series.cc

// -*- mode:C++ ; compile-command: "g++-3.4 -I.. -g -c series.cc  -DIN_GIAC -DHAVE_CONFIG_H " -*-
#include "giacPCH.h"
/*
 *  Copyright (C) 2000,14 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
 *
 *  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 3 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, see <http://www.gnu.org/licenses/>.
 */
using namespace std;
#include <stdexcept>
#include <cmath>
#include "derive.h"
#include "subst.h"
#include "series.h"
#include "symbolic.h"
#include "unary.h"
#include "usual.h"
#include "poly.h"
#include "sym2poly.h" 
#include "tex.h"
#include "prog.h"
#include "misc.h"
#include "intg.h"
#include "maple.h"
#include "lin.h"
#include "plot.h"
#include "giacintl.h"

#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC

  static int mrv_begin_order=2;

  static bool taylor_(const gen & f_x,const gen & x,const gen & lim_point,int ordre,vecteur & v,GIAC_CONTEXT){
    gen current_derf(f_x),value,factorielle(1);
    for (int i=0;;++i){
      value=subst(current_derf,x,lim_point,false,contextptr);
      if (is_undef(value)){
	// if (x.type==_IDNT) value=limit(current_derf,*x._IDNTptr,lim_point,0,contextptr);
	if (is_undef(value))
	  return false;
      }
      v.push_back(ratnormal(rdiv(value,factorielle,contextptr),contextptr));
      if (i==ordre){
	v.push_back(undef);
	return true;
      }
      factorielle = factorielle * gen(i+1);
      current_derf=ratnormal(derive(current_derf,x,contextptr),contextptr);
      if (is_undef(current_derf))
	return false;
    }
    v.dbgprint();
    return false;
  }

  bool taylor(const gen & f_x,const gen & x,const gen & lim_point,int ordre,vecteur & v,GIAC_CONTEXT){
    int i=series_flags(contextptr);
    series_flags(contextptr)=series_flags(contextptr) | (1<<7) ;
    bool b=taylor_(f_x,x,lim_point,ordre,v,contextptr);
    series_flags(i,contextptr);
    return b;
  }

  // direction is always ignored for taylor, but might not 
  // for generic series_expansion
  // shift coeff =0 for taylor
  gen taylor(const gen & lim_point,int ordre,const unary_function_ptr & f,int direction,gen & shift_coeff,GIAC_CONTEXT){
    // Special handling for sin/cos expansion inside limit
    if ( is_inf(lim_point) && ( (f==at_cos)  || (f==at_sin) ) ){
      gen g=bounded_function(contextptr);
      /*
      int i=sincosinf.size();
      sincosinf.push_back(gen(" sincosinf"+print_INT_(i)));
      gen g=sincosinf.back();
      if (!g._IDNTptr->value){
	vecteur minusone_one(2);
	minusone_one[0]=minus_one;
	minusone_one[1]=plus_one;
	gen v(vecteur(1,gen(minusone_one,_LINE__VECT)));
	gen d(_DOUBLE_);
	d.subtype=_INT_TYPE;
	gen aa(makevecteur(d,v,vecteur(0)),_ASSUME__VECT);
	g._IDNTptr->value=new gen(aa);
      }
    */
      return vecteur(1,g);
    }
    // if preprocessing is needed for f, series_expansion for ordre==-1 should 
    // push back in a global vector f and it's substitution
    if (ordre<0) 
      return 0;
    shift_coeff=0;
    if (is_undef(lim_point) || is_inf(lim_point)){
      invalidserieserr(gettext("non tractable function ")+(f.ptr()->print(contextptr)+(" at "+lim_point.print(contextptr))));
      return undef;
    }
    identificateur x(" ");
    vecteur v;
    gen fx=f(x,contextptr);
    if (taylor(fx,x,lim_point,ordre,v,contextptr)) 
      return v;
    else
      return undef;
  }

  gen porder(const sparse_poly1 & a){
    if (a.empty())
      return plus_inf;
    sparse_poly1::const_iterator a_end=a.end()-1;
    if (is_undef(a_end->coeff))
      return a_end->exponent;
    else
      return plus_inf;
  }

  bool sparse_poly12vecteur(const sparse_poly1 & p,vecteur & v,int & shift){
    sparse_poly1::const_iterator it=p.begin(),itend=p.end();
    v.clear();
    if (p.empty())
      return true;
    if (p.back().exponent.type!=_INT_)
      return false;
    int n1=p.front().exponent.val,n2=p.back().exponent.val;
    if (n1>n2 || (n2-n1)+1<0) // if n==RAND_MAX, n+1<0
      return false;
    if (n1<0)
      shift=n1;
    else 
      shift=n1=0;
    v.resize(n2-n1+1);
    for (;it!=itend;++it){
      if (it->exponent.type!=_INT_)
	return false;
      int m=it->exponent.val;
      if (m<n1 || m>n2) 
	return false;
      v[m-n1]=it->coeff;
    }
    reverse(v.begin(),v.end());
    return true;
  }

  void vecteur2sparse_poly1(const vecteur & v,sparse_poly1 & p){
    p.clear();
    vecteur::const_iterator it=v.begin(),itend=v.end();
    p.reserve(itend-it);
    for (int i=0;it!=itend;++i,++it){
      if (!is_zero(*it))
	p.push_back(monome(*it,i));
    }
  }

  sparse_poly1 gen2spol1(const gen &g){
    if (g.type!=_VECT)
      return sparse_poly1(1,monome(g,0));
    sparse_poly1 p;
    vecteur2sparse_poly1(*g._VECTptr,p);
    return p;
  }

  sparse_poly1 vecteur2sparse_poly1(const vecteur & v){
    sparse_poly1 p;
    vecteur2sparse_poly1(v,p);
    return p;
  }

  gen spol12gen(const sparse_poly1 & p,GIAC_CONTEXT){
    string t;
    t = t+series_variable_name(contextptr);
    identificateur tt(t);
    gen T(tt),remains;
    gen g=sparse_poly12gen(p,T,remains,false);
    if (!is_zero(remains))
      g += remains*order_size(T,contextptr);
    return g;
  }

  static gen spol12gen(const gen & coeff,const gen & x){
    if (coeff.type==_VECT){
      vecteur v=*coeff._VECTptr;
      int s=int(v.size());
      for (int i=0;i<s;++i){
	v[i]=spol12gen(v[i],x);
      }
      return gen(v,coeff.subtype);
    }
    if (coeff.type==_SPOL1){
      gen remains=0;
      return sparse_poly12gen(*coeff._SPOL1ptr,x,remains,true)+remains;
    }
    if (coeff.type!=_SYMB)
      return coeff;
    return symbolic(coeff._SYMBptr->sommet,spol12gen(coeff._SYMBptr->feuille,x));
  }

  gen sparse_poly12gen(const sparse_poly1 & p,const gen & x,gen & remains,bool with_order_size){
    gen res;
    remains=0;
    sparse_poly1::const_iterator it=p.begin(),itend=p.end();
    for (;it!=itend;++it){
      gen coeff=it->coeff;
      if (is_undef(coeff)){
	remains=pow(x,it->exponent,context0); // ok
	if (with_order_size)
	  return res+remains*order_size(x,context0);
	else
	  return res;
      }
      coeff=spol12gen(coeff,x);
      res = res + coeff * pow(x,it->exponent,context0); // ok
    }
    return res;
  }


  bool ptruncate(sparse_poly1 & p,const gen & ordre,GIAC_CONTEXT){
    if ( (series_flags(contextptr) & 0x2) || p.empty() ){
      sparse_poly1::iterator it=p.begin(),itend=p.end();
      gen first=it->exponent;
      for (;it!=itend;++it){
	if (is_undef(it->coeff))
	  return true;
	if (ck_is_strictly_greater(it->exponent-first,ordre,contextptr)){
	  it->coeff=undef;
	  p.erase(it+1,itend);
	  return true;
	}
      }
    }
    return true;
  }

  void poly_truncate(sparse_poly1 & p,int ordre,GIAC_CONTEXT){
    if ( (series_flags(contextptr) & 0x2) || p.empty() ){
      sparse_poly1::iterator it=p.begin(),itend=p.end();
      for (;it!=itend;++it){
	if (is_undef(it->coeff))
	  return ;
	if (ck_is_strictly_greater(it->exponent,ordre,contextptr)){
	  it->coeff=undef;
	  p.erase(it+1,itend);
	  return ;
	}
      }
    }
    return ;
  }

  static gen remove_lnexp(const gen & e,GIAC_CONTEXT);

