/** @file expairseq.cpp
 *
 *  Implementation of sequences of expression pairs. */

/*
 *  GiNaC Copyright (C) 1999-2000 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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
 */

#include <algorithm>
#include <string>
#include <stdexcept>

#include "expairseq.h"
#include "lst.h"
#include "archive.h"
#include "debugmsg.h"
#include "utils.h"

#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
#endif // ndef NO_NAMESPACE_GINAC

#ifdef EXPAIRSEQ_USE_HASHTAB
#error "FIXME: expair_needs_further_processing not yet implemented for hashtabs, sorry. A.F."
#endif // def EXPAIRSEQ_USE_HASHTAB

GINAC_IMPLEMENT_REGISTERED_CLASS(expairseq, basic)

//////////
// helper classes
//////////

class epp_is_less
{
public:
	bool operator()(const epp & lh, const epp & rh) const
	{
		return (*lh).is_less(*rh);
	}
};

//////////
// default constructor, destructor, copy constructor assignment operator and helpers
//////////

// public

expairseq::expairseq(const expairseq & other)
{
	debugmsg("expairseq copy constructor",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;
}

// protected

void expairseq::copy(const expairseq & other)
{
	inherited::copy(other);
	seq=other.seq;
	overall_coeff=other.overall_coeff;
#ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
}

//////////
// other constructors
//////////

expairseq::expairseq(const ex & lh, const ex & rh) : inherited(TINFO_expairseq)
{
	debugmsg("expairseq constructor from ex,ex",LOGLEVEL_CONSTRUCT);
	construct_from_2_ex(lh,rh);
	GINAC_ASSERT(is_canonical());
}

expairseq::expairseq(const exvector & v) : inherited(TINFO_expairseq)
{
	debugmsg("expairseq constructor from exvector",LOGLEVEL_CONSTRUCT);
	construct_from_exvector(v);
	GINAC_ASSERT(is_canonical());
}

/*
expairseq::expairseq(const epvector & v, bool do_not_canonicalize)
  : inherited(TINFO_expairseq)
{
	debugmsg("expairseq constructor from epvector",LOGLEVEL_CONSTRUCT);
	if (do_not_canonicalize) {
		seq=v;
#ifdef EXPAIRSEQ_USE_HASHTAB
		combine_same_terms(); // to build hashtab
#endif // def EXPAIRSEQ_USE_HASHTAB
	} else {
		construct_from_epvector(v);
	}
	GINAC_ASSERT(is_canonical());
}
*/

expairseq::expairseq(const epvector & v, const ex & oc)
  : inherited(TINFO_expairseq), overall_coeff(oc)
{
	debugmsg("expairseq constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
	construct_from_epvector(v);
	GINAC_ASSERT(is_canonical());
}

expairseq::expairseq(epvector * vp, const ex & oc)
  : inherited(TINFO_expairseq), overall_coeff(oc)
{
	debugmsg("expairseq constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
	GINAC_ASSERT(vp!=0);
	construct_from_epvector(*vp);
	delete vp;
	GINAC_ASSERT(is_canonical());
}

//////////
// archiving
//////////

/** Construct object from archive_node. */
expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
#ifdef EXPAIRSEQ_USE_HASHTAB
	, hashtabsize(0)
#endif
{
	debugmsg("expairseq constructor from archive_node", LOGLEVEL_CONSTRUCT);
	for (unsigned int i=0; true; i++) {
		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("overall_coeff", overall_coeff, sym_lst);
}

/** Unarchive the object. */
ex expairseq::unarchive(const archive_node &n, const lst &sym_lst)
{
	return (new expairseq(n, sym_lst))->setflag(status_flags::dynallocated);
}

/** Archive the object. */
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++;
	}
	n.add_ex("overall_coeff", overall_coeff);
}

//////////
// functions overriding virtual functions from bases classes
//////////

