X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fidx.cpp;h=a3767fe8c5c65e7dc357e712cf79b34756737347;hp=af463a80f4a71cfe9c3ebf33ec486f1fed16c1e3;hb=af040268bde04a58accd189940927c191434ed1e;hpb=e5362a33f72613b324b3714524a8c2e5f7b7f46f

diff --git a/ginac/idx.cpp b/ginac/idx.cpp
index af463a80..a3767fe8 100644
--- a/ginac/idx.cpp
+++ b/ginac/idx.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's indices. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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
@@ -20,519 +20,505 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <stdexcept>
 
 #include "idx.h"
-#include "ex.h"
+#include "symbol.h"
 #include "lst.h"
-#include "relational.h"
+#include "print.h"
 #include "archive.h"
 #include "utils.h"
-#include "debugmsg.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(idx, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS(varidx, idx)
+GINAC_IMPLEMENT_REGISTERED_CLASS(spinidx, varidx)
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-// public
+idx::idx() : inherited(TINFO_idx) {}
 
-idx::idx() : inherited(TINFO_idx), symbolic(true), covariant(false)
+varidx::varidx() : covariant(false)
 {
-	debugmsg("idx default constructor",LOGLEVEL_CONSTRUCT);
-	serial=next_serial++;
-	name=autoname_prefix()+ToString(serial);
+	tinfo_key = TINFO_varidx;
 }
 
-// protected
+spinidx::spinidx() : dotted(false)
+{
+	tinfo_key = TINFO_spinidx;
+}
 
 void idx::copy(const idx & other)
 {
 	inherited::copy(other);
-	serial=other.serial;
-	symbolic=other.symbolic;
-	name=other.name;
-	value=other.value;
-	covariant=other.covariant;
+	value = other.value;
+	dim = other.dim;
+}
+
+void varidx::copy(const varidx & other)
+{
+	inherited::copy(other);
+	covariant = other.covariant;
 }
 
-void idx::destroy(bool call_parent)
+void spinidx::copy(const spinidx & other)
 {
-	if (call_parent) inherited::destroy(call_parent);
+	inherited::copy(other);
+	dotted = other.dotted;
 }
 
+DEFAULT_DESTROY(idx)
+DEFAULT_DESTROY(varidx)
+DEFAULT_DESTROY(spinidx)
+
 //////////
 // other constructors
 //////////
 
-// public
-
-/** Construct symbolic index, using an automatically generated unique name.
- *
- *  @param cov Index is covariant (contravariant otherwise)
- *  @return newly constructed index */
-idx::idx(bool cov) : inherited(TINFO_idx), symbolic(true), covariant(cov)
+idx::idx(const ex & v, const ex & d) : inherited(TINFO_idx), value(v), dim(d)
 {
-	debugmsg("idx constructor from bool",LOGLEVEL_CONSTRUCT);
-	serial = next_serial++;
-	name = autoname_prefix()+ToString(serial);
+	if (is_dim_numeric())
+		if (!dim.info(info_flags::posint))
+			throw(std::invalid_argument("dimension of space must be a positive integer"));
 }
 
-/** Construct symbolic index with specified name.
- *
- *  @param n Symbolic index name
- *  @param cov Index is covariant (contravariant otherwise)
- *  @return newly constructed index */
-idx::idx(const std::string & n, bool cov) : inherited(TINFO_idx),  
-	symbolic(true), name(n), covariant(cov)
+varidx::varidx(const ex & v, const ex & d, bool cov) : inherited(v, d), covariant(cov)
 {
-	debugmsg("idx constructor from string,bool",LOGLEVEL_CONSTRUCT);
-	serial = next_serial++;
+	tinfo_key = TINFO_varidx;
 }
 
