* Implementation of GiNaC's special tensors. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 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
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
#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 "archive.h"
#include "utils.h"
-#include "debugmsg.h"
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)
+
+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
//////////
-#define DEFAULT_CTORS(classname) \
-classname::classname() : inherited(TINFO_##classname) \
-{ \
- debugmsg(#classname " default constructor", LOGLEVEL_CONSTRUCT); \
-} \
-void classname::copy(const classname & other) \
-{ \
- inherited::copy(other); \
-} \
-void classname::destroy(bool call_parent) \
-{ \
- if (call_parent) \
- inherited::destroy(call_parent); \
-}
-
-tensor::tensor(unsigned ti) : inherited(ti)
+tensor::tensor() : inherited(TINFO_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_CTORS(tensepsilon)
+DEFAULT_CTOR(tensdelta)
+DEFAULT_CTOR(tensmetric)
minkmetric::minkmetric() : pos_sig(false)
{
- debugmsg("minkmetric default constructor", LOGLEVEL_CONSTRUCT);
tinfo_key = TINFO_minkmetric;
}
+spinmetric::spinmetric()
+{
+ 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)
+tensepsilon::tensepsilon() : minkowski(false), pos_sig(false)
{
- inherited::copy(other);
- pos_sig = other.pos_sig;
+ tinfo_key = TINFO_tensepsilon;
}
-void minkmetric::destroy(bool call_parent)
+tensepsilon::tensepsilon(bool mink, bool ps) : minkowski(mink), pos_sig(ps)
{
- if (call_parent)
- inherited::destroy(call_parent);
+ tinfo_key = TINFO_tensepsilon;
}
//////////
// archiving
//////////
-#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); \
-} \
-ex classname::unarchive(const archive_node &n, const lst &sym_lst) \
-{ \
- return (new classname(n, sym_lst))->setflag(status_flags::dynallocated); \
-} \
-void classname::archive(archive_node &n) const \
-{ \
- inherited::archive(n); \
-}
-
DEFAULT_ARCHIVING(tensor)
DEFAULT_ARCHIVING(tensdelta)
DEFAULT_ARCHIVING(tensmetric)
-DEFAULT_ARCHIVING(tensepsilon)
+DEFAULT_ARCHIVING(spinmetric)
+DEFAULT_UNARCHIVE(minkmetric)
+DEFAULT_UNARCHIVE(tensepsilon)
-minkmetric::minkmetric(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+minkmetric::minkmetric(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT);
n.find_bool("pos_sig", pos_sig);
}
-ex minkmetric::unarchive(const archive_node &n, const lst &sym_lst)
+void minkmetric::archive(archive_node &n) const
+{
+ inherited::archive(n);
+ n.add_bool("pos_sig", pos_sig);
+}
+
+tensepsilon::tensepsilon(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- return (new minkmetric(n, sym_lst))->setflag(status_flags::dynallocated);
+ n.find_bool("minkowski", minkowski);
+ n.find_bool("pos_sig", pos_sig);
}
-void minkmetric::archive(archive_node &n) const
+void tensepsilon::archive(archive_node &n) const
{
inherited::archive(n);
+ n.add_bool("minkowski", minkowski);
n.add_bool("pos_sig", pos_sig);
}
//////////
-// 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(tensepsilon)
+DEFAULT_COMPARE(spinmetric)
int minkmetric::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, minkmetric));
+ GINAC_ASSERT(is_a<minkmetric>(other));
const minkmetric &o = static_cast<const minkmetric &>(other);
if (pos_sig != o.pos_sig)
return inherited::compare_same_type(other);
}
-void tensdelta::print(std::ostream & os, unsigned upper_precedence) const
+int tensepsilon::compare_same_type(const basic & other) const
{
- debugmsg("tensdelta print",LOGLEVEL_PRINT);
- os << "delta";
-}
+ GINAC_ASSERT(is_a<tensepsilon>(other));
+ const tensepsilon &o = static_cast<const tensepsilon &>(other);
-void tensmetric::print(std::ostream & os, unsigned upper_precedence) const
-{
- debugmsg("tensmetric print",LOGLEVEL_PRINT);
- os << "g";
-}
-
-void minkmetric::print(std::ostream & os, unsigned upper_precedence) const
-{
- debugmsg("minkmetric print",LOGLEVEL_PRINT);
- os << "eta";
+ if (minkowski != o.minkowski)
+ return minkowski ? -1 : 1;
+ else if (pos_sig != o.pos_sig)
+ return pos_sig ? -1 : 1;
+ else
+ return inherited::compare_same_type(other);
}
-void tensepsilon::print(std::ostream & os, unsigned upper_precedence) const
-{
- debugmsg("tensepsilon print",LOGLEVEL_PRINT);
- os << "eps";
-}
+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<indexed>(i));
GINAC_ASSERT(i.nops() == 3);
- GINAC_ASSERT(is_ex_of_type(i.op(0), tensdelta));
+ GINAC_ASSERT(is_a<tensdelta>(i.op(0)));
+
+ const idx & i1 = ex_to<idx>(i.op(1));
+ const idx & i2 = ex_to<idx>(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<const indexed &>(i).all_index_values_are(info_flags::integer)) {
+ int n1 = ex_to<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(i2.get_value()).to_int();
+ if (n1 == n2)
+ return _ex1;
+ else
+ return _ex0;
+ }
// No further simplifications
return i.hold();
/** 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<indexed>(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<tensmetric>(i.op(0)));
+ GINAC_ASSERT(is_a<varidx>(i.op(1)));
+ GINAC_ASSERT(is_a<varidx>(i.op(2)));
+
+ 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
/** 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<indexed>(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<minkmetric>(i.op(0)));
+ GINAC_ASSERT(is_a<varidx>(i.op(1)));
+ GINAC_ASSERT(is_a<varidx>(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<varidx>(i.op(1));
+ const varidx & i2 = ex_to<varidx>(i.op(2));
// Numeric evaluation
if (static_cast<const indexed &>(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<numeric>(i1.get_value()).to_int(), n2 = ex_to<numeric>(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);
}
-/** Contraction of an indexed delta tensor with something else. */
-bool tensdelta::contract_with(ex & self, ex & other) const
