X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=445c273ed62057b297843f880dbd1d3d78bd4363;hp=0d26bd7256cccf84df9f6909f9d418ba34d3e034;hb=f01c43a7b5cffea04d34ba3d30b41781255ad5d4;hpb=703c6cebb5d3d395437e73e6935f3691aed68e0a

diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp
index 0d26bd72..445c273e 100644
--- a/ginac/indexed.cpp
+++ b/ginac/indexed.cpp
@@ -1,9 +1,9 @@
 /** @file indexed.cpp
  *
- *  Implementation of GiNaC's index carrying objects. */
+ *  Implementation of GiNaC's indexed expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2006 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
@@ -17,247 +17,361 @@
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <string>
+#include <iostream>
+#include <sstream>
+#include <stdexcept>
 
 #include "indexed.h"
-#include "ex.h"
 #include "idx.h"
-#include "debugmsg.h"
+#include "add.h"
+#include "mul.h"
+#include "ncmul.h"
+#include "power.h"
+#include "relational.h"
+#include "symmetry.h"
+#include "operators.h"
+#include "lst.h"
+#include "archive.h"
+#include "symbol.h"
+#include "utils.h"
+#include "integral.h"
+#include "matrix.h"
+#include "inifcns.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(indexed, exprseq,
+  print_func<print_context>(&indexed::do_print).
+  print_func<print_latex>(&indexed::do_print_latex).
+  print_func<print_tree>(&indexed::do_print_tree))
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
 //////////
 
-// public
-
-indexed::indexed()
+indexed::indexed() : symtree(not_symmetric())
 {
-	debugmsg("indexed default constructor",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
+	tinfo_key = &indexed::tinfo_static;
 }
 
-indexed::~indexed()
+//////////
+// other constructors
+//////////
+
+indexed::indexed(const ex & b) : inherited(b), symtree(not_symmetric())
 {
-	debugmsg("indexed destructor",LOGLEVEL_DESTRUCT);
-	destroy(0);
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-indexed::indexed(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(not_symmetric())
 {
-	debugmsg("indexed copy constructor",LOGLEVEL_CONSTRUCT);
-	copy (other);
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-const indexed & indexed::operator=(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(not_symmetric())
 {
-	debugmsg("indexed operator=",LOGLEVEL_ASSIGNMENT);
-	if (this != &other) {
-		destroy(1);
-		copy(other);
-	}
-	return *this;
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-// protected
-
-void indexed::copy(const indexed & other)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(not_symmetric())
 {
-	inherited::copy(other);
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-void indexed::destroy(bool call_parent)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(not_symmetric())
 {
-	if (call_parent) {
-		inherited::destroy(call_parent);
-	}
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-//////////
-// other constructors
-//////////
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
+{
+	tinfo_key = &indexed::tinfo_static;
+	validate();
+}
 
-// public
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
+{
+	tinfo_key = &indexed::tinfo_static;
+	validate();
+}
 
-indexed::indexed(const ex & i1) : inherited(i1)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(symm)
 {
-	debugmsg("indexed constructor from ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-indexed::indexed(const ex & i1, const ex & i2) : inherited(i1,i2)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(not_symmetric())
 {
-	debugmsg("indexed constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	seq.insert(seq.end(), v.begin(), v.end());
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3)
-	: inherited(i1,i2,i3)
+indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
 {
-	debugmsg("indexed constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	seq.insert(seq.end(), v.begin(), v.end());
+	tinfo_key = &indexed::tinfo_static;
+	validate();
 }
 
-indexed::indexed(const ex & i1, const ex & i2, const ex & i3, const ex & i4)
-	: inherited(i1,i2,i3,i4)
+indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
 {
-	debugmsg("indexed constructor from ex,ex,ex,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	tinfo_key = &indexed::tinfo_static;
 }
 
-indexed::indexed(const exvector & iv) : inherited(iv)
+indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
 {
-	debugmsg("indexed constructor from exvector",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	tinfo_key = &indexed::tinfo_static;
 }
 
-indexed::indexed(exvector * ivp) : inherited(ivp)
+indexed::indexed(const symmetry & symm, std::auto_ptr<exvector> vp) : inherited(vp), symtree(symm)
 {
-	debugmsg("indexed constructor from exvector *",LOGLEVEL_CONSTRUCT);
-	tinfo_key=TINFO_indexed;
-	GINAC_ASSERT(all_of_type_idx());
+	tinfo_key = &indexed::tinfo_static;
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+indexed::indexed(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_indexed;
-}
-
-/** Unarchive the object. */
-ex indexed::unarchive(const archive_node &n, const lst &sym_lst)
-{
-	return (new indexed(n, sym_lst))->setflag(status_flags::dynallocated);
+	if (!n.find_ex("symmetry", symtree, sym_lst)) {
+		// GiNaC versions <= 0.9.0 had an unsigned "symmetry" property
+		unsigned symm = 0;
+		n.find_unsigned("symmetry", symm);
+		switch (symm) {
+			case 1:
+				symtree = sy_symm();
+				break;
+			case 2:
+				symtree = sy_anti();
+				break;
+			default:
+				symtree = not_symmetric();
+				break;
+		}
+		const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
+	}
 }
 
-/** Archive the object. */
 void indexed::archive(archive_node &n) const
 {
 	inherited::archive(n);
+	n.add_ex("symmetry", symtree);
 }
 
+DEFAULT_UNARCHIVE(indexed)
+
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
-// public
-
-basic * indexed::duplicate() const
+void indexed::printindices(const print_context & c, unsigned level) const
 {
-	debugmsg("indexed duplicate",LOGLEVEL_DUPLICATE);
-	return new indexed(*this);
+	if (seq.size() > 1) {
+
+		exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
+
+		if (is_a<print_latex>(c)) {
+
+			// TeX output: group by variance
+			bool first = true;
+			bool covariant = true;
+
+			while (it != itend) {
+				bool cur_covariant = (is_a<varidx>(*it) ? ex_to<varidx>(*it).is_covariant() : true);
+				if (first || cur_covariant != covariant) { // Variance changed
+					// The empty {} prevents indices from ending up on top of each other
+					if (!first)
+						c.s << "}{}";
+					covariant = cur_covariant;
+					if (covariant)
+						c.s << "_{";
+					else
+						c.s << "^{";
+				}
+				it->print(c, level);
+				c.s << " ";
+				first = false;
+				it++;
+			}
+			c.s << "}";
+
+		} else {
+
+			// Ordinary output
+			while (it != itend) {
+				it->print(c, level);
+				it++;
+			}
+		}
+	}
 }
 
-void indexed::printraw(std::ostream & os) const
+void indexed::print_indexed(const print_context & c, const char *openbrace, const char *closebrace, unsigned level) const
 {
-	debugmsg("indexed printraw",LOGLEVEL_PRINT);
-	os << "indexed(indices=";
-	printrawindices(os);
-	os << ",hash=" << hashvalue << ",flags=" << flags << ")";
+	if (precedence() <= level)
+		c.s << openbrace << '(';
+	c.s << openbrace;
+	seq[0].print(c, precedence());
+	c.s << closebrace;
+	printindices(c, level);
+	if (precedence() <= level)
+		c.s << ')' << closebrace;
 }
 