// public

basic * expairseq::duplicate() const
{
	debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
	return new expairseq(*this);
}

void expairseq::print(std::ostream & os, unsigned upper_precedence) const
{
	debugmsg("expairseq print",LOGLEVEL_PRINT);
	os << "[[";
	printseq(os,',',precedence,upper_precedence);
	os << "]]";
}

void expairseq::printraw(std::ostream & os) const
{
	debugmsg("expairseq printraw",LOGLEVEL_PRINT);

	os << "expairseq(";
	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
		os << "(";
		(*cit).rest.printraw(os);
		os << ",";
		(*cit).coeff.printraw(os);
		os << "),";
	}
	os << ")";
}

void expairseq::printtree(std::ostream & os, unsigned indent) const
{
	debugmsg("expairseq printtree",LOGLEVEL_PRINT);

	os << std::string(indent,' ') << "type=" << class_name()
	   << ", hash=" << hashvalue
	   << " (0x" << std::hex << hashvalue << std::dec << ")"
	   << ", flags=" << flags
	   << ", nops=" << nops() << std::endl;
	for (unsigned i=0; i<seq.size(); ++i) {
		seq[i].rest.printtree(os,indent+delta_indent);
		seq[i].coeff.printtree(os,indent+delta_indent);
		if (i!=seq.size()-1) {
			os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
		}
	}
	if (!overall_coeff.is_equal(default_overall_coeff())) {
		os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
		os << std::string(indent+delta_indent,' ') << "overall_coeff" << std::endl;
		overall_coeff.printtree(os,indent+delta_indent);
	}
	os << std::string(indent+delta_indent,' ') << "=====" << std::endl;
#ifdef EXPAIRSEQ_USE_HASHTAB
	os << std::string(indent+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) {
			os << std::string(indent+delta_indent,' ') 
			   << "bin " << i << " with entries ";
			for (epplist::const_iterator it=hashtab[i].begin();
				 it!=hashtab[i].end(); ++it) {
				os << *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 = pow(lambda,k)/fact*exp(-lambda);
		cum_prob += prob;
		os << std::string(indent+delta_indent,' ') << "bins with " << k << " entries: "
		   << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
		   << int(prob*1000)/10.0 << ")" << std::endl;
	}
	os << std::string(indent+delta_indent,' ') << "bins with more entries: "
	   << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
	   << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
	
	os << std::string(indent+delta_indent,' ') << "variance: "
	   << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
	   << std::endl;
	os << std::string(indent+delta_indent,' ') << "average fill: "
	   << (1.0*cum_fill)/hashtabsize
	   << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
#endif // def EXPAIRSEQ_USE_HASHTAB
}

bool expairseq::info(unsigned inf) const
{
	return inherited::info(inf);
}

unsigned expairseq::nops() const
{
	if (overall_coeff.is_equal(default_overall_coeff())) {
		return seq.size();
	}
	return seq.size()+1;
}

ex expairseq::op(int i) const
{
	if (unsigned(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)
{
	throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
}

ex expairseq::eval(int level) const
{
	if ((level==1)&&(flags & status_flags::evaluated)) {
		return *this;
	}

	epvector * vp=evalchildren(level);
	if (vp==0) {
		return this->hold();
	}

	return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
}

ex expairseq::evalf(int level) const
{
	return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
}

ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
{
	ex n = thisexpairseq(normalchildren(level),overall_coeff);
	return n.bp->basic::normal(sym_lst,repl_lst,level);
}

ex expairseq::subs(const lst & ls, const lst & lr) const
{
	epvector * vp=subschildren(ls,lr);
	if (vp==0) {
		return *this;
	}
	return thisexpairseq(vp,overall_coeff);
}

// protected

/** Implementation of ex::diff() for an expairseq. It differentiates all elements of the
 *  sequence.
 *  @see ex::diff */
ex expairseq::derivative(const symbol & s) const
{
	return thisexpairseq(diffchildren(s),overall_coeff);
}

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));

	int cmpval;
	
	// compare number of elements
	if (seq.size() != o.seq.size()) {
		return (seq.size()<o.seq.size()) ? -1 : 1;
	}

	// compare overall_coeff
	cmpval = overall_coeff.compare(o.overall_coeff);
	if (cmpval!=0) return cmpval;

	//if (seq.size()==0) return 0; // empty expairseq's are equal

#ifdef EXPAIRSEQ_USE_HASHTAB
	GINAC_ASSERT(hashtabsize==o.hashtabsize);
	if (hashtabsize==0) {
#endif // def 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;
		}

		GINAC_ASSERT(cit1==last1);
		GINAC_ASSERT(cit2==last2);
		
		return 0;
#ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
}

bool expairseq::is_equal_same_type(const basic & other) const
{
	const expairseq & o=dynamic_cast<const expairseq &>(const_cast<basic &>(other));

	// compare number of elements
	if (seq.size() != o.seq.size()) return false;

	// compare overall_coeff
	if (!overall_coeff.is_equal(o.overall_coeff)) return false;