-/** Construct symbolic index with specified name.
- *
- *  @param n Symbolic index name
- *  @param cov Index is covariant (contravariant otherwise)
- *  @return newly constructed index */
-idx::idx(const char * n, bool cov) : inherited(TINFO_idx), symbolic(true), name(n), covariant(cov)
+spinidx::spinidx(const ex & v, const ex & d, bool cov, bool dot) : inherited(v, d, cov), dotted(dot)
 {
-	debugmsg("idx constructor from char*,bool",LOGLEVEL_CONSTRUCT);
-	serial = next_serial++;
-}
-
-/** Construct numeric index with specified value.
- *
- *  @param v Numeric index value
- *  @param cov Index is covariant (contravariant otherwise)
- *  @return newly constructed index */
-idx::idx(unsigned v, bool cov) : inherited(TINFO_idx), symbolic(false), value(v), covariant(cov)
-{
-	debugmsg("idx constructor from unsigned,bool",LOGLEVEL_CONSTRUCT);
-	serial = 0;
+	tinfo_key = TINFO_spinidx;
 }
 
 //////////
 // archiving
 //////////
 
-/** Construct object from archive_node. */
 idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	debugmsg("idx constructor from archive_node", LOGLEVEL_CONSTRUCT);
-	n.find_bool("symbolic", symbolic);
-	n.find_bool("covariant", covariant);
-	if (symbolic) {
-		serial = next_serial++;
-		if (!(n.find_string("name", name)))
-			name = autoname_prefix() + ToString(serial);
-	} else {
-		serial = 0;
-		n.find_unsigned("value", value);
-	}
+	n.find_ex("value", value, sym_lst);
+	n.find_ex("dim", dim, sym_lst);
 }
 
-/** Unarchive the object. */
-ex idx::unarchive(const archive_node &n, const lst &sym_lst)
+varidx::varidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-	ex s = (new idx(n, sym_lst))->setflag(status_flags::dynallocated);
+	n.find_bool("covariant", covariant);
+}
 
-	if (ex_to_idx(s).symbolic) {
-		// If idx is in sym_lst, return the existing idx
-		for (unsigned i=0; i<sym_lst.nops(); i++) {
-			if (is_ex_of_type(sym_lst.op(i), idx) && (ex_to_idx(sym_lst.op(i)).name == ex_to_idx(s).name))
-				return sym_lst.op(i);
-		}
-	}
-	return s;
+spinidx::spinidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+	n.find_bool("dotted", dotted);
 }
 
-/** Archive the object. */
 void idx::archive(archive_node &n) const
 {
 	inherited::archive(n);
-	n.add_bool("symbolic", symbolic);
-	n.add_bool("covariant", covariant);
-	if (symbolic)
-		n.add_string("name", name);
-	else
-		n.add_unsigned("value", value);
+	n.add_ex("value", value);
+	n.add_ex("dim", dim);
 }
 
-//////////
-// functions overriding virtual functions from bases classes
-//////////
-
-// public
+void varidx::archive(archive_node &n) const
+{
+	inherited::archive(n);
+	n.add_bool("covariant", covariant);
+}
 
-basic * idx::duplicate() const
+void spinidx::archive(archive_node &n) const
 {
-	debugmsg("idx duplicate",LOGLEVEL_DUPLICATE);
-	return new idx(*this);
+	inherited::archive(n);
+	n.add_bool("dotted", dotted);
 }
 
-void idx::printraw(std::ostream & os) const
+DEFAULT_UNARCHIVE(idx)
+DEFAULT_UNARCHIVE(varidx)
+DEFAULT_UNARCHIVE(spinidx)
+
+//////////
+// functions overriding virtual functions from base classes
+//////////
+
+void idx::print(const print_context & c, unsigned level) const
 {
-	debugmsg("idx printraw",LOGLEVEL_PRINT);
+	if (is_of_type(c, print_tree)) {
 
-	os << "idx(";
+		c.s << std::string(level, ' ') << class_name()
+		    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+		    << std::endl;
+		unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
+		value.print(c, level + delta_indent);
+		dim.print(c, level + delta_indent);
 
-	if (symbolic) {
-		os << "symbolic,name=" << name;
 	} else {
-		os << "non symbolic,value=" << value;
-	}
 
-	if (covariant) {
-		os << ",covariant";
-	} else {
-		os << ",contravariant";
+		if (is_a<print_latex>(c))
+			c.s << "{";
+		else
+			c.s << ".";
+		bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
+		if (need_parens)
+			c.s << "(";
+		value.print(c);
+		if (need_parens)
+			c.s << ")";
+		if (is_a<print_latex>(c))
+			c.s << "}";
 	}
-
-	os << ",serial=" << serial;
-	os << ",hash=" << hashvalue << ",flags=" << flags;
-	os << ")";
 }
 