-void indexed::printtree(std::ostream & os, unsigned indent) const
+void indexed::do_print(const print_context & c, unsigned level) const
 {
-	debugmsg("indexed printtree",LOGLEVEL_PRINT);
-	os << std::string(indent,' ') << "indexed: " << seq.size() << " indices";
-	os << ",hash=" << hashvalue << ",flags=" << flags << std::endl;
-	printtreeindices(os,indent);
+	print_indexed(c, "", "", level);
 }
 
-void indexed::print(std::ostream & os, unsigned upper_precedence) const
+void indexed::do_print_latex(const print_latex & c, unsigned level) const
 {
-	debugmsg("indexed print",LOGLEVEL_PRINT);
-	os << "UNNAMEDINDEX";
-	printindices(os);
+	print_indexed(c, "{", "}", level);
 }
 
-void indexed::printcsrc(std::ostream & os, unsigned type,
-						unsigned upper_precedence) const
+void indexed::do_print_tree(const print_tree & c, unsigned level) const
 {
-	debugmsg("indexed print csrc",LOGLEVEL_PRINT);
-	print(os,upper_precedence);
+	c.s << std::string(level, ' ') << class_name() << " @" << this
+	    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+	    << ", " << seq.size()-1 << " indices"
+	    << ", symmetry=" << symtree << std::endl;
+	seq[0].print(c, level + c.delta_indent);
+	printindices(c, level + c.delta_indent);
 }
 
 bool indexed::info(unsigned inf) const
 {
-	if (inf==info_flags::indexed) return true;
-	if (inf==info_flags::has_indices) return seq.size()!=0;
+	if (inf == info_flags::indexed) return true;
+	if (inf == info_flags::has_indices) return seq.size() > 1;
 	return inherited::info(inf);
 }
 
-exvector indexed::get_indices(void) const
+struct idx_is_not : public std::binary_function<ex, unsigned, bool> {
+	bool operator() (const ex & e, unsigned inf) const {
+		return !(ex_to<idx>(e).get_value().info(inf));
+	}
+};
+
+bool indexed::all_index_values_are(unsigned inf) const
 {
-	return seq;
+	// No indices? Then no property can be fulfilled
+	if (seq.size() < 2)
+		return false;
 
-	/*
-	idxvector filtered_indices;
-	filtered_indices.reserve(indices.size());
-	for (idxvector::const_iterator cit=indices.begin(); cit!=indices.end(); ++cit) {
-		if ((*cit).get_type()==t) {
-			filtered_indices.push_back(*cit);
-		}
-	}
-	return filtered_indices;
-	*/
+	// Check all indices
+	return find_if(seq.begin() + 1, seq.end(), bind2nd(idx_is_not(), inf)) == seq.end();
 }
 
-// protected
+int indexed::compare_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_a<indexed>(other));
+	return inherited::compare_same_type(other);
+}
 
-/** Implementation of ex::diff() for an indexed object. It always returns 0.
- *  @see ex::diff */
-ex indexed::derivative(const symbol & s) const
+ex indexed::eval(int level) const
 {
-		return _ex0();
+	// First evaluate children, then we will end up here again
+	if (level > 1)
+		return indexed(ex_to<symmetry>(symtree), evalchildren(level));
+
+	const ex &base = seq[0];
+
+	// If the base object is 0, the whole object is 0
+	if (base.is_zero())
+		return _ex0;
+
+	// If the base object is a product, pull out the numeric factor
+	if (is_exactly_a<mul>(base) && is_exactly_a<numeric>(base.op(base.nops() - 1))) {
+		exvector v(seq);
+		ex f = ex_to<numeric>(base.op(base.nops() - 1));
+		v[0] = seq[0] / f;
+		return f * thiscontainer(v);
+	}
+
+	if(this->tinfo()==&indexed::tinfo_static && seq.size()==1)
+		return base;
+
+	// Canonicalize indices according to the symmetry properties
+	if (seq.size() > 2) {
+		exvector v = seq;
+		GINAC_ASSERT(is_exactly_a<symmetry>(symtree));
+		int sig = canonicalize(v.begin() + 1, ex_to<symmetry>(symtree));
+		if (sig != INT_MAX) {
+			// Something has changed while sorting indices, more evaluations later
+			if (sig == 0)
+				return _ex0;
+			return ex(sig) * thiscontainer(v);
+		}
+	}
+
+	// Let the class of the base object perform additional evaluations
+	return ex_to<basic>(base).eval_indexed(*this);
 }
 
-int indexed::compare_same_type(const basic & other) const
+ex indexed::real_part() const
 {
-	GINAC_ASSERT(is_of_type(other,indexed));
-	return inherited::compare_same_type(other);
+	if(op(0).info(info_flags::real))
+		return *this;
+	return real_part_function(*this).hold();
 }
 
-bool indexed::is_equal_same_type(const basic & other) const
+ex indexed::imag_part() const
 {
-	GINAC_ASSERT(is_of_type(other,indexed));
-	return inherited::is_equal_same_type(other);
+	if(op(0).info(info_flags::real))
+		return 0;
+	return imag_part_function(*this).hold();
 }
 
-unsigned indexed::return_type(void) const
+ex indexed::thiscontainer(const exvector & v) const
 {
-	return return_types::noncommutative;
+	return indexed(ex_to<symmetry>(symtree), v);
 }
-   
-unsigned indexed::return_type_tinfo(void) const
+
+ex indexed::thiscontainer(std::auto_ptr<exvector> vp) const
 {
-	return tinfo_key;
+	return indexed(ex_to<symmetry>(symtree), vp);
 }
 
-ex indexed::thisexprseq(const exvector & v) const
+unsigned indexed::return_type() const
 {
-	return indexed(v);
+	if(is_a<matrix>(op(0)))
+		return return_types::commutative;
+	else
+		return op(0).return_type();
 }
 
-ex indexed::thisexprseq(exvector * vp) const
+ex indexed::expand(unsigned options) const
 {
-	return indexed(vp);
+	GINAC_ASSERT(seq.size() > 0);
+
+	if (options & expand_options::expand_indexed) {
+		ex newbase = seq[0].expand(options);
+		if (is_exactly_a<add>(newbase)) {
+			ex sum = _ex0;
+			for (size_t i=0; i<newbase.nops(); i++) {
+				exvector s = seq;
+				s[0] = newbase.op(i);
+				sum += thiscontainer(s).expand(options);
+			}
+			return sum;
+		}
+		if (!are_ex_trivially_equal(newbase, seq[0])) {
+			exvector s = seq;
+			s[0] = newbase;
+			return ex_to<indexed>(thiscontainer(s)).inherited::expand(options);
+		}
+	}
+	return inherited::expand(options);
 }
 
 //////////
@@ -270,70 +384,1209 @@ ex indexed::thisexprseq(exvector * vp) const
 // non-virtual functions in this class
 //////////
 