#ifdef EXPAIRSEQ_USE_HASHTAB
	// compare number of elements in each hashtab entry
	if (hashtabsize!=o.hashtabsize) {
		cout << "this:" << std::endl;
		printtree(cout,0);
		cout << "other:" << std::endl;
		other.printtree(cout,0);
	}
		
	GINAC_ASSERT(hashtabsize==o.hashtabsize);
	
	if (hashtabsize==0) {
#endif // def 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;
#ifdef EXPAIRSEQ_USE_HASHTAB
	}

	for (unsigned i=0; i<hashtabsize; ++i) {
		if (hashtab[i].size() != o.hashtab[i].size()) return false;
	}

	// 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 // def EXPAIRSEQ_USE_HASHTAB
}

unsigned expairseq::return_type(void) const
{
	return return_types::noncommutative_composite;
}

unsigned expairseq::calchash(void) const
{
	unsigned v=golden_ratio_hash(tinfo());
	epvector::const_iterator last=seq.end();
	for (epvector::const_iterator cit=seq.begin(); cit!=last; ++cit) {
#ifndef EXPAIRSEQ_USE_HASHTAB
		v=rotate_left_31(v); // rotation would spoil commutativity
#endif // ndef EXPAIRSEQ_USE_HASHTAB
		v ^= (*cit).rest.gethash();
	}

	v ^= overall_coeff.gethash();
	v=v & 0x7FFFFFFFU;
	
	// store calculated hash value only if object is already evaluated
	if (flags & status_flags::evaluated) {
		setflag(status_flags::hash_calculated);
		hashvalue=v;
	}

	return v;
}

ex expairseq::expand(unsigned options) const
{
	epvector * vp = expandchildren(options);
	if (vp==0) {
		return *this;
	}
	return thisexpairseq(vp,overall_coeff);
}

//////////
// new virtual functions which can be overridden by derived classes
//////////

// protected

ex expairseq::thisexpairseq(const epvector & v, const ex & oc) const
{
	return expairseq(v,oc);
}

ex expairseq::thisexpairseq(epvector * vp, const ex & oc) const
{
	return expairseq(vp,oc);
}

void expairseq::printpair(std::ostream & os, const expair & p, unsigned upper_precedence) const
{
	os << "[[";
	p.rest.bp->print(os,precedence);
	os << ",";
	p.coeff.bp->print(os,precedence);
	os << "]]";
}

void expairseq::printseq(std::ostream & os, char delim,
                         unsigned this_precedence,
                         unsigned upper_precedence) const
{
	if (this_precedence<=upper_precedence) os << "(";
	epvector::const_iterator it,it_last;
	it_last=seq.end();
	--it_last;
	for (it=seq.begin(); it!=it_last; ++it) {
		printpair(os,*it,this_precedence);
		os << delim;
	}
	printpair(os,*it,this_precedence);
	if (!overall_coeff.is_equal(default_overall_coeff())) {
		os << delim << overall_coeff;
	}
	if (this_precedence<=upper_precedence) os << ")";
}
	
expair expairseq::split_ex_to_pair(const ex & e) const
{
	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));

	return expair(e,c);
}

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));
	
	return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
}

ex expairseq::recombine_pair_to_ex(const expair & p) const
{
	return lst(p.rest,p.coeff);
}

bool expairseq::expair_needs_further_processing(epp it)
{
	return false;
}

ex expairseq::default_overall_coeff(void) const
{
	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));
}

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)));
}

bool expairseq::can_make_flat(const expair & p) const
{
	return true;
}

	
//////////
// 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);
#ifdef EXPAIRSEQ_USE_HASHTAB
	GINAC_ASSERT((hashtabsize==0)||(hashtabsize>=minhashtabsize));
	GINAC_ASSERT(hashtabsize==calc_hashtabsize(seq.size()));
#endif // def 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()) {
#ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
				construct_from_2_expairseq(ex_to_expairseq(lh),
				                           ex_to_expairseq(rh));
#ifdef EXPAIRSEQ_USE_HASHTAB
			}
#endif // def EXPAIRSEQ_USE_HASHTAB
			return;
		} else {
#ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
				construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
#ifdef EXPAIRSEQ_USE_HASHTAB
			}
#endif // def EXPAIRSEQ_USE_HASHTAB
			return;
		}
	} else if (rh.bp->tinfo()==tinfo()) {
#ifdef 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 // def EXPAIRSEQ_USE_HASHTAB
			construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
#ifdef EXPAIRSEQ_USE_HASHTAB
		}
#endif // def EXPAIRSEQ_USE_HASHTAB
		return;
	}

#ifdef EXPAIRSEQ_USE_HASHTAB
	if (calc_hashtabsize(2)!=0) {
		construct_from_2_ex_via_exvector(lh,rh);
		return;
	}
	hashtabsize=0;
#endif // def EXPAIRSEQ_USE_HASHTAB
	
	if (is_ex_exactly_of_type(lh,numeric)) {
		if (is_ex_exactly_of_type(rh,numeric)) {
			combine_overall_coeff(lh);
			combine_overall_coeff(rh);
		} else {
			combine_overall_coeff(lh);
			seq.push_back(split_ex_to_pair(rh));
		}
	} else {
		if (is_ex_exactly_of_type(rh,numeric)) {
			combine_overall_coeff(rh);
			seq.push_back(split_ex_to_pair(lh));
		} else {
			expair p1=split_ex_to_pair(lh);
			expair p2=split_ex_to_pair(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()) {
					// no further processing is necessary, since this
					// one element will usually be recombined in eval()
					seq.push_back(p1);
				}
			} else {
				seq.reserve(2);
				if (cmpval<0) {
					seq.push_back(p1);
					seq.push_back(p2);
				} else {
					seq.push_back(p2);
					seq.push_back(p1);
				}
			}
		}
	}
}

void expairseq::construct_from_2_expairseq(const expairseq & s1,
										   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();

	seq.reserve(s1.seq.size()+s2.seq.size());

	bool needs_further_processing=false;
	
	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));
			if (!newcoeff.is_zero()) {
				seq.push_back(expair((*first1).rest,newcoeff));
				if (expair_needs_further_processing(seq.end()-1)) {
					needs_further_processing = true;
				}
			}
			++first1;
			++first2;
		} else if (cmpval<0) {
			seq.push_back(*first1);
			++first1;
		} else {
			seq.push_back(*first2);
			++first2;
		}
	}
	
	while (first1!=last1) {
		seq.push_back(*first1);
		++first1;
	}
	while (first2!=last2) {
		seq.push_back(*first2);
		++first2;
	}

	if (needs_further_processing) {
		epvector v=seq;
		seq.clear();
		construct_from_epvector(v);
	}
}

void expairseq::construct_from_expairseq_ex(const expairseq & s,
											const ex & e)
{
	combine_overall_coeff(s.overall_coeff);
	if (is_ex_exactly_of_type(e,numeric)) {
		combine_overall_coeff(e);
		seq=s.seq;
		return;
	}

	epvector::const_iterator first=s.seq.begin();
	epvector::const_iterator last=s.seq.end();
	expair p=split_ex_to_pair(e);

	seq.reserve(s.seq.size()+1);
	bool p_pushed=0;

	bool needs_further_processing=false;

	// merge p into s.seq
	while (first!=last) {
		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));
			if (!newcoeff.is_zero()) {
				seq.push_back(expair((*first).rest,newcoeff));
				if (expair_needs_further_processing(seq.end()-1)) {
					needs_further_processing = true;
				}
			}
			++first;
			p_pushed=1;
			break;
		} else if (cmpval<0) {
			seq.push_back(*first);
			++first;
		} else {
			seq.push_back(p);
			p_pushed=1;
			break;
		}
	}

	if (p_pushed) {
		// while loop exited because p was pushed, now push rest of s.seq
		while (first!=last) {
			seq.push_back(*first);
			++first;
		}
	} else {
		// while loop exited because s.seq was pushed, now push p
		seq.push_back(p);
	}

	if (needs_further_processing) {
		epvector v=seq;
		seq.clear();
		construct_from_epvector(v);
	}
}

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())
	//                  (same for (+,*) -> (*,^)

	make_flat(v);
#ifdef EXPAIRSEQ_USE_HASHTAB
	combine_same_terms();
#else
	canonicalize();
	combine_same_terms_sorted_seq();
#endif // def EXPAIRSEQ_USE_HASHTAB
}

void expairseq::construct_from_epvector(const epvector & 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())
	//                  (same for (+,*) -> (*,^)

	make_flat(v);
#ifdef EXPAIRSEQ_USE_HASHTAB
	combine_same_terms();
#else
	canonicalize();
	combine_same_terms_sorted_seq();
#endif // def EXPAIRSEQ_USE_HASHTAB
}

void expairseq::make_flat(const exvector & v)
{
	exvector::const_iterator cit, citend = v.end();

	// count number of operands which are of same expairseq derived type
	// and their cumulative number of operands
	int nexpairseqs=0;
	int noperands=0;
	cit=v.begin();
	while (cit!=citend) {
		if (cit->bp->tinfo()==tinfo()) {
			nexpairseqs++;
			noperands+=ex_to_expairseq(*cit).seq.size();
		}
		++cit;
	}

