X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fexpairseq.cpp;h=11da774902a1d17994674291f674a0a022526482;hp=b14ffb3027e7b72c61ae4642306fece67def22aa;hb=f4bae27a4390712315e0317fd9e954299341933d;hpb=e78622a06f749a124b007aa7b969de02fcc9c3d2

diff --git a/ginac/expairseq.cpp b/ginac/expairseq.cpp
index b14ffb30..11da7749 100644
--- a/ginac/expairseq.cpp
+++ b/ginac/expairseq.cpp
@@ -3,7 +3,7 @@
  *  Implementation of sequences of expression pairs. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2015 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
@@ -17,27 +17,37 @@
  *
  *  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 <algorithm>
-#include <string>
-#include <stdexcept>
-
 #include "expairseq.h"
 #include "lst.h"
-#include "print.h"
+#include "add.h"
+#include "mul.h"
+#include "power.h"
+#include "relational.h"
+#include "wildcard.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "operators.h"
 #include "utils.h"
+#include "hash_seed.h"
+#include "indexed.h"
+#include "compiler.h"
 
-#if EXPAIRSEQ_USE_HASHTAB
-#include <cmath>
-#endif // EXPAIRSEQ_USE_HASHTAB
+#include <algorithm>
+#include <iostream>
+#include <iterator>
+#include <memory>
+#include <stdexcept>
+#include <string>
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
+	
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
+  print_func<print_context>(&expairseq::do_print).
+  print_func<print_tree>(&expairseq::do_print_tree))
+
 
 //////////
 // helper classes
@@ -53,90 +63,45 @@ public:
 };
 
 //////////
-// default ctor, dtor, copy ctor assignment operator and helpers
+// default constructor
 //////////
 
 // public
 
-expairseq::expairseq(const expairseq &other)
-{
-	debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
-	copy(other);
-}
-
-const expairseq &expairseq::operator=(const expairseq &other)
-{
-	debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
-	if (this != &other) {
-		destroy(true);
-		copy(other);
-	}
-	return *this;
-}
+expairseq::expairseq() 
+{}
 
 // protected
 
-/** For use by copy ctor and assignment operator. */
-void expairseq::copy(const expairseq &other)
-{
-	inherited::copy(other);
-	seq = other.seq;
-	overall_coeff = other.overall_coeff;
-#if EXPAIRSEQ_USE_HASHTAB
-	// copy hashtab
-	hashtabsize = other.hashtabsize;
-	if (hashtabsize!=0) {
-		hashmask = other.hashmask;
-		hashtab.resize(hashtabsize);
-		epvector::const_iterator osb = other.seq.begin();
-		for (unsigned i=0; i<hashtabsize; ++i) {
-			hashtab[i].clear();
-			for (epplist::const_iterator cit=other.hashtab[i].begin();
-			     cit!=other.hashtab[i].end(); ++cit) {
-				hashtab[i].push_back(seq.begin()+((*cit)-osb));
-			}
-		}
-	} else {
-		hashtab.clear();
-	}
-#endif // EXPAIRSEQ_USE_HASHTAB
-}
-
-DEFAULT_DESTROY(expairseq)
-
 //////////
-// other ctors
+// other constructors
 //////////
 
-expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
+expairseq::expairseq(const ex &lh, const ex &rh)
 {
-	debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 	construct_from_2_ex(lh,rh);
 	GINAC_ASSERT(is_canonical());
 }
 
-expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
+expairseq::expairseq(const exvector &v)
 {
-	debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
 	construct_from_exvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
-expairseq::expairseq(const epvector &v, const ex &oc)
-  : inherited(TINFO_expairseq), overall_coeff(oc)
+expairseq::expairseq(const epvector &v, const ex &oc, bool do_index_renaming)
+  :  overall_coeff(oc)
 {
-	debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
-	construct_from_epvector(v);
+	GINAC_ASSERT(is_a<numeric>(oc));
+	construct_from_epvector(v, do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
-expairseq::expairseq(epvector *vp, const ex &oc)
-  : inherited(TINFO_expairseq), overall_coeff(oc)
+expairseq::expairseq(epvector && vp, const ex &oc, bool do_index_renaming)
+  :  overall_coeff(oc)
 {
-	debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-	GINAC_ASSERT(vp!=0);
-	construct_from_epvector(*vp);
-	delete vp;
+	GINAC_ASSERT(is_a<numeric>(oc));
+	construct_from_epvector(std::move(vp), do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
@@ -144,140 +109,99 @@ expairseq::expairseq(epvector *vp, const ex &oc)
 // archiving
 //////////
 
-expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-#if EXPAIRSEQ_USE_HASHTAB
-	, hashtabsize(0)
-#endif
+void expairseq::read_archive(const archive_node &n, lst &sym_lst) 
 {
-	debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
-	for (unsigned int i=0; true; i++) {
+	inherited::read_archive(n, sym_lst);
+	auto first = n.find_first("rest");
+	auto last = n.find_last("coeff");
+	++last;
+	seq.reserve((last-first)/2);
+
+	for (auto loc = first; loc < last;) {
 		ex rest;
 		ex coeff;
-		if (n.find_ex("rest", rest, sym_lst, i) && n.find_ex("coeff", coeff, sym_lst, i))
-			seq.push_back(expair(rest, coeff));
-		else
-			break;
+		n.find_ex_by_loc(loc++, rest, sym_lst);
+		n.find_ex_by_loc(loc++, coeff, sym_lst);
+		seq.push_back(expair(rest, coeff));
 	}
+
 	n.find_ex("overall_coeff", overall_coeff, sym_lst);
+
+	canonicalize();
+	GINAC_ASSERT(is_canonical());
 }
 
 void expairseq::archive(archive_node &n) const
 {
 	inherited::archive(n);
-	epvector::const_iterator i = seq.begin(), iend = seq.end();
-	while (i != iend) {
-		n.add_ex("rest", i->rest);
-		n.add_ex("coeff", i->coeff);
-		++i;
+	for (auto & i : seq) {
+		n.add_ex("rest", i.rest);
+		n.add_ex("coeff", i.coeff);
 	}
 	n.add_ex("overall_coeff", overall_coeff);
 }
 
-DEFAULT_UNARCHIVE(expairseq)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-basic *expairseq::duplicate() const
+void expairseq::do_print(const print_context & c, unsigned level) const
 {
-	debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
-	return new expairseq(*this);
+	c.s << "[[";
+	printseq(c, ',', precedence(), level);
+	c.s << "]]";
 }
 
-void expairseq::print(const print_context & c, unsigned level) const
+void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 {
-	debugmsg("expairseq print",LOGLEVEL_PRINT);
-
-	if (is_of_type(c, print_tree)) {
-
-		unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
-
-		c.s << std::string(level, ' ') << class_name()
-		    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
-		    << ", nops=" << nops()
-		    << std::endl;
-		for (unsigned i=0; i<seq.size(); ++i) {
-			seq[i].rest.print(c, level + delta_indent);
-			seq[i].coeff.print(c, level + delta_indent);
-			if (i != seq.size()-1)
-				c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
-		}
-		if (!overall_coeff.is_equal(default_overall_coeff())) {
-			c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
-			    << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
-			overall_coeff.print(c, level + delta_indent);
-		}
-		c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
-#if EXPAIRSEQ_USE_HASHTAB
-		c.s << std::string(level + delta_indent,' ')
-		    << "hashtab size " << hashtabsize << std::endl;
-		if (hashtabsize == 0) return;
-#define MAXCOUNT 5
-		unsigned count[MAXCOUNT+1];
-		for (int i=0; i<MAXCOUNT+1; ++i)
-			count[i] = 0;
-		unsigned this_bin_fill;
-		unsigned cum_fill_sq = 0;
-		unsigned cum_fill = 0;
-		for (unsigned i=0; i<hashtabsize; ++i) {
-			this_bin_fill = 0;
-			if (hashtab[i].size() > 0) {
-				c.s << std::string(level + delta_indent, ' ')
-				    << "bin " << i << " with entries ";
-				for (epplist::const_iterator it=hashtab[i].begin();
-				     it!=hashtab[i].end(); ++it) {
-					c.s << *it-seq.begin() << " ";
-					++this_bin_fill;
-				}
-				os << std::endl;
-				cum_fill += this_bin_fill;
-				cum_fill_sq += this_bin_fill*this_bin_fill;
-			}
-			if (this_bin_fill<MAXCOUNT)
-				++count[this_bin_fill];
-			else
-				++count[MAXCOUNT];
-		}
-		unsigned fact = 1;
-		double cum_prob = 0;
-		double lambda = (1.0*seq.size()) / hashtabsize;
-		for (int k=0; k<MAXCOUNT; ++k) {
-			if (k>0)
-				fact *= k;
-			double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
-			cum_prob += prob;
-			c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
-			    << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
-			    << int(prob*1000)/10.0 << ")" << std::endl;
-		}
-		c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
-		    << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
-		    << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
-	
-		c.s << std::string(level + delta_indent, ' ') << "variance: "
-		    << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
-		    << std::endl;
-		c.s << std::string(level + delta_indent, ' ') << "average fill: "
-		    << (1.0*cum_fill)/hashtabsize
-		    << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
-#endif // EXPAIRSEQ_USE_HASHTAB
-
-	} else {
-		c.s << "[[";
-		printseq(c, ',', precedence(), level);
-		c.s << "]]";
+	c.s << std::string(level, ' ') << class_name() << " @" << this
+	    << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+	    << ", nops=" << nops()
+	    << std::endl;
+	size_t num = seq.size();
+	for (size_t i=0; i<num; ++i) {
+		seq[i].rest.print(c, level + c.delta_indent);
+		seq[i].coeff.print(c, level + c.delta_indent);
+		if (i != num - 1)
+			c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
+	}
+	if (!overall_coeff.is_equal(default_overall_coeff())) {
+		c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
+		    << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
+		overall_coeff.print(c, level + c.delta_indent);
 	}
+	c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 }
 
 bool expairseq::info(unsigned inf) const
 {
+	switch(inf) {
+		case info_flags::expanded:
+			return (flags & status_flags::expanded);
+		case info_flags::has_indices: {
+			if (flags & status_flags::has_indices)
+				return true;
+			else if (flags & status_flags::has_no_indices)
+				return false;
+			for (auto & i : seq) {
+				if (i.rest.info(info_flags::has_indices)) {
+					this->setflag(status_flags::has_indices);
+					this->clearflag(status_flags::has_no_indices);
+					return true;
+				}
+			}
+			this->clearflag(status_flags::has_indices);
+			this->setflag(status_flags::has_no_indices);
+			return false;
+		}
+	}
 	return inherited::info(inf);
 }
 
-unsigned expairseq::nops() const
+size_t expairseq::nops() const
 {
 	if (overall_coeff.is_equal(default_overall_coeff()))
 		return seq.size();
@@ -285,65 +209,190 @@ unsigned expairseq::nops() const
 		return seq.size()+1;
 }
 
-ex expairseq::op(int i) const
+ex expairseq::op(size_t i) const
 {
-	if (unsigned(i)<seq.size())
+	if (i < seq.size())
 		return recombine_pair_to_ex(seq[i]);
 	GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
 	return overall_coeff;
 }
 
-ex &expairseq::let_op(int i)
+ex expairseq::map(map_function &f) const
 {
-	throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
+	epvector v;
+	v.reserve(seq.size()+1);
+
+	for (auto & it : seq)
+		v.push_back(split_ex_to_pair(f(recombine_pair_to_ex(it))));
+
+	if (overall_coeff.is_equal(default_overall_coeff()))
+		return thisexpairseq(std::move(v), default_overall_coeff(), true);
+	else {
+		ex newcoeff = f(overall_coeff);
+		if(is_a<numeric>(newcoeff))
+			return thisexpairseq(std::move(v), newcoeff, true);
+		else {
+			v.push_back(split_ex_to_pair(newcoeff));
+			return thisexpairseq(std::move(v), default_overall_coeff(), true);
+		}
+	}
 }
 
-ex expairseq::eval(int level) const
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
+ex expairseq::eval() const
 {
-	if ((level==1) && (flags &status_flags::evaluated))
+	if (flags &status_flags::evaluated)
 		return *this;
-	
-	epvector *vp = evalchildren(level);
-	if (vp==0)
+
+	const epvector evaled = evalchildren();
+	if (!evaled.empty())
+		return dynallocate<expairseq>(std::move(evaled), overall_coeff).setflag(status_flags::evaluated);
+	else
 		return this->hold();
-	
-	return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 }
 
-ex expairseq::evalf(int level) const
+epvector* conjugateepvector(const epvector&epv)
 {
-	return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
+	epvector *newepv = nullptr;
+	for (auto i=epv.begin(); i!=epv.end(); ++i) {
+		if (newepv) {
+			newepv->push_back(i->conjugate());
+			continue;
+		}
+		expair x = i->conjugate();
+		if (x.is_equal(*i)) {
+			continue;
+		}
+		newepv = new epvector;
+		newepv->reserve(epv.size());
+		for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
+			newepv->push_back(*j);
+		}
+		newepv->push_back(x);
+	}
+	return newepv;
 }
 
-ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
+ex expairseq::conjugate() const
 {
-	ex n = thisexpairseq(normalchildren(level),overall_coeff);
-	return n.bp->basic::normal(sym_lst,repl_lst,level);
+	std::unique_ptr<epvector> newepv(conjugateepvector(seq));
+	ex x = overall_coeff.conjugate();
+	if (newepv) {
+		return thisexpairseq(std::move(*newepv), x);
+	}
+	if (are_ex_trivially_equal(x, overall_coeff)) {
+		return *this;
+	}
+	return thisexpairseq(seq, x);
 }
 
-ex expairseq::subs(const lst &ls, const lst &lr) const
+bool expairseq::match(const ex & pattern, exmap & repl_lst) const
 {
-	epvector *vp = subschildren(ls,lr);
-	if (vp==0)
-		return inherited::subs(ls, lr);
-	
-	return thisexpairseq(vp,overall_coeff);
-}
+	// This differs from basic::match() because we want "a+b+c+d" to
+	// match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 
-// protected
+	if (typeid(*this) == typeid(ex_to<basic>(pattern))) {
+
+		// Check whether global wildcard (one that matches the "rest of the
+		// expression", like "*" above) is present
+		bool has_global_wildcard = false;
+		ex global_wildcard;
+		for (size_t i=0; i<pattern.nops(); i++) {
+			if (is_exactly_a<wildcard>(pattern.op(i))) {
+				has_global_wildcard = true;
+				global_wildcard = pattern.op(i);
+				break;
+			}
+		}
+
+		// Even if the expression does not match the pattern, some of
+		// its subexpressions could match it. For example, x^5*y^(-1)
+		// does not match the pattern $0^5, but its subexpression x^5
+		// does. So, save repl_lst in order to not add bogus entries.
+		exmap tmp_repl = repl_lst;
+
+		// Unfortunately, this is an O(N^2) operation because we can't
+		// sort the pattern in a useful way...
+
+		// Chop into terms
+		exvector ops;
+		ops.reserve(nops());
+		for (size_t i=0; i<nops(); i++)
+			ops.push_back(op(i));
+
+		// Now, for every term of the pattern, look for a matching term in
+		// the expression and remove the match
+		for (size_t i=0; i<pattern.nops(); i++) {
+			ex p = pattern.op(i);
+			if (has_global_wildcard && p.is_equal(global_wildcard))
+				continue;
+			auto it = ops.begin(), itend = ops.end();
+			while (it != itend) {
+				if (it->match(p, tmp_repl)) {
+					ops.erase(it);
+					goto found;
+				}
+				++it;
+			}
+			return false; // no match found
+found:		;
+		}
 
-/** Implementation of ex::diff() for an expairseq.
- *  It differentiates all elements of the sequence.
- *  @see ex::diff */
-ex expairseq::derivative(const symbol &s) const
+		if (has_global_wildcard) {
+
+			// Assign all the remaining terms to the global wildcard (unless
+			// it has already been matched before, in which case the matches
+			// must be equal)
+			size_t num = ops.size();
+			epvector vp;
+			vp.reserve(num);
+			for (size_t i=0; i<num; i++)
+				vp.push_back(split_ex_to_pair(ops[i]));
+			ex rest = thisexpairseq(std::move(vp), default_overall_coeff());
+			for (auto & it : tmp_repl) {
+				if (it.first.is_equal(global_wildcard)) {
+					if (rest.is_equal(it.second)) {
+						repl_lst = tmp_repl;
+						return true;
+					}
+					return false;
+				}
+			}
+			repl_lst = tmp_repl;
+			repl_lst[global_wildcard] = rest;
+			return true;
+
+		} else {
+
+			// No global wildcard, then the match fails if there are any
+			// unmatched terms left
+			if (ops.empty()) {
+				repl_lst = tmp_repl;
+				return true;
+			}
+			return false;
+		}
+	}
+	return inherited::match(pattern, repl_lst);
+}
+
+ex expairseq::subs(const exmap & m, unsigned options) const
 {
-	return thisexpairseq(diffchildren(s),overall_coeff);
+	epvector subsed = subschildren(m, options);
+	if (!subsed.empty())
+		return ex_to<basic>(thisexpairseq(std::move(subsed), overall_coeff, (options & subs_options::no_index_renaming) == 0));
+	else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
+		return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
+	else
+		return subs_one_level(m, options);
 }
 