-// protected
+/** Check whether all indices are of class idx and validate the symmetry
+ *  tree. This function is used internally to make sure that all constructed
+ *  indexed objects really carry indices and not some other classes. */
+void indexed::validate() const
+{
+	GINAC_ASSERT(seq.size() > 0);
+	exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+	while (it != itend) {
+		if (!is_a<idx>(*it))
+			throw(std::invalid_argument("indices of indexed object must be of type idx"));
+		it++;
+	}
+
+	if (!symtree.is_zero()) {
+		if (!is_exactly_a<symmetry>(symtree))
+			throw(std::invalid_argument("symmetry of indexed object must be of type symmetry"));
+		const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
+	}
+}
+
+/** Implementation of ex::diff() for an indexed object always returns 0.
+ *
+ *  @see ex::diff */
+ex indexed::derivative(const symbol & s) const
+{
+	return _ex0;
+}
+
+//////////
+// global functions
+//////////
+
+struct idx_is_equal_ignore_dim : public std::binary_function<ex, ex, bool> {
+	bool operator() (const ex &lh, const ex &rh) const
+	{
+		if (lh.is_equal(rh))
+			return true;
+		else
+			try {
+				// Replacing the dimension might cause an error (e.g. with
+				// index classes that only work in a fixed number of dimensions)
+				return lh.is_equal(ex_to<idx>(rh).replace_dim(ex_to<idx>(lh).get_dim()));
+			} catch (...) {
+				return false;
+			}
+	}
+};
+
+/** Check whether two sorted index vectors are consistent (i.e. equal). */
+static bool indices_consistent(const exvector & v1, const exvector & v2)
+{
+	// Number of indices must be the same
+	if (v1.size() != v2.size())
+		return false;
+
+	return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim());
+}
+
+exvector indexed::get_indices() const
+{
+	GINAC_ASSERT(seq.size() >= 1);
+	return exvector(seq.begin() + 1, seq.end());
+}
+
+exvector indexed::get_dummy_indices() const
+{
+	exvector free_indices, dummy_indices;
+	find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+	return dummy_indices;
+}
+
+exvector indexed::get_dummy_indices(const indexed & other) const
+{
+	exvector indices = get_free_indices();
+	exvector other_indices = other.get_free_indices();
+	indices.insert(indices.end(), other_indices.begin(), other_indices.end());
+	exvector dummy_indices;
+	find_dummy_indices(indices, dummy_indices);
+	return dummy_indices;
+}
 
-void indexed::printrawindices(std::ostream & os) const
+bool indexed::has_dummy_index_for(const ex & i) const
 {
-	if (seq.size()!=0) {
-		for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-			(*cit).printraw(os);
-			os << ",";
+	exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
+	while (it != itend) {
+		if (is_dummy_pair(*it, i))
+			return true;
+		it++;
+	}
+	return false;
+}
+
+exvector indexed::get_free_indices() const
+{
+	exvector free_indices, dummy_indices;
+	find_free_and_dummy(seq.begin() + 1, seq.end(), free_indices, dummy_indices);
+	return free_indices;
+}
+
+exvector add::get_free_indices() const
+{
+	exvector free_indices;
+	for (size_t i=0; i<nops(); i++) {
+		if (i == 0)
+			free_indices = op(i).get_free_indices();
+		else {
+			exvector free_indices_of_term = op(i).get_free_indices();
+			if (!indices_consistent(free_indices, free_indices_of_term))
+				throw (std::runtime_error("add::get_free_indices: inconsistent indices in sum"));
 		}
 	}
+	return free_indices;
+}
+
+exvector mul::get_free_indices() const
+{
+	// Concatenate free indices of all factors
+	exvector un;
+	for (size_t i=0; i<nops(); i++) {
+		exvector free_indices_of_factor = op(i).get_free_indices();
+		un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+	}
+
+	// And remove the dummy indices
+	exvector free_indices, dummy_indices;
+	find_free_and_dummy(un, free_indices, dummy_indices);
+	return free_indices;
+}
+
+exvector ncmul::get_free_indices() const
+{
+	// Concatenate free indices of all factors
+	exvector un;
+	for (size_t i=0; i<nops(); i++) {
+		exvector free_indices_of_factor = op(i).get_free_indices();
+		un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+	}
+
+	// And remove the dummy indices
+	exvector free_indices, dummy_indices;
+	find_free_and_dummy(un, free_indices, dummy_indices);
+	return free_indices;
+}
+
+struct is_summation_idx : public std::unary_function<ex, bool> {
+	bool operator()(const ex & e)
+	{
+		return is_dummy_pair(e, e);
+	}
+};
+
+exvector integral::get_free_indices() const
+{
+	if (a.get_free_indices().size() || b.get_free_indices().size())
+		throw (std::runtime_error("integral::get_free_indices: boundary values should not have free indices"));
+	return f.get_free_indices();
+}
+
+template<class T> size_t number_of_type(const exvector&v)
+{
+	size_t number = 0;
+	for(exvector::const_iterator i=v.begin(); i!=v.end(); ++i)
+		if(is_exactly_a<T>(*i))
+			++number;
+	return number;
 }
 
-void indexed::printtreeindices(std::ostream & os, unsigned indent) const
+/** Rename dummy indices in an expression.
+ *
+ *  @param e Expression to work on
+ *  @param local_dummy_indices The set of dummy indices that appear in the
+ *    expression "e"
+ *  @param global_dummy_indices The set of dummy indices that have appeared
+ *    before and which we would like to use in "e", too. This gets updated
+ *    by the function */
+template<class T> static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
 {
-	if (seq.size()!=0) {
-		for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-			os << std::string(indent+delta_indent,' ');
-			(*cit).printraw(os);
-			os << std::endl;
+	size_t global_size = number_of_type<T>(global_dummy_indices),
+	       local_size = number_of_type<T>(local_dummy_indices);
+
+	// Any local dummy indices at all?
+	if (local_size == 0)
+		return e;
+
+	if (global_size < local_size) {
+
+		// More local indices than we encountered before, add the new ones
+		// to the global set
+		size_t old_global_size = global_size;
+		int remaining = local_size - global_size;
+		exvector::const_iterator it = local_dummy_indices.begin(), itend = local_dummy_indices.end();
+		while (it != itend && remaining > 0) {
+			if (is_exactly_a<T>(*it) && find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(idx_is_equal_ignore_dim(), *it)) == global_dummy_indices.end()) {
+				global_dummy_indices.push_back(*it);
+				global_size++;
+				remaining--;
+			}
+			it++;
 		}
+
+		// If this is the first set of local indices, do nothing
+		if (old_global_size == 0)
+			return e;
+	}
+	GINAC_ASSERT(local_size <= global_size);
+
+	// Construct vectors of index symbols
+	exvector local_syms, global_syms;
+	local_syms.reserve(local_size);
+	global_syms.reserve(local_size);
+	for (size_t i=0; local_syms.size()!=local_size; i++)
+		if(is_exactly_a<T>(local_dummy_indices[i]))
+			local_syms.push_back(local_dummy_indices[i].op(0));
+	shaker_sort(local_syms.begin(), local_syms.end(), ex_is_less(), ex_swap());
+	for (size_t i=0; global_syms.size()!=local_size; i++) // don't use more global symbols than necessary
+		if(is_exactly_a<T>(global_dummy_indices[i]))
+			global_syms.push_back(global_dummy_indices[i].op(0));
+	shaker_sort(global_syms.begin(), global_syms.end(), ex_is_less(), ex_swap());
+
+	// Remove common indices
+	exvector local_uniq, global_uniq;
+	set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exvector>(local_uniq), ex_is_less());
+	set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exvector>(global_uniq), ex_is_less());
+
+	// Replace remaining non-common local index symbols by global ones
+	if (local_uniq.empty())
+		return e;
+	else {
+		while (global_uniq.size() > local_uniq.size())
+			global_uniq.pop_back();
+		return e.subs(lst(local_uniq.begin(), local_uniq.end()), lst(global_uniq.begin(), global_uniq.end()), subs_options::no_pattern);
+	}
+}
+
+/** Given a set of indices, extract those of class varidx. */
+static void find_variant_indices(const exvector & v, exvector & variant_indices)
+{
+	exvector::const_iterator it1, itend;
+	for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+		if (is_exactly_a<varidx>(*it1))
+			variant_indices.push_back(*it1);
 	}
 }
 
-void indexed::printindices(std::ostream & os) const
+/** Raise/lower dummy indices in a single indexed objects to canonicalize their
+ *  variance.
+ *
+ *  @param e Object to work on
+ *  @param variant_dummy_indices The set of indices that might need repositioning (will be changed by this function)
+ *  @param moved_indices The set of indices that have been repositioned (will be changed by this function)
+ *  @return true if 'e' was changed */
+bool reposition_dummy_indices(ex & e, exvector & variant_dummy_indices, exvector & moved_indices)
 {
-	if (seq.size()!=0) {
-		if (seq.size()>1) {
-			os << "{";
+	bool something_changed = false;
+
+	// Find dummy symbols that occur twice in the same indexed object.
+	exvector local_var_dummies;
+	local_var_dummies.reserve(e.nops()/2);
+	for (size_t i=1; i<e.nops(); ++i) {
+		if (!is_a<varidx>(e.op(i)))
+			continue;
+		for (size_t j=i+1; j<e.nops(); ++j) {
+			if (is_dummy_pair(e.op(i), e.op(j))) {
+				local_var_dummies.push_back(e.op(i));
+				for (exvector::iterator k = variant_dummy_indices.begin();
+						k!=variant_dummy_indices.end(); ++k) {
+					if (e.op(i).op(0) == k->op(0)) {
+						variant_dummy_indices.erase(k);
+						break;
+					}
+				}
+				break;
+			}
+		}
+	}
+
+	// In the case where a dummy symbol occurs twice in the same indexed object
+	// we try all posibilities of raising/lowering and keep the least one in
+	// the sense of ex_is_less.
+	ex optimal_e = e;
+	size_t numpossibs = 1 << local_var_dummies.size();
+	for (size_t i=0; i<numpossibs; ++i) {
+		ex try_e = e;
+		for (size_t j=0; j<local_var_dummies.size(); ++j) {
+			exmap m;
+			if (1<<j & i) {
+				ex curr_idx = local_var_dummies[j];
+				ex curr_toggle = ex_to<varidx>(curr_idx).toggle_variance();
+				m[curr_idx] = curr_toggle;
+				m[curr_toggle] = curr_idx;
+			}
+			try_e = e.subs(m, subs_options::no_pattern);
 		}
-		exvector::const_iterator last=seq.end()-1;
-		exvector::const_iterator cit=seq.begin();
-		for (; cit!=last; ++cit) {
-			(*cit).print(os);
-			os << ",";
+		if(ex_is_less()(try_e, optimal_e))
+		{	optimal_e = try_e;
+			something_changed = true;
 		}
-		(*cit).print(os);
-		if (seq.size()>1) {
-			os << "}";
+	}
+	e = optimal_e;
+
+	if (!is_a<indexed>(e))
+		return true;
+
+	exvector seq = ex_to<indexed>(e).seq;
+
+	// If a dummy index is encountered for the first time in the
+	// product, pull it up, otherwise, pull it down
+	for (exvector::iterator it2 = seq.begin()+1, it2end = seq.end();
+			it2 != it2end; ++it2) {
+		if (!is_exactly_a<varidx>(*it2))
+			continue;
+
+		exvector::iterator vit, vitend;
+		for (vit = variant_dummy_indices.begin(), vitend = variant_dummy_indices.end(); vit != vitend; ++vit) {
+			if (it2->op(0).is_equal(vit->op(0))) {
+				if (ex_to<varidx>(*it2).is_covariant()) {
+					/*
+					 * N.B. we don't want to use
+					 *
+					 *  e = e.subs(lst(
+					 *  *it2 == ex_to<varidx>(*it2).toggle_variance(),
+					 *  ex_to<varidx>(*it2).toggle_variance() == *it2
+					 *  ), subs_options::no_pattern);
+					 *
+					 * since this can trigger non-trivial repositioning of indices,
+					 * e.g. due to non-trivial symmetry properties of e, thus
+					 * invalidating iterators
+					 */
+					*it2 = ex_to<varidx>(*it2).toggle_variance();
+					something_changed = true;
+				}
+				moved_indices.push_back(*vit);
+				variant_dummy_indices.erase(vit);
+				goto next_index;
+			}
 		}
+
+		for (vit = moved_indices.begin(), vitend = moved_indices.end(); vit != vitend; ++vit) {
+			if (it2->op(0).is_equal(vit->op(0))) {
+				if (ex_to<varidx>(*it2).is_contravariant()) {
+					*it2 = ex_to<varidx>(*it2).toggle_variance();
+					something_changed = true;
+				}
+				goto next_index;
+			}
+		}
+
+next_index: ;
 	}
+
+	if (something_changed)
+		e = ex_to<indexed>(e).thiscontainer(seq);
+
+	return something_changed;
 }
 
-bool indexed::all_of_type_idx(void) const
+/* Ordering that only compares the base expressions of indexed objects. */
+struct ex_base_is_less : public std::binary_function<ex, ex, bool> {
+	bool operator() (const ex &lh, const ex &rh) const
+	{
+		return (is_a<indexed>(lh) ? lh.op(0) : lh).compare(is_a<indexed>(rh) ? rh.op(0) : rh) < 0;
+	}
+};
+
+/* An auxiliary function used by simplify_indexed() and expand_dummy_sum() 
+ * It returns an exvector of factors from the supplied product */
+static void product_to_exvector(const ex & e, exvector & v, bool & non_commutative)
 {
-	// used only inside of ASSERTs
-	for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if (!is_ex_of_type(*cit,idx)) return false;
+	// Remember whether the product was commutative or noncommutative
+	// (because we chop it into factors and need to reassemble later)
+	non_commutative = is_exactly_a<ncmul>(e);
+
+	// Collect factors in an exvector, store squares twice
+	v.reserve(e.nops() * 2);
+
+	if (is_exactly_a<power>(e)) {
+		// We only get called for simple squares, split a^2 -> a*a
+		GINAC_ASSERT(e.op(1).is_equal(_ex2));
+		v.push_back(e.op(0));
+		v.push_back(e.op(0));
+	} else {
+		for (size_t i=0; i<e.nops(); i++) {
+			ex f = e.op(i);
+			if (is_exactly_a<power>(f) && f.op(1).is_equal(_ex2)) {
+				v.push_back(f.op(0));
+				v.push_back(f.op(0));
+			} else if (is_exactly_a<ncmul>(f)) {
+				// Noncommutative factor found, split it as well
+				non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
+				for (size_t j=0; j<f.nops(); j++)
+					v.push_back(f.op(j));
+			} else
+				v.push_back(f);
+		}
 	}
-	return true;
 }
 
-//////////
-// static member variables
-//////////
+template<class T> ex idx_symmetrization(const ex& r,const exvector& local_dummy_indices)
+{	exvector dummy_syms;
+	dummy_syms.reserve(r.nops());
+	for (exvector::const_iterator it = local_dummy_indices.begin(); it != local_dummy_indices.end(); ++it)
+			if(is_exactly_a<T>(*it))
+				dummy_syms.push_back(it->op(0));
+	if(dummy_syms.size() < 2)
+		return r;
+	ex q=symmetrize(r, dummy_syms);
+	return q;
+}
 
-// none
+// Forward declaration needed in absence of friend injection, C.f. [namespace.memdef]:
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp);
+
+/** Simplify product of indexed expressions (commutative, noncommutative and
+ *  simple squares), return list of free indices. */
+ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
+{
+	// Collect factors in an exvector
+	exvector v;
+
+	// Remember whether the product was commutative or noncommutative
+	// (because we chop it into factors and need to reassemble later)
+	bool non_commutative;
+	product_to_exvector(e, v, non_commutative);
+
+	// Perform contractions
+	bool something_changed = false;
+	GINAC_ASSERT(v.size() > 1);
+	exvector::iterator it1, itend = v.end(), next_to_last = itend - 1;
+	for (it1 = v.begin(); it1 != next_to_last; it1++) {
+
+try_again:
+		if (!is_a<indexed>(*it1))
+			continue;
+
+		bool first_noncommutative = (it1->return_type() != return_types::commutative);
+
+		// Indexed factor found, get free indices and look for contraction
+		// candidates
+		exvector free1, dummy1;
+		find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free1, dummy1);
+
+		exvector::iterator it2;
+		for (it2 = it1 + 1; it2 != itend; it2++) {
+
+			if (!is_a<indexed>(*it2))
+				continue;
+
+			bool second_noncommutative = (it2->return_type() != return_types::commutative);
+
+			// Find free indices of second factor and merge them with free
+			// indices of first factor
+			exvector un;
+			find_free_and_dummy(ex_to<indexed>(*it2).seq.begin() + 1, ex_to<indexed>(*it2).seq.end(), un, dummy1);
+			un.insert(un.end(), free1.begin(), free1.end());
+
+			// Check whether the two factors share dummy indices
+			exvector free, dummy;
+			find_free_and_dummy(un, free, dummy);
+			size_t num_dummies = dummy.size();
+			if (num_dummies == 0)
+				continue;
+
+			// At least one dummy index, is it a defined scalar product?
+			bool contracted = false;
+			if (free.empty() && it1->nops()==2 && it2->nops()==2) {
+
+				ex dim = minimal_dim(
+					ex_to<idx>(it1->op(1)).get_dim(),
+					ex_to<idx>(it2->op(1)).get_dim()
+				);
+
+				// User-defined scalar product?
+				if (sp.is_defined(*it1, *it2, dim)) {
+
+					// Yes, substitute it
+					*it1 = sp.evaluate(*it1, *it2, dim);
+					*it2 = _ex1;
+					goto contraction_done;
+				}
+			}
+
+			// Try to contract the first one with the second one
+			contracted = ex_to<basic>(it1->op(0)).contract_with(it1, it2, v);
+			if (!contracted) {
+
+				// That didn't work; maybe the second object knows how to
+				// contract itself with the first one
+				contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
+			}
+			if (contracted) {
+contraction_done:
+				if (first_noncommutative || second_noncommutative
+				 || is_exactly_a<add>(*it1) || is_exactly_a<add>(*it2)
+				 || is_exactly_a<mul>(*it1) || is_exactly_a<mul>(*it2)
+				 || is_exactly_a<ncmul>(*it1) || is_exactly_a<ncmul>(*it2)) {
+
+					// One of the factors became a sum or product:
+					// re-expand expression and run again
+					// Non-commutative products are always re-expanded to give
+					// eval_ncmul() the chance to re-order and canonicalize
+					// the product
+					ex r = (non_commutative ? ex(ncmul(v, true)) : ex(mul(v)));
+					return simplify_indexed(r, free_indices, dummy_indices, sp);
+				}
+
+				// Both objects may have new indices now or they might
+				// even not be indexed objects any more, so we have to
+				// start over
+				something_changed = true;
+				goto try_again;
+			}
+		}
+	}
+
+	// Find free indices (concatenate them all and call find_free_and_dummy())
+	// and all dummy indices that appear
+	exvector un, individual_dummy_indices;
+	for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+		exvector free_indices_of_factor;
+		if (is_a<indexed>(*it1)) {
+			exvector dummy_indices_of_factor;
+			find_free_and_dummy(ex_to<indexed>(*it1).seq.begin() + 1, ex_to<indexed>(*it1).seq.end(), free_indices_of_factor, dummy_indices_of_factor);
+			individual_dummy_indices.insert(individual_dummy_indices.end(), dummy_indices_of_factor.begin(), dummy_indices_of_factor.end());
+		} else
+			free_indices_of_factor = it1->get_free_indices();
+		un.insert(un.end(), free_indices_of_factor.begin(), free_indices_of_factor.end());
+	}
+	exvector local_dummy_indices;
+	find_free_and_dummy(un, free_indices, local_dummy_indices);
+	local_dummy_indices.insert(local_dummy_indices.end(), individual_dummy_indices.begin(), individual_dummy_indices.end());
+
+	// Filter out the dummy indices with variance
+	exvector variant_dummy_indices;
+	find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+	// Any indices with variance present at all?
+	if (!variant_dummy_indices.empty()) {
+
+		// Yes, bring the product into a canonical order that only depends on
+		// the base expressions of indexed objects
+		if (!non_commutative)
+			std::sort(v.begin(), v.end(), ex_base_is_less());
+
+		exvector moved_indices;
+
+		// Iterate over all indexed objects in the product
+		for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
+			if (!is_a<indexed>(*it1))
+				continue;
+
+			if (reposition_dummy_indices(*it1, variant_dummy_indices, moved_indices))
+				something_changed = true;
+		}
+	}
+
+	ex r;
+	if (something_changed)
+		r = non_commutative ? ex(ncmul(v, true)) : ex(mul(v));
+	else
+		r = e;
+
+	// The result should be symmetric with respect to exchange of dummy
+	// indices, so if the symmetrization vanishes, the whole expression is
+	// zero. This detects things like eps.i.j.k * p.j * p.k = 0.
+	ex q = idx_symmetrization<idx>(r, local_dummy_indices);
+	if (q.is_zero()) {
+		free_indices.clear();
+		return _ex0;
+	}
+	q = idx_symmetrization<varidx>(q, local_dummy_indices);
+	if (q.is_zero()) {
+		free_indices.clear();
+		return _ex0;
+	}
+	q = idx_symmetrization<spinidx>(q, local_dummy_indices);
+	if (q.is_zero()) {
+		free_indices.clear();
+		return _ex0;
+	}
+
+	// Dummy index renaming
+	r = rename_dummy_indices<idx>(r, dummy_indices, local_dummy_indices);
+	r = rename_dummy_indices<varidx>(r, dummy_indices, local_dummy_indices);
+	r = rename_dummy_indices<spinidx>(r, dummy_indices, local_dummy_indices);
+
+	// Product of indexed object with a scalar?
+	if (is_exactly_a<mul>(r) && r.nops() == 2
+	 && is_exactly_a<numeric>(r.op(1)) && is_a<indexed>(r.op(0)))
+		return ex_to<basic>(r.op(0).op(0)).scalar_mul_indexed(r.op(0), ex_to<numeric>(r.op(1)));
+	else
+		return r;
+}
+
+/** This structure stores the original and symmetrized versions of terms
+ *  obtained during the simplification of sums. */
+class terminfo {
+public:
+	terminfo(const ex & orig_, const ex & symm_) : orig(orig_), symm(symm_) {}
+
+	ex orig; /**< original term */
+	ex symm; /**< symmtrized term */
+};
+
+class terminfo_is_less {
+public:
+	bool operator() (const terminfo & ti1, const terminfo & ti2) const
+	{
+		return (ti1.symm.compare(ti2.symm) < 0);
+	}
+};
+
+/** This structure stores the individual symmetrized terms obtained during
+ *  the simplification of sums. */
+class symminfo {
+public:
+	symminfo() : num(0) {}
+
+	symminfo(const ex & symmterm_, const ex & orig_, size_t num_) : orig(orig_), num(num_)
+	{
+		if (is_exactly_a<mul>(symmterm_) && is_exactly_a<numeric>(symmterm_.op(symmterm_.nops()-1))) {
+			coeff = symmterm_.op(symmterm_.nops()-1);
+			symmterm = symmterm_ / coeff;
+		} else {
+			coeff = 1;
+			symmterm = symmterm_;
+		}
+	}
+
+	ex symmterm;  /**< symmetrized term */
+	ex coeff;     /**< coefficient of symmetrized term */
+	ex orig;      /**< original term */
+	size_t num; /**< how many symmetrized terms resulted from the original term */
+};
+
+class symminfo_is_less_by_symmterm {
+public:
+	bool operator() (const symminfo & si1, const symminfo & si2) const
+	{
+		return (si1.symmterm.compare(si2.symmterm) < 0);
+	}
+};
+
+class symminfo_is_less_by_orig {
+public:
+	bool operator() (const symminfo & si1, const symminfo & si2) const
+	{
+		return (si1.orig.compare(si2.orig) < 0);
+	}
+};
+
+bool hasindex(const ex &x, const ex &sym)
+{	
+	if(is_a<idx>(x) && x.op(0)==sym)
+		return true;
+	else
+		for(size_t i=0; i<x.nops(); ++i)
+			if(hasindex(x.op(i), sym))
+				return true;
+	return false;
+}
+
+/** Simplify indexed expression, return list of free indices. */
+ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
+{
+	// Expand the expression
+	ex e_expanded = e.expand();
+
+	// Simplification of single indexed object: just find the free indices
+	// and perform dummy index renaming/repositioning
+	if (is_a<indexed>(e_expanded)) {
+
+		// Find the dummy indices
+		const indexed &i = ex_to<indexed>(e_expanded);
+		exvector local_dummy_indices;
+		find_free_and_dummy(i.seq.begin() + 1, i.seq.end(), free_indices, local_dummy_indices);
+
+		// Filter out the dummy indices with variance
+		exvector variant_dummy_indices;
+		find_variant_indices(local_dummy_indices, variant_dummy_indices);
+
+		// Any indices with variance present at all?
+		if (!variant_dummy_indices.empty()) {
+
+			// Yes, reposition them
+			exvector moved_indices;
+			reposition_dummy_indices(e_expanded, variant_dummy_indices, moved_indices);
+		}
+
+		// Rename the dummy indices
+		e_expanded = rename_dummy_indices<idx>(e_expanded, dummy_indices, local_dummy_indices);
+		e_expanded = rename_dummy_indices<varidx>(e_expanded, dummy_indices, local_dummy_indices);
+		e_expanded = rename_dummy_indices<spinidx>(e_expanded, dummy_indices, local_dummy_indices);
+		return e_expanded;
+	}
+
+	// Simplification of sum = sum of simplifications, check consistency of
+	// free indices in each term
+	if (is_exactly_a<add>(e_expanded)) {
+		bool first = true;
+		ex sum;
+		free_indices.clear();
+
+		for (size_t i=0; i<e_expanded.nops(); i++) {
+			exvector free_indices_of_term;
+			ex term = simplify_indexed(e_expanded.op(i), free_indices_of_term, dummy_indices, sp);
+			if (!term.is_zero()) {
+				if (first) {
+					free_indices = free_indices_of_term;
+					sum = term;
+					first = false;
+				} else {
+					if (!indices_consistent(free_indices, free_indices_of_term)) {
+						std::ostringstream s;
+						s << "simplify_indexed: inconsistent indices in sum: ";
+						s << exprseq(free_indices) << " vs. " << exprseq(free_indices_of_term);
+						throw (std::runtime_error(s.str()));
+					}
+					if (is_a<indexed>(sum) && is_a<indexed>(term))
+						sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
+					else
+						sum += term;
+				}
+			}
+		}
+
+		// If the sum turns out to be zero, we are finished
+		if (sum.is_zero()) {
+			free_indices.clear();
+			return sum;
+		}
+
+		// More than one term and more than one dummy index?
+		size_t num_terms_orig = (is_exactly_a<add>(sum) ? sum.nops() : 1);
+		if (num_terms_orig < 2 || dummy_indices.size() < 2)
+			return sum;
+
+		// Chop the sum into terms and symmetrize each one over the dummy
+		// indices
+		std::vector<terminfo> terms;
+		for (size_t i=0; i<sum.nops(); i++) {
+			const ex & term = sum.op(i);
+			exvector dummy_indices_of_term;
+			dummy_indices_of_term.reserve(dummy_indices.size());
+			for(exvector::iterator i=dummy_indices.begin(); i!=dummy_indices.end(); ++i)
+				if(hasindex(term,i->op(0)))
+					dummy_indices_of_term.push_back(*i);
+			ex term_symm = idx_symmetrization<idx>(term, dummy_indices_of_term);
+			term_symm = idx_symmetrization<varidx>(term_symm, dummy_indices_of_term);
+			term_symm = idx_symmetrization<spinidx>(term_symm, dummy_indices_of_term);
+			if (term_symm.is_zero())
+				continue;
+			terms.push_back(terminfo(term, term_symm));
+		}
+
+		// Sort by symmetrized terms
+		std::sort(terms.begin(), terms.end(), terminfo_is_less());
+
+		// Combine equal symmetrized terms
+		std::vector<terminfo> terms_pass2;
+		for (std::vector<terminfo>::const_iterator i=terms.begin(); i!=terms.end(); ) {
+			size_t num = 1;
+			std::vector<terminfo>::const_iterator j = i + 1;
+			while (j != terms.end() && j->symm == i->symm) {
+				num++;
+				j++;
+			}
+			terms_pass2.push_back(terminfo(i->orig * num, i->symm * num));
+			i = j;
+		}
+
+		// If there is only one term left, we are finished
+		if (terms_pass2.size() == 1)
+			return terms_pass2[0].orig;
+
+		// Chop the symmetrized terms into subterms
+		std::vector<symminfo> sy;
+		for (std::vector<terminfo>::const_iterator i=terms_pass2.begin(); i!=terms_pass2.end(); ++i) {
+			if (is_exactly_a<add>(i->symm)) {
+				size_t num = i->symm.nops();
+				for (size_t j=0; j<num; j++)
+					sy.push_back(symminfo(i->symm.op(j), i->orig, num));
+			} else
+				sy.push_back(symminfo(i->symm, i->orig, 1));
+		}
+
+		// Sort by symmetrized subterms
+		std::sort(sy.begin(), sy.end(), symminfo_is_less_by_symmterm());
+
+		// Combine equal symmetrized subterms
+		std::vector<symminfo> sy_pass2;
+		exvector result;
+		for (std::vector<symminfo>::const_iterator i=sy.begin(); i!=sy.end(); ) {
+
+			// Combine equal terms
+			std::vector<symminfo>::const_iterator j = i + 1;
+			if (j != sy.end() && j->symmterm == i->symmterm) {
+
+				// More than one term, collect the coefficients
+				ex coeff = i->coeff;
+				while (j != sy.end() && j->symmterm == i->symmterm) {
+					coeff += j->coeff;
+					j++;
+				}
+
+				// Add combined term to result
+				if (!coeff.is_zero())
+					result.push_back(coeff * i->symmterm);
+
+			} else {
+
+				// Single term, store for second pass
+				sy_pass2.push_back(*i);
+			}
+
+			i = j;
+		}
+
+		// Were there any remaining terms that didn't get combined?
+		if (sy_pass2.size() > 0) {
+
+			// Yes, sort by their original terms
+			std::sort(sy_pass2.begin(), sy_pass2.end(), symminfo_is_less_by_orig());
+
+			for (std::vector<symminfo>::const_iterator i=sy_pass2.begin(); i!=sy_pass2.end(); ) {
+
+				// How many symmetrized terms of this original term are left?
+				size_t num = 1;
+				std::vector<symminfo>::const_iterator j = i + 1;
+				while (j != sy_pass2.end() && j->orig == i->orig) {
+					num++;
+					j++;
+				}
+
+				if (num == i->num) {
+
+					// All terms left, then add the original term to the result
+					result.push_back(i->orig);
+
+				} else {
+
+					// Some terms were combined with others, add up the remaining symmetrized terms
+					std::vector<symminfo>::const_iterator k;
+					for (k=i; k!=j; k++)
+						result.push_back(k->coeff * k->symmterm);
+				}
+
+				i = j;
+			}
+		}
+
+		// Add all resulting terms
+		ex sum_symm = (new add(result))->setflag(status_flags::dynallocated);
+		if (sum_symm.is_zero())
+			free_indices.clear();
+		return sum_symm;
+	}
+
+	// Simplification of products
+	if (is_exactly_a<mul>(e_expanded)
+	 || is_exactly_a<ncmul>(e_expanded)
+	 || (is_exactly_a<power>(e_expanded) && is_a<indexed>(e_expanded.op(0)) && e_expanded.op(1).is_equal(_ex2)))
+		return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
+
+	// Cannot do anything
+	free_indices.clear();
+	return e_expanded;
+}
+
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible and checks whether
+ *  the free indices in sums are consistent.
+ *
+ *  @param options Simplification options (currently unused)
+ *  @return simplified expression */
+ex ex::simplify_indexed(unsigned options) const
+{
+	exvector free_indices, dummy_indices;
+	scalar_products sp;
+	return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible, checks whether
+ *  the free indices in sums are consistent, and automatically replaces
+ *  scalar products by known values if desired.
+ *
+ *  @param sp Scalar products to be replaced automatically
+ *  @param options Simplification options (currently unused)
+ *  @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp, unsigned options) const
+{
+	exvector free_indices, dummy_indices;
+	return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Symmetrize expression over its free indices. */
+ex ex::symmetrize() const
+{
+	return GiNaC::symmetrize(*this, get_free_indices());
+}
+
+/** Antisymmetrize expression over its free indices. */
+ex ex::antisymmetrize() const
+{
+	return GiNaC::antisymmetrize(*this, get_free_indices());
+}
+
+/** Symmetrize expression by cyclic permutation over its free indices. */
+ex ex::symmetrize_cyclic() const
+{
+	return GiNaC::symmetrize_cyclic(*this, get_free_indices());
+}
 
 //////////
-// global constants
+// helper classes
 //////////
 
-const indexed some_indexed;
-const type_info & typeid_indexed=typeid(some_indexed);
+spmapkey::spmapkey(const ex & v1_, const ex & v2_, const ex & dim_) : dim(dim_)
+{
+	// If indexed, extract base objects
+	ex s1 = is_a<indexed>(v1_) ? v1_.op(0) : v1_;
+	ex s2 = is_a<indexed>(v2_) ? v2_.op(0) : v2_;
+
+	// Enforce canonical order in pair
+	if (s1.compare(s2) > 0) {
+		v1 = s2;
+		v2 = s1;
+	} else {
+		v1 = s1;
+		v2 = s2;
+	}
+}
+
+bool spmapkey::operator==(const spmapkey &other) const
+{
+	if (!v1.is_equal(other.v1))
+		return false;
+	if (!v2.is_equal(other.v2))
+		return false;
+	if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
+		return true;
+	else
+		return dim.is_equal(other.dim);
+}
+
+bool spmapkey::operator<(const spmapkey &other) const
+{
+	int cmp = v1.compare(other.v1);
+	if (cmp)
+		return cmp < 0;
+	cmp = v2.compare(other.v2);
+	if (cmp)
+		return cmp < 0;
+
+	// Objects are equal, now check dimensions
+	if (is_a<wildcard>(dim) || is_a<wildcard>(other.dim))
+		return false;
+	else
+		return dim.compare(other.dim) < 0;
+}
+
+void spmapkey::debugprint() const
+{
+	std::cerr << "(" << v1 << "," << v2 << "," << dim << ")";
+}
+
+void scalar_products::add(const ex & v1, const ex & v2, const ex & sp)
+{
+	spm[spmapkey(v1, v2)] = sp;
+}
+
+void scalar_products::add(const ex & v1, const ex & v2, const ex & dim, const ex & sp)
+{
+	spm[spmapkey(v1, v2, dim)] = sp;
+}
+
+void scalar_products::add_vectors(const lst & l, const ex & dim)
+{
+	// Add all possible pairs of products
+	for (lst::const_iterator it1 = l.begin(); it1 != l.end(); ++it1)
+		for (lst::const_iterator it2 = l.begin(); it2 != l.end(); ++it2)
+			add(*it1, *it2, *it1 * *it2);
+}
+
+void scalar_products::clear()
+{
+	spm.clear();
+}
+
+/** Check whether scalar product pair is defined. */
+bool scalar_products::is_defined(const ex & v1, const ex & v2, const ex & dim) const
+{
+	return spm.find(spmapkey(v1, v2, dim)) != spm.end();
+}
+
+/** Return value of defined scalar product pair. */
+ex scalar_products::evaluate(const ex & v1, const ex & v2, const ex & dim) const
+{
+	return spm.find(spmapkey(v1, v2, dim))->second;
+}
+
+void scalar_products::debugprint() const
+{
+	std::cerr << "map size=" << spm.size() << std::endl;
+	spmap::const_iterator i = spm.begin(), end = spm.end();
+	while (i != end) {
+		const spmapkey & k = i->first;
+		std::cerr << "item key=";
+		k.debugprint();
+		std::cerr << ", value=" << i->second << std::endl;
+		++i;
+	}
+}
+
+exvector get_all_dummy_indices_safely(const ex & e)
+{
+	if (is_a<indexed>(e))
+		return ex_to<indexed>(e).get_dummy_indices();
+	else if (is_a<power>(e) && e.op(1)==2) {
+		return e.op(0).get_free_indices();
+	}	
+	else if (is_a<mul>(e) || is_a<ncmul>(e)) {
+		exvector dummies;
+		exvector free_indices;
+		for (int i=0; i<e.nops(); ++i) {
+			exvector dummies_of_factor = get_all_dummy_indices_safely(e.op(i));
+			dummies.insert(dummies.end(), dummies_of_factor.begin(),
+				dummies_of_factor.end());
+			exvector free_of_factor = e.op(i).get_free_indices();
+			free_indices.insert(free_indices.begin(), free_of_factor.begin(),
+				free_of_factor.end());
+		}
+		exvector free_out, dummy_out;
+		find_free_and_dummy(free_indices.begin(), free_indices.end(), free_out,
+			dummy_out);
+		dummies.insert(dummies.end(), dummy_out.begin(), dummy_out.end());
+		return dummies;
+	}
+	else if(is_a<add>(e)) {
+		exvector result;
+		for(int i=0; i<e.nops(); ++i) {
+			exvector dummies_of_term = get_all_dummy_indices_safely(e.op(i));
+			sort(dummies_of_term.begin(), dummies_of_term.end());
+			exvector new_vec;
+			set_union(result.begin(), result.end(), dummies_of_term.begin(),
+				dummies_of_term.end(), std::back_inserter<exvector>(new_vec),
+				ex_is_less());
+			result.swap(new_vec);
+		}
+		return result;
+	}
+	return exvector();
+}
+
+/** Returns all dummy indices from the exvector */
+exvector get_all_dummy_indices(const ex & e)
+{
+	exvector p;
+	bool nc;
+	product_to_exvector(e, p, nc);
+	exvector::const_iterator ip = p.begin(), ipend = p.end();
+	exvector v, v1;
+	while (ip != ipend) {
+		if (is_a<indexed>(*ip)) {
+			v1 = ex_to<indexed>(*ip).get_dummy_indices();
+			v.insert(v.end(), v1.begin(), v1.end());
+			exvector::const_iterator ip1 = ip+1;
+			while (ip1 != ipend) {
+				if (is_a<indexed>(*ip1)) {
+					v1 = ex_to<indexed>(*ip).get_dummy_indices(ex_to<indexed>(*ip1));
+					v.insert(v.end(), v1.begin(), v1.end());
+				}
+				++ip1;
+			}
+		}
+		++ip;
+	}
+	return v;
+}
+
+lst rename_dummy_indices_uniquely(const exvector & va, const exvector & vb)
+{
+	exvector common_indices;
+	set_intersection(va.begin(), va.end(), vb.begin(), vb.end(), std::back_insert_iterator<exvector>(common_indices), ex_is_less());
+	if (common_indices.empty()) {
+		return lst(lst(), lst());
+	} else {
+		exvector new_indices, old_indices;
+		old_indices.reserve(2*common_indices.size());
+		new_indices.reserve(2*common_indices.size());
+		exvector::const_iterator ip = common_indices.begin(), ipend = common_indices.end();
+		while (ip != ipend) {
+			ex newsym=(new symbol)->setflag(status_flags::dynallocated);
+			ex newidx;
+			if(is_exactly_a<spinidx>(*ip))
+				newidx = (new spinidx(newsym, ex_to<spinidx>(*ip).get_dim(),
+						ex_to<spinidx>(*ip).is_covariant(),
+						ex_to<spinidx>(*ip).is_dotted()))
+					-> setflag(status_flags::dynallocated);
+			else if (is_exactly_a<varidx>(*ip))
+				newidx = (new varidx(newsym, ex_to<varidx>(*ip).get_dim(),
+						ex_to<varidx>(*ip).is_covariant()))
+					-> setflag(status_flags::dynallocated);
+			else
+				newidx = (new idx(newsym, ex_to<idx>(*ip).get_dim()))
+					-> setflag(status_flags::dynallocated);
+			old_indices.push_back(*ip);
+			new_indices.push_back(newidx);
+			if(is_a<varidx>(*ip)) {
+				old_indices.push_back(ex_to<varidx>(*ip).toggle_variance());
+				new_indices.push_back(ex_to<varidx>(newidx).toggle_variance());
+			}
+			++ip;
+		}
+		return lst(lst(old_indices.begin(), old_indices.end()), lst(new_indices.begin(), new_indices.end()));
+	}
+}
+
+ex rename_dummy_indices_uniquely(const exvector & va, const exvector & vb, const ex & b)
+{
+	lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+	return (indices_subs.op(0).nops()>0 ? b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming) : b);
+}
+
+ex rename_dummy_indices_uniquely(const ex & a, const ex & b)
+{
+	exvector va = get_all_dummy_indices_safely(a);
+	if (va.size() > 0) {
+		exvector vb = get_all_dummy_indices_safely(b);
+		if (vb.size() > 0) {
+			sort(va.begin(), va.end(), ex_is_less());
+			sort(vb.begin(), vb.end(), ex_is_less());
+			lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+			if (indices_subs.op(0).nops() > 0)
+				return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
+		}
+	}
+	return b;
+}
+
+ex rename_dummy_indices_uniquely(exvector & va, const ex & b, bool modify_va)
+{
+	if (va.size() > 0) {
+		exvector vb = get_all_dummy_indices_safely(b);
+		if (vb.size() > 0) {
+			sort(vb.begin(), vb.end(), ex_is_less());
+			lst indices_subs = rename_dummy_indices_uniquely(va, vb);
+			if (indices_subs.op(0).nops() > 0) {
+				if (modify_va) {
+					for (lst::const_iterator i = ex_to<lst>(indices_subs.op(1)).begin(); i != ex_to<lst>(indices_subs.op(1)).end(); ++i)
+						va.push_back(*i);
+					exvector uncommon_indices;
+					set_difference(vb.begin(), vb.end(), indices_subs.op(0).begin(), indices_subs.op(0).end(), std::back_insert_iterator<exvector>(uncommon_indices), ex_is_less());
+					exvector::const_iterator ip = uncommon_indices.begin(), ipend = uncommon_indices.end();
+					while (ip != ipend) {
+						va.push_back(*ip);
+						++ip;
+					}
+					sort(va.begin(), va.end(), ex_is_less());
+				}
+				return b.subs(ex_to<lst>(indices_subs.op(0)), ex_to<lst>(indices_subs.op(1)), subs_options::no_pattern|subs_options::no_index_renaming);
+			}
+		}
+	}
+	return b;
+}
+
+ex expand_dummy_sum(const ex & e, bool subs_idx)
+{
+	ex e_expanded = e.expand();
+	pointer_to_map_function_1arg<bool> fcn(expand_dummy_sum, subs_idx);
+	if (is_a<add>(e_expanded) || is_a<lst>(e_expanded) || is_a<matrix>(e_expanded)) {
+		return e_expanded.map(fcn);
+	} else if (is_a<ncmul>(e_expanded) || is_a<mul>(e_expanded) || is_a<power>(e_expanded) || is_a<indexed>(e_expanded)) {
+		exvector v;
+		if (is_a<indexed>(e_expanded))
+			v = ex_to<indexed>(e_expanded).get_dummy_indices();
+		else
+			v = get_all_dummy_indices(e_expanded);
+		ex result = e_expanded;
+		for(exvector::const_iterator it=v.begin(); it!=v.end(); ++it) {
+			ex nu = *it;
+			if (ex_to<idx>(nu).get_dim().info(info_flags::nonnegint)) {
+				int idim = ex_to<numeric>(ex_to<idx>(nu).get_dim()).to_int();
+				ex en = 0;
+				for (int i=0; i < idim; i++) {
+					if (subs_idx && is_a<varidx>(nu)) {
+						ex other = ex_to<varidx>(nu).toggle_variance();
+						en += result.subs(lst(
+							nu == idx(i, idim),
+							other == idx(i, idim)
+						));
+					} else {
+						en += result.subs( nu.op(0) == i );
+					}
+				}
+				result = en;
+			}
+		}
+		return result;
+	} else {
+		return e;
+	}
+}
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC