - - exvector::iterator before_other = other - 1; - const varidx & mu = ex_to(self->op(1)); - const varidx & mu_toggle = ex_to(other->op(1)); - const varidx & alpha = ex_to(before_other->op(1)); + auto before_other = other - 1; + ex mu = self->op(1); + ex mu_toggle = other->op(1); + ex alpha = before_other->op(1); // e~mu e.mu = Tr ONE if (other - self == 1) { - if (prev_square > -1) { - *self = indexed(squared_metric, mu, mu_toggle); - v[prev_square] = _ex1; - } else { - *self = unit.get_metric(mu, mu_toggle, true); - } + *self = unit.get_metric(mu, mu_toggle, true); *other = dirac_ONE(rl); return true; } else if (other - self == 2) { if (is_a(*before_other) && ex_to(*before_other).get_representation_label() == rl) { - if (ex_to(*self).is_anticommuting()) { - // e~mu e~alpha e.mu = (2*pow(e~alpha, 2) -Tr(B)) e~alpha - if (prev_square > -1) { - *self = 2 * indexed(squared_metric, alpha, alpha) - - indexed(squared_metric, mu, mu_toggle); - v[prev_square] = _ex1; - } else { - *self = 2 * unit.get_metric(alpha, alpha, true) - unit.get_metric(mu, mu_toggle, true); - } - *other = _ex1; - return true; - - } else { - // e~mu e~alpha e.mu = 2*e~mu B(alpha, mu.toggle_variance())-Tr(B) e~alpha - *self = 2 * (*self) * unit.get_metric(alpha, mu_toggle, true) - unit.get_metric(mu, mu_toggle, true) * (*before_other); - *before_other = _ex1; - *other = _ex1; - return true; - } + // e~mu e~alpha e.mu = 2*e~mu B(alpha, mu.toggle_variance())-Tr(B) e~alpha + *self = 2 * (*self) * unit.get_metric(alpha, mu_toggle, true) - unit.get_metric(mu, mu_toggle, true) * (*before_other); + *before_other = _ex1; + *other = _ex1; + return true; + } else { // e~mu S e.mu = Tr S ONE *self = unit.get_metric(mu, mu_toggle, true); @@ -482,19 +507,10 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth return false; } - ex S = ncmul(exvector(self + 1, before_other), true); + ex S = ncmul(exvector(self + 1, before_other)); if (is_a(*before_other) && ex_to(*before_other).get_representation_label() == rl) { - if (ex_to(*self).is_anticommuting()) { - if (prev_square > -1) { - *self = 2 * (*before_other) * S * indexed(squared_metric, alpha, alpha) - - (*self) * S * (*other) * (*before_other); - } else { - *self = 2 * (*before_other) * S * unit.get_metric(alpha, alpha, true) - (*self) * S * (*other) * (*before_other); - } - } else { - *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other); - } + *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other); } else { // simply commutes *self = (*self) * S * (*other) * (*before_other); @@ -516,11 +532,9 @@ ex clifford::eval_ncmul(const exvector & v) const s.reserve(v.size()); // Remove superfluous ONEs - exvector::const_iterator cit = v.begin(), citend = v.end(); - while (cit != citend) { - if (!is_a(*cit) || !is_a(cit->op(0))) - s.push_back(*cit); - cit++; + for (auto & it : v) { + if (!is_a(it) || !is_a(it.op(0))) + s.push_back(it); } bool something_changed = false; @@ -528,11 +542,11 @@ ex clifford::eval_ncmul(const exvector & v) const // Anticommutate gamma5/L/R's to the front if (s.size() >= 2) { - exvector::iterator first = s.begin(), next_to_last = s.end() - 2; + auto first = s.begin(), next_to_last = s.end() - 2; while (true) { - exvector::iterator it = next_to_last; + auto it = next_to_last; while (true) { - exvector::iterator it2 = it + 1; + auto it2 = it + 1; if (is_a(*it) && is_a(*it2)) { ex e1 = it->op(0), e2 = it2->op(0); @@ -612,8 +626,10 @@ ex clifford::eval_ncmul(const exvector & v) const bool a_is_cliffordunit = is_a(ag); bool b_is_cliffordunit = is_a(bg); - if (a_is_cliffordunit && b_is_cliffordunit && ex_to(a).same_metric(b)) { - + if (a_is_cliffordunit && b_is_cliffordunit && ex_to(a).same_metric(b) + && (ex_to(a).get_commutator_sign() == -1)) { + // This is done only for Clifford algebras + const ex & ia = a.op(1); const ex & ib = b.op(1); if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha @@ -657,7 +673,7 @@ ex clifford::eval_ncmul(const exvector & v) const } else if (!a_is_cliffordunit && !b_is_cliffordunit && ag.is_equal(bg)) { // a\ a\ -> a^2 - varidx ix((new symbol)->setflag(status_flags::dynallocated), ex_to(a.op(1)).minimal_dim(ex_to(b.op(1)))); + varidx ix(dynallocate(), ex_to(a.op(1)).minimal_dim(ex_to(b.op(1)))); a = indexed(ag, ix) * indexed(ag, ix.toggle_variance()); b = dirac_ONE(representation_label); @@ -676,12 +692,12 @@ ex clifford::eval_ncmul(const exvector & v) const ex clifford::thiscontainer(const exvector & v) const { - return clifford(representation_label, get_metric(), is_anticommuting(), v); + return clifford(representation_label, metric, commutator_sign, v); } -ex clifford::thiscontainer(std::auto_ptr vp) const +ex clifford::thiscontainer(exvector && v) const { - return clifford(representation_label, get_metric(), is_anticommuting(), vp); + return clifford(representation_label, metric, commutator_sign, std::move(v)); } ex diracgamma5::conjugate() const @@ -691,12 +707,12 @@ ex diracgamma5::conjugate() const ex diracgammaL::conjugate() const { - return (new diracgammaR)->setflag(status_flags::dynallocated); + return dynallocate(); } ex diracgammaR::conjugate() const { - return (new diracgammaL)->setflag(status_flags::dynallocated); + return dynallocate(); } ////////// @@ -705,86 +721,90 @@ ex diracgammaR::conjugate() const ex dirac_ONE(unsigned char rl) { - static ex ONE = (new diracone)->setflag(status_flags::dynallocated); - return clifford(ONE, rl, false); + static ex ONE = dynallocate(); + return clifford(ONE, rl); } -ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting) +static unsigned get_dim_uint(const ex& e) { - static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated); + 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) +{ + ex unit = dynallocate(); if (!is_a(mu)) throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx")); - if (ex_to(mu).is_symbolic() && !is_a(mu)) - throw(std::invalid_argument("clifford_unit(): symbolic index of Clifford unit must be of type varidx (not idx)")); + exvector indices = metr.get_free_indices(); - if (is_a(metr)) { - exvector indices = ex_to(metr).get_indices(); - if ((indices.size() == 2) && is_a(indices[0]) && is_a(indices[1])) { - return clifford(unit, mu, metr, rl, anticommuting); - } else { - throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be indexed exactly by two indices of same type as the given index")); - } - } else if (is_a(metr)) { - 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()); - return clifford(unit, mu, indexed(metr, xi, chi), rl, anticommuting); + 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; - anticommuting = true; - static varidx 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())) { + //static idx xi(dynallocate(), n), + // chi(dynallocate(), n); + idx xi(dynallocate(), n), + chi(dynallocate(), n); + 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; } - if (M(i, j) != -M(j, i)) { - anticommuting = false; - } } } - return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl, anticommuting); + return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl); } else { throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index")); } - } else { - throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type indexed, tensormetric or matrix")); - } + } else if (indices.size() == 0) { // a tensor or other expression without indices + //static varidx xi(dynallocate(), ex_to(mu).get_dim()), + // chi(dynallocate(), ex_to(mu).get_dim()); + varidx xi(dynallocate(), ex_to(mu).get_dim()), + chi(dynallocate(), 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")); } ex dirac_gamma(const ex & mu, unsigned char rl) { - static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated); + static