  bool padd(const sparse_poly1 & a,const sparse_poly1 &b, sparse_poly1 & res,GIAC_CONTEXT){
    // Series addition
    if (a.empty()){
      if (&b!=&res)
	res=b;
      return true;
    }
    if (b.empty()){
      if (&a!=&res)
	res=a;
      return true;
    }
    sparse_poly1::const_iterator a_cur,a_end,b_cur,b_end;
    sparse_poly1 temp_a,temp_b;
    if (&res==&a){ // must make a copy of a
      temp_a=a;
      a_cur=temp_a.begin();
      a_end=temp_a.end();
    }
    else {
      a_cur=a.begin();
      a_end=a.end();
    }
    if (&res==&b){ // must make a copy of b
      temp_b=b;
      b_cur=temp_b.begin();
      b_end=temp_b.end();
    }
    else {
      b_cur=b.begin();
      b_end=b.end();
    }
    res.clear();
    res.reserve((a_end-a_cur)+(b_end-b_cur));
    for (;(a_cur!=a_end) && (b_cur!=b_end) ;) {
      gen a_pow=a_cur->exponent;
      gen b_pow=b_cur->exponent;
      // a and b are non-empty, compare powers
      if (ck_is_strictly_greater(b_pow,a_pow,contextptr)) {
	// get coefficient from a
	res.push_back(*a_cur);
	if (is_undef(a_cur->coeff)){
	  return true;
	}
	++a_cur;
	continue;
      }
      if (ck_is_strictly_greater(a_pow,b_pow,contextptr)) {
	// get coefficient from b
	res.push_back(*b_cur);
	if (is_undef(b_cur->coeff)){
	  return true;
	}
	++b_cur;
	continue;
      }
      // Add coefficient of a and b
      gen sum=a_cur->coeff+b_cur->coeff;
      if (sum.type>_POLY && sum.type!=_FRAC &&(res.empty() || (series_flags(contextptr) & 0x1) ) ){
	//cerr << sum << " ";
	sum=recursive_normal(remove_lnexp(sum,contextptr),contextptr);
	//cerr << sum << '\n';
      }
      // gen sum=(a_cur->coeff+b_cur->coeff);
      if (!is_zero(sum))
	res.push_back(monome(sum,a_pow));
      if (is_undef(sum)){
	return true;
      }
      ++a_cur;
      ++b_cur;
    }
    for (;a_cur!=a_end;++a_cur)
      res.push_back(*a_cur);
    for (;b_cur!=b_end;++b_cur)
      res.push_back(*b_cur);
    return true;
  }

  sparse_poly1 spadd(const sparse_poly1 & a,const sparse_poly1 &b,GIAC_CONTEXT){
    sparse_poly1 res;
    padd(a,b,res,contextptr);
    return res;
  }

  sparse_poly1 spsub(const sparse_poly1 & a,const sparse_poly1 &b,GIAC_CONTEXT){
    sparse_poly1 res(b);
    pneg(b,res,contextptr);
    padd(a,res,res,contextptr);
    return res;
  }


  bool pmul(const sparse_poly1 & a,const gen & b_orig, sparse_poly1 & res,GIAC_CONTEXT){
    gen b(b_orig);
    if (&a==&res){
      if (is_one(b_orig)) return true;
      sparse_poly1::iterator it=res.begin(),itend=res.end();
      for (;it!=itend;++it){
	gen g=it->coeff * b;
	if (g.type>_POLY && g.type!=_FRAC) 
	  g=ratnormal(g,contextptr) ;
	it->coeff = g;
      }
      return true;
    }
    sparse_poly1::const_iterator it=a.begin(),itend=a.end();
    res.clear();
    res.reserve(itend-it);
    for (;it!=itend;++it)
      res.push_back(monome(ratnormal(it->coeff * b,contextptr), it->exponent));
    return true;
  }

  bool pmul(const gen & b, const sparse_poly1 & a,sparse_poly1 & res,GIAC_CONTEXT){
    return pmul(a,b,res,contextptr);
  }

  sparse_poly1 spmul(const sparse_poly1 & a,const gen &b,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!pmul(a,b,res,contextptr))
      res=sparse_poly1(1,monome(1,undef));
    return res;
  }

  sparse_poly1 spmul(const gen & a,const sparse_poly1 &b,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!pmul(a,b,res,contextptr))
      res=sparse_poly1(1,monome(1,undef));
    return res;
  }

  struct monome_less {
    monome_less() {}
    bool operator () (const monome & a,const monome & b){
      return ck_is_strictly_greater(b.exponent,a.exponent,context0);
    }
  };

  struct symb_size_less_t {
    symb_size_less_t() {}
    bool operator () (const gen &a,const gen &b){
      return symb_size_less(a,b);
    }
  };

  bool pmul(const sparse_poly1 & celuici,const sparse_poly1 &other, sparse_poly1 & final_seq,bool n_truncate,const gen & n_valuation,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    int asize=int(celuici.size());
    int bsize=int(other.size());
    if ( (!asize) || (!bsize) ) {
      final_seq.clear();
      return true;
    }
    if (asize==1){
      gen temp(celuici.front().coeff);
      pshift(other,celuici.front().exponent,final_seq,contextptr);
      // COUT << other << "Shifted" << final_seq << '\n';
      return pmul(final_seq,temp,final_seq,contextptr);
      // COUT << other << "Multiplied" << final_seq << '\n';
    }
    if (bsize==1){
      gen temp(other.front().coeff);
      pshift(celuici,other.front().exponent,final_seq,contextptr);
      return pmul(final_seq,temp,final_seq,contextptr);
    }
    sparse_poly1 new_seq;
    new_seq.reserve(asize*bsize);
    // General sparse series multiplication: complexity is N*M*ln(N*M)
    // Storage capacity 2*N*M expair
    // That's much more than O(N+M) for dense poly *but*
    // it works for non integer powers
    // COUT << celuici << "pmul" << other << '\n';
    // First find the order product
    gen a_max = porder(celuici);
    gen b_max = porder(other);
    gen a_min = celuici.front().exponent;
    gen b_min = other.front().exponent;
    gen c_min = normal(a_min + b_min,contextptr);
    gen c_max = min(normal(a_min + b_max,contextptr),normal(b_min + a_max,contextptr),contextptr);
    if (c_max.type==_SYMB && c_max._SYMBptr->sommet==at_max)
      return false; // setsizeerr(gettext("series.cc/pmul"));
    // compute all products term by term, with optimization for dense poly
    // (coeff are sorted for dense poly)
    sparse_poly1::const_iterator itb = other.begin(),itbend = other.end();
    sparse_poly1::const_iterator ita = celuici.begin(),ita_end=celuici.end();
    sparse_poly1::const_iterator itabegin = ita;
    gen old_pow=normal(ita->exponent+itb->exponent,contextptr);
    gen res(0);
    for ( ; ita!=ita_end; ++ita ){
      sparse_poly1::const_iterator itacur=ita;
      sparse_poly1::const_iterator itbcur=itb;
      for (;;) {
#ifdef TIMEOUT
	control_c();
#endif
	if (ctrl_c || interrupted) {
	  interrupted=ctrl_c=true;
	  return false;
	}
	gen cur_pow=normal(itacur->exponent+itbcur->exponent,contextptr);
	if ((n_truncate && ck_is_strictly_greater(n_valuation,cur_pow,contextptr)) || ck_is_greater(c_max,cur_pow,contextptr)){
	  if (cur_pow!=old_pow){
	    new_seq.push_back( monome(res,old_pow ));
	    res=itacur->coeff * itbcur->coeff;
	    old_pow=cur_pow;
	  }
	  else
	    res=res+ itacur->coeff  * itbcur->coeff;
	}
	if (itacur==itabegin)
	  break;
	--itacur;
	++itbcur;
	if (itbcur==itbend)
	  break;
      }
    }
    --ita;
    ++itb;
    for ( ; itb!=itbend;++itb){
      sparse_poly1::const_iterator itacur=ita;
      sparse_poly1::const_iterator itbcur=itb;
      for (;;) {
#ifdef TIMEOUT
	control_c();
#endif
	if (ctrl_c || interrupted) {
	  interrupted=ctrl_c=true;
	  return false;
	}
	gen cur_pow=normal(itacur->exponent + itbcur->exponent,contextptr);
	if ((n_truncate && ck_is_strictly_greater(n_valuation,cur_pow,contextptr)) || ck_is_greater(c_max,cur_pow,contextptr)){
	  if (cur_pow!=old_pow){
	    new_seq.push_back( monome(res ,old_pow ));
	    res= itacur->coeff  * itbcur->coeff ;
	    old_pow=cur_pow;
	  }
	  else
	    res=res+ itacur->coeff  * itbcur->coeff ;
	}
	if (itacur==itabegin)
	  break;
	--itacur;
	++itbcur;
	if (itbcur==itbend)
	  break;
      }
    }
    new_seq.push_back( monome(res ,old_pow ));
    final_seq.clear();
    sparse_poly1::const_iterator it=new_seq.begin();
    sparse_poly1::const_iterator itend=new_seq.end();
    const int MAXS=512;
    int m=MAXS,M=-MAXS,N=itend-it;
    final_seq.reserve(N);
#ifdef FXCG
    if (N<MAXS){
      for (;it!=itend;++it){
	if (it->exponent.type!=_INT_)
	  break;
	int cur=it->exponent.val;
	if (cur<m)
	  m=cur;
	if (cur>M)
	  M=cur;
      }
      if (it==itend){
	gen tab[M-m+1];
	memset(tab,sizeof(tab),0);
	for (it=new_seq.begin();it!=itend;++it){
	  tab[it->exponent.val-m] += it->coeff;
	}
	for (int i=m;i<=M;++i){
	  gen res=tab[i-m];
	  if (is_zero(res))
	    continue;
	  if (is_undef(res)){
	    final_seq.push_back(monome(res,i));
	    return true;
	  }
	  if (series_flags(contextptr) & 0x1)
	    res=recursive_normal(res,contextptr);
	  if (!is_zero(res))
	    final_seq.push_back(monome(res,i));
	}
	return true;
      }
    }
#endif
    // COUT << new_seq << '\n';
    // sort by asc. power
    sort( new_seq.begin(),new_seq.end(),monome_less());
    // COUT << "Sorted" << new_seq << '\n';
    // add terms with same power
    it=new_seq.begin();
    // itend=new_seq.end();
    while (it!=itend){
      gen res=it->coeff;
      gen pow=it->exponent;
      if (is_undef(res)){
	final_seq.push_back(*it);
	return true;
      }
      ++it;
      while ( (it!=itend) && (it->exponent==pow)){
#ifdef TIMEOUT
	control_c();
#endif
	if (ctrl_c || interrupted) {
	  interrupted=ctrl_c=true;
	  return false;
	}
	if (is_undef(it->coeff)){
	  final_seq.push_back(*it);
	  return true;
	}
	res=res+it->coeff;
	++it;
      }
      if (series_flags(contextptr) & 0x1)
	res=recursive_normal(res,contextptr);
      if (!is_zero(res))
	final_seq.push_back(monome(res, pow));
    }
    if (c_max!=plus_inf)
      final_seq.push_back(monome(undef, c_max));
    return true;
    //COUT << final_seq.back().coeff << '\n';
    //return true;
  }

