Add support for Texinfo-5.0.
[ginac.git] / ginac / color.cpp
index 675d327..34ab4d8 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's color (SU(3) Lie algebra) objects. */
 
 /*
- *  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 <algorithm>
-#include <stdexcept>
-
 #include "color.h"
-#include "ex.h"
 #include "idx.h"
 #include "ncmul.h"
+#include "symmetry.h"
+#include "operators.h"
 #include "numeric.h"
+#include "mul.h"
 #include "power.h" // for sqrt()
+#include "symbol.h"
 #include "archive.h"
-#include "debugmsg.h"
 #include "utils.h"
 
+#include <iostream>
+#include <stdexcept>
+
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3one, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3t, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3f, tensor)
-GINAC_IMPLEMENT_REGISTERED_CLASS(su3d, tensor)
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor,
+  print_func<print_dflt>(&su3one::do_print).
+  print_func<print_latex>(&su3one::do_print_latex))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor,
+  print_func<print_dflt>(&su3t::do_print).
+  print_func<print_latex>(&su3t::do_print))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor,
+  print_func<print_dflt>(&su3f::do_print).
+  print_func<print_latex>(&su3f::do_print))
+
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor,
+  print_func<print_dflt>(&su3d::do_print).
+  print_func<print_latex>(&su3d::do_print))
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructors
 //////////
 
 color::color() : representation_label(0)
 {
-       debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_color;
-}
-
-void color::copy(const color & other)
-{
-       inherited::copy(other);
-       representation_label = other.representation_label;
 }
 
-DEFAULT_DESTROY(color)
-DEFAULT_CTORS(su3one)
-DEFAULT_CTORS(su3t)
-DEFAULT_CTORS(su3f)
-DEFAULT_CTORS(su3d)
+DEFAULT_CTOR(su3one)
+DEFAULT_CTOR(su3t)
+DEFAULT_CTOR(su3f)
+DEFAULT_CTOR(su3d)
 
 //////////
 // other constructors
@@ -70,62 +75,61 @@ DEFAULT_CTORS(su3d)
 /** Construct object without any color index. This constructor is for
  *  internal use only. Use the color_ONE() function instead.
  *  @see color_ONE */
-color::color(const ex & b, unsigned rl = 0) : inherited(b), representation_label(rl)
+color::color(const ex & b, unsigned char rl) : inherited(b), representation_label(rl)
 {
-       debugmsg("color constructor from ex,unsigned", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_color;
 }
 
 /** Construct object with one color index. This constructor is for internal
  *  use only. Use the color_T() function instead.
  *  @see color_T */
-color::color(const ex & b, const ex & i1, unsigned rl = 0) : inherited(b, i1), representation_label(rl)
+color::color(const ex & b, const ex & i1, unsigned char rl) : inherited(b, i1), representation_label(rl)
 {
-       debugmsg("color constructor from ex,ex,unsigned", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_color;
 }
 
-color::color(unsigned rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
+color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl)
 {
-       debugmsg("color constructor from unsigned,exvector", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_color;
 }
 
-color::color(unsigned rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
+color::color(unsigned char rl, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl)
 {
-       debugmsg("color constructor from unsigned,exvector *", LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_color;
+}
+
+return_type_t color::return_type_tinfo() const
+{
+       return make_return_type_t<color>(representation_label);
 }
 
 //////////
 // archiving
 //////////
 
-color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+void color::read_archive(const archive_node& n, lst& sym_lst)
 {
-       debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
-       n.find_unsigned("representation", representation_label);
+       inherited::read_archive(n, sym_lst);
+       unsigned rl;
+       n.find_unsigned("label", rl);
+       representation_label = rl;
 }
 
 void color::archive(archive_node &n) const
 {
        inherited::archive(n);
-       n.add_unsigned("representation", representation_label);
+       n.add_unsigned("label", representation_label);
 }
 
