- dirac_trace() handles arbitrary expressions (even unexpanded), including
[ginac.git] / ginac / color.cpp
index b59e4b4ce1a030b340b1a248a6be6d4b070ef34e..e36c1cbe9796effef77d085d228bb4f5be614894 100644 (file)
@@ -1,10 +1,9 @@
 /** @file color.cpp
  *
 /** @file color.cpp
  *
- *  Implementation of GiNaC's color objects.
- *  No real implementation yet, to be done.     */
+ *  Implementation of GiNaC's color (SU(3) Lie algebra) objects. */
 
 /*
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2001 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
  *
  *  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
  */
 
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
-#include <string>
-#include <list>
 #include <algorithm>
 #include <algorithm>
-#include <iostream>
 #include <stdexcept>
 
 #include "color.h"
 #include "ex.h"
 #include <stdexcept>
 
 #include "color.h"
 #include "ex.h"
-#include "coloridx.h"
+#include "idx.h"
 #include "ncmul.h"
 #include "numeric.h"
 #include "ncmul.h"
 #include "numeric.h"
-#include "relational.h"
+#include "power.h" // for sqrt()
+#include "symbol.h"
+#include "print.h"
+#include "archive.h"
 #include "debugmsg.h"
 #include "debugmsg.h"
+#include "utils.h"
 
 namespace GiNaC {
 
 
 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)
+
 //////////
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
 //////////
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
-// public
-
-color::color() : type(invalid), representation_label(0)
-{
-    debugmsg("color default constructor",LOGLEVEL_CONSTRUCT);
-    tinfo_key=TINFO_color;
-}
-
-color::~color()
-{
-    debugmsg("color destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
-}
-
-color::color(color const & other)
+color::color() : representation_label(0)
 {
 {
-    debugmsg("color copy constructor",LOGLEVEL_CONSTRUCT);
-    copy (other);
+       debugmsg("color default constructor", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_color;
 }
 
 }
 
-color const & color::operator=(color const & other)
+void color::copy(const color & other)
 {
 {
-    debugmsg("color operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-       copy(other);
-    }
-    return *this;
+       inherited::copy(other);
+       representation_label = other.representation_label;
 }
 
 }
 
-// protected
-
-void color::copy(color const & other)
-{
-    indexed::copy(other);
-    type=other.type;
-    representation_label=other.representation_label;
-}
-
-void color::destroy(bool call_parent)
-{
-    if (call_parent) {
-        indexed::destroy(call_parent);
-    }
-}
+DEFAULT_DESTROY(color)
+DEFAULT_CTORS(su3one)
+DEFAULT_CTORS(su3t)
+DEFAULT_CTORS(su3f)
+DEFAULT_CTORS(su3d)
 
 //////////
 // other constructors
 //////////
 
 
 //////////
 // other constructors
 //////////
 
-// protected
-
-color::color(color_types const t, unsigned const rl) : type(t), representation_label(rl)
+/** 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 char rl) : inherited(b), representation_label(rl)
 {
 {
-    debugmsg("color constructor from color_types,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       debugmsg("color constructor from ex,unsigned char", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_color;
 }
 
 }
 
-color::color(color_types const t, ex const & i1, unsigned const rl)
-    : indexed(i1), type(t), representation_label(rl)
+/** 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 char rl) : inherited(b, i1), representation_label(rl)
 {
 {
-    debugmsg("color constructor from color_types,ex,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       debugmsg("color constructor from ex,ex,unsigned char", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_color;
 }
 
 }
 
-color::color(color_types const t, ex const & i1, ex const & i2, unsigned const rl)
-    : indexed(i1,i2), type(t), representation_label(rl)
+color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(indexed::unknown, v, discardable), representation_label(rl)
 {
 {
-    debugmsg("color constructor from color_types,ex,ex,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       debugmsg("color constructor from unsigned char,exvector", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_color;
 }
 
 }
 
-color::color(color_types const t, ex const & i1, ex const & i2, ex const & i3,
-             unsigned const rl) : indexed(i1,i2,i3), type(t), representation_label(rl)
+color::color(unsigned char rl, exvector * vp) : inherited(indexed::unknown, vp), representation_label(rl)
 {
 {
-    debugmsg("color constructor from color_types,ex,ex,ex,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       debugmsg("color constructor from unsigned char,exvector *", LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_color;
 }
 
 }
 
-color::color(color_types const t, exvector const & iv, unsigned const rl)
-    : indexed(iv), type(t), representation_label(rl)
+//////////
+// archiving
+//////////
+
+color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
 {
-    debugmsg("color constructor from color_types,exvector,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
+       unsigned rl;
+       n.find_unsigned("label", rl);
+       representation_label = rl;
 }
 
 }
 
-color::color(color_types const t, exvector * ivp, unsigned const rl)
-    : indexed(ivp), type(t), representation_label(rl)
+void color::archive(archive_node &n) const
 {
 {
-    debugmsg("color constructor from color_types,exvector *,unsigned",LOGLEVEL_CONSTRUCT);
-    ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-    tinfo_key=TINFO_color;
-    ASSERT(all_of_type_coloridx());
+       inherited::archive(n);
+       n.add_unsigned("label", representation_label);
 }
 
 }
 
+DEFAULT_UNARCHIVE(color)
+DEFAULT_ARCHIVING(su3one)
+DEFAULT_ARCHIVING(su3t)
+DEFAULT_ARCHIVING(su3f)
+DEFAULT_ARCHIVING(su3d)
+
 //////////
 // functions overriding virtual functions from bases classes
 //////////
 
 //////////
 // functions overriding virtual functions from bases classes
 //////////
 
-// public
-
-basic * color::duplicate() const
+int color::compare_same_type(const basic & other) const
 {
 {
-    debugmsg("color duplicate",LOGLEVEL_DUPLICATE);
-    return new color(*this);
-}
+       GINAC_ASSERT(other.tinfo() == TINFO_color);
+       const color &o = static_cast<const color &>(other);
 
 
-void color::printraw(ostream & os) const
-{
-    debugmsg("color printraw",LOGLEVEL_PRINT);
-    os << "color(type=" << (unsigned)type
-       << ",representation_label=" << representation_label
-       << ",indices=";
-    printrawindices(os);
-    os << ",hash=" << hashvalue << ",flags=" << flags << ")";
+       if (representation_label != o.representation_label) {
+               // different representation label
+               return representation_label < o.representation_label ? -1 : 1;
+       }
+
+       return inherited::compare_same_type(other);
 }
 
 }
 
-void color::printtree(ostream & os, unsigned indent) const
+DEFAULT_COMPARE(su3one)
+DEFAULT_COMPARE(su3t)
+DEFAULT_COMPARE(su3f)
+DEFAULT_COMPARE(su3d)
+
+DEFAULT_PRINT(su3one, "ONE")
+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
 {
 {
-    debugmsg("color printtree",LOGLEVEL_PRINT);
-    os << string(indent,' ') << "color object: "
-       << "type=" << (unsigned)type
-       << ",representation_label=" << representation_label << ", ";
-    os << seq.size() << " indices" << endl;
-    printtreeindices(os,indent);
-    os << string(indent,' ') << "hash=" << hashvalue
-       << " (0x" << hex << hashvalue << dec << ")"
-       << ", flags=" << flags << endl;
+       //!! TODO: sort by representation label
+       exvector s;
+       s.reserve(v.size());
+
+       exvector::const_iterator it = v.begin(), itend = v.end();
+       while (it != itend) {
+               if (!is_ex_of_type(it->op(0), su3one))
+                       s.push_back(*it);
+               it++;
+       }
+
+       if (s.size() == 0)
+               return color(su3one());
+       else if (s.size() == v.size())
+               return simplified_ncmul(v);
+       else
+               return simplified_ncmul(s);
 }
 
 }
 
-void color::print(ostream & os, unsigned upper_precedence) const
+ex color::thisexprseq(const exvector & v) const
 {
 {
-    debugmsg("color print",LOGLEVEL_PRINT);
-    switch (type) {
-    case color_T:
-        os << "T";
-        if (representation_label!=0) {
-            os << "^(" << representation_label << ")";
-        }
-        break;
-    case color_f:
-        os << "f";
-        break;
-    case color_d:
-        os << "d";
-        break;
-    case color_delta8:
-        os << "delta8";
-        break;
-    case color_ONE:
-        os << "color_ONE";
-        break;
-    case invalid:
-    default:
-        os << "INVALID_COLOR_OBJECT";
-        break;
-    }
-    printindices(os);
+       return color(representation_label, v);
 }
 
 }
 
-void color::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
+ex color::thisexprseq(exvector * vp) const
 {
 {
-    debugmsg("color print csrc",LOGLEVEL_PRINT);
-    print(os,upper_precedence);
+       return color(representation_label, vp);
 }
 
 }
 
-bool color::info(unsigned inf) const
+/** Given a vector iv3 of three indices and a vector iv2 of two indices that
+ *  is a subset of iv3, return the (free) index that is in iv3 but not in
+ *  iv2 and the sign introduced by permuting that index to the front.
+ *
+ *  @param iv3 Vector of 3 indices
+ *  @param iv2 Vector of 2 indices, must be a subset of iv3
+ *  @param sig Returs sign introduced by index permutation
+ *  @return the free index (the one that is in iv3 but not in iv2) */
+static ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int & sig)
 {
 {
-    return indexed::info(inf);
-}
+       GINAC_ASSERT(iv3.size() == 3);
+       GINAC_ASSERT(iv2.size() == 2);
 
 
-#define CMPINDICES(A,B,C) ((idx1.get_value()==(A))&&(idx2.get_value()==(B))&&(idx3.get_value()==(C)))
+       sig = 1;
 
 
-ex color::eval(int level) const
-{
-    // canonicalize indices
-    
-    bool antisymmetric=false;
-    
-    switch (type) {
-    case color_f:
-        antisymmetric=true; // no break here!
-    case color_d:
-    case color_delta8:
-        {
-            exvector iv=seq;
-            int sig=canonicalize_indices(iv,antisymmetric);
-            if (sig!=INT_MAX) {
-                // something has changed while sorting indices, more evaluations later
-                if (sig==0) return exZERO();
-                return ex(sig)*color(type,iv,representation_label);
-            }
-        }
-        break;
-    default:
-        // nothing to canonicalize
-        break;
-    }
-
-    switch (type) {
-    case color_delta8:
-        {
-            ASSERT(seq.size()==2);
-            coloridx const & idx1=ex_to_coloridx(seq[0]);
-            coloridx const & idx2=ex_to_coloridx(seq[1]);
-            
-            // check for delta8_{a,a} where a is a symbolic index, replace by 8
-            if ((idx1.is_symbolic())&&(idx1.is_equal_same_type(idx2))) {
-                return ex(COLOR_EIGHT);
-            }
-
-            // check for delta8_{a,b} where a and b are numeric indices, replace by 0 or 1
-            if ((!idx1.is_symbolic())&&(!idx2.is_symbolic())) {
-                if ((idx1.get_value()!=idx2.get_value())) {
-                    return exONE();
-                } else {
-                    return exZERO();
-                }
-            }
+#define TEST_PERMUTATION(A,B,C,P) \
+       if (iv3[B].is_equal(iv2[0]) && iv3[C].is_equal(iv2[1])) { \
+               sig = P; \
+               return iv3[A]; \
+       }
+       
+       TEST_PERMUTATION(0,1,2,  1);
+       TEST_PERMUTATION(0,2,1, -1);
+       TEST_PERMUTATION(1,0,2, -1);
+       TEST_PERMUTATION(1,2,0,  1);
+       TEST_PERMUTATION(2,0,1,  1);
+       TEST_PERMUTATION(2,1,0, -1);
+
+       throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
+}
+
+/** 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(i.nops() == 4);
+       GINAC_ASSERT(is_ex_of_type(i.op(0), su3d));
+
+       // Convolutions are zero
+       if (static_cast<const indexed &>(i).get_dummy_indices().size() != 0)
+               return _ex0();
+
+       // Numeric evaluation
+       if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+
+               // 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();
+               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]);
+
+#define CMPINDICES(A,B,C) ((v[0] == (A)) && (v[1] == (B)) && (v[2] == (C)))
+
+               // 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();
+               else if (CMPINDICES(2,4,7) || CMPINDICES(3,6,6) || CMPINDICES(3,7,7))
+                       return _ex_1_2();
+               else if (CMPINDICES(1,1,8) || CMPINDICES(2,2,8) || CMPINDICES(3,3,8))
+                       return sqrt(_ex3())/3;
+               else if (CMPINDICES(8,8,8))
+                       return -sqrt(_ex3())/3;
+               else if (CMPINDICES(4,4,8) || CMPINDICES(5,5,8)
+                     || CMPINDICES(6,6,8) || CMPINDICES(7,7,8))
+                       return -sqrt(_ex3())/6;
+               else
+                       return _ex0();
        }
        }
-        break;
-    case color_d:
-        // check for d_{a,a,c} (=0) when a is symbolic
-        {
-            ASSERT(seq.size()==3);
-            coloridx const & idx1=ex_to_coloridx(seq[0]);
-            coloridx const & idx2=ex_to_coloridx(seq[1]);
-            coloridx const & idx3=ex_to_coloridx(seq[2]);
-            
-            if (idx1.is_equal_same_type(idx2) && idx1.is_symbolic()) {
-                return exZERO();
-            } else if (idx2.is_equal_same_type(idx3) && idx2.is_symbolic()) {
-                return exZERO();
-            }
-            
-            // check for three numeric indices
-            if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
-                ASSERT(idx1.get_value()<=idx2.get_value());
-                ASSERT(idx2.get_value()<=idx3.get_value());
-                if (CMPINDICES(1,4,6)||CMPINDICES(1,5,7)||CMPINDICES(2,5,6)||
-                    CMPINDICES(3,4,4)||CMPINDICES(3,5,5)) {
-                    return exHALF();
-                } else if (CMPINDICES(2,4,7)||CMPINDICES(3,6,6)||CMPINDICES(3,7,7)) {
-                    return -exHALF();
-                } else if (CMPINDICES(1,1,8)||CMPINDICES(2,2,8)||CMPINDICES(3,3,8)) {
-                    return 1/sqrt(numeric(3));
-                } else if (CMPINDICES(8,8,8)) {
-                    return -1/sqrt(numeric(3));
-                } else if (CMPINDICES(4,4,8)||CMPINDICES(5,5,8)||CMPINDICES(6,6,8)||CMPINDICES(7,7,8)) {
-                    return -1/(2*sqrt(numeric(3)));
-                }
-                return exZERO();
-            }
-        }
-        break;
-    case color_f:
-        {
-            ASSERT(seq.size()==3);
-            coloridx const & idx1=ex_to_coloridx(seq[0]);
-            coloridx const & idx2=ex_to_coloridx(seq[1]);
-            coloridx const & idx3=ex_to_coloridx(seq[2]);
-            
-            // check for three numeric indices
-            if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
-                ASSERT(idx1.get_value()<=idx2.get_value());
-                ASSERT(idx2.get_value()<=idx3.get_value());
-                if (CMPINDICES(1,2,3)) {
-                    return exONE();
-                } else if (CMPINDICES(1,4,7)||CMPINDICES(2,4,6)||
-                           CMPINDICES(2,5,7)||CMPINDICES(3,4,5)) {
-                    return exHALF();
-                } else if (CMPINDICES(1,5,6)||CMPINDICES(3,6,7)) {
-                    return -exHALF();
-                } else if (CMPINDICES(4,5,8)||CMPINDICES(6,7,8)) {
-                    return sqrt(numeric(3))/2;
-                } else if (CMPINDICES(8,8,8)) {
-                    return -1/sqrt(numeric(3));
-                } else if (CMPINDICES(4,4,8)||CMPINDICES(5,5,8)||CMPINDICES(6,6,8)||CMPINDICES(7,7,8)) {
-                    return -1/(2*sqrt(numeric(3)));
-                }
-                return exZERO();
-            }
-            break;
-        }
-    default:
-        // nothing to evaluate
-        break;
-    }
-    
-    return this->hold();
-}
-    
-// protected
 
 
-int color::compare_same_type(basic const & other) const
-{
-    ASSERT(other.tinfo() == TINFO_color);
-    const color *o = static_cast<const color *>(&other);
-    if (type==o->type) {
-        if (representation_label==o->representation_label) {
-            return indexed::compare_same_type(other);
-        }
-        return representation_label < o->representation_label ? -1 : 1;
-    }
-    return type < o->type ? -1 : 1;
-}
+       // No further simplifications
+       return i.hold();
+}
+
+/** 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(i.nops() == 4);
+       GINAC_ASSERT(is_ex_of_type(i.op(0), su3f));
+
+       // Numeric evaluation
+       if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+
+               // 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();
+               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; }
+               if (v[1] > v[2]) { std::swap(v[1], v[2]); sign = -sign; }
+
+               // Check for non-zero elements
+               if (CMPINDICES(1,2,3))
+                       return sign;
+               else if (CMPINDICES(1,4,7) || CMPINDICES(2,4,6)
+                     || CMPINDICES(2,5,7) || CMPINDICES(3,4,5))
+                       return _ex1_2() * sign;
+               else if (CMPINDICES(1,5,6) || CMPINDICES(3,6,7))
+                       return _ex_1_2() * sign;
+               else if (CMPINDICES(4,5,8) || CMPINDICES(6,7,8))
+                       return sqrt(_ex3())/2 * sign;
+               else
+                       return _ex0();
+       }
 
 
-bool color::is_equal_same_type(basic const & other) const
-{
-    ASSERT(other.tinfo() == TINFO_color);
-    const color *o = static_cast<const color *>(&other);
-    if (type!=o->type) return false;
-    if (representation_label!=o->representation_label) return false;
-    return indexed::is_equal_same_type(other);
+       // No further simplifications
+       return i.hold();
 }
 
 }
 
-#include <iostream>
 
 
-ex color::simplify_ncmul(exvector const & v) const
+/** Contraction of an indexed symmetric structure constant with something else. */
+bool su3d::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
 {
-    // simplifications: contract delta8_{a,b} where possible
-    //                  sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...
-    //                  remove superfluous ONEs
-    
-    // contract indices of delta8_{a,b} if they are different and symbolic
-
-    exvector v_contracted=v;
-    unsigned replacements;
-    bool something_changed=false;
-
-    exvector::iterator it=v_contracted.begin();
-    while (it!=v_contracted.end()) {
-        // process only delta8 objects
-        if (is_ex_exactly_of_type(*it,color) && (ex_to_color(*it).type==color_delta8)) {
-            color & d8=ex_to_nonconst_color(*it);
-            ASSERT(d8.seq.size()==2);
-            coloridx const & first_idx=ex_to_coloridx(d8.seq[0]);
-            coloridx const & second_idx=ex_to_coloridx(d8.seq[1]);
-            // delta8_{a,a} should have been contracted in color::eval()
-            ASSERT((!first_idx.is_equal(second_idx))||(!first_idx.is_symbolic()));
-            ex saved_delta8=*it; // save to restore it later
-
-            // try to contract first index
-            replacements=1;
-            if (first_idx.is_symbolic()) {
-                replacements = subs_index_in_exvector(v_contracted,first_idx,second_idx);
-                if (replacements==1) {
-                    // not contracted except in itself, restore delta8 object
-                    *it=saved_delta8;
-                } else {
-                    // a contracted index should occur exactly twice
-                    ASSERT(replacements==2);
-                    *it=exONE();
-                    something_changed=true;
-                }
-            }
-
-            // try second index only if first was not contracted
-            if ((replacements==1)&&(second_idx.is_symbolic())) {
-                // first index not contracted, *it is guaranteed to be the original delta8 object
-                replacements = subs_index_in_exvector(v_contracted,second_idx,first_idx);
-                if (replacements==1) {
-                    // not contracted except in itself, restore delta8 object
-                    *it=saved_delta8;
-                } else {
-                    // a contracted index should occur exactly twice
-                    ASSERT(replacements==2);
-                    *it=exONE();
-                    something_changed=true;
-                }
-            }
-        }
-        ++it;
-    }
-
-    if (something_changed) {
-        // do more simplifications later
-        return nonsimplified_ncmul(v_contracted);
-    }
-
-    // there were no indices to contract
-    // sort delta8,f,d,T(rl=0),T(rl=1),...,ONE(rl=0),ONE(rl=1),...,unknown
-    // (if there is at least one unknown object, all Ts will be unknown to not change the order)
-    
-    exvector delta8vec;
-    exvector fvec;
-    exvector dvec;
-    vector<exvector> Tvecs;
-    Tvecs.resize(MAX_REPRESENTATION_LABELS);
-    vector<exvector> ONEvecs;
-    ONEvecs.resize(MAX_REPRESENTATION_LABELS);
-    exvector unknownvec;
-    
-    split_color_string_in_parts(v,delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
-
-    // d_{a,k,l} f_{b,k,l}=0 (includes case a=b)
-    if ((dvec.size()>=1)&&(fvec.size()>=1)) {
-        for (exvector::iterator it1=dvec.begin(); it1!=dvec.end(); ++it1) {
-            for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
-                ASSERT(is_ex_exactly_of_type(*it1,color));
-                ASSERT(is_ex_exactly_of_type(*it2,color));
-                color const & col1=ex_to_color(*it1);
-                color const & col2=ex_to_color(*it2);
-                exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
-                if (iv_intersect.size()>=2) return exZERO();
-            }
-        }
-    }
-    
-    // d_{a,k,l} d_{b,k,l}=5/3 delta8_{a,b} (includes case a=b)
-    if (dvec.size()>=2) {
-        for (exvector::iterator it1=dvec.begin(); it1!=dvec.end()-1; ++it1) {
-            for (exvector::iterator it2=it1+1; it2!=dvec.end(); ++it2) {
-                ASSERT(is_ex_exactly_of_type(*it1,color));
-                ASSERT(is_ex_exactly_of_type(*it2,color));
-                color const & col1=ex_to_color(*it1);
-                color const & col2=ex_to_color(*it2);
-                exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
-                if (iv_intersect.size()>=2) {
-                    if (iv_intersect.size()==3) {
-                        *it1=numeric(40)/numeric(3);
-                        *it2=exONE();
-                    } else {
-                        int sig1, sig2; // unimportant, since symmetric
-                        ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,false,&sig1);
-                        ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,false,&sig2);
-                        *it1=numeric(5)/numeric(3)*color(color_delta8,idx1,idx2);
-                        *it2=exONE();
-                    }
-                    return nonsimplified_ncmul(recombine_color_string(
-                           delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                }
-            }
-        }
-    }
-
-    // f_{a,k,l} f_{b,k,l}=3 delta8_{a,b} (includes case a=b)
-    if (fvec.size()>=2) {
-        for (exvector::iterator it1=fvec.begin(); it1!=fvec.end()-1; ++it1) {
-            for (exvector::iterator it2=it1+1; it2!=fvec.end(); ++it2) {
-                ASSERT(is_ex_exactly_of_type(*it1,color));
-                ASSERT(is_ex_exactly_of_type(*it2,color));
-                color const & col1=ex_to_color(*it1);
-                color const & col2=ex_to_color(*it2);
-                exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
-                if (iv_intersect.size()>=2) {
-                    if (iv_intersect.size()==3) {
-                        *it1=numeric(24);
-                        *it2=exONE();
-                    } else {
-                        int sig1, sig2;
-                        ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,true,&sig1);
-                        ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,true,&sig2);
-                        *it1=numeric(sig1*sig2*5)/numeric(3)*color(color_delta8,idx1,idx2);
-                        *it2=exONE();
-                    }
-                    return nonsimplified_ncmul(recombine_color_string(
-                           delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                }
-            }
-        }
-    }
-
-    // d_{a,b,c} T_b T_c = 5/6 T_a
-    // f_{a,b,c} T_b T_c = 3/2 I T_a
-    for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
-        if ((Tvecs[rl].size()>=2)&&((dvec.size()>=1)||(fvec.size()>=1))) {
-            for (exvector::iterator it1=Tvecs[rl].begin(); it1!=Tvecs[rl].end()-1; ++it1) {
-                exvector iv;
-                ASSERT(is_ex_exactly_of_type(*it1,color)&&ex_to_color(*it1).type==color_T);
-                ASSERT(is_ex_exactly_of_type(*(it1+1),color)&&ex_to_color(*(it1+1)).type==color_T);
-                iv.push_back(ex_to_color(*it1).seq[0]);
-                iv.push_back(ex_to_color(*(it1+1)).seq[0]);
-                
-                // d_{a,b,c} T_b T_c = 5/6 T_a
-                for (exvector::iterator it2=dvec.begin(); it2!=dvec.end(); ++it2) {
-                    ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_d);
-                    color const & dref=ex_to_color(*it2);
-                    exvector iv_intersect=idx_intersect(dref.seq,iv);
-                    if (iv_intersect.size()==2) {
-                        int sig; // unimportant, since symmetric
-                        ex free_idx=permute_free_index_to_front(dref.seq,iv,false,&sig);
-                        *it1=color(color_T,free_idx,rl);
-                        *(it1+1)=color(color_ONE,rl);
-                        *it2=numeric(5)/numeric(6);
-                        return nonsimplified_ncmul(recombine_color_string(
-                               delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                    }
-                }
-
-                // f_{a,b,c} T_b T_c = 3/2 I T_a
-                for (exvector::iterator it2=fvec.begin(); it2!=fvec.end(); ++it2) {
-                    ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_f);
-                    color const & fref=ex_to_color(*it2);
-                    exvector iv_intersect=idx_intersect(fref.seq,iv);
-                    if (iv_intersect.size()==2) {
-                        int sig;
-                        ex free_idx=permute_free_index_to_front(fref.seq,iv,true,&sig);
-                        *it1=color(color_T,free_idx,rl);
-                        *(it1+1)=color(color_ONE,rl);
-                        *it2=numeric(sig*3)/numeric(2)*I;
-                        return nonsimplified_ncmul(recombine_color_string(
-                               delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                    }
-                }
-            }
-        }
-    }
-    
-    // clear all ONEs when there is at least one corresponding color_T
-    // in this representation, retain one ONE otherwise
-    for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
-        if (Tvecs[rl].size()!=0) {
-            ONEvecs[rl].clear();
-        } else if (ONEvecs[rl].size()!=0) {
-            ONEvecs[rl].clear();
-            ONEvecs[rl].push_back(color(color_ONE,rl));
-        }
-    }
-
-    // return a sorted vector
-    return simplified_ncmul(recombine_color_string(delta8vec,fvec,dvec,Tvecs,
-                                                   ONEvecs,unknownvec));
-}
+       GINAC_ASSERT(is_ex_of_type(*self, indexed));
+       GINAC_ASSERT(is_ex_of_type(*other, indexed));
+       GINAC_ASSERT(self->nops() == 4);
+       GINAC_ASSERT(is_ex_of_type(self->op(0), su3d));
 
 
-ex color::thisexprseq(exvector const & v) const
-{
-    return color(type,v,representation_label);
-}
+       if (is_ex_exactly_of_type(other->op(0), su3d)) {
 
 
-ex color::thisexprseq(exvector * vp) const
-{
-    return color(type,vp,representation_label);
-}
+               // Find the dummy indices of the contraction
+               exvector dummy_indices;
+               dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 
 
-bool color::all_of_type_coloridx(void) const
-{
-    // used only inside of ASSERTs
-    for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        if (!is_ex_of_type(*cit,coloridx)) return false;
-    }
-    return true;
-}
+               // d.abc*d.abc=40/3
+               if (dummy_indices.size() == 3) {
+                       *self = numeric(40, 3);
+                       *other = _ex1();
+                       return true;
 
 
-//////////
-// virtual functions which can be overridden by derived classes
-//////////
+               // 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();
+                       return true;
+               }
+       }
 
 
-// none
+       return false;
+}
 
 
-//////////
-// non-virtual functions in this class
-//////////
+/** 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(self->nops() == 4);
+       GINAC_ASSERT(is_ex_of_type(self->op(0), su3f));
 
 
-//////////
-// static member variables
-//////////
+       if (is_ex_exactly_of_type(other->op(0), su3f)) { // f*d is handled by su3d class
 
 
-// none
+               // Find the dummy indices of the contraction
+               exvector dummy_indices;
+               dummy_indices = ex_to_indexed(*self).get_dummy_indices(ex_to_indexed(*other));
 
 
-//////////
-// global constants
-//////////
+               // f.abc*f.abc=24
+               if (dummy_indices.size() == 3) {
+                       *self = 24;
+                       *other = _ex1();
+                       return true;
 
 
-const color some_color;
-type_info const & typeid_color=typeid(some_color);
+               // 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);
+                       *self = sign1 * sign2 * 3 * delta_tensor(a, b);
+                       *other = _ex1();
+                       return true;
+               }
+       }
+
+       return false;
+}
 
 //////////
 
 //////////
-// friend functions
+// global functions
 //////////
 
 //////////
 
-color color_ONE(unsigned const rl)
+ex color_ONE(unsigned char rl)
 {
 {
-    return color(color::color_ONE,rl);
+       return color(su3one(), rl);
 }
 
 }
 
-color color_T(ex const & a, unsigned const rl)
+ex color_T(const ex & a, unsigned char rl)
 {
 {
-    return color(color::color_T,a,rl);
-}
+       if (!is_ex_of_type(a, idx))
+               throw(std::invalid_argument("indices of color_T must be of type idx"));
+       if (!ex_to_idx(a).get_dim().is_equal(8))
+               throw(std::invalid_argument("index dimension for color_T must be 8"));
 
 
-color color_f(ex const & a, ex const & b, ex const & c)
-{
-    return color(color::color_f,a,b,c);
+       return color(su3t(), a, rl);
 }
 
 }
 
-color color_d(ex const & a, ex const & b, ex const & c)
+ex color_f(const ex & a, const ex & b, const ex & c)
 {
 {
-    return color(color::color_d,a,b,c);
-}
+       if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+               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))
+               throw(std::invalid_argument("index dimension for color_f must be 8"));
 
 
-ex color_h(ex const & a, ex const & b, ex const & c)
-{
-    return color(color::color_d,a,b,c)+I*color(color::color_f,a,b,c);
+       return indexed(su3f(), indexed::antisymmetric, a, b, c);
 }
 
 }
 
-color color_delta8(ex const & a, ex const & b)
+ex color_d(const ex & a, const ex & b, const ex & c)
 {
 {
-    return color(color::color_delta8,a,b);
-}
+       if (!is_ex_of_type(a, idx) || !is_ex_of_type(b, idx) || !is_ex_of_type(c, idx))
+               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))
+               throw(std::invalid_argument("index dimension for color_d must be 8"));
 
 
-void split_color_string_in_parts(exvector const & v, exvector & delta8vec,
-                                 exvector & fvec, exvector & dvec,
-                                 vector<exvector> & Tvecs,
-                                 vector<exvector> & ONEvecs,
-                                 exvector & unknownvec)
-{
-    // if not all elements are of type color, put all Ts in unknownvec to
-    // retain the ordering
-    bool all_color=true;
-    for (exvector::const_iterator cit=v.begin(); cit!=v.end(); ++cit) {
-        if (!is_ex_exactly_of_type(*cit,color)) {
-            all_color=false;
-            break;
-        }
-    }
-    
-    for (exvector::const_iterator cit=v.begin(); cit!=v.end(); ++cit) {
-        if (is_ex_exactly_of_type(*cit,color)) {
-            switch (ex_to_color(*cit).type) {
-            case color::color_delta8:
-                delta8vec.push_back(*cit);
-                break;
-            case color::color_f:
-                fvec.push_back(*cit);
-                break;
-            case color::color_d:
-                dvec.push_back(*cit);
-                break;
-            case color::color_T:
-                ASSERT(ex_to_color(*cit).representation_label<MAX_REPRESENTATION_LABELS);
-                if (all_color) {
-                    Tvecs[ex_to_color(*cit).representation_label].push_back(*cit);
-                } else {
-                    unknownvec.push_back(*cit);
-                }
-                break;
-            case color::color_ONE:
-                ASSERT(ex_to_color(*cit).representation_label<MAX_REPRESENTATION_LABELS);
-                ONEvecs[ex_to_color(*cit).representation_label].push_back(*cit);
-                break;
-            default:
-                throw(std::logic_error("invalid type in split_color_string_in_parts()"));
-            }
-        } else {
-            unknownvec.push_back(*cit);
-        }
-    }
-}    
-
-exvector recombine_color_string(exvector & delta8vec, exvector & fvec,
-                                exvector & dvec, vector<exvector> & Tvecs,
-                                vector<exvector> & ONEvecs, exvector & unknownvec)
-{
-    unsigned sz=delta8vec.size()+fvec.size()+dvec.size()+unknownvec.size();
-    for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
-        sz += Tvecs[rl].size();
-        sz += ONEvecs[rl].size();
-    }
-    exvector v;
-    v.reserve(sz);
-    
-    append_exvector_to_exvector(v,delta8vec);
-    append_exvector_to_exvector(v,fvec);
-    append_exvector_to_exvector(v,dvec);
-    for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
-        append_exvector_to_exvector(v,Tvecs[rl]);
-        append_exvector_to_exvector(v,ONEvecs[rl]);
-    }
-    append_exvector_to_exvector(v,unknownvec);
-    return v;
+       return indexed(su3d(), indexed::symmetric, a, b, c);
 }
 
 }
 
-ex color_trace_of_one_representation_label(exvector const & v)
+ex color_h(const ex & a, const ex & b, const ex & c)
 {
 {
-    if (v.size()==0) {
-        return numeric(COLOR_THREE);
-    } else if (v.size()==1) {
-        ASSERT(is_ex_exactly_of_type(*(v.begin()),color));
-        return exZERO();
-    }
-    exvector v1=v;
-    ex last_element=v1.back();
-    ASSERT(is_ex_exactly_of_type(last_element,color));
-    ASSERT(ex_to_color(last_element).type==color::color_T);
-    v1.pop_back();
-    ex next_to_last_element=v1.back();
-    ASSERT(is_ex_exactly_of_type(next_to_last_element,color));
-    ASSERT(ex_to_color(next_to_last_element).type==color::color_T);
-    v1.pop_back();
-    exvector v2=v1;
-
-    ex const & last_index=ex_to_color(last_element).seq[0];
-    ex const & next_to_last_index=ex_to_color(next_to_last_element).seq[0];
-    ex summation_index=coloridx();
-
-    v2.push_back(color_T(summation_index)); // don't care about the representation_label
-    
-    // FIXME: check this formula for SU(N) with N!=3
-    return numeric(1)/numeric(2*COLOR_THREE)*color_delta8(next_to_last_index,last_index)
-           % color_trace_of_one_representation_label(v1)
-          +numeric(1)/numeric(2)*color_h(next_to_last_index,last_index,summation_index)
-           % color_trace_of_one_representation_label(v2);
-    /*
-    ex term1=numeric(1)/numeric(2*COLOR_THREE)*color_delta8(next_to_last_index,last_index)
-           % color_trace_of_one_representation_label(v1);
-    cout << "term 1 of trace of " << v.size() << " ts=" << term1 << endl;
-    ex term2=numeric(1)/numeric(2)*color_h(next_to_last_index,last_index,summation_index)
-           % color_trace_of_one_representation_label(v2);
-    cout << "term 2 of trace of " << v.size() << " ts=" << term2 << endl;
-    return term1+term2;
-    */
+       return color_d(a, b, c) + I * color_f(a, b, c);
 }
 
 }
 
-ex color_trace(exvector const & v, unsigned const rl)
+/** Check whether a given tinfo key (as returned by return_type_tinfo()
+ *  is that of a color object with the specified representation label. */
+static bool is_color_tinfo(unsigned ti, unsigned char rl)
 {
 {
-    ASSERT(rl<MAX_REPRESENTATION_LABELS);
-    
-    exvector v_rest;
-    v_rest.reserve(v.size()+1); // max size if trace is empty
-    
-    exvector delta8vec;
-    exvector fvec;
-    exvector dvec;
-    vector<exvector> Tvecs;
-    Tvecs.resize(MAX_REPRESENTATION_LABELS);
-    vector<exvector> ONEvecs;
-    ONEvecs.resize(MAX_REPRESENTATION_LABELS);
-    exvector unknownvec;
-
-    split_color_string_in_parts(v,delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
-
-    if (unknownvec.size()!=0) {
-        throw(std::invalid_argument("color_trace(): expression must be expanded"));
-    }
-
-    append_exvector_to_exvector(v_rest,delta8vec);
-    append_exvector_to_exvector(v_rest,fvec);
-    append_exvector_to_exvector(v_rest,dvec);
-    for (unsigned i=0; i<MAX_REPRESENTATION_LABELS; ++i) {
-        if (i!=rl) {
-            append_exvector_to_exvector(v_rest,Tvecs[i]);
-            append_exvector_to_exvector(v_rest,ONEvecs[i]);
-        } else {
-            if (Tvecs[i].size()!=0) {
-                v_rest.push_back(color_trace_of_one_representation_label(Tvecs[i]));
-            } else if (ONEvecs[i].size()!=0) {
-                v_rest.push_back(numeric(COLOR_THREE));
-            } else {
-                throw(std::logic_error("color_trace(): representation_label not in color string"));
-            }
-        }
-    }
-
-    return nonsimplified_ncmul(v_rest);
+       return ti == (TINFO_color + rl);
 }
 
 }
 
-ex simplify_pure_color_string(ex const & e)
-{
-    ASSERT(is_ex_exactly_of_type(e,ncmul));
-
-    exvector delta8vec;
-    exvector fvec;
-    exvector dvec;
-    vector<exvector> Tvecs;
-    Tvecs.resize(MAX_REPRESENTATION_LABELS);
-    vector<exvector> ONEvecs;
-    ONEvecs.resize(MAX_REPRESENTATION_LABELS);
-    exvector unknownvec;
-
-    split_color_string_in_parts(ex_to_ncmul(e).get_factors(),delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec);
-
-    // search for T_k S T_k (=1/2 Tr(S) - 1/6 S)
-    for (unsigned rl=0; rl<MAX_REPRESENTATION_LABELS; ++rl) {
-        if (Tvecs[rl].size()>=2) {
-            for (unsigned i=0; i<Tvecs[rl].size()-1; ++i) {
-                for (unsigned j=i+1; j<Tvecs[rl].size(); ++j) {
-                    ex & t1=Tvecs[rl][i];
-                    ex & t2=Tvecs[rl][j];
-                    ASSERT(is_ex_exactly_of_type(t1,color)&&
-                           (ex_to_color(t1).type==color::color_T)&&
-                           (ex_to_color(t1).seq.size()==1));
-                    ASSERT(is_ex_exactly_of_type(t2,color)&&
-                           (ex_to_color(t2).type==color::color_T)&&
-                           (ex_to_color(t2).seq.size()==1));
-                    coloridx const & idx1=ex_to_coloridx(ex_to_color(t1).seq[0]);
-                    coloridx const & idx2=ex_to_coloridx(ex_to_color(t2).seq[0]);
-                    
-                    if (idx1.is_equal(idx2) && idx1.is_symbolic()) {
-                        exvector S;
-                        for (unsigned k=i+1; k<j; ++k) {
-                            S.push_back(Tvecs[rl][k]);
-                        }
-                        t1=exONE();
-                        t2=exONE();
-                        ex term1=numeric(-1)/numeric(6)*nonsimplified_ncmul(recombine_color_string(
-                                 delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                        for (unsigned k=i+1; k<j; ++k) {
-                            S.push_back(exONE());
-                        }
-                        t1=color_trace_of_one_representation_label(S);
-                        ex term2=numeric(1)/numeric(2)*nonsimplified_ncmul(recombine_color_string(
-                                 delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-                        return simplify_color(term1+term2);
-                    }
-                }
-            }
-        }
-    }
-    
-    // FIXME: higher contractions
-    
-    return e;
-}
-    
-ex simplify_color(ex const & e)
+ex color_trace(const ex & e, unsigned char rl)
 {
 {
-    // all simplification is done on expanded objects
-    ex e_expanded=e.expand();
-
-    // simplification of sum=sum of simplifications
-    if (is_ex_exactly_of_type(e_expanded,add)) {
-        ex sum=exZERO();
-        for (int i=0; i<e_expanded.nops(); ++i) {
-            sum += simplify_color(e_expanded.op(i));
-        }
-        return sum;
-    }
-
-    // simplification of commutative product=commutative product of simplifications
-    if (is_ex_exactly_of_type(e_expanded,mul)) {
-        ex prod=exONE();
-        for (int i=0; i<e_expanded.nops(); ++i) {
-            prod *= simplify_color(e_expanded.op(i));
-        }
-        return prod;
-    }
-
-    // simplification of noncommutative product: test if everything is color
-    if (is_ex_exactly_of_type(e_expanded,ncmul)) {
-        bool all_color=true;
-        for (int i=0; i<e_expanded.nops(); ++i) {
-            if (!is_ex_exactly_of_type(e_expanded.op(i),color)) {
-                all_color=false;
-                break;
-            }
-        }
-        if (all_color) {
-            return simplify_pure_color_string(e_expanded);
-        }
-    }
-
-    // cannot do anything
-    return e_expanded;
-}
+       if (is_ex_of_type(e, color)) {
 
 
-ex brute_force_sum_color_indices(ex const & e)
-{
-    exvector iv_all=e.get_indices();
-    exvector iv_double;
-    
-    // find double symbolic indices
-    if (iv_all.size()<2) return e;
-    for (exvector::const_iterator cit1=iv_all.begin(); cit1!=iv_all.end()-1; ++cit1) {
-        ASSERT(is_ex_of_type(*cit1,coloridx));
-        for (exvector::const_iterator cit2=cit1+1; cit2!=iv_all.end(); ++cit2) {
-            ASSERT(is_ex_of_type(*cit2,coloridx));
-            if (ex_to_coloridx(*cit1).is_symbolic() && 
-                ex_to_coloridx(*cit1).is_equal(ex_to_coloridx(*cit2))) {
-                iv_double.push_back(*cit1);
-                break;
-            }
-        }
-    }
-
-    vector<int> counter;
-    counter.resize(iv_double.size());
-    int l;
-    for (l=0; unsigned(l)<iv_double.size(); ++l) {
-        counter[l]=1;
-    }
-
-    ex sum=exZERO();
-    
-    while (1) {
-        ex term=e;
-        for (l=0; unsigned(l)<iv_double.size(); ++l) {
-            term=term.subs(iv_double[l]==coloridx((unsigned)(counter[l])));
-            //iv_double[l].print(cout);
-            //cout << " " << counter[l] << " ";
-        }
-        //cout << endl;
-        sum += term;
-        
-        // increment counter[]
-        l=iv_double.size()-1;
-        while ((l>=0)&&((++counter[l])>(int)COLOR_EIGHT)) {
-            counter[l]=1;    
-            l--;
-        }
-        if (l<2) { cout << counter[0] << counter[1] << endl; }
-        if (l<0) break;
-    }
-    
-    return sum;
-}
+               if (ex_to_color(e).get_representation_label() == rl
+                && is_ex_of_type(e.op(0), su3one))
+                       return _ex3();
+               else
+                       return _ex0();
 
 
-void append_exvector_to_exvector(exvector & dest, exvector const & source)
-{
-    for (exvector::const_iterator cit=source.begin(); cit!=source.end(); ++cit) {
-        dest.push_back(*cit);
-    }
+       } else if (is_ex_exactly_of_type(e, add)) {
+
+               // Trace of sum = sum of traces
+               ex sum = _ex0();
+               for (unsigned i=0; i<e.nops(); i++)
+                       sum += color_trace(e.op(i), rl);
+               return sum;
+
+       } else if (is_ex_exactly_of_type(e, mul)) {
+
+               // Trace of product: pull out non-color factors
+               ex prod = _ex1();
+               for (unsigned i=0; i<e.nops(); i++) {
+                       const ex &o = e.op(i);
+                       if (is_color_tinfo(o.return_type_tinfo(), rl))
+                               prod *= color_trace(o, rl);
+                       else
+                               prod *= o;
+               }
+               return prod;
+
+       } else if (is_ex_exactly_of_type(e, ncmul)) {
+
+               if (!is_color_tinfo(e.return_type_tinfo(), rl))
+                       return _ex0();
+
+               // Expand product, if necessary
+               ex e_expanded = e.expand();
+               if (!is_ex_of_type(e_expanded, ncmul))
+                       return color_trace(e_expanded, rl);
+
+               unsigned 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 (int 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;
+               }
+       }
+
+       return _ex0();
 }
 
 } // namespace GiNaC
 }
 
 } // namespace GiNaC