X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=97b503b851eb46a29bd5905b0207a772efe49108;hp=da638b2c15c75063040442e229ab3c72b7f5367a;hb=98fa99a4c097b9baee1ce09124a24bced4b1abbb;hpb=b4631c1661b1945c85b3ea2e8ce1d3e58d1e6e79 diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index da638b2c..97b503b8 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) 1999-2004 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2006 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 @@ -17,9 +17,11 @@ * * 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 */ +#include + #include "clifford.h" #include "ex.h" @@ -44,6 +46,8 @@ 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)) @@ -72,15 +76,9 @@ 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()) +clifford::clifford() : representation_label(0), metric(0), anticommuting(true), commutator_sign(-1) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } DEFAULT_CTOR(diracone) @@ -97,48 +95,53 @@ 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) : inherited(b), representation_label(rl), metric(0) +clifford::clifford(const ex & b, unsigned char rl, bool anticommut) : inherited(b), representation_label(rl), metric(0), anticommuting(anticommut), commutator_sign(-1) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } /** 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) : inherited(b, mu), representation_label(rl), metric(metr) +clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl, bool anticommut, int comm_sign) : inherited(b, mu), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign) { GINAC_ASSERT(is_a(mu)); - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } -clifford::clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr) +clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, int comm_sign, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } -clifford::clifford(unsigned char rl, const ex & metr, std::auto_ptr vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr) +clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, int comm_sign, std::auto_ptr vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } ////////// // archiving ////////// -clifford::clifford(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst) +clifford::clifford(const archive_node & n, lst & sym_lst) : inherited(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 +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) @@ -149,23 +152,85 @@ DEFAULT_ARCHIVING(diracgamma5) DEFAULT_ARCHIVING(diracgammaL) DEFAULT_ARCHIVING(diracgammaR) + +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)), + 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 metric.subs(lst(metric.op(1) == i, metric.op(2) == j), subs_options::no_pattern); + } + } else { + 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 +{ + 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::get_metric(const ex & i, const ex & j) const +ex clifford::op(size_t i) const { - return indexed(metric, symmetric2(), i, j); + GINAC_ASSERT(i(other)) { - return get_metric().is_equal(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; + 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 @@ -186,7 +251,7 @@ 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) @@ -200,7 +265,7 @@ void clifford::do_print_dflt(const print_dflt & c, unsigned level) const { // dirac_slash() object is printed differently if (is_dirac_slash(seq[0])) { - seq[0].print(c, level); + seq[0].print(c, precedence()); c.s << "\\"; } else this->print_dispatch(c, level); @@ -211,10 +276,12 @@ void clifford::do_print_latex(const print_latex & c, unsigned level) const // dirac_slash() object is printed differently if (is_dirac_slash(seq[0])) { c.s << "{"; - seq[0].print(c, level); + seq[0].print(c, precedence()); c.s << "\\hspace{-1.0ex}/}"; - } else + } else { + c.s << "\\clifford[" << int(representation_label) << "]"; this->print_dispatch(c, level); + } } DEFAULT_COMPARE(diracone) @@ -224,7 +291,7 @@ DEFAULT_COMPARE(diracgamma5) DEFAULT_COMPARE(diracgammaL) DEFAULT_COMPARE(diracgammaR) -DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}") +DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbf{1}") DEFAULT_PRINT_LATEX(cliffordunit, "e", "e") DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma") DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}") @@ -235,7 +302,7 @@ 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); @@ -373,15 +440,16 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other * used in cliffordunit::contract_with(). */ static int find_same_metric(exvector & v, ex & c) { - for (int i=0; i(v[i]) && is_a(v[i]) - && ex_to(c).same_metric(v[i]) - && (ex_to(c.op(1)) == ex_to(v[i]).get_indices()[0] - || ex_to(c.op(1)).toggle_variance() == ex_to(v[i]).get_indices()[0])) { - return ++i; // next to found + 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 term } } - return 0; //nothing found + return -1; //nothing found } /** Contraction of a Clifford unit with something else. */ @@ -401,70 +469,88 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth return false; // Find if a previous contraction produces the square of self - int prev_square = find_same_metric(v, self[0]); - varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to(self->op(1)).get_dim()); - ex squared_metric = unit.get_metric(self->op(1), d) * unit.get_metric(d.toggle_variance(), other->op(1)); + 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)); // e~mu e.mu = Tr ONE if (other - self == 1) { - if (prev_square != 0) { - *self = squared_metric; - v[prev_square-1] = _ex1; - } else - *self = unit.get_metric(self->op(1), other->op(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); + } *other = dirac_ONE(rl); return true; - // e~mu e~alpha e.mu = (2e~alpha^2-Tr) e~alpha - } else if (other - self == 2 - && is_a(self[1])) { - - const ex & ia = self[1].op(1); - const ex & ib = self[1].op(1); - if (is_a(unit.get_metric())) - *self = 2 - unit.get_metric(self->op(1), other->op(1)); - else if (prev_square != 0) { - *self = 2-squared_metric; - v[prev_square-1] = _ex1; - } else - *self = 2*unit.get_metric(ia, ib) - unit.get_metric(self->op(1), other->op(1)); - *other = _ex1; - return true; - - // e~mu S e~alpha e.mu = 2 e~alpha^3 S - e~mu S e.mu e~alpha + } 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; + } + } else { + // e~mu S e.mu = Tr S ONE + *self = unit.get_metric(mu, mu_toggle, true); + *other = dirac_ONE(rl); + return true; + } + } else { + // e~mu S e~alpha e.mu = 2 e~mu S B(alpha, mu.toggle_variance()) - e~mu S e.mu e~alpha // (commutate contracted indices towards each other, simplify_indexed() // will re-expand and re-run the simplification) - } else { - exvector::iterator it = self + 1, next_to_last = other - 1; - while (it != other) { - if (!is_a(*it)) - return false; - ++it; + if (std::find_if(self + 1, other, is_not_a_clifford()) != other) { + return false; } - - it = self + 1; - ex S = _ex1; - while (it != next_to_last) { - S *= *it; - *it++ = _ex1; + + ex S = ncmul(exvector(self + 1, before_other), true); + + 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); + } + } else { + // simply commutes + *self = (*self) * S * (*other) * (*before_other); } - - const ex & ia = next_to_last->op(1); - const ex & ib = next_to_last->op(1); - if (is_a(unit.get_metric())) - *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last); - else if (prev_square != 0) { - *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last)*unit.get_metric(self->op(1),self->op(1)); - v[prev_square-1] = _ex1; - } else - *self = 2 * (*next_to_last) * S* unit.get_metric(ia,ib) - (*self) * S * (*other) * (*next_to_last); - *next_to_last = _ex1; - *other = _ex1; + + std::fill(self + 1, other + 1, _ex1); return true; } - - } - + } return false; } @@ -573,12 +659,14 @@ 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 - a = ex_to(a).get_metric(ia, ib); + a = ex_to(a).get_metric(ia, ib, true); b = dirac_ONE(representation_label); something_changed = true; } @@ -628,7 +716,7 @@ ex clifford::eval_ncmul(const exvector & v) const } if (s.empty()) - return clifford(diracone(), representation_label) * sign; + return dirac_ONE(representation_label) * sign; if (something_changed) return reeval_ncmul(s) * sign; else @@ -637,12 +725,12 @@ ex clifford::eval_ncmul(const exvector & v) const ex clifford::thiscontainer(const exvector & v) const { - return clifford(representation_label, get_metric(), v); + return clifford(representation_label, metric, anticommuting, commutator_sign, v); } ex clifford::thiscontainer(std::auto_ptr vp) const { - return clifford(representation_label, get_metric(), vp); + return clifford(representation_label, metric, anticommuting, commutator_sign, vp); } ex diracgamma5::conjugate() const @@ -667,22 +755,52 @@ ex diracgammaR::conjugate() const ex dirac_ONE(unsigned char rl) { static ex ONE = (new diracone)->setflag(status_flags::dynallocated); - return clifford(ONE, rl); + return clifford(ONE, rl, false); } -ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl) +ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting) { static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated); - if (!is_a(mu)) - throw(std::invalid_argument("index of Clifford unit must be of type varidx")); - - if (is_a(metr)) - return clifford(unit, mu, metr.op(0), rl); - else if(is_a(metr) || is_a(metr)) - return clifford(unit, mu, metr, rl); - else - throw(std::invalid_argument("metric for Clifford unit must be of type indexed, tensormetric or matrix")); + 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 ((indices.size() == 2) && is_a(indices[0]) && is_a(indices[1])) { + return clifford(unit, mu, metr, rl, anticommuting); + } 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())) { + for (unsigned i = 0; i < n; i++) { + for (unsigned j = i+1; j < n; j++) { + if (M(i, j) != 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); + } else { + 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()); + return clifford(unit, mu, indexed(metr, xi, chi), rl, anticommuting); + } 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) @@ -690,9 +808,11 @@ ex dirac_gamma(const ex & mu, unsigned char rl) static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated); if (!is_a(mu)) - throw(std::invalid_argument("index of Dirac gamma must be of type varidx")); + throw(std::invalid_argument("dirac_gamma(): index of Dirac gamma must