-DEFAULT_UNARCHIVE(color)
-DEFAULT_ARCHIVING(su3one)
-DEFAULT_ARCHIVING(su3t)
-DEFAULT_ARCHIVING(su3f)
-DEFAULT_ARCHIVING(su3d)
+GINAC_BIND_UNARCHIVER(color);
+GINAC_BIND_UNARCHIVER(su3one);
+GINAC_BIND_UNARCHIVER(su3t);
+GINAC_BIND_UNARCHIVER(su3f);
+GINAC_BIND_UNARCHIVER(su3d);
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 int color::compare_same_type(const basic & other) const
 {
-       GINAC_ASSERT(other.tinfo() == TINFO_color);
+       GINAC_ASSERT(is_a<color>(other));
        const color &o = static_cast<const color &>(other);
 
        if (representation_label != o.representation_label) {
@@ -136,45 +140,51 @@ int color::compare_same_type(const basic & other) const
        return inherited::compare_same_type(other);
 }
 
+bool color::match_same_type(const basic & other) const
+{
+       GINAC_ASSERT(is_a<color>(other));
+       const color &o = static_cast<const color &>(other);
+
+       return representation_label == o.representation_label;
+}
+
 DEFAULT_COMPARE(su3one)
 DEFAULT_COMPARE(su3t)
 DEFAULT_COMPARE(su3f)
 DEFAULT_COMPARE(su3d)
 
-DEFAULT_PRINT(su3one, "ONE")
+DEFAULT_PRINT_LATEX(su3one, "ONE", "\\mathbb{1}")
 DEFAULT_PRINT(su3t, "T")
 DEFAULT_PRINT(su3f, "f")
 DEFAULT_PRINT(su3d, "d")
 
 /** Perform automatic simplification on noncommutative product of color
  *  objects. This removes superfluous ONEs. */
-ex color::simplify_ncmul(const exvector & v) const
+ex color::eval_ncmul(const exvector & v) const
 {
-       //!! TODO: sort by representation label
        exvector s;
        s.reserve(v.size());
 
+       // Remove superfluous ONEs
        exvector::const_iterator it = v.begin(), itend = v.end();
        while (it != itend) {
-               if (!is_ex_of_type(it->op(0), su3one))
+               if (!is_a<su3one>(it->op(0)))
                        s.push_back(*it);
                it++;
        }
 
-       if (s.size() == 0)
-               return color(su3one());
-       else if (s.size() == v.size())
-               return simplified_ncmul(v);
+       if (s.empty())
+               return color(su3one(), representation_label);
        else
-               return simplified_ncmul(s);
+               return hold_ncmul(s);
 }
 
-ex color::thisexprseq(const exvector & v) const
+ex color::thiscontainer(const exvector & v) const
 {
        return color(representation_label, v);
 }
 
-ex color::thisexprseq(exvector * vp) const
+ex color::thiscontainer(std::auto_ptr<exvector> vp) const
 {
        return color(representation_label, vp);
 }
@@ -213,13 +223,13 @@ static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2
 /** Automatic symbolic evaluation of indexed symmetric structure constant. */
 ex su3d::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 4);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
+       GINAC_ASSERT(is_a<su3d>(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)) {
@@ -227,7 +237,7 @@ ex su3d::eval_indexed(const basic & i) const
                // Sort indices
                int v[3];
                for (unsigned j=0; j<3; j++)
-                       v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
+                       v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
                if (v[0] > v[1]) std::swap(v[0], v[1]);
                if (v[0] > v[2]) std::swap(v[0], v[2]);
                if (v[1] > v[2]) std::swap(v[1], v[2]);
@@ -237,18 +247,18 @@ ex su3d::eval_indexed(const basic & i) const
                // Check for non-zero elements
                if (CMPINDICES(1,4,6) || CMPINDICES(1,5,7) || CMPINDICES(2,5,6)
                 || CMPINDICES(3,4,4) || CMPINDICES(3,5,5))
-                       return _ex1_2();
+                       return _ex1_2;
                else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
-                       return _ex_1_2();
+                       return _ex_1_2;
                else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
-                       return sqrt(_ex3())/3;
+                       return sqrt(_ex3)*_ex1_3;
                else if (CMPINDICES(8,8,8))
-                       return -sqrt(_ex3())/3;
+                       return sqrt(_ex3)*_ex_1_3;
                else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
                      || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
-                       return -sqrt(_ex3())/6;
+                       return sqrt(_ex3)/_ex_6;
                else
-                       return _ex0();
+                       return _ex0;
        }
 
        // No further simplifications
@@ -258,9 +268,9 @@ ex su3d::eval_indexed(const basic & i) const
 /** Automatic symbolic evaluation of indexed antisymmetric structure constant. */
 ex su3f::eval_indexed(const basic & i) const
 {
-       GINAC_ASSERT(is_of_type(i, indexed));
+       GINAC_ASSERT(is_a<indexed>(i));
        GINAC_ASSERT(i.nops() == 4);
-       GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
+       GINAC_ASSERT(is_a<su3f>(i.op(0)));
 
        // Numeric evaluation
        if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
@@ -268,7 +278,7 @@ ex su3f::eval_indexed(const basic & i) const
                // Sort indices, remember permutation sign
                int v[3];
                for (unsigned j=0; j<3; j++)
-                       v[j] = ex_to_numeric(ex_to_idx(i.op(j + 1)).get_value()).to_int();
+                       v[j] = ex_to<numeric>(ex_to<idx>(i.op(j + 1)).get_value()).to_int();
                int sign = 1;
                if (v[0] > v[1]) { std::swap(v[0], v[1]); sign = -sign; }
                if (v[0] > v[2]) { std::swap(v[0], v[2]); sign = -sign; }
@@ -279,13 +289,13 @@ ex su3f::eval_indexed(const basic & i) const
                        return sign;
                else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
                      || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
-                       return _ex1_2() * sign;
+                       return _ex1_2 * sign;
                else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
-                       return _ex_1_2() * sign;
+                       return _ex_1_2 * sign;
                else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
-                       return sqrt(_ex3())/2 * sign;
+                       return sqrt(_ex3)/2 * sign;
                else
-                       return _ex0();
+                       return _ex0;
        }
 
        // No further simplifications
@@ -293,34 +303,113 @@ ex su3f::eval_indexed(const basic & i) const
 }
 
 
+/** Contraction of generator with something else. */
+bool su3t::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() == 2);
+       GINAC_ASSERT(is_a<su3t>(self->op(0)));
+       unsigned char rl = ex_to<color>(*self).get_representation_label();
+
+       if (is_exactly_a<su3t>(other->op(0))) {
+
+               // Contraction only makes sense if the represenation labels are equal
+               GINAC_ASSERT(is_a<color>(*other));
+               if (ex_to<color>(*other).get_representation_label() != rl)
+                       return false;
+
+               // T.a T.a = 4/3 ONE
+               if (other - self == 1) {
+                       *self = numeric(4, 3);
+                       *other = color_ONE(rl);
+                       return true;
+
+               // T.a T.b T.a = -1/6 T.b
+               } else if (other - self == 2
+                       && is_a<color>(self[1])) {
+                       *self = numeric(-1, 6);
+                       *other = _ex1;
+                       return true;
+
+               // T.a S T.a = 1/2 Tr(S) - 1/6 S
+               } else {
+                       exvector::iterator it = self + 1;
+                       while (it != other) {
+                               if (!is_a<color>(*it)) {
+                                       return false;
+                               }
+                               it++;
+                       }
+
+                       it = self + 1;
+                       ex S = _ex1;
+                       while (it != other) {
+                               S *= *it;
+                               *it++ = _ex1;
+                       }
+
+                       *self = color_trace(S, rl) * color_ONE(rl) / 2 - S / 6;
+                       *other = _ex1;
+                       return true;
+               }
+       }
+
+       return false;
+}
+
 /** Contraction of an indexed symmetric structure constant with something else. */
 bool su3d::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() == 4);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
+       GINAC_ASSERT(is_a<su3d>(self->op(0)));
 
-       if (is_ex_exactly_of_type(other->op(0), su3d)) {
+       if (is_exactly_a<su3d>(other->op(0))) {
 
                // Find the dummy indices of the contraction
-               exvector dummy_indices;
-               dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
-
-               // d.abc*d.abc=40/3
+               exvector self_indices = ex_to<indexed>(*self).get_indices();
+               exvector other_indices = ex_to<indexed>(*other).get_indices();
+               exvector all_indices = self_indices;
+               all_indices.insert(all_indices.end(), other_indices.begin(), other_indices.end());
+               exvector free_indices, dummy_indices;
+               find_free_and_dummy(all_indices, free_indices, dummy_indices);
+
+               // d.abc d.abc = 40/3
                if (dummy_indices.size() == 3) {
                        *self = numeric(40, 3);
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
 
-               // d.akl*d.bkl=5/3*delta.ab
+               // d.akl d.bkl = 5/3 delta.ab
                } else if (dummy_indices.size() == 2) {
-                       exvector a = index_set_difference(ex_to_indexed(*self).get_indices(), dummy_indices);
-                       exvector b = index_set_difference(ex_to_indexed(*other).get_indices(), dummy_indices);
-                       GINAC_ASSERT(a.size() > 0);
-                       GINAC_ASSERT(b.size() > 0);
-                       *self = numeric(5, 3) * delta_tensor(a[0], b[0]);
-                       *other = _ex1();
+                       exvector a;
+                       std::back_insert_iterator<exvector> ita(a);
+                       ita = set_difference(self_indices.begin(), self_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
+                       ita = set_difference(other_indices.begin(), other_indices.end(), dummy_indices.begin(), dummy_indices.end(), ita, ex_is_less());
+                       GINAC_ASSERT(a.size() == 2);
+                       *self = numeric(5, 3) * delta_tensor(a[0], a[1]);
+                       *other = _ex1;
+                       return true;
+               }
+
+       } else if (is_exactly_a<su3t>(other->op(0))) {
+
+               // d.abc T.b T.c = 5/6 T.a
+               if (other+1 != v.end()
+                && is_exactly_a<su3t>(other[1].op(0))
+                && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
+
+                       exvector self_indices = ex_to<indexed>(*self).get_indices();
+                       exvector dummy_indices;
+                       dummy_indices.push_back(other[0].op(1));
+                       dummy_indices.push_back(other[1].op(1));
+                       int sig;
+                       ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
+                       *self = numeric(5, 6);
+                       other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
+                       other[1] = _ex1;
                        return true;
                }
        }
@@ -331,30 +420,49 @@ bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exve
 /** Contraction of an indexed antisymmetric structure constant with something else. */
 bool su3f::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() == 4);
-       GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
+       GINAC_ASSERT(is_a<su3f>(self->op(0)));
 
-       if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
+       if (is_exactly_a<su3f>(other->op(0))) { // f*d is handled by su3d class
 
                // Find the dummy indices of the contraction
                exvector dummy_indices;
-               dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
+               dummy_indices = ex_to<indexed>(*self).get_dummy_indices(ex_to<indexed>(*other));
 
-               // f.abc*f.abc=24
+               // f.abc f.abc = 24
                if (dummy_indices.size() == 3) {
                        *self = 24;
-                       *other = _ex1();
+                       *other = _ex1;
                        return true;
 
-               // f.akl*f.bkl=3*delta.ab
+               // f.akl f.bkl = 3 delta.ab
                } else if (dummy_indices.size() == 2) {
                        int sign1, sign2;
-                       ex a = permute_free_index_to_front(ex_to_indexed(*self).get_indices(), dummy_indices, sign1);
-                       ex b = permute_free_index_to_front(ex_to_indexed(*other).get_indices(), dummy_indices, sign2);
+                       ex a = permute_free_index_to_front(ex_to<indexed>(*self).get_indices(), dummy_indices, sign1);
+                       ex b = permute_free_index_to_front(ex_to<indexed>(*other).get_indices(), dummy_indices, sign2);
                        *self = sign1 * sign2 * 3 * delta_tensor(a, b);
-                       *other = _ex1();
+                       *other = _ex1;
+                       return true;
+               }
+
+       } else if (is_exactly_a<su3t>(other->op(0))) {
+
+               // f.abc T.b T.c = 3/2 I T.a
+               if (other+1 != v.end()
+                && is_exactly_a<su3t>(other[1].op(0))
+                && ex_to<indexed>(*self).has_dummy_index_for(other[1].op(1))) {
+
+                       exvector self_indices = ex_to<indexed>(*self).get_indices();
+                       exvector dummy_indices;
+                       dummy_indices.push_back(other[0].op(1));
+                       dummy_indices.push_back(other[1].op(1));
+                       int sig;
+                       ex a = permute_free_index_to_front(self_indices, dummy_indices, sig);
+                       *self = numeric(3, 2) * sig * I;
+                       other[0] = color_T(a, ex_to<color>(other[0]).get_representation_label());
+                       other[1] = _ex1;
                        return true;
                }
        }
@@ -366,39 +474,46 @@ bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exve
 // global functions
 //////////
 
-ex color_ONE(unsigned rl)
+ex color_ONE(unsigned char rl)
 {
-       return color(su3one(), rl);
+       static ex ONE = (new su3one)->setflag(status_flags::dynallocated);
+       return color(ONE, rl);
 }
 
-ex color_T(const ex & a, unsigned rl)
+ex color_T(const ex & a, unsigned char rl)
 {
-       if (!is_ex_of_type(a, idx))
+       static ex t = (new su3t)->setflag(status_flags::dynallocated);
+
+       if (!is_a<idx>(a))
                throw(std::invalid_argument("indices of color_T must be of type idx"));
-       if (!ex_to_idx(a).get_dim().is_equal(8))
+       if (!ex_to<idx>(a).get_dim().is_equal(8))
                throw(std::invalid_argument("index dimension for color_T must be 8"));
 
-       return color(su3t(), a, rl);
+       return color(t, a, rl);
 }
 
 ex color_f(const ex & a, const ex & b, const ex & c)
 {
-       if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+       static ex f = (new su3f)->setflag(status_flags::dynallocated);
+
+       if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
                throw(std::invalid_argument("indices of color_f must be of type idx"));
-       if (!ex_to_idx(a).get_dim().is_equal(8) || !ex_to_idx(b).get_dim().is_equal(8) || !ex_to_idx(c).get_dim().is_equal(8))
+       if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
                throw(std::invalid_argument("index dimension for color_f must be 8"));
 
-       return indexed(su3f(), indexed::antisymmetric, a, b, c);
+       return indexed(f, antisymmetric3(), a, b, c);
 }
 
 ex color_d(const ex & a, const ex & b, const ex & c)
 {
-       if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+       static ex d = (new su3d)->setflag(status_flags::dynallocated);
+
+       if (!is_a<idx>(a) || !is_a<idx>(b) || !is_a<idx>(c))
                throw(std::invalid_argument("indices of color_d must be of type idx"));
-       if (!ex_to_idx(a).get_dim().is_equal(8) || !ex_to_idx(b).get_dim().is_equal(8) || !ex_to_idx(c).get_dim().is_equal(8))
+       if (!ex_to<idx>(a).get_dim().is_equal(8) || !ex_to<idx>(b).get_dim().is_equal(8) || !ex_to<idx>(c).get_dim().is_equal(8))
                throw(std::invalid_argument("index dimension for color_d must be 8"));
 
-       return indexed(su3d(), indexed::symmetric, a, b, c);
+       return indexed(d, symmetric3(), a, b, c);
 }
 
 ex color_h(const ex & a, const ex & b, const ex & c)
@@ -406,4 +521,125 @@ ex color_h(const ex & a, const ex & b, const ex & c)
        return color_d(a, b, c) + I * color_f(a, b, c);
 }
 
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ *  is that of a color object (with an arbitrary representation label). */
+static bool is_color_tinfo(const return_type_t& ti)
+{
+       return *(ti.tinfo) == typeid(color);
+}
+
+/** Extract representation label from tinfo key (as returned by
+ *  return_type_tinfo()). */
+static unsigned char get_representation_label(const return_type_t& ti)
+{
+       return (unsigned char)ti.rl;
+}
+
+ex color_trace(const ex & e, const std::set<unsigned char> & rls)
+{
+       if (is_a<color>(e)) {
+
+               unsigned char rl = ex_to<color>(e).get_representation_label();
+
+               // Are we taking the trace over this object's representation label?
+               if (rls.find(rl) == rls.end())
+                       return e;
+
+               // Yes, all generators are traceless, except for color_ONE
+               if (is_a<su3one>(e.op(0)))
+                       return _ex3;
+               else
+                       return _ex0;
+
+       } else if (is_exactly_a<mul>(e)) {
+
+               // Trace of product: pull out non-color factors
+               ex prod = _ex1;
+               for (size_t i=0; i<e.nops(); i++) {
+                       const ex &o = e.op(i);
+                       if (is_color_tinfo(o.return_type_tinfo()))
+                               prod *= color_trace(o, rls);
+                       else
+                               prod *= o;
+               }
+               return prod;
+
+       } else if (is_exactly_a<ncmul>(e)) {
+
+               unsigned char rl = get_representation_label(e.return_type_tinfo());
+
+               // Are we taking the trace over this string's representation label?
+               if (rls.find(rl) == rls.end())
+                       return e;
+
+               // Yes, expand product if necessary
+               ex e_expanded = e.expand();
+               if (!is_a<ncmul>(e_expanded))
+                       return color_trace(e_expanded, rls);
+
+               size_t num = e.nops();
+
+               if (num == 2) {
+
+                       // Tr T_a T_b = 1/2 delta_a_b
+                       return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
+
+               } else if (num == 3) {
+
+                       // Tr T_a T_b T_c = 1/4 h_a_b_c
+                       return color_h(e.op(0).op(1), e.op(1).op(1), e.op(2).op(1)) / 4;
+
+               } else {
+
+                       // Traces of 4 or more generators are computed recursively:
+                       // Tr T_a1 .. T_an =
+                       //     1/6 delta_a(n-1)_an Tr T_a1 .. T_a(n-2)
+                       //   + 1/2 h_a(n-1)_an_k Tr T_a1 .. T_a(n-2) T_k
+                       const ex &last_index = e.op(num - 1).op(1);
+                       const ex &next_to_last_index = e.op(num - 2).op(1);
+                       idx summation_index((new symbol)->setflag(status_flags::dynallocated), 8);
+
+                       exvector v1;
+                       v1.reserve(num - 2);
+                       for (size_t i=0; i<num-2; i++)
+                               v1.push_back(e.op(i));
+
+                       exvector v2 = v1;
+                       v2.push_back(color_T(summation_index, rl));
+
+                       return delta_tensor(next_to_last_index, last_index) * color_trace(ncmul(v1), rl) / 6
+                              + color_h(next_to_last_index, last_index, summation_index) * color_trace(ncmul(v2), rl) / 2;
+               }
+
+       } else if (e.nops() > 0) {
+
+               // Trace maps to all other container classes (this includes sums)
+               pointer_to_map_function_1arg<const std::set<unsigned char> &> fcn(color_trace, rls);
+               return e.map(fcn);
+
+       } else
+               return _ex0;
+}
+
+ex color_trace(const ex & e, const lst & rll)
+{
+       // Convert list to set
+       std::set<unsigned char> rls;
+       for (lst::const_iterator i = rll.begin(); i != rll.end(); ++i) {
+               if (i->info(info_flags::nonnegint))
+                       rls.insert(ex_to<numeric>(*i).to_int());
+       }
+
+       return color_trace(e, rls);
+}
+
+ex color_trace(const ex & e, unsigned char rl)
+{
+       // Convert label to set
+       std::set<unsigned char> rls;
+       rls.insert(rl);
+
+       return color_trace(e, rls);
+}
+
 } // namespace GiNaC