+// protected
+
 int expairseq::compare_same_type(const basic &other) const
 {
-	GINAC_ASSERT(is_of_type(other, expairseq));
-	const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
+	GINAC_ASSERT(is_a<expairseq>(other));
+	const expairseq &o = static_cast<const expairseq &>(other);
 	
 	int cmpval;
 	
@@ -356,59 +405,22 @@ int expairseq::compare_same_type(const basic &other) const
 	if (cmpval!=0)
 		return cmpval;
 	
-#if EXPAIRSEQ_USE_HASHTAB
-	GINAC_ASSERT(hashtabsize==o.hashtabsize);
-	if (hashtabsize==0) {
-#endif // EXPAIRSEQ_USE_HASHTAB
-		epvector::const_iterator cit1 = seq.begin();
-		epvector::const_iterator cit2 = o.seq.begin();
-		epvector::const_iterator last1 = seq.end();
-		epvector::const_iterator last2 = o.seq.end();
-		
-		for (; (cit1!=last1)&&(cit2!=last2); ++cit1, ++cit2) {
-			cmpval = (*cit1).compare(*cit2);
-			if (cmpval!=0) return cmpval;
-		}
+	auto cit1 = seq.begin(), last1 = seq.end();
+	auto cit2 = o.seq.begin(), last2 = o.seq.end();
+	for (; (cit1!=last1) && (cit2!=last2); ++cit1, ++cit2) {
+		cmpval = (*cit1).compare(*cit2);
+		if (cmpval!=0) return cmpval;
+	}
 		
-		GINAC_ASSERT(cit1==last1);
-		GINAC_ASSERT(cit2==last2);
+	GINAC_ASSERT(cit1==last1);
+	GINAC_ASSERT(cit2==last2);
 		
-		return 0;
-#if EXPAIRSEQ_USE_HASHTAB
-	}
-	
-	// compare number of elements in each hashtab entry
-	for (unsigned i=0; i<hashtabsize; ++i) {
-		unsigned cursize=hashtab[i].size();
-		if (cursize != o.hashtab[i].size())
-			return (cursize < o.hashtab[i].size()) ? -1 : 1;
-	}
-	
-	// compare individual (sorted) hashtab entries
-	for (unsigned i=0; i<hashtabsize; ++i) {
-		unsigned sz = hashtab[i].size();
-		if (sz>0) {
-			const epplist &eppl1 = hashtab[i];
-			const epplist &eppl2 = o.hashtab[i];
-			epplist::const_iterator it1 = eppl1.begin();
-			epplist::const_iterator it2 = eppl2.begin();
-			while (it1!=eppl1.end()) {
-				cmpval = (*(*it1)).compare(*(*it2));
-				if (cmpval!=0)
-					return cmpval;
-				++it1;
-				++it2;
-			}
-		}
-	}
-	
-	return 0; // equal
-#endif // EXPAIRSEQ_USE_HASHTAB
+	return 0;
 }
 
 bool expairseq::is_equal_same_type(const basic &other) const
 {
-	const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
+	const expairseq &o = static_cast<const expairseq &>(other);
 	
 	// compare number of elements
 	if (seq.size()!=o.seq.size())
@@ -418,80 +430,32 @@ bool expairseq::is_equal_same_type(const basic &other) const
 	if (!overall_coeff.is_equal(o.overall_coeff))
 		return false;
 	
-#if EXPAIRSEQ_USE_HASHTAB
-	// compare number of elements in each hashtab entry
-	if (hashtabsize!=o.hashtabsize) {
-		std::cout << "this:" << std::endl;
-		print(print_tree(std::cout));
-		std::cout << "other:" << std::endl;
-		other.print(print_tree(std::cout));
-	}
-		
-	GINAC_ASSERT(hashtabsize==o.hashtabsize);
-	
-	if (hashtabsize==0) {
-#endif // EXPAIRSEQ_USE_HASHTAB
-		epvector::const_iterator cit1 = seq.begin();
-		epvector::const_iterator cit2 = o.seq.begin();
-		epvector::const_iterator last1 = seq.end();
-		
-		while (cit1!=last1) {
-			if (!(*cit1).is_equal(*cit2)) return false;
-			++cit1;
-			++cit2;
-		}
-		
-		return true;
-#if EXPAIRSEQ_USE_HASHTAB
-	}
-	
-	for (unsigned i=0; i<hashtabsize; ++i) {
-		if (hashtab[i].size() != o.hashtab[i].size())
+	auto cit2 = o.seq.begin();
+	for (auto & cit1 : seq) {
+		if (!cit1.is_equal(*cit2))
 			return false;
+		++cit2;
 	}
 
-	// compare individual sorted hashtab entries
-	for (unsigned i=0; i<hashtabsize; ++i) {
-		unsigned sz = hashtab[i].size();
-		if (sz>0) {
-			const epplist &eppl1 = hashtab[i];
-			const epplist &eppl2 = o.hashtab[i];
-			epplist::const_iterator it1 = eppl1.begin();
-			epplist::const_iterator it2 = eppl2.begin();
-			while (it1!=eppl1.end()) {
-				if (!(*(*it1)).is_equal(*(*it2))) return false;
-				++it1;
-				++it2;
-			}
-		}
-	}
-	
 	return true;
-#endif // EXPAIRSEQ_USE_HASHTAB
 }
 
-unsigned expairseq::return_type(void) const
+unsigned expairseq::return_type() const
 {
 	return return_types::noncommutative_composite;
 }
 
-unsigned expairseq::calchash(void) const
+unsigned expairseq::calchash() const
 {
-	unsigned v = golden_ratio_hash(tinfo());
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-#if !EXPAIRSEQ_USE_HASHTAB
-		v = rotate_left_31(v); // rotation would spoil commutativity
-#endif // EXPAIRSEQ_USE_HASHTAB
-		v ^= cit->rest.gethash();
-#if !EXPAIRSEQ_USE_HASHTAB
-		v = rotate_left_31(v);
-		v ^= cit->coeff.gethash();
-#endif // EXPAIRSEQ_USE_HASHTAB
+	unsigned v = make_hash_seed(typeid(*this));
+	for (auto & i : seq) {
+		v ^= i.rest.gethash();
+		v = rotate_left(v);
+		v ^= i.coeff.gethash();
 	}
-	
+
 	v ^= overall_coeff.gethash();
-	v &= 0x7FFFFFFFU;
-	
+
 	// store calculated hash value only if object is already evaluated
 	if (flags &status_flags::evaluated) {
 		setflag(status_flags::hash_calculated);
@@ -503,14 +467,11 @@ unsigned expairseq::calchash(void) const
 
 ex expairseq::expand(unsigned options) const
 {
-	epvector *vp = expandchildren(options);
-	if (vp==0) {
-		// the terms have not changed, so it is safe to declare this expanded
-		setflag(status_flags::expanded);
-		return *this;
+	epvector expanded = expandchildren(options);
+	if (!expanded.empty()) {
+		return thisexpairseq(std::move(expanded), overall_coeff);
 	}
-	
-	return thisexpairseq(vp,overall_coeff);
+	return (options == 0) ? setflag(status_flags::expanded) : *this;
 }
 
 //////////
@@ -524,25 +485,25 @@ ex expairseq::expand(unsigned options) const
  *  has (at least) two possible different semantics but we want to inherit
  *  methods thus avoiding code duplication.  Sometimes a method in expairseq
  *  has to create a new one of the same semantics, which cannot be done by a
- *  ctor because the name (add, mul,...) is unknown on the expaiseq level.  In
+ *  ctor because the name (add, mul,...) is unknown on the expairseq level.  In
  *  order for this trick to work a derived class must of course override this
  *  definition. */
-ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
+ex expairseq::thisexpairseq(const epvector &v, const ex &oc, bool do_index_renaming) const
 {
-	return expairseq(v,oc);
+	return expairseq(v, oc, do_index_renaming);
 }
 
-ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
+ex expairseq::thisexpairseq(epvector && vp, const ex &oc, bool do_index_renaming) const
 {
-	return expairseq(vp,oc);
+	return expairseq(std::move(vp), oc, do_index_renaming);
 }
 
 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 {
 	c.s << "[[";
-	p.rest.bp->print(c, precedence());
+	p.rest.print(c, precedence());
 	c.s << ",";
-	p.coeff.bp->print(c, precedence());
+	p.coeff.print(c, precedence());
 	c.s << "]]";
 }
 
@@ -552,8 +513,8 @@ void expairseq::printseq(const print_context & c, char delim,
 {
 	if (this_precedence <= upper_precedence)
 		c.s << "(";
-	epvector::const_iterator it, it_last = seq.end() - 1;
-	for (it=seq.begin(); it!=it_last; ++it) {
+	auto it = seq.begin(), it_last = seq.end() - 1;
+	for (; it!=it_last; ++it) {
 		printpair(c, *it, this_precedence);
 		c.s << delim;
 	}
@@ -572,14 +533,14 @@ void expairseq::printseq(const print_context & c, char delim,
  *  @see expairseq::recombine_pair_to_ex() */
 expair expairseq::split_ex_to_pair(const ex &e) const
 {
-	return expair(e,_ex1());
+	return expair(e,_ex1);
 }
 
 
 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
                                                 const ex &c) const
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
 	
 	return expair(e,c);
 }
@@ -588,10 +549,10 @@ expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
                                                   const ex &c) const
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+	GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
 	
-	return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
+	return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 }
 
 
@@ -599,36 +560,33 @@ expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
  *  @see expairseq::split_ex_to_pair() */
 ex expairseq::recombine_pair_to_ex(const expair &p) const
 {
-	return lst(p.rest,p.coeff);
+	return lst{p.rest, p.coeff};
 }
 
 bool expairseq::expair_needs_further_processing(epp it)
 {
-#if EXPAIRSEQ_USE_HASHTAB
-	//#  error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
-#endif // EXPAIRSEQ_USE_HASHTAB
 	return false;
 }
 
-ex expairseq::default_overall_coeff(void) const
+ex expairseq::default_overall_coeff() const
 {
-	return _ex0();
+	return _ex0;
 }
 
 void expairseq::combine_overall_coeff(const ex &c)
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
-	overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
+	GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
+	overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 }
 
 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
-	overall_coeff = ex_to_numeric(overall_coeff).
-	                add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
+	GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c1));
+	GINAC_ASSERT(is_exactly_a<numeric>(c2));
+	overall_coeff = ex_to<numeric>(overall_coeff).
+	                add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 }
 
 bool expairseq::can_make_flat(const expair &p) const
@@ -641,73 +599,31 @@ bool expairseq::can_make_flat(const expair &p) const
 // non-virtual functions in this class
 //////////
 
-void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
-{
-	exvector v;
-	v.reserve(2);
-	v.push_back(lh);
-	v.push_back(rh);
-	construct_from_exvector(v);
-#if EXPAIRSEQ_USE_HASHTAB
-	GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
-	GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
-#endif // EXPAIRSEQ_USE_HASHTAB
-}
-
 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 {
-	if (lh.bp->tinfo()==tinfo()) {
-		if (rh.bp->tinfo()==tinfo()) {
-#if EXPAIRSEQ_USE_HASHTAB
-			unsigned totalsize = ex_to_expairseq(lh).seq.size() +
-			                     ex_to_expairseq(rh).seq.size();
-			if (calc_hashtabsize(totalsize)!=0) {
-				construct_from_2_ex_via_exvector(lh,rh);
-			} else {
-#endif // EXPAIRSEQ_USE_HASHTAB
-				construct_from_2_expairseq(ex_to_expairseq(lh),
-				                           ex_to_expairseq(rh));
-#if EXPAIRSEQ_USE_HASHTAB
+	if (typeid(ex_to<basic>(lh)) == typeid(*this)) {
+		if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
+			if (is_a<mul>(lh) && lh.info(info_flags::has_indices) && 
+				rh.info(info_flags::has_indices)) {
+				ex newrh=rename_dummy_indices_uniquely(lh, rh);
+				construct_from_2_expairseq(ex_to<expairseq>(lh),
+				                           ex_to<expairseq>(newrh));
 			}
-#endif // EXPAIRSEQ_USE_HASHTAB
+			else
+				construct_from_2_expairseq(ex_to<expairseq>(lh),
+				                           ex_to<expairseq>(rh));
 			return;
 		} else {
-#if EXPAIRSEQ_USE_HASHTAB
-			unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
-			if (calc_hashtabsize(totalsize)!=0) {
-				construct_from_2_ex_via_exvector(lh, rh);
-			} else {
-#endif // EXPAIRSEQ_USE_HASHTAB
-				construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
-#if EXPAIRSEQ_USE_HASHTAB
-			}
-#endif // EXPAIRSEQ_USE_HASHTAB
+			construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 			return;
 		}
-	} else if (rh.bp->tinfo()==tinfo()) {
-#if EXPAIRSEQ_USE_HASHTAB
-		unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
-		if (calc_hashtabsize(totalsize)!=0) {
-			construct_from_2_ex_via_exvector(lh,rh);
-		} else {
-#endif // EXPAIRSEQ_USE_HASHTAB
-			construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
-#if EXPAIRSEQ_USE_HASHTAB
-		}
-#endif // EXPAIRSEQ_USE_HASHTAB
-		return;
-	}
-	
-#if EXPAIRSEQ_USE_HASHTAB
-	if (calc_hashtabsize(2)!=0) {
-		construct_from_2_ex_via_exvector(lh,rh);
+	} else if (typeid(ex_to<basic>(rh)) == typeid(*this)) {
+		construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 		return;
 	}
-	hashtabsize = 0;
-#endif // EXPAIRSEQ_USE_HASHTAB
 	
-	if (is_ex_exactly_of_type(lh,numeric)) {
-		if (is_ex_exactly_of_type(rh,numeric)) {
+	if (is_exactly_a<numeric>(lh)) {
+		if (is_exactly_a<numeric>(rh)) {
 			combine_overall_coeff(lh);
 			combine_overall_coeff(rh);
 		} else {
@@ -715,7 +631,7 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 			seq.push_back(split_ex_to_pair(rh));
 		}
 	} else {
-		if (is_ex_exactly_of_type(rh,numeric)) {
+		if (is_exactly_a<numeric>(rh)) {
 			combine_overall_coeff(rh);
 			seq.push_back(split_ex_to_pair(lh));
 		} else {
@@ -724,8 +640,8 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 			
 			int cmpval = p1.rest.compare(p2.rest);
 			if (cmpval==0) {
-				p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
-				if (!ex_to_numeric(p1.coeff).is_zero()) {
+				p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
+				if (!ex_to<numeric>(p1.coeff).is_zero()) {
 					// no further processing is necessary, since this
 					// one element will usually be recombined in eval()
 					seq.push_back(p1);
@@ -745,15 +661,13 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 }
 
 void expairseq::construct_from_2_expairseq(const expairseq &s1,
-										   const expairseq &s2)
+                                           const expairseq &s2)
 {
 	combine_overall_coeff(s1.overall_coeff);
 	combine_overall_coeff(s2.overall_coeff);
 
-	epvector::const_iterator first1 = s1.seq.begin();
-	epvector::const_iterator last1 = s1.seq.end();
-	epvector::const_iterator first2 = s2.seq.begin();
-	epvector::const_iterator last2 = s2.seq.end();
+	auto first1 = s1.seq.begin(), last1 = s1.seq.end();
+	auto first2 = s2.seq.begin(), last2 = s2.seq.end();
 
 	seq.reserve(s1.seq.size()+s2.seq.size());
 
@@ -761,12 +675,13 @@ void expairseq::construct_from_2_expairseq(const expairseq &s1,
 	
 	while (first1!=last1 && first2!=last2) {
 		int cmpval = (*first1).rest.compare((*first2).rest);
+
 		if (cmpval==0) {
 			// combine terms
-			const numeric &newcoeff = ex_to_numeric((*first1).coeff).
-			                           add(ex_to_numeric((*first2).coeff));
+			const numeric &newcoeff = ex_to<numeric>(first1->coeff).
+			                           add(ex_to<numeric>(first2->coeff));
 			if (!newcoeff.is_zero()) {
-				seq.push_back(expair((*first1).rest,newcoeff));
+				seq.push_back(expair(first1->rest,newcoeff));
 				if (expair_needs_further_processing(seq.end()-1)) {
 					needs_further_processing = true;
 				}
@@ -792,24 +707,23 @@ void expairseq::construct_from_2_expairseq(const expairseq &s1,
 	}
 	
 	if (needs_further_processing) {
-		epvector v = seq;
-		seq.clear();
-		construct_from_epvector(v);
+		// Clear seq and start over.
+		epvector v = std::move(seq);
+		construct_from_epvector(std::move(v));
 	}
 }
 
 void expairseq::construct_from_expairseq_ex(const expairseq &s,
-											const ex &e)
+                                            const ex &e)
 {
 	combine_overall_coeff(s.overall_coeff);
-	if (is_ex_exactly_of_type(e,numeric)) {
+	if (is_exactly_a<numeric>(e)) {
 		combine_overall_coeff(e);
 		seq = s.seq;
 		return;
 	}
 	
-	epvector::const_iterator first = s.seq.begin();
-	epvector::const_iterator last = s.seq.end();
+	auto first = s.seq.begin(), last = s.seq.end();
 	expair p = split_ex_to_pair(e);
 	
 	seq.reserve(s.seq.size()+1);
@@ -819,16 +733,15 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
 	
 	// merge p into s.seq
 	while (first!=last) {
-		int cmpval=(*first).rest.compare(p.rest);
+		int cmpval = (*first).rest.compare(p.rest);
 		if (cmpval==0) {
 			// combine terms
-			const numeric &newcoeff = ex_to_numeric((*first).coeff).
-			                           add(ex_to_numeric(p.coeff));
+			const numeric &newcoeff = ex_to<numeric>(first->coeff).
+			                           add(ex_to<numeric>(p.coeff));
 			if (!newcoeff.is_zero()) {
-				seq.push_back(expair((*first).rest,newcoeff));
-				if (expair_needs_further_processing(seq.end()-1)) {
+				seq.push_back(expair(first->rest,newcoeff));
+				if (expair_needs_further_processing(seq.end()-1))
 					needs_further_processing = true;
-				}
 			}
 			++first;
 			p_pushed = true;
@@ -855,9 +768,9 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
 	}
 
 	if (needs_further_processing) {
-		epvector v = seq;
-		seq.clear();
-		construct_from_epvector(v);
+		// Clear seq and start over.
+		epvector v = std::move(seq);
+		construct_from_epvector(std::move(v));
 	}
 }
 
@@ -865,523 +778,190 @@ void expairseq::construct_from_exvector(const exvector &v)
 {
 	// simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 	//                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
-	//                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
+	//                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
 	//                  (same for (+,*) -> (*,^)
 
 	make_flat(v);
-#if EXPAIRSEQ_USE_HASHTAB
-	combine_same_terms();
-#else
 	canonicalize();
 	combine_same_terms_sorted_seq();
-#endif // EXPAIRSEQ_USE_HASHTAB
-	return;
 }
 
-void expairseq::construct_from_epvector(const epvector &v)
+void expairseq::construct_from_epvector(const epvector &v, bool do_index_renaming)
 {
 	// simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
 	//                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
-	//                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric())
-	//                  (same for (+,*) -> (*,^)
+	//                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
+	//                  same for (+,*) -> (*,^)
 
-	make_flat(v);
-#if EXPAIRSEQ_USE_HASHTAB
-	combine_same_terms();
-#else
+	make_flat(v, do_index_renaming);
+	canonicalize();
+	combine_same_terms_sorted_seq();
+}
+
+void expairseq::construct_from_epvector(epvector &&v, bool do_index_renaming)
+{
+	// simplifications: +(a,+(b,c),d) -> +(a,b,c,d) (associativity)
+	//                  +(d,b,c,a) -> +(a,b,c,d) (canonicalization)
+	//                  +(...,x,*(x,c1),*(x,c2)) -> +(...,*(x,1+c1+c2)) (c1, c2 numeric)
+	//                  same for (+,*) -> (*,^)
+
+	make_flat(std::move(v), do_index_renaming);
 	canonicalize();
 	combine_same_terms_sorted_seq();
-#endif // EXPAIRSEQ_USE_HASHTAB
-	return;
 }
 
 /** Combine this expairseq with argument exvector.
  *  It cares for associativity as well as for special handling of numerics. */
 void expairseq::make_flat(const exvector &v)
 {
-	exvector::const_iterator cit;
-	
 	// count number of operands which are of same expairseq derived type
 	// and their cumulative number of operands
 	int nexpairseqs = 0;
 	int noperands = 0;
+	bool do_idx_rename = false;
 	
-	cit = v.begin();
-	while (cit!=v.end()) {
-		if (cit->bp->tinfo()==this->tinfo()) {
+	for (auto & cit : v) {
+		if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
 			++nexpairseqs;
-			noperands += ex_to_expairseq(*cit).seq.size();
+			noperands += ex_to<expairseq>(cit).seq.size();
 		}
-		++cit;
+		if (is_a<mul>(*this) && (!do_idx_rename) &&
+		    cit.info(info_flags::has_indices))
+			do_idx_rename = true;
 	}
 	
 	// reserve seq and coeffseq which will hold all operands
 	seq.reserve(v.size()+noperands-nexpairseqs);
 	
 	// copy elements and split off numerical part
-	cit = v.begin();
-	while (cit!=v.end()) {
-		if (cit->bp->tinfo()==this->tinfo()) {
-			const expairseq &subseqref = ex_to_expairseq(*cit);
+	make_flat_inserter mf(v, do_idx_rename);
+	for (auto & cit : v) {
+		if (typeid(ex_to<basic>(cit)) == typeid(*this)) {
+			ex newfactor = mf.handle_factor(cit, _ex1);
+			const expairseq &subseqref = ex_to<expairseq>(newfactor);
 			combine_overall_coeff(subseqref.overall_coeff);
-			epvector::const_iterator cit_s = subseqref.seq.begin();
-			while (cit_s!=subseqref.seq.end()) {
-				seq.push_back(*cit_s);
-				++cit_s;
+			for (auto & cit_s : subseqref.seq) {
+				seq.push_back(cit_s);
 			}
 		} else {
-			if (is_ex_exactly_of_type(*cit,numeric))
-				combine_overall_coeff(*cit);
-			else
-				seq.push_back(split_ex_to_pair(*cit));
+			if (is_exactly_a<numeric>(cit))
+				combine_overall_coeff(cit);
+			else {
+				ex newfactor = mf.handle_factor(cit, _ex1);
+				seq.push_back(split_ex_to_pair(newfactor));
+			}
 		}
-		++cit;
 	}
-	
-	return;
 }
 
 /** Combine this expairseq with argument epvector.
  *  It cares for associativity as well as for special handling of numerics. */
-void expairseq::make_flat(const epvector &v)
+void expairseq::make_flat(const epvector &v, bool do_index_renaming)
 {
-	epvector::const_iterator cit;
-	
 	// count number of operands which are of same expairseq derived type
 	// and their cumulative number of operands
 	int nexpairseqs = 0;
 	int noperands = 0;
+	bool really_need_rename_inds = false;
 	
-	cit = v.begin();
-	while (cit!=v.end()) {
-		if (cit->rest.bp->tinfo()==this->tinfo()) {
+	for (auto & cit : v) {
+		if (typeid(ex_to<basic>(cit.rest)) == typeid(*this)) {
 			++nexpairseqs;
-			noperands += ex_to_expairseq((*cit).rest).seq.size();
+			noperands += ex_to<expairseq>(cit.rest).seq.size();
 		}
-		++cit;
+		if ((!really_need_rename_inds) && is_a<mul>(*this) &&
+		    cit.rest.info(info_flags::has_indices))
+			really_need_rename_inds = true;
 	}
+	do_index_renaming = do_index_renaming && really_need_rename_inds;
 	
 	// reserve seq and coeffseq which will hold all operands
 	seq.reserve(v.size()+noperands-nexpairseqs);
+	make_flat_inserter mf(v, do_index_renaming);
 	
 	// copy elements and split off numerical part
-	cit = v.begin();
-	while (cit!=v.end()) {
-		if (cit->rest.bp->tinfo()==this->tinfo() &&
-		    this->can_make_flat(*cit)) {
-			const expairseq &subseqref = ex_to_expairseq((*cit).rest);
-			combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
-			                                    ex_to_numeric((*cit).coeff));
-			epvector::const_iterator cit_s = subseqref.seq.begin();
-			while (cit_s!=subseqref.seq.end()) {
-				seq.push_back(expair((*cit_s).rest,
-				                     ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
-				//seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
-				//                                              (*cit).coeff));
-				++cit_s;
+	for (auto & cit : v) {
+		if (typeid(ex_to<basic>(cit.rest)) == typeid(*this) &&
+		    this->can_make_flat(cit)) {
+			ex newrest = mf.handle_factor(cit.rest, cit.coeff);
+			const expairseq &subseqref = ex_to<expairseq>(newrest);
+			combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
+			                      ex_to<numeric>(cit.coeff));
+			for (auto & cit_s : subseqref.seq) {
+				seq.push_back(expair(cit_s.rest,
+				                     ex_to<numeric>(cit_s.coeff).mul_dyn(ex_to<numeric>(cit.coeff))));
 			}
 		} else {
-			if (cit->is_canonical_numeric())
-				combine_overall_coeff(cit->rest);
-			else
-				seq.push_back(*cit);
+			if (cit.is_canonical_numeric())
+				combine_overall_coeff(mf.handle_factor(cit.rest, _ex1));
+			else {
+				ex rest = cit.rest;
+				ex newrest = mf.handle_factor(rest, cit.coeff);
+				if (are_ex_trivially_equal(newrest, rest))
+					seq.push_back(cit);
+				else
+					seq.push_back(expair(newrest, cit.coeff));
+			}
 		}
-		++cit;
 	}
-	return;
 }
 
 /** Brings this expairseq into a sorted (canonical) form. */
-void expairseq::canonicalize(void)
+void expairseq::canonicalize()
 {
-	// canonicalize
-	sort(seq.begin(),seq.end(),expair_is_less());
-	return;
+	std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 }
 
 
 /** Compact a presorted expairseq by combining all matching expairs to one
  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
  *  instance. */
-void expairseq::combine_same_terms_sorted_seq(void)
+void expairseq::combine_same_terms_sorted_seq()
 {
-	bool needs_further_processing = false;
-	
-	if (seq.size()>1) {
-		epvector::iterator itin1 = seq.begin();
-		epvector::iterator itin2 = itin1+1;
-		epvector::iterator itout = itin1;
-		epvector::iterator last = seq.end();
-		// must_copy will be set to true the first time some combination is 
-		// possible from then on the sequence has changed and must be compacted
-		bool must_copy = false;
-		while (itin2!=last) {
-			if ((*itin1).rest.compare((*itin2).rest)==0) {
-				(*itin1).coeff = ex_to_numeric((*itin1).coeff).
-				                 add_dyn(ex_to_numeric((*itin2).coeff));
-				if (expair_needs_further_processing(itin1))
-					needs_further_processing = true;
-				must_copy = true;
-			} else {
-				if (!ex_to_numeric((*itin1).coeff).is_zero()) {
-					if (must_copy)
-						*itout = *itin1;
-					++itout;
-				}
-				itin1 = itin2;
-			}
-			++itin2;
-		}
-		if (!ex_to_numeric((*itin1).coeff).is_zero()) {
-			if (must_copy)
-				*itout = *itin1;
-			++itout;
-		}
-		if (itout!=last)
-			seq.erase(itout,last);
-	}
-	
-	if (needs_further_processing) {
-		epvector v = seq;
-		seq.clear();
-		construct_from_epvector(v);
-	}
-	return;
-}
-
-#if EXPAIRSEQ_USE_HASHTAB
-
-unsigned expairseq::calc_hashtabsize(unsigned sz) const
-{
-	unsigned size;
-	unsigned nearest_power_of_2 = 1 << log2(sz);
-	// if (nearest_power_of_2 < maxhashtabsize/hashtabfactor) {
-	//  size = nearest_power_of_2*hashtabfactor;
-	size = nearest_power_of_2/hashtabfactor;
-	if (size<minhashtabsize)
-		return 0;
-	GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
-	// hashtabsize must be a power of 2
-	GINAC_ASSERT((1U << log2(size))==size);
-	return size;
-}
-
-unsigned expairseq::calc_hashindex(const ex &e) const
-{
-	// calculate hashindex
-	unsigned hash = e.gethash();
-	unsigned hashindex;
-	if (is_a_numeric_hash(hash)) {
-		hashindex = hashmask;
-	} else {
-		hashindex = hash &hashmask;
-		// last hashtab entry is reserved for numerics
-		if (hashindex==hashmask) hashindex = 0;
-	}
-	GINAC_ASSERT(hashindex>=0);
-	GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
-	return hashindex;
-}
-
-void expairseq::shrink_hashtab(void)
-{
-	unsigned new_hashtabsize;
-	while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
-		GINAC_ASSERT(new_hashtabsize<hashtabsize);
-		if (new_hashtabsize==0) {
-			hashtab.clear();
-			hashtabsize = 0;
-			canonicalize();
-			return;
-		}
-		
-		// shrink by a factor of 2
-		unsigned half_hashtabsize = hashtabsize/2;
-		for (unsigned i=0; i<half_hashtabsize-1; ++i)
-			hashtab[i].merge(hashtab[i+half_hashtabsize],epp_is_less());
-		// special treatment for numeric hashes
-		hashtab[0].merge(hashtab[half_hashtabsize-1],epp_is_less());
-		hashtab[half_hashtabsize-1] = hashtab[hashtabsize-1];
-		hashtab.resize(half_hashtabsize);
-		hashtabsize = half_hashtabsize;
-		hashmask = hashtabsize-1;
-	}
-}
-
-void expairseq::remove_hashtab_entry(epvector::const_iterator element)
-{
-	if (hashtabsize==0)
-		return; // nothing to do
-	
-	// calculate hashindex of element to be deleted
-	unsigned hashindex = calc_hashindex((*element).rest);
-
-	// find it in hashtab and remove it
-	epplist &eppl = hashtab[hashindex];
-	epplist::iterator epplit = eppl.begin();
-	bool erased = false;
-	while (epplit!=eppl.end()) {
-		if (*epplit == element) {
-			eppl.erase(epplit);
-			erased = true;
-			break;
-		}
-		++epplit;
-	}
-	if (!erased) {
-		printtree(cout,0);
-		cout << "tried to erase " << element-seq.begin() << std::endl;
-		cout << "size " << seq.end()-seq.begin() << std::endl;
-
-		unsigned hashindex = calc_hashindex((*element).rest);
-		epplist &eppl = hashtab[hashindex];
-		epplist::iterator epplit=eppl.begin();
-		bool erased=false;
-		while (epplit!=eppl.end()) {
-			if (*epplit == element) {
-				eppl.erase(epplit);
-				erased = true;
-				break;
-			}
-			++epplit;
-		}
-		GINAC_ASSERT(erased);
-	}
-	GINAC_ASSERT(erased);
-}
-
-void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
-                                   epvector::iterator newpos)
-{
-	GINAC_ASSERT(hashtabsize!=0);
-	
-	// calculate hashindex of element which was moved
-	unsigned hashindex=calc_hashindex((*newpos).rest);
-
-	// find it in hashtab and modify it
-	epplist &eppl = hashtab[hashindex];
-	epplist::iterator epplit = eppl.begin();
-	while (epplit!=eppl.end()) {
-		if (*epplit == oldpos) {
-			*epplit = newpos;
-			break;
-		}
-		++epplit;
-	}
-	GINAC_ASSERT(epplit!=eppl.end());
-}
-
-void expairseq::sorted_insert(epplist &eppl, epp elem)
-{
-	epplist::iterator current = eppl.begin();
-	while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
-		++current;
-	}
-	eppl.insert(current,elem);
-}    
+	if (seq.size()<2)
+		return;
 
-void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
-                                          epvector::iterator &last_non_zero,
-                                          std::vector<bool> &touched,
-                                          unsigned &number_of_zeroes)
-{
-	epp current=seq.begin();
+	bool needs_further_processing = false;
 
-	while (current!=first_numeric) {
-		if (is_ex_exactly_of_type((*current).rest,numeric)) {
-			--first_numeric;
-			iter_swap(current,first_numeric);
+	auto itin1 = seq.begin();
+	auto itin2 = itin1 + 1;
+	auto itout = itin1;
+	auto last = seq.end();
+	// must_copy will be set to true the first time some combination is 
+	// possible from then on the sequence has changed and must be compacted
+	bool must_copy = false;
+	while (itin2!=last) {
+		if (itin1->rest.compare(itin2->rest)==0) {
+			itin1->coeff = ex_to<numeric>(itin1->coeff).
+			               add_dyn(ex_to<numeric>(itin2->coeff));
+			if (expair_needs_further_processing(itin1))
+				needs_further_processing = true;
+			must_copy = true;
 		} else {
-			// calculate hashindex
-			unsigned currenthashindex = calc_hashindex((*current).rest);
-
-			// test if there is already a matching expair in the hashtab-list
-			epplist &eppl=hashtab[currenthashindex];
-			epplist::iterator epplit = eppl.begin();
-			while (epplit!=eppl.end()) {
-				if ((*current).rest.is_equal((*(*epplit)).rest))
-					break;
-				++epplit;
-			}
-			if (epplit==eppl.end()) {
-				// no matching expair found, append this to end of list
-				sorted_insert(eppl,current);
-				++current;
-			} else {
-				// epplit points to a matching expair, combine it with current
-				(*(*epplit)).coeff = ex_to_numeric((*(*epplit)).coeff).
-				                     add_dyn(ex_to_numeric((*current).coeff));
-				
-				// move obsolete current expair to end by swapping with last_non_zero element
-				// if this was a numeric, it is swapped with the expair before first_numeric 
-				iter_swap(current,last_non_zero);
-				--first_numeric;
-				if (first_numeric!=last_non_zero) iter_swap(first_numeric,current);
-				--last_non_zero;
-				++number_of_zeroes;
-				// test if combined term has coeff 0 and can be removed is done later
-				touched[(*epplit)-seq.begin()]=true;
+			if (!ex_to<numeric>(itin1->coeff).is_zero()) {
+				if (must_copy)
+					*itout = *itin1;
+				++itout;
 			}
+			itin1 = itin2;
 		}
+		++itin2;
 	}
-}
-
-void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
-                                   epvector::iterator &last_non_zero,
-                                   std::vector<bool> &touched,
-                                   unsigned &number_of_zeroes)
-{
-	// move terms with coeff 0 to end and remove them from hashtab
-	// check only those elements which have been touched
-	epp current = seq.begin();
-	unsigned i = 0;
-	while (current!=first_numeric) {
-		if (!touched[i]) {
-			++current;
-			++i;
-		} else if (!ex_to_numeric((*current).coeff).is_zero()) {
-			++current;
-			++i;
-		} else {
-			remove_hashtab_entry(current);
-			
-			// move element to the end, unless it is already at the end
-			if (current!=last_non_zero) {
-				iter_swap(current,last_non_zero);
-				--first_numeric;
-				bool numeric_swapped=first_numeric!=last_non_zero;
-				if (numeric_swapped) iter_swap(first_numeric,current);
-				epvector::iterator changed_entry;
-
-				if (numeric_swapped)
-					changed_entry = first_numeric;
-				else
-					changed_entry = last_non_zero;
-				
-				--last_non_zero;
-				++number_of_zeroes;
-
-				if (first_numeric!=current) {
-
-					// change entry in hashtab which referred to first_numeric or last_non_zero to current
-					move_hashtab_entry(changed_entry,current);
-					touched[current-seq.begin()] = touched[changed_entry-seq.begin()];
-				}
-			} else {
-				--first_numeric;
-				--last_non_zero;
-				++number_of_zeroes;
-			}
-		}
+	if (!ex_to<numeric>(itin1->coeff).is_zero()) {
+		if (must_copy)
+			*itout = *itin1;
+		++itout;
 	}
-	GINAC_ASSERT(i==current-seq.begin());
-}
-
-/** True if one of the coeffs vanishes, otherwise false.
- *  This would be an invariant violation, so this should only be used for
- *  debugging purposes. */
-bool expairseq::has_coeff_0(void) const
-{
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if ((*cit).coeff.is_zero())
-			return true;
-	}
-	return false;
-}
-
-void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
-										epvector::const_iterator last_non_zero)
-{
-	if (first_numeric==seq.end()) return; // no numerics    
-	
-	epvector::iterator current = first_numeric;
-	epvector::const_iterator last = last_non_zero+1;
-	while (current!=last) {
-		sorted_insert(hashtab[hashmask],current);
-		++current;
-	}
-}
+	if (itout!=last)
+		seq.erase(itout,last);
 
-void expairseq::combine_same_terms(void)
-{
-	// combine same terms, drop term with coeff 0, move numerics to end
-	
-	// calculate size of hashtab
-	hashtabsize = calc_hashtabsize(seq.size());
-	
-	// hashtabsize is a power of 2
-	hashmask = hashtabsize-1;
-	
-	// allocate hashtab
-	hashtab.clear();
-	hashtab.resize(hashtabsize);
-	
-	if (hashtabsize==0) {
-		canonicalize();
-		combine_same_terms_sorted_seq();
-		GINAC_ASSERT(!has_coeff_0());
-		return;
-	}
-	
-	// iterate through seq, move numerics to end,
-	// fill hashtab and combine same terms
-	epvector::iterator first_numeric = seq.end();
-	epvector::iterator last_non_zero = seq.end()-1;
-	
-	std::vector<bool> touched;
-	touched.reserve(seq.size());
-	for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
-	
-	unsigned number_of_zeroes = 0;
-	
-	GINAC_ASSERT(!has_coeff_0());
-	build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
-	/*
-	cout << "in combine:" << std::endl;
-	printtree(cout,0);
-	cout << "size=" << seq.end() - seq.begin() << std::endl;
-	cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
-	cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
-	for (unsigned i=0; i<seq.size(); ++i) {
-		if (touched[i]) cout << i << " is touched" << std::endl;
-	}
-	cout << "end in combine" << std::endl;
-	*/
-	
-	// there should not be any terms with coeff 0 from the beginning,
-	// so it should be safe to skip this step
-	if (number_of_zeroes!=0) {
-		drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
-		/*
-		cout << "in combine after drop:" << std::endl;
-		printtree(cout,0);
-		cout << "size=" << seq.end() - seq.begin() << std::endl;
-		cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
-		cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
-		for (unsigned i=0; i<seq.size(); ++i) {
-			if (touched[i]) cout << i << " is touched" << std::endl;
-		}
-		cout << "end in combine after drop" << std::endl;
-		*/
-	}
-	
-	add_numerics_to_hashtab(first_numeric,last_non_zero);
-	
-	// pop zero elements
-	for (unsigned i=0; i<number_of_zeroes; ++i) {
-		seq.pop_back();
+	if (needs_further_processing) {
+		// Clear seq and start over.
+		epvector v = std::move(seq);
+		construct_from_epvector(std::move(v));
 	}
-	
-	// shrink hashtabsize to calculated value
-	GINAC_ASSERT(!has_coeff_0());
-	
-	shrink_hashtab();
-	
-	GINAC_ASSERT(!has_coeff_0());
 }
 
-#endif // EXPAIRSEQ_USE_HASHTAB
-
 /** Check if this expairseq is in sorted (canonical) form.  Useful mainly for
  *  debugging or in assertions since being sorted is an invariance. */
 bool expairseq::is_canonical() const
@@ -1389,29 +969,25 @@ bool expairseq::is_canonical() const
 	if (seq.size() <= 1)
 		return 1;
 	
-#if EXPAIRSEQ_USE_HASHTAB
-	if (hashtabsize > 0) return 1; // not canoncalized
-#endif // EXPAIRSEQ_USE_HASHTAB
-	
-	epvector::const_iterator it = seq.begin();
-	epvector::const_iterator it_last = it;
-	for (++it; it!=seq.end(); it_last=it, ++it) {
-		if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
-			if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
-				!is_ex_exactly_of_type((*it).rest,numeric)) {
+	auto it = seq.begin(), itend = seq.end();
+	auto it_last = it;
+	for (++it; it!=itend; it_last=it, ++it) {
+		if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
+			if (!is_exactly_a<numeric>(it_last->rest) ||
+				!is_exactly_a<numeric>(it->rest)) {
 				// double test makes it easier to set a breakpoint...
-				if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
-					!is_ex_exactly_of_type((*it).rest,numeric)) {
+				if (!is_exactly_a<numeric>(it_last->rest) ||
+					!is_exactly_a<numeric>(it->rest)) {
 					printpair(std::clog, *it_last, 0);
 					std::clog << ">";
 					printpair(std::clog, *it, 0);
 					std::clog << "\n";
 					std::clog << "pair1:" << std::endl;
-					(*it_last).rest.print(print_tree(std::clog));
-					(*it_last).coeff.print(print_tree(std::clog));
+					it_last->rest.print(print_tree(std::clog));
+					it_last->coeff.print(print_tree(std::clog));
 					std::clog << "pair2:" << std::endl;
-					(*it).rest.print(print_tree(std::clog));
-					(*it).coeff.print(print_tree(std::clog));
+					it->rest.print(print_tree(std::clog));
+					it->coeff.print(print_tree(std::clog));
 					return 0;
 				}
 			}
@@ -1420,221 +996,175 @@ bool expairseq::is_canonical() const
 	return 1;
 }
 
-
 /** Member-wise expand the expairs in this sequence.
  *
  *  @see expairseq::expand()
- *  @return pointer to epvector containing expanded pairs or zero pointer,
- *  if no members were changed. */
-epvector * expairseq::expandchildren(unsigned options) const
+ *  @return epvector containing expanded pairs, empty if no members
+ *    had to be changed. */
+epvector expairseq::expandchildren(unsigned options) const
 {
-	epvector::const_iterator last = seq.end();
-	epvector::const_iterator cit = seq.begin();
+	auto cit = seq.begin(), last = seq.end();
 	while (cit!=last) {
-		const ex &expanded_ex = (*cit).rest.expand(options);
-		if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
+		const ex expanded_ex = cit->rest.expand(options);
+		if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
 			
 			// something changed, copy seq, eval and return it
-			epvector *s = new epvector;
-			s->reserve(seq.size());
+			epvector s;
+			s.reserve(seq.size());
 			
 			// copy parts of seq which are known not to have changed
-			epvector::const_iterator cit2 = seq.begin();
-			while (cit2!=cit) {
-				s->push_back(*cit2);
-				++cit2;
-			}
+			s.insert(s.begin(), seq.begin(), cit);
+
 			// copy first changed element
-			s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
-			                                           (*cit2).coeff));
-			++cit2;
+			s.push_back(expair(expanded_ex, cit->coeff));
+			++cit;
+
 			// copy rest
-			while (cit2!=last) {
-				s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
-				                                           (*cit2).coeff));
-				++cit2;
+			while (cit != last) {
+				s.push_back(expair(cit->rest.expand(options), cit->coeff));
+				++cit;
 			}
 			return s;
 		}
+
 		++cit;
 	}
 	
-	return 0; // signalling nothing has changed
+	return epvector(); // empty signalling nothing has changed
 }
 
 
 /** Member-wise evaluate the expairs in this sequence.
  *
  *  @see expairseq::eval()
- *  @return pointer to epvector containing evaluated pairs or zero pointer,
- *  if no members were changed. */
-epvector * expairseq::evalchildren(int level) const
+ *  @return epvector containing evaluated pairs, empty if no members
+ *    had to be changed. */
+epvector expairseq::evalchildren() const
 {
-	// returns a NULL pointer if nothing had to be evaluated
-	// returns a pointer to a newly created epvector otherwise
-	// (which has to be deleted somewhere else)
-
-	if (level==1)
-		return 0;
-	
-	if (level == -max_recursion_level)
-		throw(std::runtime_error("max recursion level reached"));
-	
-	--level;
-	epvector::const_iterator last=seq.end();
-	epvector::const_iterator cit=seq.begin();
+	auto cit = seq.begin(), last = seq.end();
 	while (cit!=last) {
-		const ex &evaled_ex = (*cit).rest.eval(level);
-		if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
-			
-			// something changed, copy seq, eval and return it
-			epvector *s = new epvector;
-			s->reserve(seq.size());
-			
+		const expair evaled_pair = combine_ex_with_coeff_to_pair(cit->rest, cit->coeff);
+		if (unlikely(!evaled_pair.is_equal(*cit))) {
+
+			// something changed: copy seq, eval and return it
+			epvector s;
+			s.reserve(seq.size());
+
 			// copy parts of seq which are known not to have changed
-			epvector::const_iterator cit2=seq.begin();
-			while (cit2!=cit) {
-				s->push_back(*cit2);
-				++cit2;
-			}
+			s.insert(s.begin(), seq.begin(), cit);
+
 			// copy first changed element
-			s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
-			                                           (*cit2).coeff));
-			++cit2;
+			s.push_back(evaled_pair);
+			++cit;
+
 			// copy rest
-			while (cit2!=last) {
-				s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
-				                                           (*cit2).coeff));
-				++cit2;
+			while (cit != last) {
+				s.push_back(combine_ex_with_coeff_to_pair(cit->rest, cit->coeff));
+				++cit;
 			}
 			return s;
 		}
+
 		++cit;
 	}
-	
-	return 0; // signalling nothing has changed
-}
 
+	return epvector(); // signalling nothing has changed
+}
 
-/** Member-wise evaluate numerically all expairs in this sequence.
+/** Member-wise substitute in this sequence.
  *
- *  @see expairseq::evalf()
- *  @return epvector with all entries evaluated numerically. */
-epvector expairseq::evalfchildren(int level) const
-{
-	if (level==1)
-		return seq;
-	
-	if (level==-max_recursion_level)
-		throw(std::runtime_error("max recursion level reached"));
-	
-	epvector s;
-	s.reserve(seq.size());
-	
-	--level;
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
-		                                          (*it).coeff.evalf(level)));
+ *  @see expairseq::subs()
+ *  @return epvector containing expanded pairs, empty if no members
+ *    had to be changed. */
+epvector expairseq::subschildren(const exmap & m, unsigned options) const
+{
+	// When any of the objects to be substituted is a product or power
+	// we have to recombine the pairs because the numeric coefficients may
+	// be part of the search pattern.
+	if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
+
+		// Search the list of substitutions and cache our findings
+		for (auto & it : m) {
+			if (is_exactly_a<mul>(it.first) || is_exactly_a<power>(it.first)) {
+				options |= subs_options::pattern_is_product;
+				break;
+			}
+		}
+		if (!(options & subs_options::pattern_is_product))
+			options |= subs_options::pattern_is_not_product;
 	}
-	return s;
-}
 
+	if (options & subs_options::pattern_is_product) {
 
-/** Member-wise normalize all expairs in this sequence.
- *
- *  @see expairseq::normal()
- *  @return epvector with all entries normalized. */
-epvector expairseq::normalchildren(int level) const
-{
-	if (level==1)
-		return seq;
-	
-	if (level==-max_recursion_level)
-		throw(std::runtime_error("max recursion level reached"));
-	
-	epvector s;
-	s.reserve(seq.size());
-	
-	--level;
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
-		                                          (*it).coeff));
-	}
-	return s;
-}
+		// Substitute in the recombined pairs
+		auto cit = seq.begin(), last = seq.end();
+		while (cit != last) {
 
+			const ex &orig_ex = recombine_pair_to_ex(*cit);
+			const ex &subsed_ex = orig_ex.subs(m, options);
+			if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
 
-/** Member-wise differentiate all expairs in this sequence.
- *
- *  @see expairseq::diff()
- *  @return epvector with all entries differentiated. */
-epvector expairseq::diffchildren(const symbol &y) const
-{
-	epvector s;
-	s.reserve(seq.size());
-	
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
-		                                          (*it).coeff));
-	}
-	return s;
-}
+				// Something changed: copy seq, subs and return it
+				epvector s;
+				s.reserve(seq.size());
 
+				// Copy parts of seq which are known not to have changed
+				s.insert(s.begin(), seq.begin(), cit);
 
-/** Member-wise substitute in this sequence.
- *
- *  @see expairseq::subs()
- *  @return pointer to epvector containing pairs after application of subs or zero
- *  pointer, if no members were changed. */
-epvector * expairseq::subschildren(const lst &ls, const lst &lr) const
-{
-	// returns a NULL pointer if nothing had to be substituted
-	// returns a pointer to a newly created epvector otherwise
-	// (which has to be deleted somewhere else)
-	GINAC_ASSERT(ls.nops()==lr.nops());
-	
-	epvector::const_iterator last = seq.end();
-	epvector::const_iterator cit = seq.begin();
-	while (cit!=last) {
-		const ex &subsed_ex=(*cit).rest.subs(ls,lr);
-		if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
+				// Copy first changed element
+				s.push_back(split_ex_to_pair(subsed_ex));
+				++cit;
+
+				// Copy rest
+				while (cit != last) {
+					s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(m, options)));
+					++cit;
+				}
+				return s;
+			}
+
+			++cit;
+		}
+
+	} else {
+
+		// Substitute only in the "rest" part of the pairs
+		auto cit = seq.begin(), last = seq.end();
+		while (cit != last) {
+
+			const ex subsed_rest = cit->rest.subs(m, options);
+			const expair subsed_pair = combine_ex_with_coeff_to_pair(subsed_rest, cit->coeff);
+			if (!subsed_pair.is_equal(*cit)) {
 			
-			// something changed, copy seq, subs and return it
-			epvector *s = new epvector;
-			s->reserve(seq.size());
+				// Something changed: copy seq, subs and return it
+				epvector s;
+				s.reserve(seq.size());
+
+				// Copy parts of seq which are known not to have changed
+				s.insert(s.begin(), seq.begin(), cit);
 			
-			// copy parts of seq which are known not to have changed
-			epvector::const_iterator cit2 = seq.begin();
-			while (cit2!=cit) {
-				s->push_back(*cit2);
-				++cit2;
-			}
-			// copy first changed element
-			s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
-			                                           (*cit2).coeff));
-			++cit2;
-			// copy rest
-			while (cit2!=last) {
-				s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
-				                                           (*cit2).coeff));
-				++cit2;
+				// Copy first changed element
+				s.push_back(subsed_pair);
+				++cit;
+
+				// Copy rest
+				while (cit != last) {
+					s.push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(m, options), cit->coeff));
+					++cit;
+				}
+				return s;
 			}
-			return s;
+
+			++cit;
 		}
-		++cit;
 	}
 	
-	return 0; // signalling nothing has changed
+	// Nothing has changed
+	return epvector();
 }
 
 //////////
 // static member variables
 //////////
 
-#if EXPAIRSEQ_USE_HASHTAB
-unsigned expairseq::maxhashtabsize = 0x4000000U;
-unsigned expairseq::minhashtabsize = 0x1000U;
-unsigned expairseq::hashtabfactor = 1;
-#endif // EXPAIRSEQ_USE_HASHTAB
-
 } // namespace GiNaC