be of type varidx")); - return clifford(gamma, mu, default_metric(), rl); + 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((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl, true); } ex dirac_gamma5(unsigned char rl) @@ -718,28 +838,25 @@ 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); + static varidx xi((new symbol)->setflag(status_flags::dynallocated), dim), + chi((new symbol)->setflag(status_flags::dynallocated), dim); + return clifford(e, varidx(0, dim), indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl, true); } /** 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) +bool is_clifford_tinfo(tinfo_t ti) { - return (ti & ~0xff) == TINFO_clifford; + p_int start_loc=(p_int)&clifford::return_type_tinfo_static; + return (p_int)ti>=start_loc && (p_int)tifirst; - ex rhs = i->second; - - if (is_exactly_a(rhs) - && rhs.return_type() == return_types::noncommutative - && is_clifford_tinfo(rhs.return_type_tinfo())) { - - // Expand product, if necessary - ex rhs_expanded = rhs.expand(); - if (!is_a(rhs_expanded)) { - i->second = canonicalize_clifford(rhs_expanded); - continue; - - } else if (!is_a(rhs.op(0))) - continue; - - exvector v; - v.reserve(rhs.nops()); - for (size_t j=0; j(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) * b1 * b2).simplify_indexed(); - it[1] = v.size() == 2 ? _ex2 * dirac_ONE(ex_to(it[1]).get_representation_label()) : _ex2; - ex sum = ncmul(v); - it[0] = save1; - it[1] = save0; - sum -= ncmul(v, true); - i->second = canonicalize_clifford(sum); - goto next_sym; + pointer_to_map_function fcn(canonicalize_clifford); + + if (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) { + + ex lhs = i->first; + ex rhs = i->second; + + if (is_exactly_a(rhs) + && rhs.return_type() == return_types::noncommutative + && is_clifford_tinfo(rhs.return_type_tinfo())) { + + // Expand product, if necessary + ex rhs_expanded = rhs.expand(); + if (!is_a(rhs_expanded)) { + i->second = canonicalize_clifford(rhs_expanded); + continue; + + } else if (!is_a(rhs.op(0))) + continue; + + exvector v; + v.reserve(rhs.nops()); + for (size_t j=0; j(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); + // 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 += ex_to(save0).get_commutator_sign() * ncmul(v, true); + i->second = canonicalize_clifford(sum); + goto next_sym; + } + ++it; } - ++it; - } next_sym: ; + } } + return aux.subs(srl, subs_options::no_pattern).simplify_indexed(); } - return aux.subs(srl, subs_options::no_pattern).simplify_indexed(); } ex clifford_prime(const ex & e) @@ -997,9 +1125,8 @@ 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)) { - return e.map(fcn); - } else if (is_a(e)) { + } else if (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)); @@ -1007,70 +1134,115 @@ ex clifford_prime(const ex & e) return e; } -ex remove_dirac_ONE(const ex & e) +ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options) { - pointer_to_map_function fcn(remove_dirac_ONE); - if (is_a(e) && is_a(e.op(0))) { - return 1; - } else if (is_a(e)) { - return e.map(fcn); - } else if (is_a(e)) { - return e.map(fcn); - } else if (is_a(e)) { - return e.map(fcn); - } else if (is_a(e)) { - return pow(remove_dirac_ONE(e.op(0)), e.op(1)); - } else - return e; + pointer_to_map_function_2args fcn(remove_dirac_ONE, rl, options | 1); + bool need_reevaluation = false; + ex e1 = e; + if (! (options & 1) ) { // is not a child + if (options & 2) + e1 = expand_dummy_sum(e, true); + e1 = canonicalize_clifford(e1); + } + + if (is_a(e1) && ex_to(e1).get_representation_label() >= rl) { + if (is_a(e1.op(0))) + return 1; + 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) || e1.info(info_flags::list)) { + if (options & 3) // is a child or was already expanded + return e1.map(fcn); + else + try { + return e1.map(fcn); + } catch (std::exception &p) { + need_reevaluation = true; + } + } else if (is_a(e1)) { + if (options & 3) // is a child or was already expanded + return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1)); + else + try { + return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1)); + } catch (std::exception &p) { + need_reevaluation = true; + } + } + if (need_reevaluation) + return remove_dirac_ONE(e, rl, options | 2); + return e1; } -ex clifford_norm(const ex & e) +char clifford_max_label(const ex & e, bool ignore_ONE) { - return sqrt(remove_dirac_ONE(canonicalize_clifford(e * clifford_bar(e)).simplify_indexed())); + if (is_a(e)) + if (ignore_ONE && is_a(e.op(0))) + return -1; + else + return ex_to(e).get_representation_label(); + else { + char 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; + } } +ex clifford_norm(const ex & e) +{ + return sqrt(remove_dirac_ONE(e * clifford_bar(e))); +} + ex clifford_inverse(const ex & e) { ex norm = clifford_norm(e); if (!norm.is_zero()) return clifford_bar(e) / pow(norm, 2); else - throw(std::invalid_argument("Cannot find inverse of Clifford number with zero norm!")); + 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) +ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl, bool anticommuting) { - unsigned min, max; if (!ex_to(mu).is_dim_numeric()) - throw(std::invalid_argument("Index should have a numeric dimension")); - unsigned dim = (ex_to(ex_to(mu).get_dim())).to_int(); - ex c = clifford_unit(mu, metr, rl); - - if (is_a(v)) { - if (ex_to(v).cols() > ex_to(v).rows()) { - min = ex_to(v).rows(); - max = ex_to(v).cols(); - } else { - min = ex_to(v).cols(); - max = ex_to(v).rows(); - } - if (min == 1) { - if (dim == max) - if (is_a(mu)) // need to swap variance - return indexed(v, ex_to(mu).toggle_variance()) * c; + throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension")); + ex e = clifford_unit(mu, metr, rl, anticommuting); + return lst_to_clifford(v, e); +} + +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(); + + if (is_a(v)) { + if (ex_to(v).cols() > ex_to(v).rows()) { + min = ex_to(v).rows(); + max = ex_to(v).cols(); + } else { + min = ex_to(v).cols(); + max = ex_to(v).rows(); + } + if (min == 1) { + if (dim == max) + return indexed(v, ex_to(mu).toggle_variance()) * e; else - return indexed(v, mu) * c; + 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)), ex_to(mu).toggle_variance()) * e; else - throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch")); + throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch")); } else - throw(std::invalid_argument("First argument should be a vector vector")); - } else if (is_a(v)) { - if (dim == ex_to(v).nops()) - return indexed(matrix(dim, 1, ex_to(v)), ex_to(mu).toggle_variance()) * c; - else - throw(std::invalid_argument("List length and dimension of clifford unit mismatch")); + throw(std::invalid_argument("lst_to_clifford(): cannot construct from anything but list or vector")); } else - throw(std::invalid_argument("Cannot construct from anything but list or vector")); + 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 @@ -1078,87 +1250,125 @@ ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char r static ex get_clifford_comp(const ex & e, const ex & c) { 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)) + if (is_a(e) || e.info(info_flags::list) // || 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 - int ival = ex_to(ex_to(c.op(1)).get_value()).to_int(); + // 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 - throw(std::invalid_argument("Expression is a Clifford multi-vector")); + 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) { - exvector ind_vec = ex_to(e.op(j)).get_dummy_indices(ex_to(e.op(ind))); - if (ind_vec.size() > 0) { - 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 + if (j != ind) + if (same_value_index) S = S * e.op(j); - } - return S; + 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 - throw(std::invalid_argument("Expression is not a Clifford vector to the given units")); + 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 - throw(std::invalid_argument("Expression is not handlable as a Clifford vector")); - + 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()) ) + return 0; + else + return 1; + 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) +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()) - throw(std::invalid_argument("Index should have a numeric dimension")); + throw(std::invalid_argument("clifford_to_lst(): index should have a numeric dimension")); unsigned int D = 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) == 0) + if (pow(c.subs(mu == i, subs_options::no_pattern), 2).is_zero() + or (not is_a(pow(c.subs(mu == i, subs_options::no_pattern), 2)))) algebraic = false; lst V; - if (algebraic) + 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)))); - else { + simplify_indexed(canonicalize_clifford(e * c.subs(mu == i, subs_options::no_pattern) + c.subs(mu == i, subs_options::no_pattern) * e)) + / (2*pow(c.subs(mu == i, subs_options::no_pattern), 2)))); + } else { ex e1 = canonicalize_clifford(e); - for (unsigned int i = 0; i < D; i++) - V.append(get_clifford_comp(e1, c.subs(c.op(1) == i))); + 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)); + for (unsigned int i = 0; i < D; 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) +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 x, D; - if (is_a(G)) - D = ex_to(G.op(1)); - else - throw(std::invalid_argument("metric should be an indexed object")); + ex x, D, cu; + + if (! is_a(v) && ! v.info(info_flags::list)) + throw(std::invalid_argument("clifford_moebius_map(): parameter v should be either vector or list")); - varidx mu ((new symbol)->setflag(status_flags::dynallocated), ex_to(D).get_dim()); - - if (! is_a(v) && ! is_a(v)) - throw(std::invalid_argument("parameter v should be either vector or list")); - - x = lst_to_clifford(v, mu, G); - ex e = simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d))); - ex cu = clifford_unit(mu, G); - return clifford_to_lst(e, cu, false); + if (is_a(G)) { + cu = G; + } else { + if (is_a(G)) + D = ex_to(G.op(1)).get_dim(); + 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")); + + varidx mu((new symbol)->setflag(status_flags::dynallocated), D); + cu = clifford_unit(mu, G, rl, anticommuting); + } + + x = lst_to_clifford(v, cu); + 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) +{ + 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); + else + throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a matrix")); } + } // namespace GiNaC