X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Findexed.cpp;h=d63711044b03fbff787a47aeba51a14908c79d72;hp=9ddff040fd509c3d4f7773df99fcd7db7d34d8bf;hb=0c718e0dda0d2de1224f39ec5e3c39720e0abfc2;hpb=444d1e293d87b78f0497a55c6a4dabad010f5b62

diff --git a/ginac/indexed.cpp b/ginac/indexed.cpp
index 9ddff040..d6371104 100644
--- a/ginac/indexed.cpp
+++ b/ginac/indexed.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's indexed expressions. */
 
 /*
- *  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
@@ -20,8 +20,9 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
+#include <sstream>
 #include <stdexcept>
-#include <algorithm>
 
 #include "indexed.h"
 #include "idx.h"
@@ -29,30 +30,30 @@
 #include "mul.h"
 #include "ncmul.h"
 #include "power.h"
+#include "relational.h"
+#include "symmetry.h"
 #include "lst.h"
 #include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(indexed, exprseq)
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-indexed::indexed() : symmetry(unknown)
+indexed::indexed() : symtree(sy_none())
 {
-	debugmsg("indexed default constructor", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
 }
 
 void indexed::copy(const indexed & other)
 {
 	inherited::copy(other);
-	symmetry = other.symmetry;
+	symtree = other.symtree;
 }
 
 DEFAULT_DESTROY(indexed)
@@ -61,97 +62,81 @@ DEFAULT_DESTROY(indexed)
 // other constructors
 //////////
 
-indexed::indexed(const ex & b) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b) : inherited(b), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1) : inherited(b, i1), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(unknown)
+indexed::indexed(const ex & b, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2) : inherited(b, i1, i2), symtree(symm)
 {
-	debugmsg("indexed constructor from ex,symmetry,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const ex & i1, const ex & i2, const ex & i3) : inherited(b, i1, i2, i3), symtree(symm)
 {
-	debugmsg("indexed constructor from ex,symmetry,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, symmetry_type symm, const ex & i1, const ex & i2, const ex & i3, const ex & i4) : inherited(b, i1, i2, i3, i4), symmetry(symm)
+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,symmetry,ex,ex,ex,ex", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, const exvector & v) : inherited(b), symmetry(unknown)
+indexed::indexed(const ex & b, const exvector & v) : inherited(b), symtree(sy_none())
 {
-	debugmsg("indexed constructor from ex,exvector", LOGLEVEL_CONSTRUCT);
 	seq.insert(seq.end(), v.begin(), v.end());
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(const ex & b, symmetry_type symm, const exvector & v) : inherited(b), symmetry(symm)
+indexed::indexed(const ex & b, const symmetry & symm, const exvector & v) : inherited(b), symtree(symm)
 {
-	debugmsg("indexed constructor from ex,symmetry,exvector", LOGLEVEL_CONSTRUCT);
 	seq.insert(seq.end(), v.begin(), v.end());
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
+	validate();
 }
 
-indexed::indexed(symmetry_type symm, const exprseq & es) : inherited(es), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exprseq & es) : inherited(es), symtree(symm)
 {
-	debugmsg("indexed constructor from symmetry,exprseq", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
 }
 
-indexed::indexed(symmetry_type symm, const exvector & v, bool discardable) : inherited(v, discardable), symmetry(symm)
+indexed::indexed(const symmetry & symm, const exvector & v, bool discardable) : inherited(v, discardable), symtree(symm)
 {
-	debugmsg("indexed constructor from symmetry,exvector", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
 }
 
-indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(symm)
+indexed::indexed(const symmetry & symm, exvector * vp) : inherited(vp), symtree(symm)
 {
-	debugmsg("indexed constructor from symmetry,exvector *", LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_indexed;
-	assert_all_indices_of_type_idx();
 }
 
 //////////
@@ -160,61 +145,66 @@ indexed::indexed(symmetry_type symm, exvector * vp) : inherited(vp), symmetry(sy
 
 indexed::indexed(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("indexed constructor from archive_node", LOGLEVEL_CONSTRUCT);
-	unsigned int symm;
-	if (!(n.find_unsigned("symmetry", symm)))
-		throw (std::runtime_error("unknown indexed symmetry type in archive"));
+	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 = sy_none();
+				break;
+		}
+		const_cast<symmetry &>(ex_to<symmetry>(symtree)).validate(seq.size() - 1);
+	}
 }
 
 void indexed::archive(archive_node &n) const
 {
 	inherited::archive(n);
-	n.add_unsigned("symmetry", symmetry);
+	n.add_ex("symmetry", symtree);
 }
 
