X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fcolor.cpp;h=9a364c4395427198a842d765c0c057e34a6200b0;hp=5a9229b189e0f2d075d1188a7799bcab9d564e1e;hb=6d7bf9ee5a7ce05cb3a23dae664e781d7325d7b8;hpb=7cbe7effc515e4575b4d1fd1d6d75f0148eb8a89

diff --git a/ginac/color.cpp b/ginac/color.cpp
index 5a9229b1..9a364c43 100644
--- a/ginac/color.cpp
+++ b/ginac/color.cpp
@@ -1,10 +1,9 @@
 /** @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) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -21,985 +20,581 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
-#include <string>
-#include <list>
-#include <algorithm>
 #include <iostream>
 #include <stdexcept>
 
 #include "color.h"
-#include "ex.h"
-#include "coloridx.h"
+#include "idx.h"
 #include "ncmul.h"
+#include "symmetry.h"
+#include "operators.h"
 #include "numeric.h"
-#include "relational.h"
+#include "mul.h"
+#include "power.h" // for sqrt()
+#include "symbol.h"
 #include "archive.h"
-#include "debugmsg.h"
 #include "utils.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(color, indexed)
 
-//////////
-// 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;
-}
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3one, tensor,
+  print_func<print_dflt>(&su3one::do_print).
+  print_func<print_latex>(&su3one::do_print_latex))
 
-color::~color()
-{
-	debugmsg("color destructor",LOGLEVEL_DESTRUCT);
-	destroy(false);
-}
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3t, tensor,
+  print_func<print_dflt>(&su3t::do_print).
+  print_func<print_latex>(&su3t::do_print))
 
-color::color(const color & other)
-{
-	debugmsg("color copy constructor",LOGLEVEL_CONSTRUCT);
-	copy (other);
-}
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3f, tensor,
+  print_func<print_dflt>(&su3f::do_print).
+  print_func<print_latex>(&su3f::do_print))
 
-const color & color::operator=(const color & other)
-{
-	debugmsg("color operator=",LOGLEVEL_ASSIGNMENT);
-	if (this != &other) {
-		destroy(true);
-		copy(other);
-	}
-	return *this;
-}
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(su3d, tensor,
+  print_func<print_dflt>(&su3d::do_print).
+  print_func<print_latex>(&su3d::do_print))
 
-// protected
+//////////
+// default constructors
+//////////
 
-void color::copy(const color & other)
+color::color() : representation_label(0)
 {
-	inherited::copy(other);
-	type=other.type;
-	representation_label=other.representation_label;
+	tinfo_key = TINFO_color;
 }
 
-void color::destroy(bool call_parent)
-{
-	if (call_parent) {
-		inherited::destroy(call_parent);
-	}
-}
+DEFAULT_CTOR(su3one)
+DEFAULT_CTOR(su3t)
+DEFAULT_CTOR(su3f)
+DEFAULT_CTOR(su3d)
 
 //////////
 // other constructors
 //////////
 
-// protected
-
-color::color(color_types const t, unsigned rl) : type(t), representation_label(rl)
-{
-	debugmsg("color constructor from color_types,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
-}
-
-color::color(color_types const t, const ex & i1, unsigned rl)
-  : inherited(i1), 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,ex,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
+	tinfo_key = TINFO_color;
 }
 
-color::color(color_types const t, const ex & i1, const ex & i2, unsigned rl)
-  : inherited(i1,i2), 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,ex,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
+	tinfo_key = TINFO_color;
 }
 
-color::color(color_types const t, const ex & i1, const ex & i2, const ex & i3,
-             unsigned rl) : inherited(i1,i2,i3), type(t), representation_label(rl)
+color::color(unsigned char rl, const exvector & v, bool discardable) : inherited(sy_none(), v, discardable), representation_label(rl)
 {
-	debugmsg("color constructor from color_types,ex,ex,ex,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
+	tinfo_key = TINFO_color;
 }
 