+/** Automatic symbolic evaluation of an indexed metric tensor. */
+ex spinmetric::eval_indexed(const basic & i) 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));
+ GINAC_ASSERT(is_a<indexed>(i));
+ GINAC_ASSERT(i.nops() == 3);
+ GINAC_ASSERT(is_a<spinmetric>(i.op(0)));
+ GINAC_ASSERT(is_a<spinidx>(i.op(1)));
+ GINAC_ASSERT(is_a<spinidx>(i.op(2)));
- // 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 spinidx & i1 = ex_to<spinidx>(i.op(1));
+ const spinidx & i2 = ex_to<spinidx>(i.op(2));
+
+ // Convolutions are zero
+ if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
+ return _ex0;
+
+ // Numeric evaluation
+ if (static_cast<const indexed &>(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();
+ 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_a<indexed>(i));
+ GINAC_ASSERT(i.nops() > 1);
+ GINAC_ASSERT(is_a<tensepsilon>(i.op(0)));
+
+ // Convolutions are zero
+ if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
+ return _ex0;
+
+ // Numeric evaluation
+ if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+
+ // Get sign of index permutation (the indices should already be in
+ // a canonic order but we can't assume what exactly that order is)
+ std::vector<int> v;
+ v.reserve(i.nops() - 1);
+ 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 (size_t j=1; j<i.nops(); j++) {
+ const ex & x = i.op(j);
+ 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())
+ sign = (pos_sig ? -sign : sign);
+ else
+ sign = (pos_sig ? sign : -sign);
+ }
+ }
+
+ return sign;
+ }
+
+ // No further simplifications
+ return i.hold();
+}
+
+bool tensor::replace_contr_index(exvector::iterator self, exvector::iterator other) const
+{
+ // 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 (int i=1; i<other.nops(); i++) {
- const idx &other_idx = ex_to_idx(other.op(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 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<idx>(self->op(2));
+ free_idx = &ex_to<idx>(self->op(1));
first_index_tried = true;
goto 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<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(ex & self, ex & other) const
+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(self.nops() == 3);
- GINAC_ASSERT(is_ex_of_type(self.op(0), tensmetric));
+ GINAC_ASSERT(is_a<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<tensmetric>(self->op(0)));
// 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<tensdelta>(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<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(self->nops() == 3);
+ GINAC_ASSERT(is_a<spinmetric>(self->op(0)));
+
+ // Contractions between spinor metrics
+ 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));
+ const idx &other_i2 = ex_to<idx>(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_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));
+ 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;
+ int sign = 1;
again:
if (self_idx->is_symbolic()) {
- for (int i=1; i<other.nops(); i++) {
- const idx &other_idx = ex_to_idx(other.op(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 = _ex1();
- other = other.subs(other_idx == *free_idx);
+ // 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;
}
}
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<idx>(self->op(2));
+ free_idx = &ex_to<idx>(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<indexed>(*self));
+ GINAC_ASSERT(is_a<indexed>(*other));
+ GINAC_ASSERT(is_a<tensepsilon>(self->op(0)));
+ size_t num = self->nops() - 1;
+
+ if (is_exactly_a<tensepsilon>(other->op(0)) && num+1 == other->nops()) {
+
+ // Contraction of two epsilon tensors is a determinant
+ bool variance = is_a<varidx>(self->op(1));
+ matrix M(num, num);
+ 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 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))
+ 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(), indexed::symmetric, i1, i2);
+ return indexed(tensdelta(), sy_symm(), i1, i2);
}
ex metric_tensor(const ex & i1, const ex & i2)
{
- if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
+ 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(), i1, i2);
+ return indexed(tensmetric(), sy_symm(), 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))
+ 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), indexed::symmetric, i1, i2);
+ return indexed(minkmetric(pos_sig), sy_symm(), i1, i2);
+}
+
+ex spinor_metric(const ex & i1, const ex & i2)
+{
+ 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);
}
ex epsilon_tensor(const ex & i1, const ex & i2)
{
- if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
+ 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 (!dim.is_equal(ex_to<idx>(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))
+ throw(std::runtime_error("index dimension of epsilon tensor must match number of indices"));
+
+ return indexed(tensepsilon(), sy_anti(), i1, i2);
+}
+
+ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
+{
+ 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"));
- if (!ex_to_idx(i1).get_dim().is_equal(_ex2()) || !ex_to_idx(i2).get_dim().is_equal(_ex2()))
- throw(std::invalid_argument("index dimension of epsilon tensor must match number of indices"));
- return indexed(tensepsilon(), indexed::antisymmetric, i1, i2);
+ 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()))
+ throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
+ 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);
+}
+
+ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool pos_sig)
+{
+ 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 (!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()))
+ throw(std::invalid_argument("all indices of epsilon tensor must have the same dimension"));
+ 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);
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff