X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.cpp;h=42056ed150d61668c5a5923fd26fa159bebd340d;hp=8440a56c3151af093628db82f8a24ce9ecba1241;hb=073bf40a73e419a3dbcb6dfa190947ce2cc3bdce;hpb=0348291b295769a3a6a6488a50776a8eb2159268 diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp index 8440a56c..42056ed1 100644 --- a/ginac/tensor.cpp +++ b/ginac/tensor.cpp @@ -3,7 +3,7 @@ * Implementation of GiNaC's special tensors. */ /* - * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2011 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 @@ -17,131 +17,91 @@ * * 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 - #include "tensor.h" #include "idx.h" #include "indexed.h" +#include "symmetry.h" #include "relational.h" +#include "operators.h" +#include "lst.h" #include "numeric.h" +#include "matrix.h" #include "archive.h" #include "utils.h" -#include "debugmsg.h" + +#include +#include +#include namespace GiNaC { GINAC_IMPLEMENT_REGISTERED_CLASS(tensor, basic) -GINAC_IMPLEMENT_REGISTERED_CLASS(tensdelta, tensor) -GINAC_IMPLEMENT_REGISTERED_CLASS(tensmetric, tensor) -GINAC_IMPLEMENT_REGISTERED_CLASS(minkmetric, tensmetric) -GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor) -////////// -// default constructor, destructor, copy constructor assignment operator and helpers -////////// +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensdelta, tensor, + print_func(&tensdelta::do_print). + print_func(&tensdelta::do_print_latex)) -#define DEFAULT_DESTROY(classname) \ -void classname::destroy(bool call_parent) \ -{ \ - if (call_parent) \ - inherited::destroy(call_parent); \ -} +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensmetric, tensor, + print_func(&tensmetric::do_print). + print_func(&tensmetric::do_print)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(minkmetric, tensmetric, + print_func(&minkmetric::do_print). + print_func(&minkmetric::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinmetric, tensmetric, + print_func(&spinmetric::do_print). + print_func(&spinmetric::do_print_latex)) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensepsilon, tensor, + print_func(&tensepsilon::do_print). + print_func(&tensepsilon::do_print_latex)) -#define DEFAULT_CTORS(classname) \ -classname::classname() : inherited(TINFO_##classname) \ -{ \ - debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \ -} \ -void classname::copy(const classname & other) \ -{ \ - inherited::copy(other); \ -} \ -DEFAULT_DESTROY(classname) +////////// +// constructors +////////// -tensor::tensor(unsigned ti) : inherited(ti) +tensor::tensor() { - debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \ + setflag(status_flags::evaluated | status_flags::expanded); } -DEFAULT_CTORS(tensor) -DEFAULT_CTORS(tensdelta) -DEFAULT_CTORS(tensmetric) -DEFAULT_DESTROY(minkmetric) -DEFAULT_DESTROY(tensepsilon) +DEFAULT_CTOR(tensdelta) +DEFAULT_CTOR(tensmetric) minkmetric::minkmetric() : pos_sig(false) { - debugmsg("minkmetric default constructor", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_minkmetric; } -minkmetric::minkmetric(bool ps) : pos_sig(ps) +spinmetric::spinmetric() { - debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_minkmetric; } -void minkmetric::copy(const minkmetric & other) +minkmetric::minkmetric(bool ps) : pos_sig(ps) { - inherited::copy(other); - pos_sig = other.pos_sig; } tensepsilon::tensepsilon() : minkowski(false), pos_sig(false) { - debugmsg("tensepsilon default constructor", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_tensepsilon; } tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps) { - debugmsg("tensepsilon constructor from bool,bool", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_tensepsilon; -} - -void tensepsilon::copy(const tensepsilon & other) -{ - inherited::copy(other); - minkowski = other.minkowski; - pos_sig = other.pos_sig; } ////////// // archiving ////////// -#define DEFAULT_UNARCHIVE(classname) \ -ex classname::unarchive(const archive_node &n, const lst &sym_lst) \ -{ \ - return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \ -} - -#define DEFAULT_ARCHIVING(classname) \ -classname::classname(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) \ -{ \ - debugmsg(#classname " constructor from archive_node", LOGLEVEL_CONSTRUCT); \ -} \ -DEFAULT_UNARCHIVE(classname) \ -void classname::archive(archive_node &n) const \ -{ \ - inherited::archive(n); \ -} - -DEFAULT_ARCHIVING(tensor) -DEFAULT_ARCHIVING(tensdelta) -DEFAULT_ARCHIVING(tensmetric) -DEFAULT_UNARCHIVE(minkmetric) -DEFAULT_UNARCHIVE(tensepsilon) - -minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +void minkmetric::read_archive(const archive_node& n, lst& sym_lst) { - debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT); + inherited::read_archive(n, sym_lst); n.find_bool("pos_sig", pos_sig); } +GINAC_BIND_UNARCHIVER(minkmetric); void minkmetric::archive(archive_node &n) const { @@ -149,12 +109,13 @@ void minkmetric::archive(archive_node &n) const n.add_bool("pos_sig", pos_sig); } -tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst) +void tensepsilon::read_archive(const archive_node& n, lst& sym_lst) { - debugmsg("tensepsilon constructor from archive_node", LOGLEVEL_CONSTRUCT); + inherited::read_archive(n, sym_lst); n.find_bool("minkowski", minkowski); n.find_bool("pos_sig", pos_sig); } +GINAC_BIND_UNARCHIVER(tensepsilon); void tensepsilon::archive(archive_node &n) const { @@ -163,24 +124,38 @@ void tensepsilon::archive(archive_node &n) const n.add_bool("pos_sig", pos_sig); } +GINAC_BIND_UNARCHIVER(tensdelta); +GINAC_BIND_UNARCHIVER(tensmetric); +GINAC_BIND_UNARCHIVER(spinmetric); + ////////// -// functions overriding virtual functions from bases classes +// functions overriding virtual functions from base classes ////////// -#define DEFAULT_COMPARE(classname) \ -int classname::compare_same_type(const basic & other) const \ -{ \ - /* by default, two tensors of the same class are always identical */ \ - return 0; \ -} - DEFAULT_COMPARE(tensor) DEFAULT_COMPARE(tensdelta) DEFAULT_COMPARE(tensmetric) +DEFAULT_COMPARE(spinmetric) + +bool tensdelta::info(unsigned inf) const +{ + if(inf == info_flags::real) + return true; + + return false; +} + +bool tensmetric::info(unsigned inf) const +{ + if(inf == info_flags::real) + return true; + + return false; +} int minkmetric::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_of_type(other, minkmetric)); + GINAC_ASSERT(is_a(other)); const minkmetric &o = static_cast(other); if (pos_sig != o.pos_sig) @@ -189,9 +164,17 @@ int minkmetric::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } +bool minkmetric::info(unsigned inf) const +{ + if(inf == info_flags::real) + return true; + + return false; +} + int tensepsilon::compare_same_type(const basic & other) const { - GINAC_ASSERT(is_of_type(other, tensepsilon)); + GINAC_ASSERT(is_a(other)); const tensepsilon &o = static_cast(other); if (minkowski != o.minkowski) @@ -202,43 +185,65 @@ int tensepsilon::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } -void tensdelta::print(std::ostream & os, unsigned upper_precedence) const +bool tensepsilon::info(unsigned inf) const { - debugmsg("tensdelta print",LOGLEVEL_PRINT); - os << "delta"; -} + if(inf == info_flags::real) + return true; -void tensmetric::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("tensmetric print",LOGLEVEL_PRINT); - os << "g"; + return false; } -void minkmetric::print(std::ostream & os, unsigned upper_precedence) const +bool spinmetric::info(unsigned inf) const { - debugmsg("minkmetric print",LOGLEVEL_PRINT); - os << "eta"; -} + if(inf == info_flags::real) + return true; -void tensepsilon::print(std::ostream & os, unsigned upper_precedence) const -{ - debugmsg("tensepsilon print",LOGLEVEL_PRINT); - os << "eps"; + return false; } +DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta") +DEFAULT_PRINT(tensmetric, "g") +DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta") +DEFAULT_PRINT_LATEX(spinmetric, "eps", "\\varepsilon") +DEFAULT_PRINT_LATEX(tensepsilon, "eps", "\\varepsilon") + /** Automatic symbolic evaluation of an indexed delta tensor. */ ex tensdelta::eval_indexed(const basic & i) const { - GINAC_ASSERT(is_of_type(i, indexed)); + GINAC_ASSERT(is_a(i)); GINAC_ASSERT(i.nops() == 3); - GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta)); + GINAC_ASSERT(is_a(i.op(0))); + + const idx & i1 = ex_to(i.op(1)); + const idx & i2 = ex_to(i.op(2)); + + // The dimension of the indices must be equal, otherwise we use the minimal + // dimension + if (!i1.get_dim().is_equal(i2.get_dim())) { + ex min_dim = i1.minimal_dim(i2); + exmap m; + m[i1] = i1.replace_dim(min_dim); + m[i2] = i2.replace_dim(min_dim); + return i.subs(m, subs_options::no_pattern); + } - const idx & i1 = ex_to_idx(i.op(1)); - const idx & i2 = ex_to_idx(i.op(2)); + // Trace of delta tensor is the (effective) dimension of the space + if (is_dummy_pair(i1, i2)) { + try { + return i1.minimal_dim(i2); + } catch (std::exception &e) { + return i.hold(); + } + } - // Trace of delta tensor is the dimension of the space - if (is_dummy_pair(i1, i2)) - return i1.get_dim(); + // Numeric evaluation + if (static_cast(i).all_index_values_are(info_flags::integer)) { + int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(i2.get_value()).to_int(); + if (n1 == n2) + return _ex1; + else + return _ex0; + } // No further simplifications return i.hold(); @@ -247,14 +252,24 @@ ex tensdelta::eval_indexed(const basic & i) const /** Automatic symbolic evaluation of an indexed metric tensor. */ ex tensmetric::eval_indexed(const basic & i) const { - GINAC_ASSERT(is_of_type(i, indexed)); + GINAC_ASSERT(is_a(i)); GINAC_ASSERT(i.nops() == 3); - GINAC_ASSERT(is_ex_of_type(i.op(0), tensmetric)); - GINAC_ASSERT(is_ex_of_type(i.op(1), varidx)); - GINAC_ASSERT(is_ex_of_type(i.op(2), varidx)); - - const varidx & i1 = ex_to_varidx(i.op(1)); - const varidx & i2 = ex_to_varidx(i.op(2)); + GINAC_ASSERT(is_a(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); + + const varidx & i1 = ex_to(i.op(1)); + const varidx & i2 = ex_to(i.op(2)); + + // The dimension of the indices must be equal, otherwise we use the minimal + // dimension + if (!i1.get_dim().is_equal(i2.get_dim())) { + ex min_dim = i1.minimal_dim(i2); + exmap m; + m[i1] = i1.replace_dim(min_dim); + m[i2] = i2.replace_dim(min_dim); + return i.subs(m, subs_options::no_pattern); + } // A metric tensor with one covariant and one contravariant index gets // replaced by a delta tensor @@ -268,40 +283,71 @@ ex tensmetric::eval_indexed(const basic & i) const /** Automatic symbolic evaluation of an indexed Lorentz metric tensor. */ ex minkmetric::eval_indexed(const basic & i) const { - GINAC_ASSERT(is_of_type(i, indexed)); + GINAC_ASSERT(is_a(i)); GINAC_ASSERT(i.nops() == 3); - GINAC_ASSERT(is_ex_of_type(i.op(0), minkmetric)); - GINAC_ASSERT(is_ex_of_type(i.op(1), varidx)); - GINAC_ASSERT(is_ex_of_type(i.op(2), varidx)); + GINAC_ASSERT(is_a(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); - const varidx & i1 = ex_to_varidx(i.op(1)); - const varidx & i2 = ex_to_varidx(i.op(2)); + const varidx & i1 = ex_to(i.op(1)); + const varidx & i2 = ex_to(i.op(2)); // Numeric evaluation if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { - int n1 = ex_to_numeric(i1.get_value()).to_int(), n2 = ex_to_numeric(i2.get_value()).to_int(); + int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(i2.get_value()).to_int(); if (n1 != n2) - return _ex0(); + return _ex0; else if (n1 == 0) - return pos_sig ? _ex_1() : _ex1(); + return pos_sig ? _ex_1 : _ex1; else - return pos_sig ? _ex1() : _ex_1(); + return pos_sig ? _ex1 : _ex_1; } // Perform the usual evaluations of a metric tensor return inherited::eval_indexed(i); } +/** Automatic symbolic evaluation of an indexed metric tensor. */ +ex spinmetric::eval_indexed(const basic & i) const +{ + GINAC_ASSERT(is_a(i)); + GINAC_ASSERT(i.nops() == 3); + GINAC_ASSERT(is_a(i.op(0))); + GINAC_ASSERT(is_a(i.op(1))); + GINAC_ASSERT(is_a(i.op(2))); + + const spinidx & i1 = ex_to(i.op(1)); + const spinidx & i2 = ex_to(i.op(2)); + + // Convolutions are zero + if (!(static_cast(i).get_dummy_indices().empty())) + return _ex0; + + // Numeric evaluation + if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { + int n1 = ex_to(i1.get_value()).to_int(), n2 = ex_to(i2.get_value()).to_int(); + if (n1 == n2) + return _ex0; + else if (n1 < n2) + return _ex1; + else + return _ex_1; + } + + // No further simplifications + return i.hold(); +} + /** Automatic symbolic evaluation of an indexed epsilon tensor. */ ex tensepsilon::eval_indexed(const basic & i) const { - GINAC_ASSERT(is_of_type(i, indexed)); + GINAC_ASSERT(is_a(i)); GINAC_ASSERT(i.nops() > 1); - GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon)); + GINAC_ASSERT(is_a(i.op(0))); // Convolutions are zero - if (static_cast(i).get_dummy_indices().size() != 0) - return _ex0(); + if (!(static_cast(i).get_dummy_indices().empty())) + return _ex0; // Numeric evaluation if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { @@ -310,21 +356,25 @@ ex tensepsilon::eval_indexed(const basic & i) const // a canonic order but we can't assume what exactly that order is) std::vector v; v.reserve(i.nops() - 1); - for (unsigned j=1; j(ex_to(i.op(j)).get_value()).to_int()); + int sign = permutation_sign(v.begin(), v.end()); // In a Minkowski space, check for covariant indices if (minkowski) { - for (unsigned j=1; j(x)) { throw(std::runtime_error("indices of epsilon tensor in Minkowski space must be of type varidx")); - if (ex_to_varidx(x).is_covariant()) - if (ex_to_idx(x).get_value().is_zero()) + } + if (ex_to(x).is_covariant()) { + if (ex_to(x).get_value().is_zero()) { sign = (pos_sig ? -sign : sign); - else + } + else { sign = (pos_sig ? sign : -sign); + } + } } } @@ -335,39 +385,41 @@ ex tensepsilon::eval_indexed(const basic & i) const return i.hold(); } -/** Contraction of an indexed delta tensor with something else. */ -bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const { - GINAC_ASSERT(is_ex_of_type(*self, indexed)); - GINAC_ASSERT(is_ex_of_type(*other, indexed)); - GINAC_ASSERT(self->nops() == 3); - GINAC_ASSERT(is_ex_of_type(self->op(0), tensdelta)); - - // Try to contract first index - const idx *self_idx = &ex_to_idx(self->op(1)); - const idx *free_idx = &ex_to_idx(self->op(2)); + // Try to contract the first index + const idx *self_idx = &ex_to(self->op(1)); + const idx *free_idx = &ex_to(self->op(2)); bool first_index_tried = false; again: if (self_idx->is_symbolic()) { - for (int i=1; inops(); i++) { - const idx &other_idx = ex_to_idx(other->op(i)); + for (size_t i=1; inops(); i++) { + if (! is_a(other->op(i))) + continue; + const idx &other_idx = ex_to(other->op(i)); if (is_dummy_pair(*self_idx, other_idx)) { - // Contraction found, remove delta tensor and substitute - // index in second object - *self = _ex1(); - *other = other->subs(other_idx == *free_idx); - return true; + // Contraction found, remove this tensor and substitute the + // index in the second object + try { + // minimal_dim() throws an exception when index dimensions are not comparable + ex min_dim = self_idx->minimal_dim(other_idx); + *other = other->subs(other_idx == free_idx->replace_dim(min_dim)); + *self = _ex1; // *other is assigned first because assigning *self invalidates free_idx + return true; + } catch (std::exception &e) { + return false; + } } } } if (!first_index_tried) { - // No contraction with first index found, try second index - self_idx = &ex_to_idx(self->op(2)); - free_idx = &ex_to_idx(self->op(1)); + // No contraction with the first index found, try the second index + self_idx = &ex_to(self->op(2)); + free_idx = &ex_to(self->op(1)); first_index_tried = true; goto again; } @@ -375,34 +427,99 @@ again: return false; } +/** Contraction of an indexed delta tensor with something else. */ +bool tensdelta::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +{ + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 3); + GINAC_ASSERT(is_a(self->op(0))); + + // Replace the dummy index with this tensor's other index and remove + // the tensor (this is valid for contractions with all other tensors) + return replace_contr_index(self, other); +} + /** Contraction of an indexed metric tensor with something else. */ bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const { - GINAC_ASSERT(is_ex_of_type(*self, indexed)); - GINAC_ASSERT(is_ex_of_type(*other, indexed)); + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(self->nops() == 3); + GINAC_ASSERT(is_a(self->op(0))); + + // If contracting with the delta tensor, let the delta do it + // (don't