-color::color(color_types const t, const exvector & iv, unsigned rl)
-  : inherited(iv), type(t), representation_label(rl)
+color::color(unsigned char rl, std::auto_ptr<exvector> vp) : inherited(sy_none(), vp), representation_label(rl)
 {
-	debugmsg("color constructor from color_types,exvector,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
-}
-
-color::color(color_types const t, exvector * ivp, unsigned rl)
-  : inherited(ivp), type(t), representation_label(rl)
-{
-	debugmsg("color constructor from color_types,exvector *,unsigned",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(representation_label<MAX_REPRESENTATION_LABELS);
-	tinfo_key=TINFO_color;
-	GINAC_ASSERT(all_of_type_coloridx());
+	tinfo_key = TINFO_color;
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-color::color(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
-	debugmsg("color constructor from archive_node", LOGLEVEL_CONSTRUCT);
-	unsigned int ty;
-	if (!(n.find_unsigned("type", ty)))
-		throw (std::runtime_error("unknown color type in archive"));
-	type = (color_types)ty;
-	if (!(n.find_unsigned("representation", representation_label)))
-		throw (std::runtime_error("unknown color representation label in archive"));
-}
-
-/** Unarchive the object. */
-ex color::unarchive(const archive_node &n, const lst &sym_lst)
+color::color(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 {
-	return (new color(n, sym_lst))->setflag(status_flags::dynallocated);
+	unsigned rl;
+	n.find_unsigned("label", rl);
+	representation_label = rl;
 }
 
-/** Archive the object. */
 void color::archive(archive_node &n) const
 {
 	inherited::archive(n);
-	n.add_unsigned("type", type);
-	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)
+
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base 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(is_a<color>(other));
+	const color &o = static_cast<const color &>(other);
 
-void color::printraw(std::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(std::ostream & os, unsigned indent) const
+bool color::match_same_type(const basic & other) const
 {
-	debugmsg("color printtree",LOGLEVEL_PRINT);
-	os << std::string(indent,' ') << "color object: "
-	   << "type=" << (unsigned)type
-	   << ",representation_label=" << representation_label << ", ";
-	os << seq.size() << " indices" << std::endl;
-	printtreeindices(os,indent);
-	os << std::string(indent,' ') << "hash=" << hashvalue
-	   << " (0x" << std::hex << hashvalue << std::dec << ")"
-	   << ", flags=" << flags << std::endl;
+	GINAC_ASSERT(is_a<color>(other));
+	const color &o = static_cast<const color &>(other);
+
+	return representation_label == o.representation_label;
 }
 
-void color::print(std::ostream & os, unsigned upper_precedence) const
+DEFAULT_COMPARE(su3one)
+DEFAULT_COMPARE(su3t)
+DEFAULT_COMPARE(su3f)
+DEFAULT_COMPARE(su3d)
+
+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::eval_ncmul(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;
+	exvector s;
+	s.reserve(v.size());
+
+	// Remove superfluous ONEs
+	exvector::const_iterator it = v.begin(), itend = v.end();
+	while (it != itend) {
+		if (!is_a<su3one>(it->op(0)))
+			s.push_back(*it);
+		it++;
 	}
-	printindices(os);
+
+	if (s.empty())
+		return color(su3one(), representation_label);
+	else
+		return hold_ncmul(s);
 }
 
-void color::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+ex color::thiscontainer(const exvector & v) const
 {
-	debugmsg("color print csrc",LOGLEVEL_PRINT);
-	print(os,upper_precedence);
+	return color(representation_label, v);
 }
 
-bool color::info(unsigned inf) const
+ex color::thiscontainer(std::auto_ptr<exvector> vp) const
 {
-	return inherited::info(inf);
+	return color(representation_label, vp);
 }
 
-#define CMPINDICES(A,B,C) ((idx1.get_value()==(A))&&(idx2.get_value()==(B))&&(idx3.get_value()==(C)))
-
-ex color::eval(int level) 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)
 {
-	// 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 _ex0();
-				return ex(sig)*color(type,iv,representation_label);
-			}
-		}
-		break;
-	default:
-		// nothing to canonicalize
-		break;
-	}
+	GINAC_ASSERT(iv3.size() == 3);
+	GINAC_ASSERT(iv2.size() == 2);
 
-	switch (type) {
-	case color_delta8:
-		{
-			GINAC_ASSERT(seq.size()==2);
-			const coloridx & idx1=ex_to_coloridx(seq[0]);
-			const coloridx & 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);
-			}
+	sig = 1;
 