  sparse_poly1 spmul(const sparse_poly1 & a,const sparse_poly1 &b,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!pmul(a,b,res,false,0,contextptr))
      res=sparse_poly1(1,monome(1,undef));
    return res;
  }

  bool pneg(const sparse_poly1 & a,sparse_poly1 & res,GIAC_CONTEXT){
    if (&a==&res){
      sparse_poly1::iterator it=res.begin(),itend=res.end();
      for (;it!=itend;++it)
	it->coeff=-it->coeff;
      return true;
    }
    sparse_poly1::const_iterator it=a.begin(),itend=a.end();
    res.clear();
    res.reserve(itend-it);
    for (;it!=itend;++it)
      res.push_back(monome(-it->coeff, it->exponent));
    return true;
  }

  sparse_poly1 spneg(const sparse_poly1 & a,GIAC_CONTEXT){
    sparse_poly1 res;
    pneg(a,res,contextptr);
    return res;
  }
  
  bool pshift(const sparse_poly1 & a,const gen & b_orig, sparse_poly1 & res,GIAC_CONTEXT){
    if (is_zero(b_orig)){
      if (&a!=&res)
	res=a;
      return true;
    }
    gen b(b_orig);
    if (&a==&res){
      sparse_poly1::iterator it=res.begin(),itend=res.end();
      for (;it!=itend;++it)
	it->exponent = normal(it->exponent + b,contextptr);
      return true;
    }
    sparse_poly1::const_iterator it=a.begin(),itend=a.end();
    res.clear();
    res.reserve(itend-it);
    for (;it!=itend;++it)
      res.push_back(monome(it->coeff , normal(it->exponent +b,contextptr)));
    return true;
  }

  // ascending order division
  bool pdiv(const sparse_poly1 & a,const sparse_poly1 &b_orig, sparse_poly1 & res,int ordre_orig,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    //if (debug_infolevel) CERR << CLOCK()*1e-6 << " pdiv begin" <<'\n';
    sparse_poly1 b(b_orig);
    ptruncate(b,ordre_orig,contextptr);
    if (b.empty()){
      // divisionby0err(a);
      return false;
    }
    gen b0=b.front().coeff;
    if (is_undef(b0)){
      if (&b!=&res)
	res=b;
      return true;
    }
    if (b.size()==1){
      pshift(a,-b.front().exponent,res,contextptr);
      return pdiv(res,b0,res,contextptr);
    }
    // COUT << a << "/" << b << '\n';
    if (&res==&b){
      // setsizeerr(gettext("series.cc/pdiv"));
      return false;
    }
    gen e0=b.front().exponent;
    gen ordre=min(min(porder(a),porder(b)-e0,contextptr),ordre_orig,contextptr);
    if (ordre==plus_inf)
      ordre=series_default_order(contextptr);
    // COUT << ordre << '\n';
    if (ordre.type==_SYMB && ordre._SYMBptr->sommet==at_max)
      return false; // setsizeerr(gettext("series.cc/pdiv"));
    sparse_poly1 rem(a);
    res.clear();
    sparse_poly1 bshift;
    gen q_cur,e_cur; // current quotient, current exponent
    for (;;){
      if (is_undef(rem.front().coeff)){
	res.push_back(monome(undef,rem.front().exponent-e0));
	// COUT << "=" << res << '\n';
	return true;
      }
      q_cur=rdiv(rem.front().coeff,b0,contextptr);
      e_cur=rem.front().exponent-e0;
      res.push_back(monome(q_cur,e_cur));
      pshift(b,e_cur,bshift,contextptr);
      sparse_poly1::iterator it=bshift.begin(),itend=bshift.end();
      for (;it!=itend;++it){
	if (is_undef(it->coeff))
	  break;
	if (ck_is_strictly_greater(it->exponent,ordre,contextptr)){
	  it->coeff=undef;
	  bshift.erase(it+1,itend);
	  break;
	}
      }
      if (!pmul(-q_cur,bshift,bshift,contextptr))
	return false;
      padd(rem,bshift,rem,contextptr);
      // COUT << rem.front().exponent << " " << e0+ordre << '\n';
      if (ck_is_strictly_greater(rem.front().exponent,a.front().exponent+ordre,contextptr)){
	res.push_back(monome(undef,a.front().exponent+ordre+1-e0));
	return true;
      }
    }
    return true;
  }

  sparse_poly1 spdiv(const sparse_poly1 & a,const sparse_poly1 &b,GIAC_CONTEXT){
    sparse_poly1 res;
    gen og=min(porder(a),porder(b),contextptr);
    int o=series_default_order(contextptr);
    if (og.type==_INT_)
      o=og.val;
    if (!pdiv(a,b,res,o,contextptr))
      res=sparse_poly1(1,monome(1,undef));
    return res;
  }

  bool pdiv(const sparse_poly1 & a,const gen & b_orig, sparse_poly1 & res,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    if (is_zero(b_orig))
      return false; // divisionby0err(a);
    if (is_one(b_orig)){
      if (&a!=&res)
	res=a;
      return true;
    }
    gen b(b_orig);
    if (&a==&res){
      sparse_poly1::iterator it=res.begin(),itend=res.end();
      for (;it!=itend;++it){
	it->coeff=rdiv(it->coeff, b,contextptr);
	if (series_flags(contextptr) & 0x1)
	  it->coeff=normal(it->coeff,contextptr);
      }
      // it->coeff=rdiv(it->coeff, b,contextptr);
      return true;
    }
    sparse_poly1::const_iterator it=a.begin(),itend=a.end();
    res.clear();
    res.reserve(itend-it);
    gen tmp;
    for (;it!=itend;++it){
      tmp=rdiv(it->coeff,b,contextptr);
      if (series_flags(contextptr) & 0x1)
	tmp=normal(tmp,contextptr);
      res.push_back(monome(tmp , it->exponent));
    }
    // res.push_back(monome(rdiv(it->coeff,b,contextptr) , it->exponent));
    return true;
  }

  sparse_poly1 spdiv(const sparse_poly1 & a,const gen &b,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!pdiv(a,b,res,contextptr))
      res=sparse_poly1(1,undef);
    return res;
  }
  
  // v is replaced by e*v where e*v has no denominator 
  void lcmdeno(vecteur &v,gen & e,GIAC_CONTEXT){
    if (v.empty()){
      e=1;
      return;
    }
    if (is_undef(v.front())){
      v.erase(v.begin());
      lcmdeno(v,e,contextptr);
      v.insert(v.begin(),undef);
      return;
    }
    vecteur l;
    lvar(v,l);
    //int l_size(l.size());
    vecteur w;
    w.reserve(2*v.size());
    gen common=1,f,num,den;
    // compute lcm of denominators in common
    vecteur::iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it){
      if (is_integer(*it)){
	num=*it; den=1;
      }
      else {
	if (it->type==_FRAC && is_integer(it->_FRACptr->num) && is_integer(it->_FRACptr->den))
	  f=*it;
	else
	  f=e2r(*it,l,contextptr);
	fxnd(f,num,den);
      }
      w.push_back(num);
      w.push_back(den);
      // replace common by lcm of common and den
#if !defined USE_GMP_REPLACEMENTS && !defined BF2GMP_H
      if (common.type==_ZINT && common.ref_count()==1 && is_integer(den)){
	if (den.type==_ZINT)
	  mpz_lcm(*common._ZINTptr,*common._ZINTptr,*den._ZINTptr);
	else
	  mpz_lcm_ui(*common._ZINTptr,*common._ZINTptr,absint(den.val));
      }
      else
	common = lcm(common,den);
#else
      common = lcm(common,den);
#endif
    }
    // compute e and recompute v
    e=r2sym(common,l,contextptr);
    it=v.begin();
    for (int i=0;it!=itend;++it,i=i+2){
      if (it->type==_FRAC && is_integer(it->_FRACptr->num) && is_integer(it->_FRACptr->den) && is_integer(common))
	*it=w[i]*rdiv(common,w[i+1],contextptr);
      else
	*it=r2sym(w[i]*rdiv(common,w[i+1],contextptr),l,contextptr);
    }
  }

  void lcmdeno_converted(vecteur &v,gen & e,GIAC_CONTEXT){
    if (v.empty()){
      e=1;
      return;
    }
    if (is_undef(v.front())){
      v.erase(v.begin());
      lcmdeno_converted(v,e,contextptr);
      v.insert(v.begin(),undef);
      return;
    }
    vecteur w;
    w.reserve(2*v.size());
    gen common=1,f,num,den;
    // compute lcm of denominators in common
    vecteur::iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it){
      fxnd(*it,num,den);
      w.push_back(num);
      w.push_back(den);
      // replace common by lcm of common and den
      common = lcm(common,den);
    }
    // compute e and recompute v
    e=common;
    it=v.begin();
    for (int i=0;it!=itend;++it,i=i+2)
      *it=w[i]*rdiv(common,w[i+1],contextptr);
  }

  void lcmdeno(sparse_poly1 &v,gen & e,GIAC_CONTEXT){
    if (v.empty()){
      e=1;
      return;
    }
    if (is_undef(v.back().coeff)){
      monome last=v.back();
      v.pop_back();
      lcmdeno(v,e,contextptr);
      v.push_back(last);
      return;
    }
    vecteur l;
    lvar(v,l);
    int l_size(int(l.size()));
    vector<gen> w;
    w.reserve(2*l_size);
    gen common=1,num,den,f;
    // compute lcm of denominators in common
    sparse_poly1::iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it){
      f=e2r(it->coeff,l,contextptr);
      fxnd(f,num,den);
      w.push_back(num);
      w.push_back(den);
      common=lcm(common,den);
    }
    // compute e and recompute v
    e=r2sym(common,l,contextptr);
    it=v.begin();
    for (int i=0;it!=itend;++it,i=i+2){
      it->coeff=r2sym(w[i]*rdiv(common,w[i+1],contextptr),l,contextptr);
    }
  }

  void vreverse(iterateur a,iterateur aend){
    iterateur b=aend-1;
    for (;a<b;++a,--b){
      swapgen(*a,*b);
    }
  }
  
  bool pcompose(const vecteur & v,const sparse_poly1 & p, sparse_poly1 & res,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    if (v.empty()){
      res.clear();
      return true;
    }
    if ( p.empty() ){
      res.clear();
      if (!is_zero(v.front())) 
	res.push_back(monome(v.front(),0));
      return true;
    }
    // Conversion of p and v to "internal" polynomial form
    vecteur l; // will contain the list of variables common to v and p
    alg_lvar(v,l);
    alg_lvar(p,l);
    // int l_size(l.size());
    gen plcm=plus_one,vlcm=plus_one,f,num,den;
    // compute lcm of denominators of p in plcm
    sparse_poly1::const_iterator its=p.begin(),itsend=p.end();
    vecteur ptemp;
    ptemp.reserve(2*(itsend-its));
    for (;its!=itsend;++its){
      f=e2r(its->coeff,l,contextptr);
      fxnd(f,num,den);
      ptemp.push_back(num);
      ptemp.push_back(den);
      plcm=lcm(den,plcm);
    }
    // compute pcopy such that pcopy/plcm=p
    its=p.begin();
    sparse_poly1 pcopy;
    pcopy.reserve(itsend-its);
    for (int i=0;its!=itsend;++its,i=i+2){
      num=ptemp[i]*rdiv(plcm,ptemp[i+1],contextptr);
      pcopy.push_back(monome(num,its->exponent));
    }
    // do the same thing on v
    vecteur w;
    // compute lcm of denominators in common
    vecteur::const_iterator it=v.begin(),itend=v.end();
    w.reserve(2*(itend-it));
    for (;it!=itend;++it){
      f=e2r(*it,l,contextptr);
      fxnd(f,num,den);
      w.push_back(num);
      w.push_back(den);
      vlcm=lcm(vlcm,den);
    }
    // compute vcopy
    it=v.begin();
    vecteur vcopy;
    vcopy.reserve(itend-it);
    for (int i=0;it!=itend;++it,i=i+2)
      vcopy.push_back(w[i]*rdiv(vlcm,w[i+1],contextptr));
    vreverse(vcopy.begin(),vcopy.end());
    if (vcopy.empty()  ){
      res=sparse_poly1(1,monome(undef,minus_inf));
      return true;
    }
    // COUT << "compose " << vcopy << " with " << pcopy << '\n';
    it=vcopy.begin(),itend=vcopy.end();
    int n=int(itend-it)-1;
    bool n_truncate=false; 
    gen n_valuation;
    if (is_undef(*it)){
      ++it;
      n_truncate=true;
      n_valuation=gen(n)*p.front().exponent;
      // add undef order term
      gen cur_ordre=porder(p);
      // compare cur_ordre with n*valuation(pcopy)
      if ( (cur_ordre==plus_inf) || (ck_is_strictly_greater(cur_ordre,n_valuation,contextptr)) ){
	// remove greater order terms from pcopy
	for (;!pcopy.empty();){
	  if (ck_is_strictly_greater(pcopy.back().exponent,n_valuation,contextptr))
	    pcopy.pop_back();
	  else
	    break;
	}
	// insert undef
	if (pcopy.empty() || (!is_undef(pcopy.back().coeff)) )
	  pcopy.push_back(monome(undef,n_valuation));
      }
    }
    // Skip 0 coeffs in the reverse list vcopy
    for (;it!=itend;++it){
      if (!is_zero(*it))
	break;
    }
    if (it==itend){
      res=sparse_poly1(1,monome(undef));
      return true;
    }
    res=sparse_poly1(1,monome(*it));
    // COUT << res << '\n';
    ++it;
    if (it==itend && is_undef(pcopy.back().coeff))
      res.push_back(monome(undef,min(n_valuation,pcopy.back().exponent,contextptr)));
    gen plcmn=plus_one;
    for (;it!=itend;++it){
      plcmn=plcmn*plcm;
      // COUT << res << "*" << pcopy << '\n' ;
      if (!pmul(res,pcopy,res,n_truncate,n_valuation,contextptr))
	return false;
      if (n_truncate){ // Remove all terms of order > n_valuation
	sparse_poly1::iterator sit=res.begin(),sitend=res.end();
	for (;sit!=sitend;++sit){
	  if (ck_is_greater(sit->exponent,n_valuation,contextptr)){
	    res.erase(sit,sitend);
	    res.push_back(monome(undef,n_valuation));
	    break;
	  }
	}
      }
      // COUT << res << '\n';
      if (!is_zero(*it))
	padd(res,sparse_poly1(1,monome(*it*plcmn)),res,contextptr);
      // COUT << res << '\n';
    }
    den=vlcm*plcmn;
    // back conversion from res to symbolic form
    sparse_poly1::iterator sit=res.begin(),sitend=res.end();
    for (;sit!=sitend;++sit){
      num=den;
      sit->coeff=r2sym(fraction(sit->coeff,num).normal(),l,contextptr);
    }
    return true;
  }

  bool ppow(const sparse_poly1 & base,int m,int ordre,sparse_poly1 & res,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    if (m==0){
      res.clear();
      return true;
    }
    if (m==1){
      if (&base!=&res)
	res=base;
      return true;
    }
    sparse_poly1 temp;
    if (!pmul(base,base,temp,true,ordre,contextptr))
      return false;
    ptruncate(temp,ordre,contextptr);
    if (m%2){
      if (!ppow(temp,m/2,ordre,temp,contextptr) ||
	  !pmul(temp,base,res,true,ordre,contextptr))
	return false;
    }
    else {
      if (!ppow(temp,m/2,ordre,res,contextptr))
	return false;
    }
    ptruncate(res,ordre,contextptr);
    return true;
  }
  
  // constant power, otherwise use exp(ln)
  bool ppow(const sparse_poly1 & base,const gen & e,int ordre,int direction,sparse_poly1 & res,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    if (base.size()==1){
      gen basepow;
      if (e.type==_FRAC && e._FRACptr->den==2 && is_positive(-base.front().coeff,contextptr))
	basepow=pow(cst_i,e._FRACptr->num,contextptr)*pow(-base.front().coeff,e,contextptr);
      else
	basepow=pow(base.front().coeff,e,contextptr);
      if (&base==&res){
	res.front().coeff=basepow;
	res.front().exponent=res.front().exponent*e;	
      }
      else 
	res=sparse_poly1(1,monome(basepow,base.front().exponent*e));
      return true;
    }
    gen n=porder(base);
    if ((n==plus_inf) && (e.type==_INT_) && (e.val>=0) ){ // exact power
      int m=e.val;
      return ppow(base,m,ordre,res,contextptr);
    }
    if (base.empty()){
      if (ck_is_positive(e,contextptr))
	res.clear();
      else
	return false; // divisionby0err(base);
      return true;
    }
    // series expansion to a constant power
    monome first(base.front());
    sparse_poly1 basecopy(base);
    basecopy.erase(basecopy.begin());
    pshift(basecopy,-first.exponent,basecopy,contextptr);
    if (!pdiv(basecopy,first.coeff,basecopy,contextptr))
      return false;
    if (n==plus_inf && !basecopy.empty()){ // add an O() error term
      monome last(undef,ordre+1);
      basecopy.push_back(last);
    }
    // If first.exponent!=0 and direction==0 we can not find 
    // first.exponent^e consistently around 0
    if (!direction && !is_integer(e) && !is_zero(first.exponent) ){
      *logptr(contextptr) << gettext("Warning: vanishing non integral power expansion") << '\n';
      /*
      res.clear();
      first.coeff=pow(first.coeff,e,contextptr);
      first.exponent = first.exponent*e;
      res.push_back(first);
      first.coeff=undef;
      first.exponent += basecopy[0].exponent;
      res.push_back(first);      
      return;
      */
    }
    // answer=first.coeff^e*x^(first.exponent*e)*(1+base)^e
    // first (1+base)^e -> compose( [1,e,e(e-1)/2,...], base)
    vecteur v(1,plus_one);
    gen produit(e),factorielle(1);
    for (int i=1;i<=ordre;++i){
      v.push_back(rdiv(produit,factorielle,contextptr));
      produit=produit*(e-gen(i));
      factorielle=factorielle*gen(i+1);
    }
    if (e.type!=_INT_ || e.val>ordre)
      v.push_back(undef);
    // COUT << v << '\n';
    if (!pcompose(v,basecopy,res,contextptr))
      return false;
    // COUT << res << '\n';
    // final multiplication ans shift
    pshift(res,first.exponent*e,res,contextptr);
    return pmul(res,normalize_sqrt(pow(first.coeff,e,contextptr),contextptr),res,contextptr);
  }

  sparse_poly1 sppow(const sparse_poly1 & a,const gen &b,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!ppow(a,b,series_default_order(contextptr),0,res,contextptr))
      res=sparse_poly1(1,monome(1,undef));
    return res;
  }

  bool pintegrate(sparse_poly1 & p,const gen & t,GIAC_CONTEXT){
    sparse_poly1::iterator it=p.begin(),itend=p.end();
    identificateur idu("u"); gen u(idu);
    for (;it!=itend;++it){
#if 1
      it->coeff=integrate_gen(it->coeff,t,contextptr);
#else
      gen tmp=subst(it->coeff,t,u,false,contextptr);
      it->coeff=_integrate(makesequence(tmp,u,0,t),contextptr);
#endif
    }
    return true;
  }