-void idx::printtree(std::ostream & os, unsigned indent) const
+void varidx::print(const print_context & c, unsigned level) const
 {
-	debugmsg("idx printtree",LOGLEVEL_PRINT);
-
-	os << std::string(indent,' ') << "idx: ";
+	if (is_of_type(c, print_tree)) {
 
-	if (symbolic) {
-		os << "symbolic,name=" << name;
-	} else {
-		os << "non symbolic,value=" << value;
-	}
+		c.s << std::string(level, ' ') << class_name()
+		    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+		    << (covariant ? ", covariant" : ", contravariant")
+		    << std::endl;
+		unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
+		value.print(c, level + delta_indent);
+		dim.print(c, level + delta_indent);
 
-	if (covariant) {
-		os << ",covariant";
 	} else {
-		os << ",contravariant";
+		if (is_a<print_latex>(c))
+			c.s << "{";
+		else {
+			if (covariant)
+				c.s << ".";
+			else
+				c.s << "~";
+		}
+		bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
+		if (need_parens)
+			c.s << "(";
+		value.print(c);
+		if (need_parens)
+			c.s << ")";
+		if (is_a<print_latex>(c))
+			c.s << "}";
 	}
-
-	os << ", serial=" << serial
-	   << ", hash=" << hashvalue
-	   << " (0x" << std::hex << hashvalue << std::dec << ")"
-	   << ", flags=" << flags << std::endl;
 }
 
-void idx::print(std::ostream & os, unsigned upper_precedence) const
+void spinidx::print(const print_context & c, unsigned level) const
 {
-	debugmsg("idx print",LOGLEVEL_PRINT);
+	if (is_of_type(c, print_tree)) {
+
+		c.s << std::string(level, ' ') << class_name()
+		    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+		    << (covariant ? ", covariant" : ", contravariant")
+		    << (dotted ? ", dotted" : ", undotted")
+		    << std::endl;
+		unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
+		value.print(c, level + delta_indent);
+		dim.print(c, level + delta_indent);
 
-	if (covariant) {
-		os << "_";
-	} else {
-		os << "~";
-	}
-	if (symbolic) {
-		os << name;
 	} else {
-		os << value;
+
+		bool is_tex = is_of_type(c, print_latex);
+		if (is_tex) {
+			if (covariant)
+				c.s << "_{";
+			else
+				c.s << "^{";
+		} else {
+			if (covariant)
+				c.s << ".";
+			else
+				c.s << "~";
+		}
+		if (dotted) {
+			if (is_tex)
+				c.s << "\\dot{";
+			else
+				c.s << "*";
+		}
+		bool need_parens = !(is_ex_exactly_of_type(value, numeric) || is_ex_of_type(value, symbol));
+		if (need_parens)
+			c.s << "(";
+		value.print(c);
+		if (need_parens)
+			c.s << ")";
+		if (is_tex && dotted)
+			c.s << "}";
+		if (is_tex)
+			c.s << "}";
 	}
 }
 
 bool idx::info(unsigned inf) const
 {
-	if (inf==info_flags::idx) return true;
+	if (inf == info_flags::idx)
+		return true;
 	return inherited::info(inf);
 }
 
-ex idx::subs(const lst & ls, const lst & lr) const
+unsigned idx::nops() const
 {
-	GINAC_ASSERT(ls.nops()==lr.nops());
-#ifdef DO_GINAC_ASSERT
-	for (unsigned i=0; i<ls.nops(); i++) {
-		GINAC_ASSERT(is_ex_exactly_of_type(ls.op(i),symbol)||
-			   is_ex_of_type(ls.op(i),idx));
-	}
-#endif // def DO_GINAC_ASSERT
-
-	for (unsigned i=0; i<ls.nops(); i++) {
-		if (is_equal(*(ls.op(i)).bp)) {
-			return lr.op(i);
-		}
-	}
-	return *this;
+	// don't count the dimension as that is not really a sub-expression
+	return 1;
 }
 
-// protected
+ex & idx::let_op(int i)
+{
+	GINAC_ASSERT(i == 0);
+	return value;
+}
 
+/** Returns order relation between two indices of the same type. The order
+ *  must be such that dummy indices lie next to each other. */
 int idx::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_of_type(other,idx));
-	const idx &o = static_cast<const idx &>(&other);
-
-	if (covariant!=o.covariant) {
-		// different co/contravariant
-		return covariant ? -1 : 1;
-	}
+	GINAC_ASSERT(is_a<idx>(other));
+	const idx &o = static_cast<const idx &>(other);
 
-	if ((!symbolic) && (!o.symbolic)) {
-		// non-symbolic, of equal type: compare values
-		if (value==o.value) {
-			return 0;
-		}
-		return value<o.value ? -1 : 1;
-	}
+	int cmpval = value.compare(o.value);
+	if (cmpval)
+		return cmpval;
+	return dim.compare(o.dim);
+}
 
-	if (symbolic && o.symbolic) {
-		// both symbolic: compare serials
-		if (serial==o.serial) {
-			return 0;
-		}
-		return serial<o.serial ? -1 : 1;
-	}
+bool idx::match_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_a<idx>(other));
+	const idx &o = static_cast<const idx &>(other);
 
-	// one symbolic, one value: value is sorted first
-	return o.symbolic ? -1 : 1;
+	return dim.is_equal(o.dim);
 }
 
-bool idx::is_equal_same_type(const basic & other) const
+int varidx::compare_same_type(const basic & other) const
 {
-	GINAC_ASSERT(is_of_type(other,idx));
-	const idx &o = static_cast<const idx &>(other);
+	GINAC_ASSERT(is_a<varidx>(other));
+	const varidx &o = static_cast<const varidx &>(other);
+
+	int cmpval = inherited::compare_same_type(other);
+	if (cmpval)
+		return cmpval;
 
-	if (covariant != o.covariant) return false;
-	if (symbolic != o.symbolic) return false;
-	if (symbolic && o.symbolic) return serial==o.serial;
-	return value==o.value;
-}    
+	// Check variance last so dummy indices will end up next to each other
+	if (covariant != o.covariant)
+		return covariant ? -1 : 1;
+	return 0;
+}
 
-unsigned idx::calchash(void) const
+bool varidx::match_same_type(const basic & other) const
 {
-	hashvalue=golden_ratio_hash(golden_ratio_hash(tinfo_key ^ serial));
-	setflag(status_flags::hash_calculated);
-	return hashvalue;
+	GINAC_ASSERT(is_a<varidx>(other));
+	const varidx &o = static_cast<const varidx &>(other);
+
+	if (covariant != o.covariant)
+		return false;
+	return inherited::match_same_type(other);
 }
 
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
+int spinidx::compare_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_a<spinidx>(other));
+	const spinidx &o = static_cast<const spinidx &>(other);
+
+	// Check dottedness first so dummy indices will end up next to each other
+	if (dotted != o.dotted)
+		return dotted ? -1 : 1;
 
-// public
+	int cmpval = inherited::compare_same_type(other);
+	if (cmpval)
+		return cmpval;
 
-/** Check whether the index forms a co-/contravariant pair with another
- *  index (i.e. same name/value but opposite co-/contravariance). */
-bool idx::is_co_contra_pair(const basic & other) const
+	return 0;
+}
+
+bool spinidx::match_same_type(const basic & other) const
 {
-	// like is_equal_same_type(), but tests for different covariant status
-	GINAC_ASSERT(is_of_type(other,idx));
-	const idx & o=static_cast<const idx &>(const_cast<basic &>(other));
+	GINAC_ASSERT(is_a<spinidx>(other));
+	const spinidx &o = static_cast<const spinidx &>(other);
 
-	if (covariant==o.covariant) return false;
-	if (symbolic!=o.symbolic) return false;
-	if (symbolic && o.symbolic) return serial==o.serial;
-	return value==o.value;
-}    
+	if (dotted != o.dotted)
+		return false;
+	return inherited::match_same_type(other);
+}
 
-/** Toggle co-/contravariance of index. */
-ex idx::toggle_covariant(void) const
+/** By default, basic::evalf would evaluate the index value but we don't want
+ *  a.1 to become a.(1.0). */
+ex idx::evalf(int level) const
 {
-	idx * i_copy=static_cast<idx *>(duplicate());
-	i_copy->covariant = !i_copy->covariant;
+	return *this;
+}
+
+ex idx::subs(const lst & ls, const lst & lr, bool no_pattern) const
+{
+	GINAC_ASSERT(ls.nops() == lr.nops());
+
+	// First look for index substitutions
+	for (unsigned i=0; i<ls.nops(); i++) {
+		if (is_equal(ex_to<basic>(ls.op(i)))) {
+
+			// Substitution index->index
+			if (is_ex_of_type(lr.op(i), idx))
+				return lr.op(i);
+
+			// Otherwise substitute value
+			idx *i_copy = static_cast<idx *>(duplicate());
+			i_copy->value = lr.op(i);
+			i_copy->clearflag(status_flags::hash_calculated);
+			return i_copy->setflag(status_flags::dynallocated);
+		}
+	}
+
+	// None, substitute objects in value (not in dimension)
+	const ex &subsed_value = value.subs(ls, lr, no_pattern);
+	if (are_ex_trivially_equal(value, subsed_value))
+		return *this;
+
+	idx *i_copy = static_cast<idx *>(duplicate());
+	i_copy->value = subsed_value;
 	i_copy->clearflag(status_flags::hash_calculated);
 	return i_copy->setflag(status_flags::dynallocated);
 }
 
+/** Implementation of ex::diff() for an index always returns 0.
+ *
+ *  @see ex::diff */
+ex idx::derivative(const symbol & s) const
+{
+	return _ex0;
+}
+
 //////////
-// non-virtual functions in this class
+// new virtual functions
 //////////
 
-// private
+bool idx::is_dummy_pair_same_type(const basic & other) const
+{
+	const idx &o = static_cast<const idx &>(other);
+
+	// Only pure symbols form dummy pairs, "2n+1" doesn't
+	if (!is_ex_of_type(value, symbol))
+		return false;
 
-std::string & idx::autoname_prefix(void)
+	// Value must be equal, of course
+	if (!value.is_equal(o.value))
+		return false;
+
+	// Also the dimension
+	return dim.is_equal(o.dim);
+}
+
+bool varidx::is_dummy_pair_same_type(const basic & other) const
 {
-	static std::string * s = new std::string("index");
-	return *s;
+	const varidx &o = static_cast<const varidx &>(other);
+
+	// Variance must be opposite
+	if (covariant == o.covariant)
+		return false;
+
+	return inherited::is_dummy_pair_same_type(other);
+}
+
+bool spinidx::is_dummy_pair_same_type(const basic & other) const
+{
+	const spinidx &o = static_cast<const spinidx &>(other);
+
+	// Dottedness must be the same
+	if (dotted != o.dotted)
+		return false;
+
+	return inherited::is_dummy_pair_same_type(other);
 }
 
+
 //////////
-// static member variables
+// non-virtual functions
 //////////
 
-// protected
+ex varidx::toggle_variance(void) const
+{
+	varidx *i_copy = static_cast<varidx *>(duplicate());
+	i_copy->covariant = !i_copy->covariant;
+	i_copy->clearflag(status_flags::hash_calculated);
+	return i_copy->setflag(status_flags::dynallocated);
+}
 
-unsigned idx::next_serial=0;
+ex spinidx::toggle_dot(void) const
+{
+	spinidx *i_copy = static_cast<spinidx *>(duplicate());
+	i_copy->dotted = !i_copy->dotted;
+	i_copy->clearflag(status_flags::hash_calculated);
+	return i_copy->setflag(status_flags::dynallocated);
+}
+
+ex spinidx::toggle_variance_dot(void) const
+{
+	spinidx *i_copy = static_cast<spinidx *>(duplicate());
+	i_copy->covariant = !i_copy->covariant;
+	i_copy->dotted = !i_copy->dotted;
+	i_copy->clearflag(status_flags::hash_calculated);
+	return i_copy->setflag(status_flags::dynallocated);
+}
 
 //////////
-// other functions
+// global functions
 //////////
 
-/** 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 iv Index vector
- *  @param antisymmetric Whether the object carrying the indices is antisymmetric (symmetric otherwise)
- *  @return the sign introduced by the reordering of the indices. For symmetric
- *          objects this is always +1. For antisymmetric objects this is either
- *          +1 or -1 or 0 (if two equal indices were encountered). If the index
- *          vector was unchanged this function returns INT_MAX. */
-int canonicalize_indices(exvector & iv, bool antisymmetric)
-{
-	if (iv.size()<2) {
-		// nothing do to for 0 or 1 indices
-		return INT_MAX;
-	}
-
-	bool something_changed=false;
-	int sig=1;
-
-	// simple bubble sort algorithm should be sufficient for the small number of indices needed
-	exvector::const_iterator last_idx=iv.end();
-	exvector::const_iterator next_to_last_idx=iv.end()-1;
-	for (exvector::iterator it1=iv.begin(); it1!=next_to_last_idx; ++it1) {
-		for (exvector::iterator it2=it1+1; it2!=last_idx; ++it2) {
-			int cmpval=(*it1).compare(*it2);
-			if (cmpval==1) {
-				iter_swap(it1,it2);
-				something_changed=true;
-				if (antisymmetric) sig=-sig;
-			} else if ((cmpval==0) && antisymmetric) {
-				something_changed=true;
-				sig=0;
-			}
-		}
-	}
+bool is_dummy_pair(const idx & i1, const idx & i2)
+{
+	// The indices must be of exactly the same type
+	if (i1.tinfo() != i2.tinfo())
+		return false;
 
-	return something_changed ? sig : INT_MAX;
-}
-
-/** Build a vector of indices as the set intersection of two other index
- *  vectors (i.e. the returned vector contains the indices which appear in
- *  both source vectors). */
-exvector idx_intersect(const exvector & iv1, const exvector & iv2)
-{
-	// Create union vector
-	exvector iv_union;
-	iv_union.reserve(iv1.size() + iv2.size());
-	iv_union.insert(iv_union.end(), iv1.begin(), iv1.end());
-	iv_union.insert(iv_union.end(), iv2.begin(), iv2.end());
-
-	// Sort it
-	canonicalize_indices(iv_union);
-
-	// Look for duplicates
-	exvector iv_intersect;
-	exvector::const_iterator cit = iv_union.begin(), citend = iv_union.end();
-	ex e;
-	if (cit != citend)
-		e = *cit++;
-	while (cit != citend) {
-		if (e.is_equal(*cit)) {
-			iv_intersect.push_back(e);
-			do {
-				cit++;
-			} while (cit != citend && e.is_equal(*cit));
-			if (cit == citend)
-				break;
-		}
-		e = *cit++;
-	}
-	return iv_intersect;
+	// Same type, let the indices decide whether they are paired
+	return i1.is_dummy_pair_same_type(i2);
 }
 
-/** Given a vector iv3 of three indices and a vector iv2 of two indices
- *  where iv2 is a subset of iv3, return the (free) index that is in iv3
- *  but not in iv2 and the sign introduced by permuting that index to the
- *  front.
- *
- *  @param iv3 Vector of 3 indices
- *  @param iv2 Vector of 2 indices, must be a subset of iv3
- *  @param sig Returns the sign introduced by permuting the free index to the
- *             front if the object carrying the indices was antisymmetric (if
- *             it's symmetric, you can just ignore the returned value).
- *  @return the free index (the one that is in iv3 but not in iv2) */
-ex permute_free_index_to_front(const exvector & iv3, const exvector & iv2, int * sig)
-{
-	// match (return value,iv2) to iv3 by permuting indices
-	// iv3 is always cyclic
-
-	GINAC_ASSERT(iv3.size()==3);
-	GINAC_ASSERT(iv2.size()==2);
-
-	*sig=1;
-
-#define TEST_PERMUTATION(A,B,C,P) \
-	if ((iv3[B].is_equal(iv2[0]))&&(iv3[C].is_equal(iv2[1]))) { \
-		*sig=P; \
-		return iv3[A]; \
-	}
-	
-	TEST_PERMUTATION(0,1,2,  1);
-	TEST_PERMUTATION(0,2,1, -1);
-	TEST_PERMUTATION(1,0,2, -1);
-	TEST_PERMUTATION(1,2,0,  1);
-	TEST_PERMUTATION(2,0,1,  1);
-	TEST_PERMUTATION(2,1,0, -1);
-	throw(std::logic_error("permute_free_index_to_front(): no valid permutation found"));
-}
-	
-/** Substitute one index in a vector of expressions.
- *
- *  @param v Vector to substitute in (will be modified)
- *  @param is Index being substituted
- *  @param ir Index to replace by
- *  @return number of performed substitutions */
-unsigned subs_index_in_exvector(exvector & v, const ex & is, const ex & ir)
-{
-	exvector::iterator it;
-	unsigned replacements=0;
-	unsigned current_replacements;
-
-	GINAC_ASSERT(is_ex_of_type(is,idx));
-	GINAC_ASSERT(is_ex_of_type(ir,idx));
-   
-	for (it=v.begin(); it!=v.end(); ++it) {
-		current_replacements=count_index(*it,is);
-		if (current_replacements>0) {
-			(*it)=(*it).subs(is==ir);
-		}
-		replacements += current_replacements;
-	}
-	return replacements;
+bool is_dummy_pair(const ex & e1, const ex & e2)
+{
+	// The expressions must be indices
+	if (!is_ex_of_type(e1, idx) || !is_ex_of_type(e2, idx))
+		return false;
+
+	return is_dummy_pair(ex_to<idx>(e1), ex_to<idx>(e2));
 }
 
-/** Count number of times a given index appears in the index vector of an
- *  indexed object.
- *
- *  @param e Indexed object
- *  @param i Index to look for
- *  @return number of times the index was found */
-unsigned count_index(const ex & e, const ex & i)
-{
-	exvector idxv=e.get_indices();
-	unsigned count=0;
-	for (exvector::const_iterator cit=idxv.begin(); cit!=idxv.end(); ++cit) {
-		if ((*cit).is_equal(i)) count++;
+void find_free_and_dummy(exvector::const_iterator it, exvector::const_iterator itend, exvector & out_free, exvector & out_dummy)
+{
+	out_free.clear();
+	out_dummy.clear();
+
+	// No indices? Then do nothing
+	if (it == itend)
+		return;
+
+	// Only one index? Then it is a free one if it's not numeric
+	if (itend - it == 1) {
+		if (ex_to<idx>(*it).is_symbolic())
+			out_free.push_back(*it);
+		return;
 	}
-	return count;
-}
 
-/** Substitute multiple indices in an expression.
- *
- *  @param e Expression to substitute in
- *  @param idxv_subs Vector of indices being substituted
- *  @param idxv_repl Vector of indices to replace by (1:1 correspondence to idxv_subs)
- *  @return expression with substituted indices */
-ex subs_indices(const ex & e, const exvector & idxv_subs, const exvector & idxv_repl)
-{
-	GINAC_ASSERT(idxv_subs.size()==idxv_repl.size());
-	ex res=e;
-	for (unsigned i=0; i<idxv_subs.size(); ++i) {
-		res=res.subs(idxv_subs[i]==idxv_repl[i]);
+	// Sort index vector. This will cause dummy indices come to lie next
+	// to each other (because the sort order is defined to guarantee this).
+	exvector v(it, itend);
+	shaker_sort(v.begin(), v.end(), ex_is_less(), ex_swap());
+
+	// Find dummy pairs and free indices
+	it = v.begin(); itend = v.end();
+	exvector::const_iterator last = it++;
+	while (it != itend) {
+		if (is_dummy_pair(*it, *last)) {
+			out_dummy.push_back(*last);
+			it++;
+			if (it == itend)
+				return;
+		} else {
+			if (!it->is_equal(*last) && ex_to<idx>(*last).is_symbolic())
+				out_free.push_back(*last);
+		}
+		last = it++;
 	}
-	return res;
+	if (ex_to<idx>(*last).is_symbolic())
+		out_free.push_back(*last);
 }
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC