metric tensors now silently replace their indices' dimensions with their
[ginac.git] / ginac / tensor.cpp
index 414225d23d27294b17d86120ec2e12a9a6fb3f81..0c36a68002423d712f4d8afa5ec903716ffba7e7 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's special tensors. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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 "lst.h"
 #include "numeric.h"
+#include "matrix.h"
+#include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
@@ -38,32 +42,33 @@ 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)
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-tensor::tensor(unsigned ti) : inherited(ti)
-{
-       debugmsg("tensor constructor from unsigned", LOGLEVEL_CONSTRUCT); \
-}
-
 DEFAULT_CTORS(tensor)
 DEFAULT_CTORS(tensdelta)
 DEFAULT_CTORS(tensmetric)
+DEFAULT_COPY(spinmetric)
+DEFAULT_DESTROY(spinmetric)
 DEFAULT_DESTROY(minkmetric)
 DEFAULT_DESTROY(tensepsilon)
 
 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;
 }
 
@@ -75,13 +80,11 @@ void minkmetric::copy(const minkmetric & other)
 
 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;
 }
 
@@ -99,12 +102,12 @@ void tensepsilon::copy(const tensepsilon & other)
 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)
 {
-       debugmsg("minkmetric constructor from archive_node", LOGLEVEL_CONSTRUCT);
        n.find_bool("pos_sig", pos_sig);
 }
 
@@ -116,7 +119,6 @@ void minkmetric::archive(archive_node &n) const
 
 tensepsilon::tensepsilon(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-       debugmsg("tensepsilon constructor from archive_node", LOGLEVEL_CONSTRUCT);
        n.find_bool("minkowski", minkowski);
        n.find_bool("pos_sig", pos_sig);
 }
@@ -129,16 +131,17 @@ void tensepsilon::archive(archive_node &n) const
 }
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 DEFAULT_COMPARE(tensor)
 DEFAULT_COMPARE(tensdelta)
 DEFAULT_COMPARE(tensmetric)
+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)
@@ -149,7 +152,7 @@ int minkmetric::compare_same_type(const basic & other) const
 
 int tensepsilon::compare_same_type(const basic & other) const
 {
-       GINAC_ASSERT(is_of_type(other, tensepsilon));
+       GINAC_ASSERT(is_a<tensepsilon>(other));
        const tensepsilon &o = static_cast<const tensepsilon &>(other);
 
        if (minkowski != o.minkowski)
@@ -160,32 +163,38 @@ int tensepsilon::compare_same_type(const basic & other) const
                return inherited::compare_same_type(other);
 }
 
-DEFAULT_PRINT(tensdelta, "delta")
+DEFAULT_PRINT_LATEX(tensdelta, "delta", "\\delta")
 DEFAULT_PRINT(tensmetric, "g")
-DEFAULT_PRINT(minkmetric, "eta")
-DEFAULT_PRINT(tensepsilon, "eps")
+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));
+       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();
+       // 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)) {
-               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 _ex1();
+                       return _ex1;
                else
-                       return _ex0();
+                       return _ex0;
        }
 
        // No further simplifications
@@ -195,14 +204,21 @@ 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<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);
+               return i.subs(lst(i1 == i1.replace_dim(min_dim), i2 == i2.replace_dim(min_dim)));
+       }
 
        // A metric tensor with one covariant and one contravariant index gets
        // replaced by a delta tensor
@@ -216,40 +232,71 @@ 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<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);
 }
 
+/** Automatic symbolic evaluation of an indexed metric tensor. */
+ex spinmetric::eval_indexed(const basic & i) const
+{
+       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)));
+
+       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_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() > 1);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), tensepsilon));
+       GINAC_ASSERT(is_a<tensepsilon>(i.op(0)));
 
        // Convolutions are zero
-       if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
-               return _ex0();
+       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)) {
@@ -259,8 +306,8 @@ ex tensepsilon::eval_indexed(const basic & i) const
                std::vector<int> v;
                v.reserve(i.nops() - 1);
                for (unsigned 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);
+                       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) {
@@ -268,8 +315,8 @@ ex tensepsilon::eval_indexed(const basic & i) const
                                const ex & x = i.op(j);
                                if (!is_ex_of_type(x, varidx))
                                        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
                                                sign = (pos_sig ? sign : -sign);
@@ -283,39 +330,39 @@ 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
-       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<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 (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 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);
+                                       *self = _ex1;
+                                       *other = other->subs(other_idx == free_idx->replace_dim(min_dim));
+                                       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;
        }
@@ -323,13 +370,76 @@ 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(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<indexed>(*self));
+       GINAC_ASSERT(is_a<indexed>(*other));
        GINAC_ASSERT(self->nops() == 3);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), tensmetric));
+       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_of_type(other->op(0), tensdelta))
+               return false;
+
+       // 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 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_ex_of_type(other->op(0), spinmetric)) {
+               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)
@@ -337,19 +447,20 @@ bool tensmetric::contract_with(exvector::iterator self, exvector::iterator other
                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 (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();
+                               *self = (static_cast<const spinidx *>(self_idx)->is_covariant() ? sign : -sign);
                                *other = other->subs(other_idx == *free_idx);
                                return true;
                        }
@@ -359,15 +470,46 @@ 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<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)));
+       unsigned num = self->nops() - 1;
+
+       if (is_ex_exactly_of_type(other->op(0), tensepsilon) && num+1 == other->nops()) {
+
+               // Contraction of two epsilon tensors is a determinant
+               ex dim = ex_to<idx>(self->op(1)).get_dim();
+               matrix M(num, num);
+               for (int i=0; i<num; i++) {
+                       for (int j=0; j<num; j++) {
+                               if (minkowski)
+                                       M(i, j) = lorentz_g(self->op(i+1), other->op(j+1), pos_sig);
+                               else
+                                       M(i, j) = metric_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
 //////////
@@ -377,7 +519,7 @@ ex delta_tensor(const ex & i1, const ex & i2)
        if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
                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)
@@ -385,7 +527,7 @@ ex metric_tensor(const ex & i1, const ex & i2)
        if (!is_ex_of_type(i1, varidx) || !is_ex_of_type(i2, varidx))
                throw(std::invalid_argument("indices of metric tensor must be of type varidx"));
 
-       return indexed(tensmetric(), indexed::symmetric, i1, i2);
+       return indexed(tensmetric(), sy_symm(), i1, i2);
 }
 
 ex lorentz_g(const ex & i1, const ex & i2, bool pos_sig)
@@ -393,7 +535,17 @@ 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))
                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_ex_of_type(i1, spinidx) || !is_ex_of_type(i2, spinidx))
+               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)
@@ -401,13 +553,13 @@ ex epsilon_tensor(const ex & i1, const ex & i2)
        if (!is_ex_of_type(i1, idx) || !is_ex_of_type(i2, idx))
                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<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()))
+       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(), indexed::antisymmetric, i1, i2);
+       return indexed(tensepsilon(), sy_anti(), i1, i2);
 }
 
 ex epsilon_tensor(const ex & i1, const ex & i2, const ex & i3)
@@ -415,13 +567,13 @@ 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))
                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<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()))
+       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(), indexed::antisymmetric, i1, i2, i3);
+       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)
@@ -429,13 +581,13 @@ ex lorentz_eps(const ex & i1, const ex & i2, const ex & i3, const ex & i4, bool
        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 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<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()))
+       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), indexed::antisymmetric, i1, i2, i3, i4);
+       return indexed(tensepsilon(true, pos_sig), sy_anti(), i1, i2, i3, i4);
 }
 
 } // namespace GiNaC