X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fclifford.cpp;h=af54d77bbcb665ef7478c6dfd300c2d4aa4dd109;hp=610073899543b4256769bcf50d401d693e5987db;hb=f303227c240827857e2fb0631c537f553a9845e2;hpb=6dfb8aee92f97422e9c0e2b7aa4706ecf13cac84 diff --git a/ginac/clifford.cpp b/ginac/clifford.cpp index 61007389..af54d77b 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) 1999-2006 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 @@ -46,6 +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)) @@ -74,15 +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()), anticommuting(false) +clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } DEFAULT_CTOR(diracone) @@ -99,29 +95,29 @@ 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; + 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, 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; + tinfo_key = &clifford::tinfo_static; } -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, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } -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, std::auto_ptr vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), commutator_sign(comm_sign) { - tinfo_key = TINFO_clifford; + tinfo_key = &clifford::tinfo_static; } ////////// @@ -134,7 +130,8 @@ clifford::clifford(const archive_node & n, lst & sym_lst) : inherited(n, sym_lst 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 @@ -142,7 +139,7 @@ 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) @@ -153,37 +150,85 @@ DEFAULT_ARCHIVING(diracgamma5) DEFAULT_ARCHIVING(diracgammaL) DEFAULT_ARCHIVING(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) @@ -255,7 +300,7 @@ 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); @@ -389,22 +434,6 @@ 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 { @@ -421,53 +450,25 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth && 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)); + 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); @@ -485,16 +486,7 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth 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); - } + *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); @@ -612,8 +604,10 @@ 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 @@ -676,12 +670,12 @@ 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 { - return clifford(representation_label, get_metric(), is_anticommuting(), vp); + return clifford(representation_label, metric, commutator_sign, vp); } ex diracgamma5::conjugate() const @@ -706,56 +700,45 @@ ex diracgammaR::conjugate() const ex dirac_ONE(unsigned char rl) { static ex ONE = (new diracone)->setflag(status_flags::dynallocated); - return clifford(ONE, rl, false); + return clifford(ONE, rl); } -ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting) +ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl) { static 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")); - 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) && is_a(indices[0]) && is_a(indices[1])) { + 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())) { + 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); + 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((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")); } ex dirac_gamma(const ex & mu, unsigned char rl) @@ -767,7 +750,7 @@ ex dirac_gamma(const ex & mu, unsigned char 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(default_metric(), symmetric2(), xi, chi), rl, true); + return clifford(gamma, mu, indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl); } ex dirac_gamma5(unsigned char rl) @@ -793,28 +776,25 @@ 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); } /** 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)ti(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_); @@ -1051,18 +1031,21 @@ ex canonicalize_clifford(const ex & e_) exvector::iterator 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); + sum += ex_to(save0).get_commutator_sign() * ncmul(v, true); i->second = canonicalize_clifford(sum); goto next_sym; } @@ -1081,7 +1064,7 @@ ex clifford_prime(const ex & e) 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 +1089,7 @@ 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 @@ -1159,11 +1142,11 @@ 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 +1154,10 @@ 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 = (ex_to(ex_to(mu).get_dim())).to_int(); if (is_a(v)) { if (ex_to(v).cols() > ex_to(v).rows()) { @@ -1184,14 +1169,14 @@ 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; + return indexed(v, 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 throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch")); } else @@ -1205,9 +1190,9 @@ ex lst_to_clifford(const ex & v, const ex & e) { 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(); + 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) + 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)) { @@ -1222,8 +1207,8 @@ static ex get_clifford_comp(const ex & e, const ex & c) 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()) ); + 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) @@ -1235,7 +1220,12 @@ static ex get_clifford_comp(const ex & e, const ex & c) 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); + ex curridx = *it; + ex curridx_toggle = is_a(curridx) + ? ex_to(curridx).toggle_variance() + : curridx; + S = S * e.op(j).subs(lst(curridx == ival, + curridx_toggle == ival), subs_options::no_pattern); ++it; } } else @@ -1247,8 +1237,8 @@ static ex get_clifford_comp(const ex & e, const ex & c) } 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()) ) + 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; @@ -1260,43 +1250,43 @@ static ex get_clifford_comp(const ex & e, const ex & c) 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() + or (not is_a(pow(c.subs(mu == i, subs_options::no_pattern), 2)))) algebraic = false; lst V; 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(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); try { 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))); } 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))); + 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)) { @@ -1309,19 +1299,19 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, 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); + cu = clifford_unit(mu, G, rl); } 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); + ex_to(M)(1,0), ex_to(M)(1,1), v, G, rl); else throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a matrix")); }