X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Ftensor.cpp;h=eafe7f1870ac3c65fd79ff61ed6253d40d1edd45;hp=7b3d1417cf40362dfe38cbef2c3312061e38cbfd;hb=ed914545e01d60ecf2544e6141d6c5142c01327f;hpb=d1a4416a1bb37290a42250d871b7b52e35f64e0a diff --git a/ginac/tensor.cpp b/ginac/tensor.cpp index 7b3d1417..eafe7f18 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) 1999-2016 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 @@ -17,110 +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 "print.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(spinmetric, tensmetric) -GINAC_IMPLEMENT_REGISTERED_CLASS(tensepsilon, tensor) + +GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensdelta, tensor, + print_func(&tensdelta::do_print). + print_func(&tensdelta::do_print_latex)) + +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)) ////////// -// default constructor, destructor, copy constructor assignment operator and helpers +// 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_COPY(spinmetric) -DEFAULT_DESTROY(spinmetric) -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; } spinmetric::spinmetric() { - debugmsg("spinmetric default constructor", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_spinmetric; } minkmetric::minkmetric(bool ps) : pos_sig(ps) { - debugmsg("minkmetric constructor from bool", LOGLEVEL_CONSTRUCT); - tinfo_key = TINFO_minkmetric; -} - -void minkmetric::copy(const minkmetric & other) -{ - 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 ////////// -DEFAULT_ARCHIVING(tensor) -DEFAULT_ARCHIVING(tensdelta) -DEFAULT_ARCHIVING(tensmetric) -DEFAULT_ARCHIVING(spinmetric) -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 { @@ -128,12 +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 { @@ -142,6 +124,10 @@ 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 base classes ////////// @@ -151,9 +137,25 @@ 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) @@ -162,9 +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) @@ -175,6 +185,22 @@ int tensepsilon::compare_same_type(const basic & other) const return inherited::compare_same_type(other); } +bool tensepsilon::info(unsigned inf) const +{ + if(inf == info_flags::real) + return true; + + return false; +} + +bool spinmetric::info(unsigned inf) const +{ + if(inf == info_flags::real) + return true; + + return false; +} + DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta") DEFAULT_PRINT(tensmetric, "g") DEFAULT_PRINT_LATEX(minkmetric, "eta", "\\eta") @@ -184,24 +210,39 @@ 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)); - // Trace of delta tensor is the dimension of the space - if (is_dummy_pair(i1, i2)) - return i1.get_dim(); + // 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); + } + + // 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(); + } + } // 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(); + return _ex1; else - return _ex0(); + return _ex0; } // No further simplifications @@ -211,15 +252,25 @@ 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)); + 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 if (i1.is_covariant() != i2.is_covariant()) @@ -232,11 +283,11 @@ 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(i.op(1)); const varidx & i2 = ex_to(i.op(2)); @@ -245,11 +296,11 @@ ex minkmetric::eval_indexed(const basic & i) const 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(); + 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 @@ -259,28 +310,28 @@ ex minkmetric::eval_indexed(const basic & i) const /** Automatic symbolic evaluation of an indexed metric tensor. */ ex spinmetric::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), spinmetric)); - GINAC_ASSERT(is_ex_of_type(i.op(1), spinidx)); - GINAC_ASSERT(is_ex_of_type(i.op(2), spinidx)); + 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(); + 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(); + return _ex0; else if (n1 < n2) - return _ex1(); + return _ex1; else - return _ex_1(); + return _ex_1; } // No further simplifications @@ -290,13 +341,13 @@ ex spinmetric::eval_indexed(const basic & i) const /** 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().empty())) - return _ex0(); + return _ex0; // Numeric evaluation if (static_cast(i).all_index_values_are(info_flags::nonnegint)) { @@ -305,21 +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(x).is_covariant()) - if (ex_to(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); + } + } } } @@ -330,37 +385,39 @@ 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 + // 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 (unsigned i=1; inops(); 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 + // 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; @@ -370,61 +427,47 @@ 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_ex_of_type(self->op(0), tensmetric)); + 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_ex_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(self->op(1)); - const idx *free_idx = &ex_to(self->op(2)); - bool first_index_tried = false; - -again: - if (self_idx->is_symbolic()) { - for (unsigned 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(); - *other = other->subs(other_idx == *free_idx); - return true; - } - } - } - - if (!first_index_tried) { - - // No contraction with first index found, try second index - self_idx = &ex_to(self->op(2)); - free_idx = &ex_to(self->op(1)); - first_index_tried = true; - goto again; - } - - 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_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_ex_of_type(self->op(0), spinmetric)); + GINAC_ASSERT(is_a(self->op(0))); // Contractions between spinor metrics - if (is_ex_of_type(other->op(0), spinmetric)) { + 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)); @@ -432,32 +475,32 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other if (is_dummy_pair(self_i1, other_i1)) { if (is_dummy_pair(self_i2, other_i2)) - *self = _ex2(); + *self = _ex2; else *self = delta_tensor(self_i2, other_i2); - *other = _ex1(); + *other = _ex1; return true; } else if (is_dummy_pair(self_i1, other_i2)) { if (is_dummy_pair(self_i2, other_i1)) - *self = _ex_2(); + *self = _ex_2; else *self = -delta_tensor(self_i2, other_i1); - *other = _ex1(); + *other = _ex1; return true; } else if (is_dummy_pair(self_i2, other_i1)) { *self = -delta_tensor(self_i1, other_i2); - *other = _ex1(); + *other = _ex1; return true; } else if (is_dummy_pair(self_i2, other_i2)) { *self = delta_tensor(self_i1, other_i1); - *other = _ex1(); + *other = _ex1; return true; } } // If contracting with the delta tensor, let the delta do it // (don't raise/lower delta indices) - if (is_ex_of_type(other->op(0), tensdelta)) + if (is_a(other->op(0))) return false; // Try to contract first index @@ -468,14 +511,15 @@ bool spinmetric::contract_with(exvector::iterator self, exvector::iterator other again: if (self_idx->is_symbolic()) { - for (unsigned i=1; inops(); 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 = (static_cast(self_idx)->is_covariant() ? sign : -sign); + // 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; } } @@ -497,66 +541,30 @@ again: /** Contraction of epsilon tensor with something else. */ bool tensepsilon::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_ex_of_type(self->op(0), tensepsilon)); - unsigned num = self->nops() - 1; + 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_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) { + if (is_exactly_a(other->op(0)) && num+1 == other->nops()) { // Contraction of two epsilon tensors is a determinant - ex dim = ex_to(self->op(1)).get_dim(); + bool variance = is_a(self->op(1)); matrix M(num, num); - for (int i=0; iop(i+1), other->op(j+1), pos_sig); - else + 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(); + *other = _ex1; return true; - - } else if (other->return_type() == return_types::commutative) { - -#if 0 - // This handles eps.i.j.k * p.j * p.k = 0 - // Maybe something like this should go to simplify_indexed() because - // such relations are true for any antisymmetric tensors... - exvector c; - - // Handle all indices of the epsilon tensor - for (int i=0; iop(i+1); - - // Look whether there's a contraction with this index - exvector::const_iterator ait, aitend = v.end(); - for (ait = v.begin(); ait != aitend; ait++) { - if (ait == self) - continue; - if (is_a(*ait) && ait->return_type() == return_types::commutative && ex_to(*ait).has_dummy_index_for(idx) && ait->nops() == 2) { - - // Yes, did we already have another contraction with the same base expression? - ex base = ait->op(0); - if (std::find_if(c.begin(), c.end(), bind2nd(ex_is_equal(), base)) == c.end()) { - - // No, add the base expression to the list - c.push_back(base); - - } else { - - // Yes, the contraction is zero - *self = _ex0(); - *other = _ex0(); - return true; - } - } - } - } -#endif } return false; @@ -568,90 +576,103 @@ bool tensepsilon::contract_with(exvector::iterator self, exvector::iterator othe 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 = dynallocate(); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of delta tensor must be of type idx")); - return indexed(tensdelta(), sy_symm(), 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 = dynallocate(); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of metric tensor must be of type varidx")); - return indexed(tensmetric(), sy_symm(), 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 = dynallocate(false); + static ex metric_pos = dynallocate(true); + + 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), sy_symm(), i1, i2); + return indexed(pos_sig ? metric_pos : metric_neg, symmetric2(), i1, i2); } ex spinor_metric(const ex & i1, const ex & i2) { - if (!is_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx)) + static ex metric = dynallocate(); + + 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(spinmetric(), sy_anti(), i1, i2); + 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 = dynallocate(); + + if (!is_a(i1) || !is_a(i2)) throw(std::invalid_argument("indices of epsilon tensor must be of type idx")); 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(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(), sy_anti(), 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 = dynallocate(); + + 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(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(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(), sy_anti(), 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 = dynallocate(true, false); + static ex epsilon_pos = dynallocate(true, true); + + 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(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(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), sy_anti(), i1, i2, i3, i4); -} - -ex eps0123(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)) - throw(std::invalid_argument("indices of epsilon tensor must be of type varidx")); + 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(); - ex dim = ex_to(i1).get_dim(); - if (dim.is_equal(4)) - return lorentz_eps(i1, i2, i3, i4, pos_sig); - else - return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4); + return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4); } } // namespace GiNaC