	// 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!=citend) {
		if (cit->bp->tinfo()==tinfo()) {
			const expairseq & subseqref=ex_to_expairseq(*cit);
			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;
			}
		} else {
			if (is_ex_exactly_of_type(*cit,numeric)) {
				combine_overall_coeff(*cit);
			} else {
				seq.push_back(split_ex_to_pair(*cit));
			}
		}
		++cit;
	}

	/*
	cout << "after make flat" << std::endl;
	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
		(*cit).printraw(cout);
	}
	cout << std::endl;
	*/
}

void expairseq::make_flat(const epvector & v)
{
	epvector::const_iterator cit, citend = v.end();

	// count number of operands which are of same expairseq derived type
	// and their cumulative number of operands
	int nexpairseqs=0;
	int noperands=0;

	cit = v.begin();
	while (cit!=citend) {
		if (cit->rest.bp->tinfo()==tinfo()) {
			nexpairseqs++;
			noperands += ex_to_expairseq((*cit).rest).seq.size();
		}
		++cit;
	}

	// 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!=citend) {
		if ((cit->rest.bp->tinfo()==tinfo())&&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;
			}
		} else {
			if ((*cit).is_numeric_with_coeff_1()) {
				combine_overall_coeff((*cit).rest);
			//if (is_ex_exactly_of_type((*cit).rest,numeric)) {
			//    combine_overall_coeff(recombine_pair_to_ex(*cit));
			} else {
				seq.push_back(*cit);
			}
		}
		++cit;
	}
}

epvector * expairseq::bubblesort(epvector::iterator itbegin, epvector::iterator itend)
{
	unsigned n=itend-itbegin;

	epvector * sp=new epvector;
	sp->reserve(n);

	epvector::iterator last=itend-1;
	for (epvector::iterator it1=itbegin; it1!=last; ++it1) {
		for (epvector::iterator it2=it1+1; it2!=itend; ++it2) {
			if ((*it2).rest.compare((*it1).rest)<0) {
				iter_swap(it1,it2);
			}
		}
		sp->push_back(*it1);
	}
	sp->push_back(*last);
	return sp;
}

epvector * expairseq::mergesort(epvector::iterator itbegin, epvector::iterator itend)
{
	unsigned n=itend-itbegin;
	/*
	if (n==1) {
		epvector * sp=new epvector;
		sp->push_back(*itbegin);
		return sp;
	}
	*/
	if (n<16) return bubblesort(itbegin, itend);
	unsigned m=n/2;
	
	epvector * s1p=mergesort(itbegin, itbegin+m);
	epvector * s2p=mergesort(itbegin+m, itend);

	epvector * sp=new epvector;
	sp->reserve(s1p->size()+s2p->size());

	epvector::iterator first1=s1p->begin();
	epvector::iterator last1=s1p->end();

	epvector::iterator first2=s2p->begin();
	epvector::iterator last2=s2p->end();
	
	while (first1 != last1 && first2 != last2) {
		if ((*first1).rest.compare((*first2).rest)<0) {
			sp->push_back(*first1);
			++first1;
		} else {
			sp->push_back(*first2);
			++first2;
		}
	}

	if (first1 != last1) {
		while (first1 != last1) {
			sp->push_back(*first1);
			++first1;
		}
	} else {
		while (first2 != last2) {
			sp->push_back(*first2);
			++first2;
		}
	}

	delete s1p;
	delete s2p;
	
	return sp;
}
			

void expairseq::canonicalize(void)
{
	// canonicalize
	sort(seq.begin(),seq.end(),expair_is_less());
	/*
	sort(seq.begin(),seq.end(),expair_is_less_old());
	if (seq.size()>1) {
		if (is_ex_exactly_of_type((*(seq.begin())).rest,numeric)) {
			sort(seq.begin(),seq.end(),expair_is_less());
		} else {
			epvector::iterator last_numeric=seq.end();
			do {
				last_numeric--;
			} while (is_ex_exactly_of_type((*last_numeric).rest,numeric));
			last_numeric++;
			sort(last_numeric,seq.end(),expair_is_less());
		}
	}
	*/
	
	/*
	epvector * sorted_seqp=mergesort(seq.begin(),seq.end());
	epvector::iterator last=sorted_seqp->end();
	epvector::iterator it2=seq.begin();
	for (epvector::iterator it1=sorted_seqp->begin(); it1!=last; ++it1, ++it2) {
		iter_swap(it1,it2);
	}
	delete sorted_seqp;
	*/

	/*
	cout << "after canonicalize" << std::endl;
	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
		(*cit).printraw(cout);
	}
	cout << std::endl;
	cout.flush();
	*/
}

void expairseq::combine_same_terms_sorted_seq(void)
{
	bool needs_further_processing=false;
	
	// combine same terms, drop term with coeff 0
	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);
		}
	}

	/*
	cout << "after combine" << std::endl;
	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
		(*cit).printraw(cout);
	}
	cout << std::endl;
	cout.flush();
	*/
	
	if (needs_further_processing) {
		epvector v=seq;
		seq.clear();
		construct_from_epvector(v);
	}
}

#ifdef 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);
}    

void expairseq::build_hashtab_and_combine(epvector::iterator & first_numeric,
                                          epvector::iterator & last_non_zero,
                                          vector<bool> & touched,
                                          unsigned & number_of_zeroes)
{
	epp current=seq.begin();

	while (current!=first_numeric) {
		if (is_ex_exactly_of_type((*current).rest,numeric)) {
			--first_numeric;
			iter_swap(current,first_numeric);
		} 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;
			}
		}
	}
}    

void expairseq::drop_coeff_0_terms(epvector::iterator & first_numeric,
                                   epvector::iterator & last_non_zero,
                                   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_equal(_num0())) {
			++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;
			}
		}
	}
	GINAC_ASSERT(i==current-seq.begin());
}

bool expairseq::has_coeff_0(void) const
{
	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
		if ((*cit).coeff.is_equal(_ex0())) {
			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;
	}
}

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;

	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();
	}

	// shrink hashtabsize to calculated value
	GINAC_ASSERT(!has_coeff_0());

	shrink_hashtab();

	GINAC_ASSERT(!has_coeff_0());
}

#endif // def EXPAIRSEQ_USE_HASHTAB

bool expairseq::is_canonical() const
{
	if (seq.size()<=1) return 1;

#ifdef EXPAIRSEQ_USE_HASHTAB
	if (hashtabsize>0) return 1; // not canoncalized
#endif // def 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)) {
				// 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)) {
					printpair(std::clog,*it_last,0);
					std::clog << ">";
					printpair(std::clog,*it,0);
					std::clog << "\n";
					std::clog << "pair1:" << std::endl;
					(*it_last).rest.printtree(std::clog);
					(*it_last).coeff.printtree(std::clog);
					std::clog << "pair2:" << std::endl;
					(*it).rest.printtree(std::clog);
					(*it).coeff.printtree(std::clog);
					return 0;
				}
			}
		}
	}
	return 1;
}

epvector * expairseq::expandchildren(unsigned options) const
{
	epvector::const_iterator last = seq.end();
	epvector::const_iterator cit = seq.begin();
	while (cit!=last) {
		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());

			// 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(expanded_ex,
			                                           (*cit2).coeff));
			++cit2;
			// copy rest
			while (cit2!=last) {
				s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
				                                           (*cit2).coeff));
				++cit2;
			}
			return s;
		}
		++cit;
	}
	
	return 0; // nothing has changed
}
   
epvector * expairseq::evalchildren(int level) 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();
	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());

			// 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(evaled_ex,
			                                           (*cit2).coeff));
			++cit2;
			// copy rest
			while (cit2!=last) {
				s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
				                                           (*cit2).coeff));
				++cit2;
			}
			return s;
		}
		++cit;
	}
	
	return 0; // nothing has changed
}

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)));
	}
	return s;
}

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;
}

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;
}

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)) {
			
			// something changed, copy seq, subs and return it
			epvector *s=new epvector;
			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;
			}
			// 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;
			}
			return s;
		}
		++cit;
	}
	
	return 0; // nothing has changed
}

//////////
// static member variables
//////////

// protected

unsigned expairseq::precedence=10;

#ifdef EXPAIRSEQ_USE_HASHTAB
unsigned expairseq::maxhashtabsize=0x4000000U;
unsigned expairseq::minhashtabsize=0x1000U;
unsigned expairseq::hashtabfactor=1;
#endif // def EXPAIRSEQ_USE_HASHTAB

//////////
// global constants
//////////

const expairseq some_expairseq;
const std::type_info & typeid_expairseq = typeid(some_expairseq);

#ifndef NO_NAMESPACE_GINAC
} // namespace GiNaC
#endif // ndef NO_NAMESPACE_GINAC