 DEFAULT_UNARCHIVE(indexed)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 void indexed::print(const print_context & c, unsigned level) const
 {
-	debugmsg("indexed print", LOGLEVEL_PRINT);
 	GINAC_ASSERT(seq.size() > 0);
 
-	if (is_of_type(c, print_tree)) {
+	if (is_a<print_tree>(c)) {
 
 		c.s << std::string(level, ' ') << class_name()
 		    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
-		    << ", " << seq.size()-1 << " indices";
-		switch (symmetry) {
-			case symmetric: c.s << ", symmetric"; break;
-			case antisymmetric: c.s << ", antisymmetric"; break;
-			default: break;
-		}
-		c.s << std::endl;
+		    << ", " << seq.size()-1 << " indices"
+		    << ", symmetry=" << symtree << std::endl;
 		unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 		seq[0].print(c, level + delta_indent);
 		printindices(c, level + delta_indent);
 
 	} else {
 
-		bool is_tex = is_of_type(c, print_latex);
+		bool is_tex = is_a<print_latex>(c);
 		const ex & base = seq[0];
-		bool need_parens = is_ex_exactly_of_type(base, add) || is_ex_exactly_of_type(base, mul)
-		                || is_ex_exactly_of_type(base, ncmul) || is_ex_exactly_of_type(base, power)
-		                || is_ex_of_type(base, indexed);
+
+		if (precedence() <= level)
+			c.s << (is_tex ? "{(" : "(");
 		if (is_tex)
 			c.s << "{";
-		if (need_parens)
-			c.s << "(";
-		base.print(c);
-		if (need_parens)
-			c.s << ")";
+		base.print(c, precedence());
 		if (is_tex)
 			c.s << "}";
 		printindices(c, level);
+		if (precedence() <= level)
+			c.s << (is_tex ? ")}" : ")");
 	}
 }
 
@@ -225,9 +215,9 @@ bool indexed::info(unsigned inf) const
 	return inherited::info(inf);
 }
 
-struct idx_is_not : public binary_function<ex, unsigned, bool> {
+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));
+		return !(ex_to<idx>(e).get_value().info(inf));
 	}
 };
 
@@ -243,118 +233,55 @@ bool indexed::all_index_values_are(unsigned inf) const
 
 int indexed::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_of_type(other, indexed));
+	GINAC_ASSERT(is_a<indexed>(other));
 	return inherited::compare_same_type(other);
 }
 
-// The main difference between sort_index_vector() and canonicalize_indices()
-// is that the latter takes the symmetry of the object into account. Once we
-// implement mixed symmetries, canonicalize_indices() will only be able to
-// reorder index pairs with known symmetry properties, while sort_index_vector()
-// always sorts the whole vector.
-
-/** Bring a vector of indices into a canonic order. This operation only makes
- *  sense if the object carrying these indices is either symmetric or totally
- *  antisymmetric with respect to the indices.
- *
- *  @param itbegin Start of index vector
- *  @param itend End of index vector
- *  @param antisymm Whether the object is antisymmetric
- *  @return the sign introduced by the reordering of the indices if the object
- *          is antisymmetric (or 0 if two equal indices are encountered). For
- *          symmetric objects, this is always +1. If the index vector was
- *          already in a canonic order this function returns INT_MAX. */
-static int canonicalize_indices(exvector::iterator itbegin, exvector::iterator itend, bool antisymm)
-{
-	bool something_changed = false;
-	int sig = 1;
-
-	// Simple bubble sort algorithm should be sufficient for the small
-	// number of indices expected
-	exvector::iterator it1 = itbegin, next_to_last_idx = itend - 1;
-	while (it1 != next_to_last_idx) {
-		exvector::iterator it2 = it1 + 1;
-		while (it2 != itend) {
-			int cmpval = it1->compare(*it2);
-			if (cmpval == 1) {
-				it1->swap(*it2);
-				something_changed = true;
-				if (antisymm)
-					sig = -sig;
-			} else if (cmpval == 0 && antisymm) {
-				something_changed = true;
-				sig = 0;
-			}
-			it2++;
-		}
-		it1++;
-	}
-
-	return something_changed ? sig : INT_MAX;
-}
-
 ex indexed::eval(int level) const
 {
 	// First evaluate children, then we will end up here again
 	if (level > 1)
-		return indexed(symmetry, evalchildren(level));
+		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();
+		return _ex0;
 
 	// If the base object is a product, pull out the numeric factor
 	if (is_ex_exactly_of_type(base, mul) && is_ex_exactly_of_type(base.op(base.nops() - 1), numeric)) {
-		exvector v = seq;
-		ex f = ex_to_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 * thisexprseq(v);
 	}
 
 	// Canonicalize indices according to the symmetry properties
-	if (seq.size() > 2 && (symmetry != unknown && symmetry != mixed)) {
+	if (seq.size() > 2) {
 		exvector v = seq;
-		int sig = canonicalize_indices(v.begin() + 1, v.end(), symmetry == antisymmetric);
+		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 _ex0;
 			return ex(sig) * thisexprseq(v);
 		}
 	}
 
 	// Let the class of the base object perform additional evaluations
-	return base.bp->eval_indexed(*this);
-}
-
-int indexed::degree(const ex & s) const
-{
-	return is_equal(*s.bp) ? 1 : 0;
-}
-
-int indexed::ldegree(const ex & s) const
-{
-	return is_equal(*s.bp) ? 1 : 0;
-}
-
-ex indexed::coeff(const ex & s, int n) const
-{
-	if (is_equal(*s.bp))
-		return n==1 ? _ex1() : _ex0();
-	else
-		return n==0 ? ex(*this) : _ex0();
+	return ex_to<basic>(base).eval_indexed(*this);
 }
 
 ex indexed::thisexprseq(const exvector & v) const
 {
-	return indexed(symmetry, v);
+	return indexed(ex_to<symmetry>(symtree), v);
 }
 
 ex indexed::thisexprseq(exvector * vp) const
 {
-	return indexed(symmetry, vp);
+	return indexed(ex_to<symmetry>(symtree), vp);
 }
 
 ex indexed::expand(unsigned options) const
@@ -365,7 +292,7 @@ ex indexed::expand(unsigned options) const
 
 		// expand_indexed expands (a+b).i -> a.i + b.i
 		const ex & base = seq[0];
-		ex sum = _ex0();
+		ex sum = _ex0;
 		for (unsigned i=0; i<base.nops(); i++) {
 			exvector s = seq;
 			s[0] = base.op(i);
@@ -393,17 +320,18 @@ void indexed::printindices(const print_context & c, unsigned level) const
 
 		exvector::const_iterator it=seq.begin() + 1, itend = seq.end();
 
-		if (is_of_type(c, print_latex)) {
+		if (is_a<print_latex>(c)) {
 
 			// TeX output: group by variance
 			bool first = true;
 			bool covariant = true;
 
 			while (it != itend) {
-				bool cur_covariant = (is_ex_of_type(*it, varidx) ? ex_to_varidx(*it).is_covariant() : true);
-				if (first || cur_covariant != covariant) {
+				bool cur_covariant = (is_ex_of_type(*it, varidx) ? 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 << "}";
+						c.s << "}{}";
 					covariant = cur_covariant;
 					if (covariant)
 						c.s << "_{";
@@ -428,10 +356,10 @@ void indexed::printindices(const print_context & c, unsigned level) const
 	}
 }
 
-/** Check whether all indices are of class idx. This function is used
- *  internally to make sure that all constructed indexed objects really
- *  carry indices and not some other classes. */
-void indexed::assert_all_indices_of_type_idx(void) const
+/** 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(void) const
 {
 	GINAC_ASSERT(seq.size() > 0);
 	exvector::const_iterator it = seq.begin() + 1, itend = seq.end();
@@ -440,12 +368,42 @@ void indexed::assert_all_indices_of_type_idx(void) const
 			throw(std::invalid_argument("indices of indexed object must be of type idx"));
 		it++;
 	}
+
+	if (!symtree.is_zero()) {
+		if (!is_ex_exactly_of_type(symtree, symmetry))
+			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)
 {
@@ -453,7 +411,7 @@ static bool indices_consistent(const exvector & v1, const exvector & v2)
 	if (v1.size() != v2.size())
 		return false;
 
-	return equal(v1.begin(), v1.end(), v2.begin(), ex_is_equal());
+	return equal(v1.begin(), v1.end(), v2.begin(), idx_is_equal_ignore_dim());
 }
 
 exvector indexed::get_indices(void) const
@@ -550,7 +508,7 @@ exvector power::get_free_indices(void) const
 
 /** Rename dummy indices in an expression.
  *
- *  @param e Expression to be worked on
+ *  @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
@@ -558,8 +516,8 @@ exvector power::get_free_indices(void) const
  *    by the function */
 static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, exvector & local_dummy_indices)
 {
-	int global_size = global_dummy_indices.size(),
-	    local_size = local_dummy_indices.size();
+	unsigned global_size = global_dummy_indices.size(),
+	         local_size = local_dummy_indices.size();
 
 	// Any local dummy indices at all?
 	if (local_size == 0)
@@ -569,37 +527,122 @@ static ex rename_dummy_indices(const ex & e, exvector & global_dummy_indices, ex
 
 		// More local indices than we encountered before, add the new ones
 		// to the global set
+		int 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 (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(ex_is_equal(), *it)) == global_dummy_indices.end()) {
+			if (find_if(global_dummy_indices.begin(), global_dummy_indices.end(), bind2nd(op0_is_equal(), *it)) == global_dummy_indices.end()) {
 				global_dummy_indices.push_back(*it);
 				global_size++;
 				remaining--;
 			}
 			it++;
 		}
-	}
 
-	// Replace index symbols in expression
+		// If this is the first set of local indices, do nothing
+		if (old_global_size == 0)
+			return e;
+	}
 	GINAC_ASSERT(local_size <= global_size);
-	bool all_equal = true;
-	lst local_syms, global_syms;
-	for (unsigned i=0; i<local_size; i++) {
-		ex loc_sym = local_dummy_indices[i].op(0);
-		ex glob_sym = global_dummy_indices[i].op(0);
-		if (!loc_sym.is_equal(glob_sym)) {
-			all_equal = false;
-			local_syms.append(loc_sym);
-			global_syms.append(glob_sym);
+
+	// Construct lists of index symbols
+	exlist local_syms, global_syms;
+	for (unsigned i=0; i<local_size; 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 (unsigned i=0; i<local_size; i++) // don't use more global symbols than necessary
+		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
+	exlist local_uniq, global_uniq;
+	set_difference(local_syms.begin(), local_syms.end(), global_syms.begin(), global_syms.end(), std::back_insert_iterator<exlist>(local_uniq), ex_is_less());
+	set_difference(global_syms.begin(), global_syms.end(), local_syms.begin(), local_syms.end(), std::back_insert_iterator<exlist>(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), lst(global_uniq));
+	}
+}
+
+/** 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);
+	}
+}
+
+/** 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)
+{
+	bool something_changed = false;
+
+	// If a dummy index is encountered for the first time in the
+	// product, pull it up, otherwise, pull it down
+	exvector::const_iterator it2, it2start, it2end;
+	for (it2start = ex_to<indexed>(e).seq.begin(), it2end = ex_to<indexed>(e).seq.end(), it2 = it2start + 1; 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()) {
+					e = e.subs(lst(
+						*it2 == ex_to<varidx>(*it2).toggle_variance(),
+						ex_to<varidx>(*it2).toggle_variance() == *it2
+					));
+					something_changed = true;
+					it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
+					it2start = ex_to<indexed>(e).seq.begin();
+					it2end = ex_to<indexed>(e).seq.end();
+				}
+				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()) {
+					e = e.subs(*it2 == ex_to<varidx>(*it2).toggle_variance());
+					something_changed = true;
+					it2 = ex_to<indexed>(e).seq.begin() + (it2 - it2start);
+					it2start = ex_to<indexed>(e).seq.begin();
+					it2end = ex_to<indexed>(e).seq.end();
+				}
+				goto next_index;
+			}
+		}
+
+next_index: ;
 	}
-	if (all_equal)
-		return e;
-	else
-		return e.subs(local_syms, global_syms);
+
+	return something_changed;
 }
 
+/* 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;
+	}
+};
+
 /** 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)
@@ -614,19 +657,19 @@ ex simplify_indexed_product(const ex & e, exvector & free_indices, exvector & du
 
 	if (is_ex_exactly_of_type(e, power)) {
 		// We only get called for simple squares, split a^2 -> a*a
-		GINAC_ASSERT(e.op(1).is_equal(_ex2()));
+		GINAC_ASSERT(e.op(1).is_equal(_ex2));
 		v.push_back(e.op(0));
 		v.push_back(e.op(0));
 	} else {
-		for (int i=0; i<e.nops(); i++) {
+		for (unsigned i=0; i<e.nops(); i++) {
 			ex f = e.op(i);
-			if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2())) {
+			if (is_ex_exactly_of_type(f, power) && f.op(1).is_equal(_ex2)) {
 				v.push_back(f.op(0));
 	            v.push_back(f.op(0));
 			} else if (is_ex_exactly_of_type(f, ncmul)) {
 				// Noncommutative factor found, split it as well
 				non_commutative = true; // everything becomes noncommutative, ncmul will sort out the commutative factors later
-				for (int j=0; j<f.nops(); j++)
+				for (unsigned j=0; j<f.nops(); j++)
 					v.push_back(f.op(j));
 			} else
 				v.push_back(f);
@@ -648,7 +691,7 @@ try_again:
 		// 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);
+		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++) {
@@ -661,42 +704,33 @@ try_again:
 			// 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);
+			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);
-			if (dummy.size() == 0)
+			unsigned 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.size() == 0) {
+			if (free.empty()) {
 				if (sp.is_defined(*it1, *it2)) {
 					*it1 = sp.evaluate(*it1, *it2);
-					*it2 = _ex1();
+					*it2 = _ex1;
 					goto contraction_done;
 				}
 			}
 
-			// Contraction of symmetric with antisymmetric object is zero
-			if ((ex_to_indexed(*it1).symmetry == indexed::symmetric &&
-			     ex_to_indexed(*it2).symmetry == indexed::antisymmetric
-			  || ex_to_indexed(*it1).symmetry == indexed::antisymmetric &&
-			     ex_to_indexed(*it2).symmetry == indexed::symmetric)
-			 && dummy.size() > 1) {
-				free_indices.clear();
-				return _ex0();
-			}
-
 			// Try to contract the first one with the second one
-			contracted = it1->op(0).bp->contract_with(it1, it2, v);
+			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 = it2->op(0).bp->contract_with(it2, it1, v);
+				contracted = ex_to<basic>(it2->op(0)).contract_with(it2, it1, v);
 			}
 			if (contracted) {
 contraction_done:
@@ -726,39 +760,131 @@ contraction_done:
 	// Find free indices (concatenate them all and call find_free_and_dummy())
 	// and all dummy indices that appear
 	exvector un, individual_dummy_indices;
-	it1 = v.begin(); itend = v.end();
-	while (it1 != itend) {
+	for (it1 = v.begin(), itend = v.end(); it1 != itend; ++it1) {
 		exvector free_indices_of_factor;
 		if (is_ex_of_type(*it1, indexed)) {
 			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);
+			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());
-		it1++;
 	}
 	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_ex_of_type(*it1, indexed))
+				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.
+	if (local_dummy_indices.size() >= 2) {
+		lst dummy_syms;
+		for (int i=0; i<local_dummy_indices.size(); i++)
+			dummy_syms.append(local_dummy_indices[i].op(0));
+		if (r.symmetrize(dummy_syms).is_zero()) {
+			free_indices.clear();
+			return _ex0;
+		}
+	}
+
 	// Dummy index renaming
 	r = rename_dummy_indices(r, dummy_indices, local_dummy_indices);
 
 	// Product of indexed object with a scalar?
 	if (is_ex_exactly_of_type(r, mul) && r.nops() == 2
 	 && is_ex_exactly_of_type(r.op(1), numeric) && is_ex_of_type(r.op(0), indexed))
-		return r.op(0).op(0).bp->scalar_mul_indexed(r.op(0), ex_to_numeric(r.op(1)));
+		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_, unsigned 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 */
+	unsigned 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);
+	}
+};
+
 /** Simplify indexed expression, return list of free indices. */
 ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indices, const scalar_products & sp)
 {
@@ -766,11 +892,27 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi
 	ex e_expanded = e.expand();
 
 	// Simplification of single indexed object: just find the free indices
-	// and perform dummy index renaming
+	// and perform dummy index renaming/repositioning
 	if (is_ex_of_type(e_expanded, indexed)) {
-		const indexed &i = ex_to_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
 		return rename_dummy_indices(e_expanded, dummy_indices, local_dummy_indices);
 	}
 
@@ -778,7 +920,7 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi
 	// free indices in each term
 	if (is_ex_exactly_of_type(e_expanded, add)) {
 		bool first = true;
-		ex sum = _ex0();
+		ex sum;
 		free_indices.clear();
 
 		for (unsigned i=0; i<e_expanded.nops(); i++) {
@@ -790,23 +932,154 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi
 					sum = term;
 					first = false;
 				} else {
-					if (!indices_consistent(free_indices, free_indices_of_term))
-						throw (std::runtime_error("simplify_indexed: inconsistent indices in sum"));
+					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_ex_of_type(sum, indexed) && is_ex_of_type(term, indexed))
-						sum = sum.op(0).bp->add_indexed(sum, term);
+						sum = ex_to<basic>(sum.op(0)).add_indexed(sum, term);
 					else
 						sum += term;
 				}
 			}
 		}
 
-		return sum;
+		// 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?
+		int num_terms_orig = (is_exactly_a<add>(sum) ? sum.nops() : 1);
+		if (num_terms_orig < 2 || dummy_indices.size() < 2)
+			return sum;
+
+		// Yes, construct list of all dummy index symbols
+		lst dummy_syms;
+		for (int i=0; i<dummy_indices.size(); i++)
+			dummy_syms.append(dummy_indices[i].op(0));
+
+		// Chop the sum into terms and symmetrize each one over the dummy
+		// indices
+		std::vector<terminfo> terms;
+		for (unsigned i=0; i<sum.nops(); i++) {
+			const ex & term = sum.op(i);
+			ex term_symm = term.symmetrize(dummy_syms);
+			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(); ) {
+			unsigned 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)) {
+				unsigned num = i->symm.nops();
+				for (unsigned 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?
+				unsigned 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_ex_exactly_of_type(e_expanded, mul)
 	 || is_ex_exactly_of_type(e_expanded, ncmul)
-	 || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2())))
+	 || (is_ex_exactly_of_type(e_expanded, power) && is_ex_of_type(e_expanded.op(0), indexed) && e_expanded.op(1).is_equal(_ex2)))
 		return simplify_indexed_product(e_expanded, free_indices, dummy_indices, sp);
 
 	// Cannot do anything
@@ -814,17 +1087,47 @@ ex simplify_indexed(const ex & e, exvector & free_indices, exvector & dummy_indi
 	return e_expanded;
 }
 
-ex simplify_indexed(const ex & e)
+/** Simplify/canonicalize expression containing indexed objects. This
+ *  performs contraction of dummy indices where possible and checks whether
+ *  the free indices in sums are consistent.
+ *
+ *  @return simplified expression */
+ex ex::simplify_indexed(void) const
 {
 	exvector free_indices, dummy_indices;
 	scalar_products sp;
-	return simplify_indexed(e, free_indices, dummy_indices, sp);
+	return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
 }
 
-ex simplify_indexed(const ex & e, const scalar_products & 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
+ *  @return simplified expression */
+ex ex::simplify_indexed(const scalar_products & sp) const
 {
 	exvector free_indices, dummy_indices;
-	return simplify_indexed(e, free_indices, dummy_indices, sp);
+	return GiNaC::simplify_indexed(*this, free_indices, dummy_indices, sp);
+}
+
+/** Symmetrize expression over its free indices. */
+ex ex::symmetrize(void) const
+{
+	return GiNaC::symmetrize(*this, get_free_indices());
+}
+
+/** Antisymmetrize expression over its free indices. */
+ex ex::antisymmetrize(void) const
+{
+	return GiNaC::antisymmetrize(*this, get_free_indices());
+}
+
+/** Symmetrize expression by cyclic permutation over its free indices. */
+ex ex::symmetrize_cyclic(void) const
+{
+	return GiNaC::symmetrize_cyclic(*this, get_free_indices());
 }
 
 //////////
@@ -869,10 +1172,12 @@ ex scalar_products::evaluate(const ex & v1, const ex & v2) const
 void scalar_products::debugprint(void) const
 {
 	std::cerr << "map size=" << spm.size() << std::endl;
-	for (spmap::const_iterator cit=spm.begin(); cit!=spm.end(); ++cit) {
-		const spmapkey & k = cit->first;
+	spmap::const_iterator i = spm.begin(), end = spm.end();
+	while (i != end) {
+		const spmapkey & k = i->first;
 		std::cerr << "item key=(" << k.first << "," << k.second;
-		std::cerr << "), value=" << cit->second << std::endl;
+		std::cerr << "), value=" << i->second << std::endl;
+		++i;
 	}
 }