raise/lower delta indices) + if (is_a(other->op(0))) + return false; + + // Replace the dummy index with this tensor's other index and remove + // the tensor + return replace_contr_index(self, other); +} + +/** Contraction of an indexed spinor metric with something else. */ +bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +{ + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); GINAC_ASSERT(self->nops() == 3); - GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric)); + GINAC_ASSERT(is_a(self->op(0))); + + // Contractions between spinor metrics + if (is_a(other->op(0))) { + const idx &self_i1 = ex_to(self->op(1)); + const idx &self_i2 = ex_to(self->op(2)); + const idx &other_i1 = ex_to(other->op(1)); + const idx &other_i2 = ex_to(other->op(2)); + + if (is_dummy_pair(self_i1, other_i1)) { + if (is_dummy_pair(self_i2, other_i2)) + *self = _ex2; + else + *self = delta_tensor(self_i2, other_i2); + *other = _ex1; + return true; + } else if (is_dummy_pair(self_i1, other_i2)) { + if (is_dummy_pair(self_i2, other_i1)) + *self = _ex_2; + else + *self = -delta_tensor(self_i2, other_i1); + *other = _ex1; + return true; + } else if (is_dummy_pair(self_i2, other_i1)) { + *self = -delta_tensor(self_i1, other_i2); + *other = _ex1; + return true; + } else if (is_dummy_pair(self_i2, other_i2)) { + *self = delta_tensor(self_i1, other_i1); + *other = _ex1; + return true; + } + } // If contracting with the delta tensor, let the delta do it // (don't raise/lower delta indices) - if (is_ex_exactly_of_type(other->op(0), tensdelta)) + if (is_a(other->op(0))) return false; // Try to contract first index - const idx *self_idx = &ex_to_idx(self->op(1)); - const idx *free_idx = &ex_to_idx(self->op(2)); + const idx *self_idx = &ex_to(self->op(1)); + const idx *free_idx = &ex_to(self->op(2)); bool first_index_tried = false; + int sign = 1; again: if (self_idx->is_symbolic()) { - for (int i=1; inops(); i++) { - const idx &other_idx = ex_to_idx(other->op(i)); + for (size_t i=1; inops(); i++) { + const idx &other_idx = ex_to(other->op(i)); if (is_dummy_pair(*self_idx, other_idx)) { // Contraction found, remove metric tensor and substitute - // index in second object - *self = _ex1(); + // index in second object (assign *self last because this + // invalidates free_idx) *other = other->subs(other_idx == *free_idx); + *self = (static_cast(self_idx)->is_covariant() ? sign : -sign); return true; } } @@ -411,83 +528,151 @@ again: if (!first_index_tried) { // No contraction with first index found, try second index - self_idx = &ex_to_idx(self->op(2)); - free_idx = &ex_to_idx(self->op(1)); + self_idx = &ex_to(self->op(2)); + free_idx = &ex_to(self->op(1)); first_index_tried = true; + sign = -sign; goto again; } return false; } +/** Contraction of epsilon tensor with something else. */ +bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const +{ + GINAC_ASSERT(is_a(*self)); + GINAC_ASSERT(is_a(*other)); + GINAC_ASSERT(is_a(self->op(0))); + size_t num = self->nops() - 1; + + if (is_exactly_a(other->op(0)) && num+1 == other->nops()) { + + // Contraction of two epsilon tensors is a determinant + bool variance = is_a(self->op(1)); + matrix M(num, num); + for (size_t i=0; iop(i+1), other->op(j+1), pos_sig); + else if (variance) + M(i, j) = metric_tensor(self->op(i+1), other->op(j+1)); + else + M(i, j) = delta_tensor(self->op(i+1), other->op(j+1)); + } + } + int sign = minkowski ? -1 : 1; + *self = sign * M.determinant().simplify_indexed(); + *other = _ex1; + return true; + } + + return false; +} + ////////// // global functions ////////// ex delta_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx)) + static ex delta = (new tensdelta)->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of delta tensor must be of type idx")); - return indexed(tensdelta(), indexed::symmetric, i1, i2); + return indexed(delta, symmetric2(), i1, i2); } ex metric_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx)) + static ex metric = (new tensmetric)->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of metric tensor must be of type varidx")); - return indexed(tensmetric(), i1, i2); + return indexed(metric, symmetric2(), i1, i2); } ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig) { - if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx)) + static ex metric_neg = (new minkmetric(false))->setflag(status_flags::dynallocated); + static ex metric_pos = (new minkmetric(true))->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of metric tensor must be of type varidx")); - return indexed(minkmetric(pos_sig), indexed::symmetric, i1, i2); + return indexed(pos_sig ? metric_pos : metric_neg, symmetric2(), i1, i2); +} + +ex spinor_metric(const ex & i1, const ex & i2) +{ + static ex metric = (new spinmetric)->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2)) + throw(std::invalid_argument("indices of spinor metric must be of type spinidx")); + if (!ex_to(i1).get_dim().is_equal(2) || !ex_to(i2).get_dim().is_equal(2)) + throw(std::runtime_error("index dimension for spinor metric must be 2")); + + return indexed(metric, antisymmetric2(), i1, i2); } ex epsilon_tensor(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx)) + static ex epsilon = (new tensepsilon)->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of epsilon tensor must be of type idx")); - ex dim = ex_to_idx(i1).get_dim(); - if (!dim.is_equal(ex_to_idx(i2).get_dim())) + ex dim = ex_to(i1).get_dim(); + if (!dim.is_equal(ex_to(i2).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to_idx(i1).get_dim().is_equal(_ex2())) + if (!ex_to(i1).get_dim().is_equal(_ex2)) throw(std::runtime_error("index dimension of epsilon tensor must match number of indices")); - return indexed(tensepsilon(), indexed::antisymmetric, i1, i2); + if(is_a(i1.op(0))||is_a(i2.op(0))) + return indexed(epsilon, antisymmetric2(), i1, i2).hold(); + + return indexed(epsilon, antisymmetric2(), i1, i2); } ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3) { - if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx) || !is_ex_of_type(i3, idx)) + static ex epsilon = (new tensepsilon)->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2) || !is_a(i3)) throw(std::invalid_argument("indices of epsilon tensor must be of type idx")); - ex dim = ex_to_idx(i1).get_dim(); - if (!dim.is_equal(ex_to_idx(i2).get_dim()) || !dim.is_equal(ex_to_idx(i3).get_dim())) + ex dim = ex_to(i1).get_dim(); + if (!dim.is_equal(ex_to(i2).get_dim()) || !dim.is_equal(ex_to(i3).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to_idx(i1).get_dim().is_equal(_ex3())) + if (!ex_to(i1).get_dim().is_equal(_ex3)) throw(std::runtime_error("index dimension of epsilon tensor must match number of indices")); - return indexed(tensepsilon(), indexed::antisymmetric, i1, i2, i3); + if(is_a(i1.op(0))||is_a(i2.op(0))||is_a(i3.op(0))) + return indexed(epsilon, antisymmetric3(), i1, i2, i3).hold(); + + return indexed(epsilon, antisymmetric3(), i1, i2, i3); } ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig) { - if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx) || !is_ex_of_type(i3, varidx) || !is_ex_of_type(i4, varidx)) + static ex epsilon_neg = (new tensepsilon(true, false))->setflag(status_flags::dynallocated); + static ex epsilon_pos = (new tensepsilon(true, true))->setflag(status_flags::dynallocated); + + if (!is_a(i1) || !is_a(i2) || !is_a(i3) || !is_a(i4)) throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx")); - ex dim = ex_to_idx(i1).get_dim(); - if (!dim.is_equal(ex_to_idx(i2).get_dim()) || !dim.is_equal(ex_to_idx(i3).get_dim()) || !dim.is_equal(ex_to_idx(i4).get_dim())) + ex dim = ex_to(i1).get_dim(); + if (!dim.is_equal(ex_to(i2).get_dim()) || !dim.is_equal(ex_to(i3).get_dim()) || !dim.is_equal(ex_to(i4).get_dim())) throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension")); - if (!ex_to_idx(i1).get_dim().is_equal(_ex4())) + if (!ex_to(i1).get_dim().is_equal(_ex4)) throw(std::runtime_error("index dimension of epsilon tensor must match number of indices")); - return indexed(tensepsilon(true, pos_sig), indexed::antisymmetric, i1, i2, i3, i4); + if(is_a(i1.op(0))||is_a(i2.op(0))||is_a(i3.op(0))||is_a(i4.op(0))) + return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4).hold(); + + return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4); } } // namespace GiNaC