X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=blobdiff_plain;f=ginac%2Fidx.cpp;h=c72e478e305bc02398394aa7486ceafe3d1d9150;hb=b1da89e057fea6f9c9c6e32bd92ecb5980b6713a;hp=c24846833989386f5c78d87961dd59a6719d5414;hpb=66c0f31c678e6c1938d637636b230ea376c157c1;p=ginac.git

diff --git a/ginac/idx.cpp b/ginac/idx.cpp
index c2484683..c72e478e 100644
--- a/ginac/idx.cpp
+++ b/ginac/idx.cpp
@@ -1,8 +1,9 @@
 /** @file idx.cpp
  *
- *  Implementation of GiNaC's indices.
- *
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  Implementation of GiNaC's indices. */
+
+/*
+ *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -20,428 +21,495 @@
  */
 
 #include <stdexcept>
+#include <algorithm>
 
 #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"
+
+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
 //////////
 
-// public
-
-idx::idx() : basic(TINFO_idx), symbolic(true), covariant(false)
+idx::idx() : inherited(TINFO_idx)
 {
-    debugmsg("idx default constructor",LOGLEVEL_CONSTRUCT);
-    serial=next_serial++;
-    name="index"+ToString(serial);
+	debugmsg("idx default constructor", LOGLEVEL_CONSTRUCT);
 }
 
-idx::~idx() 
+varidx::varidx() : covariant(false)
 {
-    debugmsg("idx destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
+	debugmsg("varidx default constructor", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_varidx;
 }
 
-idx::idx(idx const & other)
+spinidx::spinidx() : dotted(false)
 {
-    debugmsg("idx copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
+	debugmsg("spinidx default constructor", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_spinidx;
 }
 
-idx const & idx::operator=(idx const & other)
+void idx::copy(const idx & other)
 {
-    debugmsg("idx operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
+	inherited::copy(other);
+	value = other.value;
+	dim = other.dim;
 }
 
-// protected
-
-void idx::copy(idx const & other)
+void varidx::copy(const varidx & other)
 {
-    basic::copy(other);
-    serial=other.serial;
-    symbolic=other.symbolic;
-    name=other.name;
-    value=other.value;
-    covariant=other.covariant;
+	inherited::copy(other);
+	covariant = other.covariant;
 }
 
-void idx::destroy(bool call_parent)
+void spinidx::copy(const spinidx & other)
 {
-    if (call_parent) basic::destroy(call_parent);
+	inherited::copy(other);
+	dotted = other.dotted;
 }
 
+DEFAULT_DESTROY(idx)
+DEFAULT_DESTROY(varidx)
+DEFAULT_DESTROY(spinidx)
+
 //////////
 // other constructors
 //////////
 
-// public
-
-idx::idx(bool cov) : basic(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="index"+ToString(serial);
+	debugmsg("idx constructor from ex,ex", LOGLEVEL_CONSTRUCT);
+	if (is_dim_numeric())
+		if (!dim.info(info_flags::posint))
+			throw(std::invalid_argument("dimension of space must be a positive integer"));
 }
 
-idx::idx(string const & n, bool cov) : basic(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++;
+	debugmsg("varidx constructor from ex,ex,bool", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_varidx;
 }
 
-idx::idx(char const * n, bool cov) : basic(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++;
+	debugmsg("spinidx constructor from ex,ex,bool,bool", LOGLEVEL_CONSTRUCT);
+	tinfo_key = TINFO_spinidx;
 }
 
-idx::idx(unsigned const v, bool cov) : basic(TINFO_idx),
-    symbolic(false), value(v), covariant(cov)
-{
-    debugmsg("idx constructor from unsigned,bool",LOGLEVEL_CONSTRUCT);
-    serial=0;
-}
-
-
 //////////
-// functions overriding virtual functions from bases classes
+// archiving
 //////////
 
-// public
-
-basic * idx::duplicate() const
+idx::idx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-    debugmsg("idx duplicate",LOGLEVEL_DUPLICATE);
-    return new idx(*this);
+	debugmsg("idx constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	n.find_ex("value", value, sym_lst);
+	n.find_ex("dim", dim, sym_lst);
 }
 
-void idx::printraw(ostream & os) const
+varidx::varidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 {
-    debugmsg("idx printraw",LOGLEVEL_PRINT);
-
-    os << "idx(";
-
-    if (symbolic) {
-        os << "symbolic,name=" << name;
-    } else {
-        os << "non symbolic,value=" << value;
-    }
+	debugmsg("varidx constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	n.find_bool("covariant", covariant);
+}
 
-    if (covariant) {
-        os << ",covariant";
-    } else {
-        os << ",contravariant";
-    }
+spinidx::spinidx(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+	debugmsg("spinidx constructor from archive_node", LOGLEVEL_CONSTRUCT);
+	n.find_bool("dotted", dotted);
+}
 
-    os << ",serial=" << serial;
-    os << ",hash=" << hashvalue << ",flags=" << flags;
-    os << ")";
+void idx::archive(archive_node &n) const
+{
+	inherited::archive(n);
+	n.add_ex("value", value);
+	n.add_ex("dim", dim);
 }
 
-void idx::printtree(ostream & os, unsigned indent) const
+void varidx::archive(archive_node &n) const
 {
-    debugmsg("idx printtree",LOGLEVEL_PRINT);
+	inherited::archive(n);
+	n.add_bool("covariant", covariant);
+}
 
-    os << string(indent,' ') << "idx: ";
+void spinidx::archive(archive_node &n) const
+{
+	inherited::archive(n);
+	n.add_bool("dotted", dotted);
+}
 
-    if (symbolic) {
-        os << "symbolic,name=" << name;
-    } else {
-        os << "non symbolic,value=" << value;
-    }
+DEFAULT_UNARCHIVE(idx)
+DEFAULT_UNARCHIVE(varidx)
+DEFAULT_UNARCHIVE(spinidx)
 
-    if (covariant) {
-        os << ",covariant";
-    } else {
-        os << ",contravariant";
-    }
+//////////
+// functions overriding virtual functions from bases classes
+//////////
 
-    os << ", serial=" << serial
-       << ", hash=" << hashvalue << " (0x" << hex << hashvalue << dec << ")"
-       << ", flags=" << flags << endl;
+void idx::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
+		    << 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);
+
+	} else {
+
+		if (!is_of_type(c, print_latex))
+			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 << ")";
+	}
 }
 
-void idx::print(ostream & os, unsigned upper_precedence) const
+void varidx::print(const print_context & c, unsigned level) const
 {
-    debugmsg("idx print",LOGLEVEL_PRINT);
+	debugmsg("varidx 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")
+		    << 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);
+
+	} else {
+
+		if (!is_of_type(c, print_latex)) {
+			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 (covariant) {
-        os << "_";
-    } else {
-        os << "~";
-    }
-    if (symbolic) {
-        os << name;
-    } else {
-        os << value;
-    }
+void spinidx::print(const print_context & c, unsigned level) const
+{
+	debugmsg("spinidx 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);
+
+	} else {
+
+		bool is_tex = is_of_type(c, print_latex);
+		if (!is_tex) {
+			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 << "}";
+	}
 }
 
 bool idx::info(unsigned inf) const
 {
-    if (inf==info_flags::idx) return true;
-    return basic::info(inf);
+	if (inf == info_flags::idx)
+		return true;
+	return inherited::info(inf);
 }
 
-ex idx::subs(lst const & ls, lst const & lr) const
+unsigned idx::nops() const
 {
-    ASSERT(ls.nops()==lr.nops());
-#ifdef DOASSERT
-    for (int i=0; i<ls.nops(); i++) {
-        ASSERT(is_ex_exactly_of_type(ls.op(i),symbol)||
-               is_ex_of_type(ls.op(i),idx));
-    }
-#endif // def DOASSERT
-
-    for (int 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;
+}
 
-int idx::compare_same_type(basic const & other) const
+/** 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
 {
-    ASSERT(is_of_type(other,idx));
-    idx const & o=static_cast<idx const &>
-                             (const_cast<basic &>(other));
+	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;
-    }
-    if ((!symbolic) && (!o.symbolic)) {
-        // non-symbolic, of equal type: compare values
-        if (value==o.value) {
-            return 0;
-        }
-        return value<o.value ? -1 : 1;
-    }
-    if (symbolic && o.symbolic) {
-        // both symbolic: compare serials
-        if (serial==o.serial) {
-            return 0;
-        }
-        return serial<o.serial ? -1 : 1;
-    }
-    // one symbolic, one value: value is sorted first
-    return o.symbolic ? -1 : 1;
+	int cmpval = value.compare(o.value);
+	if (cmpval)
+		return cmpval;
+	return dim.compare(o.dim);
 }
 
-bool idx::is_equal_same_type(basic const & other) const
+int varidx::compare_same_type(const basic & other) const
 {
-    ASSERT(is_of_type(other,idx));
-    idx const & o=static_cast<idx const &>
-                             (const_cast<basic &>(other));
+	GINAC_ASSERT(is_of_type(other, varidx));
+	const varidx &o = static_cast<const varidx &>(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;
-}    
+	int cmpval = inherited::compare_same_type(other);
+	if (cmpval)
+		return cmpval;
 
-unsigned idx::calchash(void) const
-{
-    hashvalue=golden_ratio_hash(golden_ratio_hash(tinfo_key ^ serial));
-    setflag(status_flags::hash_calculated);
-    return hashvalue;
+	// Check variance last so dummy indices will end up next to each other
+	if (covariant != o.covariant)
+		return covariant ? -1 : 1;
+	return 0;
 }
 
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
+int spinidx::compare_same_type(const basic & other) const
+{
+	GINAC_ASSERT(is_of_type(other, spinidx));
+	const spinidx &o = static_cast<const spinidx &>(other);
 
-// public
+	// Check dottedness first so dummy indices will end up next to each other
+	if (dotted != o.dotted)
+		return dotted ? -1 : 1;
 
-bool idx::is_co_contra_pair(basic const & other) const
-{
-    // like is_equal_same_type(), but tests for different covariant status
-    ASSERT(is_of_type(other,idx));
-    idx const & o=static_cast<idx const &>
-                             (const_cast<basic &>(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;
-}    
+	return 0;
+}
 
-bool idx::is_symbolic(void) const
+bool idx::match(const ex & pattern, lst & repl_lst) const
 {
-    return symbolic;
+	if (!is_ex_of_type(pattern, idx))
+		return false;
+	const idx &o = ex_to_idx(pattern);
+	if (!dim.is_equal(o.dim))
+		return false;
+	return value.match(o.value, repl_lst);
 }
 
-unsigned idx::get_value(void) const
+bool varidx::match(const ex & pattern, lst & repl_lst) const
 {
-    return value;
+	if (!is_ex_of_type(pattern, varidx))
+		return false;
+	const varidx &o = ex_to_varidx(pattern);
+	if (covariant != o.covariant)
+		return false;
+	return inherited::match(pattern, repl_lst);
 }
 
-bool idx::is_covariant(void) const
+bool spinidx::match(const ex & pattern, lst & repl_lst) const
 {
-    return covariant;
+	if (!is_ex_of_type(pattern, spinidx))
+		return false;
+	const spinidx &o = ex_to_spinidx(pattern);
+	if (dotted != o.dotted)
+		return false;
+	return inherited::match(pattern, repl_lst);
 }
 
-ex idx::toggle_covariant(void) const
+ex idx::subs(const lst & ls, const lst & lr, bool no_pattern) const
 {
-    idx * i_copy=static_cast<idx *>(duplicate());
-    i_copy->covariant = !i_copy->covariant;
-    i_copy->clearflag(status_flags::hash_calculated);
-    return i_copy->setflag(status_flags::dynallocated);
+	GINAC_ASSERT(ls.nops() == lr.nops());
+
+	// First look for index substitutions
+	for (unsigned i=0; i<ls.nops(); i++) {
+		if (is_equal(*(ls.op(i)).bp)) {
+
+			// 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);
 }
 
 //////////
-// non-virtual functions in this class
+// new virtual functions
 //////////
 
-// none
+bool idx::is_dummy_pair_same_type(const basic & other) const
+{
+	const idx &o = static_cast<const idx &>(other);
 
-//////////
-// static member variables
-//////////
+	// Only pure symbols form dummy pairs, "2n+1" doesn't
+	if (!is_ex_of_type(value, symbol))
+		return false;
 
-// protected
+	// 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
+{
+	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);
+}
 
-unsigned idx::next_serial=0;
 
 //////////
-// global constants
+// non-virtual functions
 //////////
 
-const idx some_idx;
-type_info const & typeid_idx=typeid(some_idx);
+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);
+}
+
+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
 //////////
 
-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;
-            }
-        }
-    }
-    return something_changed ? sig : INT_MAX;
-}
-
-exvector idx_intersect(exvector const & iv1, exvector const & iv2)
-{
-    // build a vector of symbolic indices contained in iv1 and iv2 simultaneously
-    // assumes (but does not test) that each index occurs at most twice
-    exvector iv_intersect;
-    for (exvector::const_iterator cit1=iv1.begin(); cit1!=iv1.end(); ++cit1) {
-        ASSERT(is_ex_of_type(*cit1,idx));
-        if (ex_to_idx(*cit1).is_symbolic()) {
-            for (exvector::const_iterator cit2=iv2.begin(); cit2!=iv2.end(); ++cit2) {
-                ASSERT(is_ex_of_type(*cit2,idx));
-                if ((*cit1).is_equal(*cit2)) {
-                    iv_intersect.push_back(*cit1);
-                    break;
-                }
-            }
-        }
-    }
-    return iv_intersect;
-}
-
-#define TEST_PERMUTATION(A,B,C,P) \
-    if ((iv3[B].is_equal(iv2[0]))&&(iv3[C].is_equal(iv2[1]))) { \
-        if (antisymmetric) *sig=P; \
-        return iv3[A]; \
-    }
-
-ex permute_free_index_to_front(exvector const & iv3, exvector const & iv2,
-                               bool antisymmetric, int * sig)
-{
-    // match (return value,iv2) to iv3 by permuting indices
-    // iv3 is always cyclic
-
-    ASSERT(iv3.size()==3);
-    ASSERT(iv2.size()==2);
-
-    *sig=1;
-    
-    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"));
-}
-    
-unsigned subs_index_in_exvector(exvector & v, ex const & is, ex const & ir)
-{
-    exvector::iterator it;
-    unsigned replacements=0;
-    unsigned current_replacements;
-
-    ASSERT(is_ex_of_type(is,idx));
-    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;
-}
-
-unsigned count_index(ex const & e, ex const & 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++;
-    }
-    return count;
-}
-
-ex subs_indices(ex const & e, exvector const & idxv_subs,
-                exvector const & idxv_repl)
-{
-    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]);
-    }
-    return res;
+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;
+
+	// Same type, let the indices decide whether they are paired
+	return i1.is_dummy_pair_same_type(i2);
 }
 
+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));
+}
 
+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;
+	}
+
+	// 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());
+
+	// 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++;
+	}
+	if (ex_to_idx(*last).is_symbolic())
+		out_free.push_back(*last);
+}
 
+} // namespace GiNaC