-			// 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 _ex1();
-				} else {
-					return _ex0();
-				}
-			}
-	}
-		break;
-	case color_d:
-		// check for d_{a,a,c} (=0) when a is symbolic
-		{
-			GINAC_ASSERT(seq.size()==3);
-			const coloridx & idx1=ex_to_coloridx(seq[0]);
-			const coloridx & idx2=ex_to_coloridx(seq[1]);
-			const coloridx & idx3=ex_to_coloridx(seq[2]);
-			
-			if (idx1.is_equal_same_type(idx2) && idx1.is_symbolic()) {
-				return _ex0();
-			} else if (idx2.is_equal_same_type(idx3) && idx2.is_symbolic()) {
-				return _ex0();
-			}
-			
-			// check for three numeric indices
-			if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
-				GINAC_ASSERT(idx1.get_value()<=idx2.get_value());
-				GINAC_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 _ex1_2();
-				} else if (CMPINDICES(2,4,7)||CMPINDICES(3,6,6)||CMPINDICES(3,7,7)) {
-					return -_ex1_2();
-				} 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 _ex0();
-			}
-		}
-		break;
-	case color_f:
-		{
-			GINAC_ASSERT(seq.size()==3);
-			const coloridx & idx1=ex_to_coloridx(seq[0]);
-			const coloridx & idx2=ex_to_coloridx(seq[1]);
-			const coloridx & idx3=ex_to_coloridx(seq[2]);
-			
-			// check for three numeric indices
-			if (!(idx1.is_symbolic()||idx2.is_symbolic()||idx3.is_symbolic())) {
-				GINAC_ASSERT(idx1.get_value()<=idx2.get_value());
-				GINAC_ASSERT(idx2.get_value()<=idx3.get_value());
-				if (CMPINDICES(1,2,3)) {
-					return _ex1();
-				} else if (CMPINDICES(1,4,7)||CMPINDICES(2,4,6)||
-				           CMPINDICES(2,5,7)||CMPINDICES(3,4,5)) {
-					return _ex1_2();
-				} else if (CMPINDICES(1,5,6)||CMPINDICES(3,6,7)) {
-					return -_ex1_2();
-				} 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 _ex0();
-			}
-			break;
-		}
-	default:
-		// nothing to evaluate
-		break;
+#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]; \
 	}
 	
-	return this->hold();
-}
-	
-// protected
+	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_a<indexed>(i));
+	GINAC_ASSERT(i.nops() == 4);
+	GINAC_ASSERT(is_a<su3d>(i.op(0)));
+
+	// Convolutions are zero
+	if (!(static_cast<const indexed &>(i).get_dummy_indices().empty()))
+		return _ex0;
+
+	// Numeric evaluation
+	if (static_cast<const indexed &>(i).all_index_values_are(info_flags::nonnegint)) {
+
+		// 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)*_ex1_3;
+		else if (CMPINDICES(8,8,8))
+			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)/_ex_6;
+		else
+			return _ex0;
+	}
 
-int color::compare_same_type(const basic & other) const
-{
-	GINAC_ASSERT(other.tinfo() == TINFO_color);
-	const color *o = static_cast<const color *>(&other);
-	if (type==o->type) {
-		if (representation_label==o->representation_label) {
-			return inherited::compare_same_type(other);
-		}
-		return representation_label < o->representation_label ? -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_a<indexed>(i));
+	GINAC_ASSERT(i.nops() == 4);
+	GINAC_ASSERT(is_a<su3f>(i.op(0)));
+
+	// 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;
 	}
-	return type < o->type ? -1 : 1;
-}
 
-bool color::is_equal_same_type(const basic & other) const
-{
-	GINAC_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 inherited::is_equal_same_type(other);
+	// No further simplifications
+	return i.hold();
 }
 
-#include <iostream>
 
-ex color::simplify_ncmul(const exvector & v) const
+/** Contraction of generator with something else. */
+bool su3t::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);
-			GINAC_ASSERT(d8.seq.size()==2);
-			const coloridx & first_idx=ex_to_coloridx(d8.seq[0]);
-			const coloridx & second_idx=ex_to_coloridx(d8.seq[1]);
-			// delta8_{a,a} should have been contracted in color::eval()
-			GINAC_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
-					GINAC_ASSERT(replacements==2);
-					*it=_ex1();
-					something_changed=true;
-				}
-			}
+	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();
 
-			// 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
-					GINAC_ASSERT(replacements==2);
-					*it=_ex1();
-					something_changed=true;
-				}
-			}
-		}
-		++it;
-	}
+	if (is_exactly_a<su3t>(other->op(0))) {
 
-	if (something_changed) {
-		// do more simplifications later
-		return nonsimplified_ncmul(v_contracted);
-	}
+		// 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;
 
-	// 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;
-	exvectorvector Tvecs;
-	Tvecs.resize(MAX_REPRESENTATION_LABELS);
-	exvectorvector 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) {
-				GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
-				GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
-				const color & col1=ex_to_color(*it1);
-				const color & col2=ex_to_color(*it2);
-				exvector iv_intersect=idx_intersect(col1.seq,col2.seq);
-				if (iv_intersect.size()>=2) return _ex0();
-			}
-		}
-	}
-	
-	// 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) {
-				GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
-				GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
-				const color & col1=ex_to_color(*it1);
-				const color & 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=_ex1();
-					} else {
-						int dummy; // sign unimportant, since symmetric
-						ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,&dummy);
-						ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,&dummy);
-						*it1=numeric(5)/numeric(3)*color(color_delta8,idx1,idx2);
-						*it2=_ex1();
-					}
-					return nonsimplified_ncmul(recombine_color_string(
-						   delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
+		// 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++;
 			}
-		}
-	}
 
-	// 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) {
-				GINAC_ASSERT(is_ex_exactly_of_type(*it1,color));
-				GINAC_ASSERT(is_ex_exactly_of_type(*it2,color));
-				const color & col1=ex_to_color(*it1);
-				const color & 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=_ex1();
-					} else {
-						int sig1, sig2;
-						ex idx1=permute_free_index_to_front(col1.seq,iv_intersect,&sig1);
-						ex idx2=permute_free_index_to_front(col2.seq,iv_intersect,&sig2);
-						*it1=numeric(sig1*sig2*5)/numeric(3)*color(color_delta8,idx1,idx2);
-						*it2=_ex1();
-					}
-					return nonsimplified_ncmul(recombine_color_string(
-						   delta8vec,fvec,dvec,Tvecs,ONEvecs,unknownvec));
-				}
+			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;
 		}
 	}
 
-	// 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;
-				GINAC_ASSERT(is_ex_exactly_of_type(*it1,color)&&ex_to_color(*it1).type==color_T);
-				GINAC_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) {
-					GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_d);
-					const color & dref=ex_to_color(*it2);
-					exvector iv_intersect=idx_intersect(dref.seq,iv);
-					if (iv_intersect.size()==2) {
-						int dummy; // sign unimportant, since symmetric
-						ex free_idx=permute_free_index_to_front(dref.seq,iv,&dummy);
-						*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) {
-					GINAC_ASSERT(is_ex_exactly_of_type(*it2,color)&&ex_to_color(*it2).type==color_f);
-					const color & 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,&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));
-					}
-				}
-			}
+	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_a<indexed>(*self));
+	GINAC_ASSERT(is_a<indexed>(*other));
+	GINAC_ASSERT(self->nops() == 4);
+	GINAC_ASSERT(is_a<su3d>(self->op(0)));
+
+	if (is_exactly_a<su3d>(other->op(0))) {
+
+		// Find the dummy indices of the contraction
+		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;
+			return true;
+
+		// d.akl d.bkl = 5/3 delta.ab
+		} else if (dummy_indices.size() == 2) {
+			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;
 		}
-	}
-	
-	// 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));
+
+	} 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;
 		}
 	}
 
-	// return a sorted vector
-	return simplified_ncmul(recombine_color_string(delta8vec,fvec,dvec,Tvecs,
-												   ONEvecs,unknownvec));
-}
-
-ex color::thisexprseq(const exvector & v) const
-{
-	return color(type,v,representation_label);
+	return false;
 }
 
-ex color::thisexprseq(exvector * vp) const
+/** Contraction of an indexed antisymmetric structure constant with something else. */
+bool su3f::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
-	return color(type,vp,representation_label);
-}
+	GINAC_ASSERT(is_a<indexed>(*self));
+	GINAC_ASSERT(is_a<indexed>(*other));
+	GINAC_ASSERT(self->nops() == 4);
+	GINAC_ASSERT(is_a<su3f>(self->op(0)));
 
-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;
-}
+	if (is_exactly_a<su3f>(other->op(0))) { // f*d is handled by su3d class
 
-//////////
-// virtual functions which can be overridden by derived classes
-//////////
+		// Find the dummy indices of the contraction
+		exvector dummy_indices;
+		dummy_indices = ex_to<indexed>(*self).get_dummy_indices(ex_to<indexed>(*other));
 
-// none
+		// f.abc f.abc = 24
+		if (dummy_indices.size() == 3) {
+			*self = 24;
+			*other = _ex1;
+			return true;
 
-//////////
-// non-virtual functions in this class
-//////////
-
-//////////
-// static member variables
-//////////
-
-// none
+		// 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;
+		}
 
-//////////
-// global constants
-//////////
+	} 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;
+		}
+	}
 
-const color some_color;
-const std::type_info & typeid_color = typeid(some_color);
+	return false;
+}
 
 //////////
-// friend functions
+// global functions
 //////////
 
-color color_ONE(unsigned rl)
+ex color_ONE(unsigned char rl)
 {
-	return color(color::color_ONE,rl);
+	return color(su3one(), rl);
 }
 
-color color_T(const ex & a, unsigned rl)
+ex color_T(const ex & a, unsigned char rl)
 {
-	return color(color::color_T,a,rl);
+	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))
+		throw(std::invalid_argument("index dimension for color_T must be 8"));
+
+	return color(su3t(), a, rl);
 }
 
-color color_f(const ex & a, const ex & b, const ex & c)
+ex color_f(const ex & a, const ex & b, const ex & c)
 {
-	return color(color::color_f,a,b,c);
+	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))
+		throw(std::invalid_argument("index dimension for color_f must be 8"));
+
+	return indexed(su3f(), sy_anti(), a, b, c);
 }
 
-color color_d(const ex & a, const ex & b, const ex & c)
+ex color_d(const ex & a, const ex & b, const ex & c)
 {
-	return color(color::color_d,a,b,c);
+	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))
+		throw(std::invalid_argument("index dimension for color_d must be 8"));
+
+	return indexed(su3d(), sy_symm(), a, b, c);
 }
 
 ex color_h(const ex & a, const ex & b, const ex & c)
 {
-	return color(color::color_d,a,b,c)+I*color(color::color_f,a,b,c);
+	return color_d(a, b, c) + I * color_f(a, b, c);
 }
 
-color color_delta8(const ex & a, const ex & b)
+/** 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)
 {
-	return color(color::color_delta8,a,b);
+	return ti == (TINFO_color + rl);
 }
 
-void split_color_string_in_parts(const exvector & v, exvector & delta8vec,
-                                 exvector & fvec, exvector & dvec,
-                                 exvectorvector & Tvecs,
-                                 exvectorvector & ONEvecs,
-                                 exvector & unknownvec)
+ex color_trace(const ex & e, unsigned char rl)
 {
-	// 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:
-				GINAC_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:
-				GINAC_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);
+	if (is_a<color>(e)) {
+
+		if (ex_to<color>(e).get_representation_label() == rl
+		 && 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(), rl))
+				prod *= color_trace(o, rl);
+			else
+				prod *= o;
 		}
-	}
-}    
+		return prod;
 
-exvector recombine_color_string(exvector & delta8vec, exvector & fvec,
-                                exvector & dvec, exvectorvector & Tvecs,
-                                exvectorvector & 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;
-}
+	} else if (is_exactly_a<ncmul>(e)) {
 
-ex color_trace_of_one_representation_label(const exvector & v)
-{
-	if (v.size()==0) {
-		return numeric(COLOR_THREE);
-	} else if (v.size()==1) {
-		GINAC_ASSERT(is_ex_exactly_of_type(*(v.begin()),color));
-		return _ex0();
-	}
-	exvector v1=v;
-	ex last_element=v1.back();
-	GINAC_ASSERT(is_ex_exactly_of_type(last_element,color));
-	GINAC_ASSERT(ex_to_color(last_element).type==color::color_T);
-	v1.pop_back();
-	ex next_to_last_element=v1.back();
-	GINAC_ASSERT(is_ex_exactly_of_type(next_to_last_element,color));
-	GINAC_ASSERT(ex_to_color(next_to_last_element).type==color::color_T);
-	v1.pop_back();
-	exvector v2=v1;
-
-	const ex & last_index=ex_to_color(last_element).seq[0];
-	const ex & 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;
-	*/
-}
+		if (!is_color_tinfo(e.return_type_tinfo(), rl))
+			return _ex0;
 
-ex color_trace(const exvector & v, unsigned rl)
-{
-	GINAC_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;
-	exvectorvector Tvecs;
-	Tvecs.resize(MAX_REPRESENTATION_LABELS);
-	exvectorvector 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"));
-	}
+		// Expand product, if necessary
+		ex e_expanded = e.expand();
+		if (!is_a<ncmul>(e_expanded))
+			return color_trace(e_expanded, rl);
 
-	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"));
-			}
-		}
-	}
+		size_t num = e.nops();
 
-	return nonsimplified_ncmul(v_rest);
-}
+		if (num == 2) {
 
-ex simplify_pure_color_string(const ex & e)
-{
-	GINAC_ASSERT(is_ex_exactly_of_type(e,ncmul));
-
-	exvector delta8vec;
-	exvector fvec;
-	exvector dvec;
-	exvectorvector Tvecs;
-	Tvecs.resize(MAX_REPRESENTATION_LABELS);
-	exvectorvector 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];
-					GINAC_ASSERT(is_ex_exactly_of_type(t1,color)&&
-						   (ex_to_color(t1).type==color::color_T)&&
-						   (ex_to_color(t1).seq.size()==1));
-					GINAC_ASSERT(is_ex_exactly_of_type(t2,color)&&
-						   (ex_to_color(t2).type==color::color_T)&&
-						   (ex_to_color(t2).seq.size()==1));
-					const coloridx & idx1=ex_to_coloridx(ex_to_color(t1).seq[0]);
-					const coloridx & 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=_ex1();
-						t2=_ex1();
-						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(_ex1());
-						}
-						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(const ex & e)
-{
-	// 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=_ex0();
-		for (unsigned i=0; i<e_expanded.nops(); ++i)
-			sum += simplify_color(e_expanded.op(i));
-		
-		return sum;
-	}
+			// Tr T_a T_b = 1/2 delta_a_b
+			return delta_tensor(e.op(0).op(1), e.op(1).op(1)) / 2;
 
-	// simplification of commutative product=commutative product of simplifications
-	if (is_ex_exactly_of_type(e_expanded,mul)) {
-		ex prod=_ex1();
-		for (unsigned i=0; i<e_expanded.nops(); ++i)
-			prod *= simplify_color(e_expanded.op(i));
-		
-		return prod;
-	}
+		} else if (num == 3) {
 
-	// simplification of noncommutative product: test if everything is color
-	if (is_ex_exactly_of_type(e_expanded,ncmul)) {
-		bool all_color=true;
-		for (unsigned 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);
-		}
-	}
+			// 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;
 
-	// cannot do anything
-	return e_expanded;
-}
+		} else {
 
-ex brute_force_sum_color_indices(const ex & 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) {
-		GINAC_ASSERT(is_ex_of_type(*cit1,coloridx));
-		for (exvector::const_iterator cit2=cit1+1; cit2!=iv_all.end(); ++cit2) {
-			GINAC_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;
-			}
-		}
-	}
+			// 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);
 
-	std::vector<int> counter;
-	counter.resize(iv_double.size());
-	int l;
-	for (l=0; unsigned(l)<iv_double.size(); ++l) {
-		counter[l]=1;
-	}
+			exvector v1;
+			v1.reserve(num - 2);
+			for (size_t i=0; i<num-2; i++)
+				v1.push_back(e.op(i));
 
-	ex sum;
-	
-	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--;
+			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;
 		}
-		if (l<2) { std::cout << counter[0] << counter[1] << std::endl; }
-		if (l<0) break;
-	}
-	
-	return sum;
-}
 
-void append_exvector_to_exvector(exvector & dest, const exvector & source)
-{
-	for (exvector::const_iterator cit=source.begin(); cit!=source.end(); ++cit) {
-		dest.push_back(*cit);
-	}
+	} else if (e.nops() > 0) {
+
+		// Trace maps to all other container classes (this includes sums)
+		pointer_to_map_function_1arg<unsigned char> fcn(color_trace, rl);
+		return e.map(fcn);
+
+	} else
+		return _ex0;
 }
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
-