* 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
*
* 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 <stdexcept>
-#include <vector>
-
#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 <iostream>
+#include <stdexcept>
+#include <vector>
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<print_dflt>(&tensdelta::do_print).
+ print_func<print_latex>(&tensdelta::do_print_latex))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensmetric, tensor,
+ print_func<print_dflt>(&tensmetric::do_print).
+ print_func<print_latex>(&tensmetric::do_print))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(minkmetric, tensmetric,
+ print_func<print_dflt>(&minkmetric::do_print).
+ print_func<print_latex>(&minkmetric::do_print_latex))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(spinmetric, tensmetric,
+ print_func<print_dflt>(&spinmetric::do_print).
+ print_func<print_latex>(&spinmetric::do_print_latex))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(tensepsilon, tensor,
+ print_func<print_dflt>(&tensepsilon::do_print).
+ print_func<print_latex>(&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
{
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
{
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
//////////
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_a<minkmetric>(other));
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_a<tensepsilon>(other));
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")
const idx & i1 = ex_to<idx>(i.op(1));
const idx & i2 = ex_to<idx>(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<const indexed &>(i).all_index_values_are(info_flags::integer)) {
const varidx & i1 = ex_to<varidx>(i.op(1));
const varidx & i2 = ex_to<varidx>(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())
// a canonic order but we can't assume what exactly that order is)
std::vector<int> v;
v.reserve(i.nops() - 1);
- for (unsigned j=1; j<i.nops(); j++)
+ for (size_t j=1; j<i.nops(); j++)
v.push_back(ex_to<numeric>(ex_to<idx>(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<i.nops(); j++) {
+ for (size_t j=1; j<i.nops(); j++) {
const ex & x = i.op(j);
- if (!is_ex_of_type(x, varidx))
+ if (!is_a<varidx>(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<varidx>(x).is_covariant()) {
+ if (ex_to<idx>(x).get_value().is_zero()) {
sign = (pos_sig ? -sign : sign);
- else
+ }
+ else {
sign = (pos_sig ? sign : -sign);
+ }
+ }
}
}
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_a<indexed>(*self));
- GINAC_ASSERT(is_a<indexed>(*other));
- GINAC_ASSERT(self->nops() == 3);
- GINAC_ASSERT(is_a<tensdelta>(self->op(0)));
-
- // Try to contract first index
+ // Try to contract the first index
const idx *self_idx = &ex_to<idx>(self->op(1));
const idx *free_idx = &ex_to<idx>(self->op(2));
bool first_index_tried = false;
again:
if (self_idx->is_symbolic()) {
- for (unsigned i=1; i<other->nops(); i++) {
+ for (size_t i=1; i<other->nops(); i++) {
+ if (! is_a<idx>(other->op(i)))
+ continue;
const idx &other_idx = ex_to<idx>(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<idx>(self->op(2));
free_idx = &ex_to<idx>(self->op(1));
first_index_tried = true;
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<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<tensdelta>(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
{
// 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<tensdelta>(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));
- bool first_index_tried = false;
-
-again:
- if (self_idx->is_symbolic()) {
- for (unsigned i=1; i<other->nops(); i++) {
- const idx &other_idx = ex_to<idx>(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<idx>(self->op(2));
- free_idx = &ex_to<idx>(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. */
GINAC_ASSERT(is_a<spinmetric>(self->op(0)));
// Contractions between spinor metrics
- if (is_ex_of_type(other->op(0), spinmetric)) {
+ if (is_a<spinmetric>(other->op(0))) {
const idx &self_i1 = ex_to<idx>(self->op(1));
const idx &self_i2 = ex_to<idx>(self->op(2));
const idx &other_i1 = ex_to<idx>(other->op(1));
// 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<tensdelta>(other->op(0)))
return false;
// Try to contract first index
again:
if (self_idx->is_symbolic()) {
- for (unsigned i=1; i<other->nops(); i++) {
+ for (size_t i=1; i<other->nops(); i++) {
const idx &other_idx = ex_to<idx>(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<const spinidx *>(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<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
return true;
}
}
GINAC_ASSERT(is_a<indexed>(*self));
GINAC_ASSERT(is_a<indexed>(*other));
GINAC_ASSERT(is_a<tensepsilon>(self->op(0)));
- unsigned num = self->nops() - 1;
+ size_t num = self->nops() - 1;
- if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) {
+ if (is_exactly_a<tensepsilon>(other->op(0)) && num+1 == other->nops()) {
// Contraction of two epsilon tensors is a determinant
- ex dim = ex_to<idx>(self->op(1)).get_dim();
+ bool variance = is_a<varidx>(self->op(1));
matrix M(num, num);
- for (int i=0; i<num; i++) {
- for (int j=0; j<num; j++) {
+ for (size_t i=0; i<num; i++) {
+ for (size_t j=0; j<num; j++) {
if (minkowski)
M(i, j) = lorentz_g(self->op(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;
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; i<num; i++) {
- ex idx = self->op(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<indexed>(*ait) && ait->return_type() == return_types::commutative && ex_to<indexed>(*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;
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<idx>(i1) || !is_a<idx>(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 = (new tensmetric)->setflag(status_flags::dynallocated);
+
+ if (!is_a<varidx>(i1) || !is_a<varidx>(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 = (new minkmetric(false))->setflag(status_flags::dynallocated);
+ static ex metric_pos = (new minkmetric(true))->setflag(status_flags::dynallocated);
+
+ if (!is_a<varidx>(i1) || !is_a<varidx>(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 = (new spinmetric)->setflag(status_flags::dynallocated);
+
+ if (!is_a<spinidx>(i1) || !is_a<spinidx>(i2))
throw(std::invalid_argument("indices of spinor metric must be of type spinidx"));
if (!ex_to<idx>(i1).get_dim().is_equal(2) || !ex_to<idx>(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 = (new tensepsilon)->setflag(status_flags::dynallocated);
+
+ if (!is_a<idx>(i1) || !is_a<idx>(i2))
throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
ex dim = ex_to<idx>(i1).get_dim();
if (!ex_to<idx>(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<wildcard>(i1.op(0))||is_a<wildcard>(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<idx>(i1) || !is_a<idx>(i2) || !is_a<idx>(i3))
throw(std::invalid_argument("indices of epsilon tensor must be of type idx"));
ex dim = ex_to<idx>(i1).get_dim();
if (!ex_to<idx>(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<wildcard>(i1.op(0))||is_a<wildcard>(i2.op(0))||is_a<wildcard>(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<varidx>(i1) || !is_a<varidx>(i2) || !is_a<varidx>(i3) || !is_a<varidx>(i4))
throw(std::invalid_argument("indices of Lorentz epsilon tensor must be of type varidx"));
ex dim = ex_to<idx>(i1).get_dim();
if (!ex_to<idx>(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<wildcard>(i1.op(0))||is_a<wildcard>(i2.op(0))||is_a<wildcard>(i3.op(0))||is_a<wildcard>(i4.op(0)))
+ return indexed(pos_sig ? epsilon_pos : epsilon_neg, antisymmetric4(), i1, i2, i3, i4).hold();
- ex dim = ex_to<idx>(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
git://www.ginac.de / ginac.git / blobdiff