ex gamma = dynallocate(); if (!is_a(mu)) throw(std::invalid_argument("dirac_gamma(): index of Dirac gamma must be of type varidx")); - 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()); - return clifford(gamma, mu, indexed(default_metric(), symmetric2(), xi, chi), rl, true); + static varidx xi(dynallocate(), ex_to(mu).get_dim()), + chi(dynallocate(), ex_to(mu).get_dim()); + return clifford(gamma, mu, indexed(dynallocate(), symmetric2(), xi, chi), rl); } ex dirac_gamma5(unsigned char rl) { - static ex gamma5 = (new diracgamma5)->setflag(status_flags::dynallocated); + static ex gamma5 = dynallocate(); return clifford(gamma5, rl); } ex dirac_gammaL(unsigned char rl) { - static ex gammaL = (new diracgammaL)->setflag(status_flags::dynallocated); + static ex gammaL = dynallocate(); return clifford(gammaL, rl); } ex dirac_gammaR(unsigned char rl) { - static ex gammaR = (new diracgammaR)->setflag(status_flags::dynallocated); + static ex gammaR = dynallocate(); return clifford(gammaR, rl); } @@ -793,28 +813,17 @@ ex dirac_slash(const ex & e, const ex & dim, unsigned char rl) // Slashed vectors are actually stored as a clifford object with the // vector as its base expression and a (dummy) index that just serves // for storing the space dimensionality - return clifford(e, varidx(0, dim), default_metric(), 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); -} - -/** Check whether a given tinfo key (as returned by return_type_tinfo() - * is that of a clifford object (with an arbitrary representation label). */ -static bool is_clifford_tinfo(unsigned ti) -{ - return (ti & ~0xff) == TINFO_clifford; + static varidx xi(dynallocate(), dim), + chi(dynallocate(), dim); + return clifford(e, varidx(0, dim), indexed(dynallocate(), symmetric2(), xi, chi), rl); } /** Extract representation label from tinfo key (as returned by * return_type_tinfo()). */ -static unsigned char get_representation_label(unsigned ti) +static unsigned char get_representation_label(const return_type_t& ti) { - return ti & 0xff; + return (unsigned char)ti.rl; } /** Take trace of a string of an even number of Dirac gammas given a vector @@ -894,10 +903,10 @@ ex dirac_trace(const ex & e, const std::set & rls, const ex & trO return e; // Substitute gammaL/R and expand product, if necessary - ex e_expanded = e.subs(lst( + ex e_expanded = e.subs(lst{ dirac_gammaL(rl) == (dirac_ONE(rl)-dirac_gamma5(rl))/2, dirac_gammaR(rl) == (dirac_ONE(rl)+dirac_gamma5(rl))/2 - ), subs_options::no_pattern).expand(); + }, subs_options::no_pattern).expand(); if (!is_a(e_expanded)) return dirac_trace(e_expanded, rls, trONE); @@ -923,7 +932,7 @@ ex dirac_trace(const ex & e, const std::set & rls, const ex & trO return trONE * I * (lorentz_eps(ex_to(i1).replace_dim(_ex4), ex_to(i2).replace_dim(_ex4), ex_to(i3).replace_dim(_ex4), ex_to(i4).replace_dim(_ex4)) * b1 * b2 * b3 * b4).simplify_indexed(); } - // Tr gamma5 S_2k = + // Tr gamma5 S_2k = // I/4! * epsilon0123.mu1.mu2.mu3.mu4 * Tr gamma.mu1 gamma.mu2 gamma.mu3 gamma.mu4 S_2k // (the epsilon is always 4-dimensional) exvector ix(num-1), bv(num-1); @@ -994,9 +1003,9 @@ ex dirac_trace(const ex & e, const lst & rll, const ex & trONE) { // Convert list to set std::set rls; - for (lst::const_iterator i = rll.begin(); i != rll.end(); ++i) { - if (i->info(info_flags::nonnegint)) - rls.insert(ex_to(*i).to_int()); + for (const auto & i : rll) { + if (i.info(info_flags::nonnegint)) + rls.insert(ex_to(i).to_int()); } return dirac_trace(e, rls, trONE); @@ -1017,17 +1026,17 @@ ex canonicalize_clifford(const ex & e_) pointer_to_map_function fcn(canonicalize_clifford); if (is_a(e_) // || is_a(e) || is_a(e) - || is_a(e_)) { + || e_.info(info_flags::list)) { return e_.map(fcn); } else { ex e=simplify_indexed(e_); // Scan for any ncmul objects exmap srl; ex aux = e.to_rational(srl); - for (exmap::iterator i = srl.begin(); i != srl.end(); ++i) { + for (auto & i : srl) { - ex lhs = i->first; - ex rhs = i->second; + ex lhs = i.first; + ex rhs = i.second; if (is_exactly_a(rhs) && rhs.return_type() == return_types::noncommutative @@ -1036,7 +1045,7 @@ ex canonicalize_clifford(const ex & e_) // Expand product, if necessary ex rhs_expanded = rhs.expand(); if (!is_a(rhs_expanded)) { - i->second = canonicalize_clifford(rhs_expanded); + i.second = canonicalize_clifford(rhs_expanded); continue; } else if (!is_a(rhs.op(0))) @@ -1048,22 +1057,25 @@ ex canonicalize_clifford(const ex & e_) v.push_back(rhs.op(j)); // Stupid recursive bubble sort because we only want to swap adjacent gammas - exvector::iterator it = v.begin(), next_to_last = v.end() - 1; + auto it = v.begin(), next_to_last = v.end() - 1; if (is_a(it->op(0)) || is_a(it->op(0)) || is_a(it->op(0))) ++it; + while (it != next_to_last) { if (it[0].compare(it[1]) > 0) { + ex save0 = it[0], save1 = it[1]; ex b1, i1, b2, i2; base_and_index(it[0], b1, i1); base_and_index(it[1], b2, i2); - it[0] = (ex_to(save0).get_metric(i1, i2, true) * b1 * b2).simplify_indexed(); - it[1] = v.size() == 2 ? _ex2 * dirac_ONE(ex_to(it[1]).get_representation_label()) : _ex2; + // for Clifford algebras (commutator_sign == -1) metric should be symmetrised + it[0] = (ex_to(save0).get_metric(i1, i2, ex_to(save0).get_commutator_sign() == -1) * b1 * b2).simplify_indexed(); + it[1] = v.size() ? _ex2 * dirac_ONE(ex_to(save0).get_representation_label()) : _ex2; ex sum = ncmul(v); it[0] = save1; it[1] = save0; - sum -= ncmul(v, true); - i->second = canonicalize_clifford(sum); + sum += ex_to(save0).get_commutator_sign() * ncmul(std::move(v)); + i.second = canonicalize_clifford(sum); goto next_sym; } ++it; @@ -1075,13 +1087,54 @@ next_sym: ; } } +ex clifford_star_bar(const ex & e, bool do_bar, unsigned options) +{ + pointer_to_map_function_2args fcn(clifford_star_bar, do_bar, options | 1); + + // is a child, no need to expand + ex e1= (options & 1 ? e : e.expand()); + + if (is_a(e1) ) { // reversing order of clifford units + exvector ev, cv; + ev.reserve(e1.nops()); + cv.reserve(e1.nops()); + // separate clifford and non-clifford entries + for (size_t i= 0; i < e1.nops(); ++i) { + if (is_a(e1.op(i)) && is_a(e1.op(i).op(0))) + cv.push_back(e1.op(i)); + else + ev.push_back(e1.op(i)); + } + for (auto i=cv.rbegin(); i!=cv.rend(); ++i) { // reverse order of Clifford units + ev.push_back(i->conjugate()); + } + // For clifford_bar an odd number of clifford units reverts the sign + if (do_bar && (cv.size() % 2 == 1)) + return -dynallocate(std::move(ev)); + else + return dynallocate(std::move(ev)); + } else if (is_a(e1) && is_a(e1.op(0))) { + if (do_bar) + return -e; + else + return e; + } else if (is_a(e1)) { + // apply the procedure to the base of a power + return pow(clifford_star_bar(e1.op(0), do_bar, 0), e1.op(1)); + } else if (is_a(e1) || is_a(e1) || e.info(info_flags::list)) { + // recurse into subexpressions + return e1.map(fcn); + } else // nothing meaningful can be done + return e; +} + ex clifford_prime(const ex & e) { pointer_to_map_function fcn(clifford_prime); if (is_a(e) && is_a(e.op(0))) { return -e; } else if (is_a(e) || is_a(e) || is_a(e) //|| is_a(e) || is_a(e) - || is_a(e) || is_a(e)) { + || is_a(e) || e.info(info_flags::list)) { return e.map(fcn); } else if (is_a(e)) { return pow(clifford_prime(e.op(0)), e.op(1)); @@ -1106,7 +1159,7 @@ ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options) else throw(std::invalid_argument("remove_dirac_ONE(): expression is a non-scalar Clifford number!")); } else if (is_a(e1) || is_a(e1) || is_a(e1) - || is_a(e1) || is_a(e1)) { + || is_a(e1) || e1.info(info_flags::list)) { if (options & 3) // is a child or was already expanded return e1.map(fcn); else @@ -1130,7 +1183,7 @@ ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options) return e1; } -char clifford_max_label(const ex & e, bool ignore_ONE) +int clifford_max_label(const ex & e, bool ignore_ONE) { if (is_a(e)) if (ignore_ONE && is_a(e.op(0))) @@ -1138,7 +1191,7 @@ char clifford_max_label(const ex & e, bool ignore_ONE) else return ex_to(e).get_representation_label(); else { - char rl = -1; + int rl = -1; for (size_t i=0; i < e.nops(); i++) rl = (rl > clifford_max_label(e.op(i), ignore_ONE)) ? rl : clifford_max_label(e.op(i), ignore_ONE); return rl; @@ -1159,11 +1212,11 @@ ex clifford_inverse(const ex & e) throw(std::invalid_argument("clifford_inverse(): cannot find inverse of Clifford number with zero norm!")); } -ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl, bool anticommuting) +ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl) { if (!ex_to(mu).is_dim_numeric()) throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension")); - ex e = clifford_unit(mu, metr, rl, anticommuting); + ex e = clifford_unit(mu, metr, rl); return lst_to_clifford(v, e); } @@ -1171,8 +1224,10 @@ ex lst_to_clifford(const ex & v, const ex & e) { unsigned min, max; if (is_a(e)) { - varidx mu = ex_to(e.op(1)); - unsigned dim = (ex_to(mu.get_dim())).to_int(); + ex mu = e.op(1); + ex mu_toggle + = is_a(mu) ? ex_to(mu).toggle_variance() : mu; + unsigned dim = get_dim_uint(mu); if (is_a(v)) { if (ex_to(v).cols() > ex_to(v).rows()) { @@ -1184,14 +1239,21 @@ ex lst_to_clifford(const ex & v, const ex & e) { } if (min == 1) { if (dim == max) - return indexed(v, ex_to(mu).toggle_variance()) * e; - else + return indexed(v, mu_toggle) * e; + 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 vector")); - } else if (is_a(v)) { + 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)), ex_to(mu).toggle_variance()) * e; + 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 @@ -1199,131 +1261,149 @@ ex lst_to_clifford(const ex & v, const ex & e) { } else throw(std::invalid_argument("lst_to_clifford(): the second argument should be a Clifford unit")); } - + /** Auxiliary structure to define a function for striping one Clifford unit * from vectors. Used in clifford_to_lst(). */ -static ex get_clifford_comp(const ex & e, const ex & c) +static ex get_clifford_comp(const ex & e, const ex & c, bool root=true) { - pointer_to_map_function_1arg fcn(get_clifford_comp, c); - int ival = ex_to(ex_to(c.op(1)).get_value()).to_int(); - - if (is_a(e) || is_a(e) // || is_a(e) || is_a(e) - || is_a(e)) - return e.map(fcn); - 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()) - ind = j; - else + // make expansion on the top-level call only + ex e1=(root? e.expand() : e); + + pointer_to_map_function_2args fcn(get_clifford_comp, c, false); + int ival = ex_to(ex_to(c.op(1)).get_value()).to_int(); + int rl=ex_to(c).get_representation_label(); + + if ( (is_a(e1) || e1.info(info_flags::list) || is_a(e1))) { + return e1.map(fcn); + } else if (is_a(e1) || is_a(e1)) { + // searches are done within products only + exvector ev, all_dummy=get_all_dummy_indices(e1); + bool found=false, same_value_found=false; + ex dummy_ind=0; + ev.reserve(e1.nops()); + for (size_t i=0; i < e1.nops(); ++i) { + // look for a Clifford unit with the same metric and representation label, + // if found remember its index + if (is_a(e1.op(i)) && ex_to(e1.op(i)).get_representation_label() == rl + && is_a(e1.op(i).op(0)) && ex_to(e1.op(i)).same_metric(c)) { // same Clifford unit + if (found) 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) - 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) { - found_dummy = true; - exvector::const_iterator it = ind_vec.begin(), itend = ind_vec.end(); - while (it != itend) { - S = S * e.op(j).subs(lst(ex_to(*it) == ival, ex_to(*it).toggle_variance() == ival), subs_options::no_pattern); - ++it; - } - } else - S = S * e.op(j); - } - return (found_dummy ? S : 0); - } else + found=true; + if (ex_to(e1.op(i).op(1)).is_numeric() && + (ival == ex_to(ex_to(e1.op(i).op(1)).get_value()).to_int())) { + same_value_found = true; // desired index value is found + } else if ((std::find(all_dummy.begin(), all_dummy.end(), e1.op(i).op(1)) != all_dummy.end()) + || (is_a(e1.op(i).op(1)) + && std::find(all_dummy.begin(), all_dummy.end(), + ex_to(e1.op(i).op(1)).toggle_variance()) != all_dummy.end())) { + dummy_ind=(e1.op(i).op(1)); // suitable dummy index found + } else + ev.push_back(e.op(i)); // another index value + } else + ev.push_back(e1.op(i)); + } + + if (! found) // no Clifford units found at all throw(std::invalid_argument("get_clifford_comp(): expression is not a Clifford vector to the given units")); - } else if (e.is_zero()) - return e; - else if (is_a(e) && ex_to(e).same_metric(c)) - if ( ex_to(e.op(1)).is_numeric() && - (ival != ex_to(ex_to(e.op(1)).get_value()).to_int()) ) + + ex res=dynallocate(std::move(ev)); + if (same_value_found) { + return res; + } else if (! dummy_ind.is_zero()) { // a dummy index was found + if (is_a(dummy_ind)) + dummy_ind = ex_to(dummy_ind).toggle_variance(); + return res.subs(dummy_ind==ival, subs_options::no_pattern); + } else // found a Clifford unit with another index return 0; - else + } else if (e1.is_zero()) { + return 0; + } else if (is_a(e1) && is_a(e1.op(0)) && ex_to(e1).same_metric(c)) { + if (ex_to(e1.op(1)).is_numeric() && + (ival == ex_to(ex_to(e1.op(1)).get_value()).to_int()) ) return 1; - else + else + return 0; + } else throw(std::invalid_argument("get_clifford_comp(): expression is not usable as a Clifford vector")); } - lst clifford_to_lst(const ex & e, const ex & c, bool algebraic) { GINAC_ASSERT(is_a(c)); - varidx mu = ex_to(c.op(1)); - if (! mu.is_dim_numeric()) + ex mu = c.op(1); + if (! ex_to(mu).is_dim_numeric()) throw(std::invalid_argument("clifford_to_lst(): index should have a numeric dimension")); - unsigned int D = ex_to(mu.get_dim()).to_int(); + unsigned int D = ex_to(ex_to(mu).get_dim()).to_int(); if (algebraic) // check if algebraic method is applicable for (unsigned int i = 0; i < D; i++) - if (pow(c.subs(mu == i), 2).is_zero() - or (not is_a(pow(c.subs(mu == i), 2)))) + if (pow(c.subs(mu == i, subs_options::no_pattern), 2).is_zero() + || (! 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)))/2; + if (! 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) + c.subs(mu == i) * e)) - / (2*pow(c.subs(mu == i), 2)))); + 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))); + 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)))/2; + if (! 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))); + V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern))); } } return V; } -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, bool anticommuting) +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) { ex x, D, cu; - if (! is_a(v) && ! is_a(v)) + if (! is_a(v) && ! v.info(info_flags::list)) throw(std::invalid_argument("clifford_moebius_map(): parameter v should be either vector or list")); 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(dynallocate(), 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(dynallocate(), 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, anticommuting); } x = lst_to_clifford(v, cu); - ex e = simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d))); - return clifford_to_lst(e, cu, false); + ex e = clifford_to_lst(simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d))), cu, false); + return (is_a(v) ? matrix(ex_to(v).rows(), ex_to(v).cols(), ex_to(e)) : e); } -ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl, bool anticommuting) +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, anticommuting); + 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