  // find q such that pcompose(p,q)=x
  // does not take care of cst coeff of p
  bool prevert(const sparse_poly1 & p_orig,sparse_poly1 & q,GIAC_CONTEXT){
    sparse_poly1 p(p_orig);
    if (p.empty())
      return false; // setsizeerr(gettext("prevert"));
    if (p.front().exponent==0)
      p.erase(p.begin());
    gen ak,k,invk,b1;
    if (p.empty() || is_undef( (ak=p.front().coeff) ) || ck_is_positive(- (k=p.front().exponent) ,contextptr) || k.type!=_INT_ )
      return false; // setsizeerr(gettext("prevert"));
    invk=gen(1)/k;
    b1=pow(ak,invk,contextptr);
    vecteur pv(1);
    sparse_poly1::const_iterator it=p.begin(),itend=p.end();
    int N=0;
    for (;it!=itend;++it){
      gen Ng=it->exponent;
      if (Ng.type!=_INT_)
	return false; // setsizeerr();
      N=Ng.val;
      if (is_undef(it->coeff))
	break;
      for (int n=int(pv.size());n<N;++n){
	pv.push_back(0);
      }
      pv.push_back(it->coeff);
    }
    if (it==itend)
      N++;
    N=k.val*N;
    q.clear();
    q.push_back(monome(gen(1)/b1,invk));
    for (int n=2;n<N;++n){
      sparse_poly1 qtemp(q),res;
      qtemp.push_back(monome(undef,(n+1)*invk));
      if (!pcompose(pv,qtemp,res,contextptr))
	return false;
      // find coeff of order (n+k-1)/k
      sparse_poly1::const_iterator jt=res.begin(),jtend=res.end();
      for (;jt!=jtend;++jt){
	if (jt->exponent==(n+k-1)/k)
	  break;
      }
      if (jt!=jtend)
	q.push_back(monome(-jt->coeff*invk/b1,gen(n)/k));
    }
    q.push_back(monome(undef,gen(N)/k));
    return true;
  }

  static bool in_series__SPOL1(const gen & e,const identificateur & x,const vecteur & lvx, const vecteur & lvx_s,int ordre,int direction,sparse_poly1 & s,GIAC_CONTEXT){
#ifdef TIMEOUT
    control_c();
#endif
    if (ctrl_c || interrupted) {
      interrupted=ctrl_c=true;
      return false;
    }
    s.clear();
    int pos=equalposcomp(lvx,e);
    if (pos){
      gen f=lvx_s[pos-1]; // since vectors begin at position 0
      if (is_zero(f)){
	return true;
      }
      if (f.type==_SPOL1){
	s=*(f._SPOL1ptr);
	return true;
      }
      if (f.type!=_VECT)
	return false; // settypeerr();
      vecteur2sparse_poly1(*f._VECTptr,s);
      return true;
    }
    if ( (e.type!=_SYMB) || !contains(e,x) ){
      gen en=normal(e,contextptr);
      if (!is_zero(en))
	s.push_back(monome(en,0));
      return true;
    }
    // do rational operations
    if (e._SYMBptr->sommet==at_plus){
      if (e._SYMBptr->feuille.type!=_VECT){
	return in_series__SPOL1(e._SYMBptr->feuille,x,lvx,lvx_s,ordre,direction,s,contextptr);
      }
      const_iterateur it=e._SYMBptr->feuille._VECTptr->begin(),itend=e._SYMBptr->feuille._VECTptr->end();
      sparse_poly1 temp;
      for (;it!=itend;++it){
	if (!in_series__SPOL1(*it,x,lvx,lvx_s,ordre,direction,temp,contextptr))
	  return false;
	padd(s,temp,s,contextptr);
      }
      return true;
    }
    if (e._SYMBptr->sommet==at_neg){
      if (e._SYMBptr->feuille.type!=_VECT){
	if (!in_series__SPOL1(e._SYMBptr->feuille,x,lvx,lvx_s,ordre,direction,s,contextptr))
	  return false;
	pneg(s,s,contextptr);
	return true;
      }
      const_iterateur it=e._SYMBptr->feuille._VECTptr->begin(),itend=e._SYMBptr->feuille._VECTptr->end();
      sparse_poly1 temp;
      for (;it!=itend;++it){
	if (!in_series__SPOL1(*it,x,lvx,lvx_s,ordre,direction,temp,contextptr))
	  return false;
	pneg(temp,temp,contextptr);
	padd(s,temp,s,contextptr);
      }
      return true;
    }
    if (e._SYMBptr->sommet==at_prod){
      if (e._SYMBptr->feuille.type!=_VECT){
	if (!in_series__SPOL1(e._SYMBptr->feuille,x,lvx,lvx_s,ordre,direction,s,contextptr))
	  return false;
	return true;
      }
      const_iterateur it=e._SYMBptr->feuille._VECTptr->begin(),itend=e._SYMBptr->feuille._VECTptr->end();
      sparse_poly1 temp;
      s=sparse_poly1(1,monome(1,0));
      for (;it!=itend;++it){
	if (!in_series__SPOL1(*it,x,lvx,lvx_s,ordre,direction,temp,contextptr) ||
	    !pmul(s,temp,s,true,ordre,contextptr))
	  return false;
      }
      return true;
    }
    if (e._SYMBptr->sommet==at_inv){
      if (e._SYMBptr->feuille.type==_VECT)
	return false; // setsizeerr(gettext("series.cc/in_series__SPOL1"));
      sparse_poly1 temp;
      if (!in_series__SPOL1(e._SYMBptr->feuille,x,lvx,lvx_s,ordre,direction,temp,contextptr))
	return false;
      return pdiv(sparse_poly1(1,monome(1,0)),temp,s,ordre,contextptr);
    }
    if (e._SYMBptr->sommet==at_pow){
      // the power is independent on x
      gen base=(*(e._SYMBptr->feuille._VECTptr))[0];
      gen exponent=(*(e._SYMBptr->feuille._VECTptr))[1];
      if (!in_series__SPOL1(base,x,lvx,lvx_s,ordre,direction,s,contextptr))
	return false;
      return ppow(s,exponent,ordre,direction,s,contextptr);
    }
    // unknown rational operator
    invalidserieserr(gettext("unknown rational operator"));
    return false; // 
  }

  static void find_image(const symbolic & temp__SYMB,gen & image_of_lim_point,sparse_poly1 & s,int direction,GIAC_CONTEXT){
    if (!s.empty()){
      if (s.begin()->exponent==0){
	image_of_lim_point=s.begin()->coeff;
	// ?? FIXME ???
	if (temp__SYMB.sommet!=at_abs){
	  s.erase(s.begin()); // remove cst coeff from s
	  for (;!s.empty();){
	    s.front().coeff=normal(s.front().coeff,contextptr);
	    if (!is_zero(s.front().coeff))
	      break;
	    s.erase(s.begin());
	  }
	}
      }
      else {
	if (ck_is_strictly_positive(s.begin()->exponent,contextptr))
	  image_of_lim_point=0;
	else {
	  image_of_lim_point=unsigned_inf;
	  if ( (s.begin()->exponent.type==_INT_) && !(s.begin()->exponent.val%2) ){ // odd negative exponent
	    if (is_strictly_positive(s.begin()->coeff,contextptr))
	      image_of_lim_point=plus_inf;
	    if (is_strictly_positive(-s.begin()->coeff,contextptr))
	      image_of_lim_point=minus_inf;
	  }
	  else { // other negative exponent
	    if (direction){
	      if (is_strictly_positive(s.begin()->coeff,contextptr))
		image_of_lim_point=plus_inf;
	      if (is_strictly_positive(-s.begin()->coeff,contextptr))
		image_of_lim_point=minus_inf;
	      if (direction<0){
		if (s.begin()->exponent.type==_INT_)
		  image_of_lim_point=-image_of_lim_point;
		else
		  image_of_lim_point=unsigned_inf;
	      }
	    }
	  }
	} // end negative leading exponent
      } // end non-zero leading exponent
    } // end non-empty series
  }

  static int find_direction(const sparse_poly1 & s,int direction,GIAC_CONTEXT){
    int image_of_direction=0;
    if (!s.empty() && fastsign(s.front().coeff,contextptr)){
      if (direction)
	image_of_direction=1;
      else {
	if (s.front().exponent.type==_INT_) {
	  if (s.front().exponent.val %2)
	    image_of_direction=direction;
	  else
	    image_of_direction=1;
	}
      }
      image_of_direction=image_of_direction*fastsign(s.front().coeff,contextptr);
      return image_of_direction;
    }
    return 0;
  }

  static int ck_is_greater(const sparse_poly1 & s1, sparse_poly1 & s2,int direction,GIAC_CONTEXT){
    sparse_poly1 s(s2);
    pneg(s,s,contextptr);
    padd(s1,s,s,contextptr);
    int image_of_direction=find_direction(s,direction,contextptr);
    if (!image_of_direction){
      cksignerr(s);
      return -1;
    }
    return image_of_direction==1;
  }

  static gen in_limit(const gen & e,const identificateur & x,const gen & lim_point,int direction,GIAC_CONTEXT);

  static bool mrv_lead_term(const gen & e,const identificateur & x,gen & coeff, gen & mrv_var, gen & exponent,sparse_poly1 & q,int begin_ordre,GIAC_CONTEXT,bool series);

  vecteur integrate(const vecteur & p,const gen & shift_coeff);

  bool series(const sparse_poly1 & s_,const unary_function_ptr & u,int direction,sparse_poly1 & res,GIAC_CONTEXT){
    sparse_poly1 s(s_);
    if (s.empty())
      return false;
    gen shift_coeff=0;
    gen o=porder(s);
    if (o==plus_inf)
      o=series_default_order(contextptr);
    else
      o=_floor(o,contextptr);
    if (o.type!=_INT_)
      return false;
    gen exponent=s.front().exponent;
    gen c=s.front().coeff;
    if (is_undef(c) || is_strictly_positive(-exponent,contextptr))
      return false;
    if (exponent==0)
      s.erase(s.begin());
    else
      c=0;
    gen se=u.ptr()->series_expansion(c,o.val,u,direction,shift_coeff,contextptr);
    if (se.type==_SPOL1){
      return false;
    }
    if (se.type!=_VECT || shift_coeff!=0)
      return false;
    if (!pcompose(*se._VECTptr,s,res,contextptr))
      return false;
    return true;
  }

  sparse_poly1 series(const sparse_poly1 & s,const unary_function_ptr & u,int direction,GIAC_CONTEXT){
    sparse_poly1 res;
    if (!series(s,u,direction,res,contextptr))
      return sparse_poly1(1,monome(undef,undef));
    return res;
  }

  bool series__SPOL1(const gen & e_orig,const identificateur & x,const gen & lim_point,int ordre,int direction,sparse_poly1 & s,GIAC_CONTEXT){
    gen e(e_orig);
    // fast check first
    if (!contains(e,x)){
      s.push_back(monome(e,0));
      return true;
    }
    if (e.type==_IDNT){
      if (!is_zero(lim_point))
	s.push_back(monome(lim_point));
      if (ordre)
	s.push_back(monome(1,1));
      else
	s.push_back(monome(undef,1));
      return true;
    }
    if (e.type!=_SYMB)
      return false; // settypeerr(); // comp not allowed
    // rewrite cos/sin/tan constants using rootof
    vecteur lv1(lvar(e)),lva,lvb;
    gen tmp;
    const_iterateur lv1_it=lv1.begin(),lv1_itend=lv1.end();
    for (;lv1_it!=lv1_itend;++lv1_it){
      if (lv1_it->type==_SYMB){
	unary_function_ptr & u =lv1_it->_SYMBptr->sommet;
	if ( (u==at_cos || u==at_sin || u==at_tan) && has_evalf(*lv1_it,tmp,1,contextptr)){
	  tmp=normal(trig2exp(*lv1_it,contextptr),contextptr);
	  if (lop(tmp,at_exp).empty()){
	    lva.push_back(*lv1_it);
	    lvb.push_back(tmp);
	  }
	}
      }
    }
    if (!lva.empty())
      e=subst(e,lva,lvb,false,contextptr);
    // find list of vars depending on x
    vecteur lvx(rlvarx(e,x));
    iterateur lvx_it=lvx.begin(),lvx_end=lvx.end();
    // find asymptotic series expansion of vars in lvx
    vecteur lvx_s;
    lvx_s.reserve(lvx_end-lvx_it);
    for (;lvx_it!=lvx_end;++lvx_it){
      if (lvx_it->type==_IDNT){
	sparse_poly1 tmp;
	if (!is_zero(lim_point))
	  tmp.push_back(monome(lim_point));
	if (ordre)
	  tmp.push_back(monome(1,1));
	else
	  tmp.push_back(monome(undef,1));
	lvx_s.push_back(tmp);
	continue;
      }
      if (lvx_it->type!=_SYMB) // just in case...
	return false; // settypeerr();
      // test for a^b
      symbolic temp__SYMB=*lvx_it->_SYMBptr;
      if (temp__SYMB.sommet==at_order_size){
	if (!is_zero(lim_point))
	  return false;
	sparse_poly1 tmp;
	tmp.push_back(monome(undef,0));
	lvx_s.push_back(tmp);
	continue;
      }
      if ( (temp__SYMB.sommet==at_pow) && (!contains((*temp__SYMB.feuille._VECTptr)[1],x) ) ){
	if (!in_series__SPOL1((*temp__SYMB.feuille._VECTptr)[0],x,lvx,lvx_s,ordre,direction,s,contextptr)||
	    !ppow(s,(*temp__SYMB.feuille._VECTptr)[1],ordre,direction,s,contextptr))
	  return false;
	lvx_s.push_back(s);
	continue;
      }
      if (temp__SYMB.sommet==at_pow)
	temp__SYMB=symbolic(at_exp,(*temp__SYMB.feuille._VECTptr)[1]*ln((*temp__SYMB.feuille._VECTptr)[0],contextptr));
      // Check here for logarithms if image_of_lim_point=+/-inf
      // In such case we must factor x^s.begin().exponent and add
      // it to the exponent 0 term of the series expansion of the ln
      if (temp__SYMB.sommet==at_ln){
	// recursive call, works since lvx is sorted by increasing size
	if (!in_series__SPOL1(temp__SYMB.feuille,x,lvx,lvx_s,ordre,direction,s,contextptr))
	  return false;
	gen exponent=s.front().exponent;
	gen c=s.front().coeff;
	s.erase(s.begin());
	bool adjust=false;
	if (is_positive(-c,contextptr)){ 
	  // im(ln(c)) is i*pi, but im(ln(c*x^exposant+...)) might be -i*pi
	  // check sign of imaginary part of expansion
	  sparse_poly1::iterator it=s.begin(),itend=s.end();
	  for (;it!=itend;++it){
	    if (is_undef(it->coeff))
	      break;
	    gen tmp=im(it->coeff,contextptr);
	    if (!is_zero(tmp)){
	      if (is_positive(-tmp,contextptr))
		adjust=true;
	      break;
	    }
	  }
	}
	if (!s.empty()){
	  pshift(s,-exponent,s,contextptr);
	  if (!pdiv(s,c,s,contextptr))
	    return false;
	  vecteur expansion(1,zero);
	  expansion.reserve(ordre);
	  for (int i=1;i<=ordre;i++){
	    if (i%2)
	      expansion.push_back(inv(gen(i),contextptr));
	    else
	      expansion.push_back(-inv(gen(i),contextptr));
	  }
	  expansion.push_back(undef);
	  if (!pcompose(expansion,s,s,contextptr))
	    return false;
	}
	if (!is_zero(exponent) || !is_one(c)){
	  c=ln(c,contextptr);
	  if (adjust)
	    c-=cst_two_pi*cst_i;
	  s.insert(s.begin(),monome(exponent*ln(x,contextptr)+c));
	}
	lvx_s.push_back(s);
	continue;
	COUT << s.back() << '\n';
      }
      // test for the special case var=f(x)
      if ((temp__SYMB.feuille.type==_IDNT) && (temp__SYMB.sommet!=at_abs)){ 
	// Since e contains x feuille of e must be x
	if (!temp__SYMB.sommet.ptr()->series_expansion){
	  *logptr(contextptr) << gettext("no taylor method for ") << temp__SYMB.sommet.ptr()->print(contextptr) << '\n';
	  return false; 
	}
	gen shift_coeff;
	gen res=temp__SYMB.sommet.ptr()->series_expansion(lim_point,ordre,temp__SYMB.sommet,direction,shift_coeff,contextptr); 
	if (res.type==_SPOL1)
	  lvx_s.push_back(*res._SPOL1ptr);
	else {// res must be a vecteur
	  if (res.type!=_VECT)
	    return false; // settypeerr(gettext("series.cc 1066"));
	  sparse_poly1 temp(vecteur2sparse_poly1(*res._VECTptr));
	  if (!is_zero(shift_coeff)){
	    pshift(temp,shift_coeff,temp,contextptr);
	    if (is_positive(shift_coeff,contextptr))
	      temp.insert(temp.begin(),monome(temp__SYMB.sommet(lim_point,contextptr))); 
	  }
	  lvx_s.push_back(temp);
	}
	continue;
      }
      // Taylor not successful: find series_expansion of arg, 
      // compose with sommet expansion
      // fixme: multiargs disabled, should return a vecteur of series_exp
      if (temp__SYMB.sommet != at_of && temp__SYMB.feuille.type==_VECT){
	int nargs=int(temp__SYMB.feuille._VECTptr->size());
	if (nargs==4 && temp__SYMB.sommet==at_sum){
	  vecteur & tempfv=*temp__SYMB.feuille._VECTptr;
	  gen k=tempfv[1],lo=tempfv[2],up=tempfv[3];
	  if (contains(k,x)){
	    invalidserieserr(gettext("Summation variable must be != from series expansion variable"));
	    return false;
	  }
	  if (k.type!=_IDNT || derive(lo,x,contextptr)!=0 || derive(up,x,contextptr)!=0)
	    return false; // setsizeerr();
	  sparse_poly1 p;
	  if (!in_series__SPOL1(tempfv[0],x,lvx,lvx_s,ordre,direction,p,contextptr))
	    return false;
	  // sum lvx_s
	  sparse_poly1::iterator it=p.begin(),itend=p.end();
	  for (;it!=itend;++it){
	    if (is_undef(it->coeff))
	      break;
	    it->coeff=_sum(makesequence(it->coeff,k,lo,up),contextptr);
	  }
	  lvx_s.push_back(p);
	  continue;
	  //invalidserieserr(gettext("taylor of sum not implemented"));
	  //return false;
	}
	if (temp__SYMB.sommet==at_euler_mac_laurin){
	  if (nargs!=5){
	    invalidserieserr(gettext("Integral must be definite"));
	    return false;
	  }
	  vecteur & tempfv=*temp__SYMB.feuille._VECTptr;
	  gen k=tempfv[2];
	  if (contains(k,x)){
	    invalidserieserr(gettext("Summation variable must be != from series expansion variable"));
	    return false;
	  }
	  if (k.type!=_IDNT)
	    return false; // setsizeerr();
	  // find upper and lower bound limit
	  gen lower=tempfv[3],upper=tempfv[4],f=tempfv[0],F=tempfv[1];
	  gen fdiff=derive(f,k,contextptr);
	  // first add integral part
	  gen eff = preval(F,k,lower,upper,contextptr);
	  eff += (limit(f,*k._IDNTptr,upper,-1,contextptr)+limit(f,*k._IDNTptr,lower,1,contextptr))/2;
	  // then Bernoulli part
	  if (is_undef(fdiff))
	    return false;
	  for (int i=1;i<ordre;i++){
	    gen add= limit(fdiff,*k._IDNTptr,upper,-1,contextptr)-limit(fdiff,*k._IDNTptr,lower,1,contextptr);
	    gen chk=limit(add/pow(x,2*i-2),x,0,1,contextptr);
	    if (!is_zero(chk)){
	      ordre=2*i-3;
	      break;
	    }
	    add=add*bernoulli(2*i)/factorial(2*i);
	    eff += add; // fdiff flimdiff 2 fois
	    fdiff=derive(fdiff,k,contextptr);
	    fdiff=ratnormal(derive(fdiff,k,contextptr),contextptr);
	    if (is_undef(fdiff))
	      return false;
	  }
	  // find order of add
	  // must do a recursive call since eff may contain new functions
	  // FIXME: "Parameters" might depend on x, search for effg 
	  // example series(sum(k/n*ln(k/n), k = 1 .. n ),n=inf);
	  gen Coeff,Mrv_var,Exponent; 
	  eff =subst(eff,x,inv(x,contextptr),true,contextptr);
	  if (!mrv_lead_term(eff,x,Coeff,Mrv_var,Exponent,s,ordre,contextptr,true))
	    return false;
	  ptruncate(s,ordre,contextptr); // add remainder term
	  s=subst(s,x,inv(x,contextptr),true,contextptr);
	  lvx_s.push_back(s);
	  continue;
	  // never reached setsizeerr();
	}
	if (temp__SYMB.sommet==at_igamma_exp){
	  if (nargs!=2){
	    invalidserieserr(gettext("igamma: bad arg number"));
	    return false;
	  }
	  vecteur & tempfv=*temp__SYMB.feuille._VECTptr;
	  gen a=tempfv[0];
	  sparse_poly1 p;
	  if (!in_series__SPOL1(tempfv[1],x,lvx,lvx_s,ordre,direction,p,contextptr))
	    return false;
	  gen image_of_lim_point;
	  find_image(temp__SYMB,image_of_lim_point,p,direction,contextptr);
	  if (!is_inf(image_of_lim_point))
	    return false;
	  // invert series expansion
	  sparse_poly1 stmp;
	  if (!pdiv(sparse_poly1(1,monome(1,0)),p,stmp,ordre,contextptr))
	    return false;
	  p=stmp;
	  // igamma(a,x)=Gamma(a)-int_x^inf exp(-t)*t^(a-1) dt
	  // =Gamma(a)-exp(-x)*x^(a-1)-(a-1)*int_x^inf exp(-t)*t^(a-2) dt
	  // ...
	  // igamma_replace(a,x)=Gamma(a)-exp(-x)*igamma_exp(a,x)
	  // therefore expansion of igamma_exp(a,x)=x^(a-1)[1+(a-1)/x+(a-1)*(a-2)/x^2...]
	  vecteur v(ordre+1); gen facti(1);
	  for (int i=0;i<=ordre;++i){
	    v[i]=facti;
	    facti=(a-i-1)*facti;
	  }
	  v.push_back(undef);
	  if (!pcompose(v,p,s,contextptr))
	    return false;
	  pshift(s,1-a,s,contextptr);
	  lvx_s.push_back(s);
	  continue;
	}
	if (temp__SYMB.sommet==at_lower_incomplete_gamma){
	  if (nargs!=2){
	    invalidserieserr(gettext("igamma: bad arg number"));
	    return false;
	  }
	  // series expansion of derivative
	  vecteur & tempfv=*temp__SYMB.feuille._VECTptr;
	  gen a=tempfv[0];
	  sparse_poly1 p;
	  if (!in_series__SPOL1(tempfv[1],x,lvx,lvx_s,ordre,direction,p,contextptr))
	    return false;
	  gen image_of_lim_point;
	  find_image(temp__SYMB,image_of_lim_point,p,direction,contextptr);
	  if (is_inf(image_of_lim_point))
	    return false; // inf is prevented by limit_symbolic_preprocessing
	  if (is_zero(image_of_lim_point)){
	    int image_of_direction=0;
	    image_of_direction = find_direction(p,direction,contextptr);
	    if (image_of_direction==0)
	      return false;
	    vecteur v(ordre+1); gen facti(1);
	    for (int i=0;i<=ordre;++i){
	      v[i]=inv(facti*(a+i),contextptr);
	      facti=-(i+1)*facti;
	    }
	    if (!pcompose(v,p,s,contextptr))
	      return false;
	    if (image_of_direction==-1)
	      pneg(p,p,contextptr);
	    if (!ppow(p,a,ordre,image_of_direction,p,contextptr))
	      return false;
	    if (image_of_direction==-1)
	      pneg(p,p,contextptr);
	    if (!pmul(p,s,s,true,ordre,contextptr))
	      return false;
	  }
	  else {
	    vecteur v;
	    gen der;
	    if (is_positive(image_of_lim_point,contextptr))
	      der=pow(x,a-1,contextptr)*exp(-x,contextptr);
	    else
	      der=-pow(-x,a-1,contextptr)*exp(-x,contextptr);	      
	    if (!taylor(der,x,image_of_lim_point,ordre,v,contextptr))
	      return false;
	    v=integrate(v,1);
	    gen intcst=_lower_incomplete_gamma(makesequence(a,lim_point),contextptr);
	    v.insert(v.begin(),intcst);
	    if (!pcompose(v,p,s,contextptr))
	      return false;
	  }
	  lvx_s.push_back(s);
	  continue;
	}
	if (temp__SYMB.sommet==at_integrate){
	  if (nargs!=4){
	    invalidserieserr(gettext("Integral must be definite"));
	    return false;
	  }
	  vecteur & tempfv=*temp__SYMB.feuille._VECTptr;
	  gen t=tempfv[1];
	  if (contains(t,x)){
	    invalidserieserr(gettext("Integration variable must be != from series expansion variable"));
	    return false;
	  }
#if 1
	  if (!contains(tempfv[0],x)){
	    vecteur v;
	    // int(f(t),t,m(x),M(x))=F(M(x))-F(m(x))
	    // hence derivative is M'(x)*f(M(x))-m'(x)*f(m(x))
	    gen g=derive(tempfv[3],x,contextptr)*subst(tempfv[0],tempfv[1],tempfv[3],false,contextptr)-derive(tempfv[2],x,contextptr)*subst(tempfv[0],tempfv[1],tempfv[2],false,contextptr);
	    g=exp2pow(g,contextptr);
	    s.clear();
	    if (!series__SPOL1(g,x,lim_point,ordre,direction,s,contextptr)){
	      return false;
	    }
	    gen s0=eval(subst(temp__SYMB,x,lim_point,false,contextptr),1,contextptr);
	    sparse_poly1 p; 
	    if (!is_zero(s0))
	      p.push_back(monome(s0,0));
	    sparse_poly1::const_iterator it=s.begin(),itend=s.end();
	    for (;it!=itend;++it){
	      gen i=it->exponent;
	      if (i==-1) // should be i<=-1?
		return false;
	      p.push_back(monome(it->coeff/(i+1),i+1));
	    }
	    lvx_s.push_back(p);
	    continue;
	  }
#else // old code
	  if (!contains(tempfv[0],x)){
	    vecteur v;
	    if (!taylor(temp__SYMB,x,lim_point,ordre,v,contextptr))
	      return false;
	    s.clear();
	    for (int i=0;i<v.size();++i){
	      s.push_back(monome(v[i],i));
	    }
	    lvx_s.push_back(s);
	    continue;
	  }
#endif
	  if (!in_series__SPOL1(tempfv[0],x,lvx,lvx_s,ordre,direction,s,contextptr))
	    return false;
	  // FIXME if tempfv[3] and tempfv[2] tends to the same limit l
	  // we may expand tempfv[0] w.r.t. t at l before integration
	  
	  // integrate s term by term wrt t
	  if (!pintegrate(s,t,contextptr))
	    return false;
	  gen remains,primit=sparse_poly12gen(s,x,remains,false);
	  // then compose primit at bounds and subtract
	  primit=subst(primit,t,tempfv[3],false,contextptr)-subst(primit,t,tempfv[2],false,contextptr);
	  if (!series__SPOL1(primit,x,lim_point,ordre,direction,s,contextptr))
	    return false;
	  // add remains to s: 
	  // int(remains,t,tempfv[2],tempfv[3]) = 
	  // (tempfv[3]-tempfv[2])*remains(theta) with theta in interval
	  remains=remains*(tempfv[3]-tempfv[2]);
	  sparse_poly1 p; 
	  if (!series__SPOL1(remains,x,lim_point,ordre,direction,p,contextptr))
	    return false;
	  if (p.empty()){
	    invalidserieserr(gettext("Can not expand remainder of integrand"));
	    return false;
	  }
	  p=sparse_poly1(p.begin(),p.begin()+1);
	  p.front().coeff=undef;
	  s=spadd(p,s,contextptr);
	  lvx_s.push_back(s);
	  continue;
	}
	const_iterateur fit=temp__SYMB.feuille._VECTptr->begin(),fitend=temp__SYMB.feuille._VECTptr->end();
	if (temp__SYMB.sommet==at_Psi || temp__SYMB.sommet==at_Eta || temp__SYMB.sommet==at_Zeta){
	  if (!in_series__SPOL1(*fit,x,lvx,lvx_s,ordre,direction,s,contextptr))
	    return false;
	}
	else {
	  bool ok=false;
	  dbgprint_vector <sparse_poly1> vs;
	  vs.reserve(fitend-fit);
	  for (;fit!=fitend;++fit){
	    if (!in_series__SPOL1(*fit,x,lvx,lvx_s,ordre,direction,s,contextptr))
	      return false;
	    vs.push_back(s);
	  }
	  if (temp__SYMB.sommet==at_max){
	    ok=true;
	    int testck=ck_is_greater(vs.front(),vs.back(),direction,contextptr);
	    if (testck==-1)
	      return false;
	    if (testck)
	      s=vs.front();
	    else
	      s=vs.back();
	  }
	  if (temp__SYMB.sommet==at_min){
	    ok=true;
	    int testck=ck_is_greater(vs.front(),vs.back(),direction,contextptr);
	    if (testck==-1)
	      return false;
	    if (testck)
	      s=vs.back();
	    else
	      s=vs.front();
	  }
	  if (!ok){
	    invalidserieserr(gettext(" multiargs not implemented"));
	    return false;
	  }
	  lvx_s.push_back(s);
	  continue;
	}
      }
      else { // 1-arg function
	if (temp__SYMB.sommet==at_of){
	  gen & tf=temp__SYMB.feuille;
	  if (tf.type==_VECT && tf._VECTptr->size()==2){
	    gen tff=tf._VECTptr->front();
	    gen tfx=tf._VECTptr->back();
	    if (!in_series__SPOL1(tfx,x,lvx,lvx_s,ordre,direction,s,contextptr)) return false; // s<-arg
	  }
	}
	else {
	  if (!in_series__SPOL1(temp__SYMB.feuille,x,lvx,lvx_s,ordre,direction,s,contextptr)) return false; // s<-arg
	}
      } // end 1-arg function
      gen image_of_lim_point;
      find_image(temp__SYMB,image_of_lim_point,s,direction,contextptr); 
      int image_of_direction=0;
      image_of_direction = find_direction(s,direction,contextptr);
      // Symbolic series expansion f(x), f is assumed to be analytic
      if (temp__SYMB.sommet==at_of){
	gen & tf=temp__SYMB.feuille;
	if (tf.type==_VECT && tf._VECTptr->size()==2){
	  gen tff=tf._VECTptr->front();
	  gen tfx=tf._VECTptr->back();
	  // Symbolic Taylor expansion of tff
	  vecteur expansion(1,symbolic(at_of,makesequence(tff,image_of_lim_point))); 
	  expansion.reserve(ordre);
	  for (int i=1;i<=ordre;i++){
	    gen fn;
	    if (i==1)
	      fn=symbolic(at_of,makesequence(symbolic(at_function_diff,tff),image_of_lim_point));
	    else
	      fn=symbolic(at_of,makesequence(symbolic(at_of,makesequence(symbolic(at_composepow,makesequence(at_function_diff,i)),tff)),image_of_lim_point));
	    expansion.push_back(fn/factorial(i));
	  }
	  expansion.push_back(undef);
	  if (!pcompose(expansion,s,s,contextptr))
	    return false;
	  lvx_s.push_back(s);
	  continue;
	}
      }
      if (temp__SYMB.sommet==at_abs){
	if (!image_of_direction){
	  *logptr(contextptr) << gettext("Sign error ") << s << '\n';
	  return false; // cksignerr(s);
	}
	if (image_of_direction==-1)
	  pneg(s,s,contextptr);
	lvx_s.push_back(s);
	continue;
      }
      if (is_inf(image_of_lim_point)){ 
	// check for sin/cos
	if (temp__SYMB.sommet==at_cos || temp__SYMB.sommet==at_sin){
	  // split the series expansion in two parts, one tending -> 0
	  sparse_poly1::iterator it=s.begin(),itend=s.end();
	  for (;it!=itend;++it){
	    if (ck_is_strictly_greater(it->exponent,zero,contextptr))
	      break;
	  }
	  sparse_poly1 s0(it,s.end()),s1(s.begin(),it);
	  // expansion is done at s0
	  image_of_lim_point=s1;
	  s=s0;
	}
	else {
	  // the function is assumed to have an expansion at infinity
	  // invert series expansion
	  sparse_poly1 stmp;
	  if (!pdiv(sparse_poly1(1,monome(1,0)),s,stmp,ordre,contextptr))
	    return false;
	  s=stmp;
	}
      }
      gen shift_coeff;
      if (!temp__SYMB.sommet.ptr()->series_expansion){
	*logptr(contextptr) << string(gettext("Not expandable "))+temp__SYMB.sommet.ptr()->s << '\n';
	return false;
      }
      int addorder=0;
      gen expansion;
      if ( (temp__SYMB.sommet==at_Psi ||temp__SYMB.sommet==at_Eta ||temp__SYMB.sommet==at_Zeta) && temp__SYMB.feuille.type==_VECT){
	if (temp__SYMB.feuille._VECTptr->size()!=2 )
	  return false; // setsizeerr();
	addorder=temp__SYMB.feuille._VECTptr->back().val;
	if (addorder<=0){
	  *logptr(contextptr) << gettext("Psi/Zeta/Eta: bad second argument") << '\n';
	  return false;
	}
	if (temp__SYMB.sommet==at_Psi)
	  expansion=at_Psi_minus_ln->ptr()->series_expansion(image_of_lim_point,ordre+addorder,temp__SYMB.sommet,image_of_direction,shift_coeff,contextptr); 
      }
      if (expansion==0)
	expansion=temp__SYMB.sommet.ptr()->series_expansion(image_of_lim_point,ordre+addorder,temp__SYMB.sommet,image_of_direction,shift_coeff,contextptr); 
      if (expansion.type==_VECT){
	if (addorder){
	  // derive expansion
	  vecteur & v =*expansion._VECTptr;
	  for (int i=0;i<addorder;++i){
	    int vs=int(v.size());
	    if (is_zero(shift_coeff)){
	      vecteur w(vs-1);
	      for (int j=1;j<vs;++j){
		w[j-1]=j*v[j];
	      }
	      v=w;
	    }
	    else {
	      for (int j=0;j<vs;++j){
		v[j]=-v[j]*(j+shift_coeff);
	      }
	      shift_coeff += 1;
	    }
	  }
	  // final correction for Psi
	  if (temp__SYMB.sommet==at_Psi){
	    v.insert(v.begin(),gen((addorder%2)?1:-1)*factorial(addorder-1));
	    shift_coeff -= 1;
	  }
	}
	if (is_zero(shift_coeff)){
	  if (!pcompose(*expansion._VECTptr,s,s,contextptr))
	    return false;
	}
	else {
	  sparse_poly1 temp;
	  if (!ppow(s,shift_coeff,ordre,direction,temp,contextptr))
	    return false;
	  if (!pcompose(*expansion._VECTptr,s,s,contextptr) ||
	      !pmul(s,temp,s,true,ordre,contextptr))
	    return false;
	  if (is_positive(shift_coeff,contextptr)){
	    gen imtemp;
	    if (addorder>0)
	      imtemp=temp__SYMB.sommet(makesequence(image_of_lim_point,addorder),contextptr);
	    else
	      imtemp=temp__SYMB.sommet(image_of_lim_point,contextptr);
	    if (!is_zero(imtemp))
	      s.insert(s.begin(),monome(imtemp));
	  }
	}
      }
      else {
	s.clear();
	s.push_back(monome(undef,minus_inf));
	return true;
      }
      lvx_s.push_back(s);
      // fixme: add support for sparse_poly1 composition
    } // end loop lvx_it!=lvx_end
    return in_series__SPOL1(e,x,lvx,lvx_s,ordre,direction,s,contextptr);
  }

  sparse_poly1 series__SPOL1(const gen & e,const identificateur & x,const gen & lim_point,int ordre,int direction,GIAC_CONTEXT){
    sparse_poly1 s;
    if (!series__SPOL1(e,x,lim_point,ordre,direction,s,contextptr))
      s=sparse_poly1(1,monome(1,undef));
    return s;
  }

  static sparse_poly1 ck_series__SPOL1(const gen & e,const identificateur & x,const gen & lim_point,int ordre,int direction,GIAC_CONTEXT){
    sparse_poly1 s;
    if (!series__SPOL1(e,x,lim_point,ordre,direction,s,contextptr)){
      s=sparse_poly1(1,monome(1,undef));
      return s;
    }
    // if s is not at order ordre, ask again with a modified ordre
    gen true_order=porder(s);
    if (true_order.type==_INT_ && true_order.val<=ordre){
      if (series__SPOL1(e,x,lim_point,ordre+1+ordre-true_order.val,direction,s,contextptr)){
	if (!s.empty())
	  ptruncate(s,ordre-s.front().exponent,contextptr);
      }
      else
	s=sparse_poly1(1,monome(1,undef));
    }
    // truncate s 
    for (unsigned i=0;i<s.size();++i){
      if (is_strictly_greater(s[i].exponent,ordre,contextptr)){
	s[i].coeff=undef;
	if (i<s.size()-1)
	  s.erase(s.begin()+i+1,s.end());
      }
    }
    return s;
  }

#ifdef DEBUG_SUPPORT
  static void inutile(sparse_poly1 & s){
    s.dbgprint();
  }
#endif

  // ***********************
  // LIMITS
  // ***********************

  bool contains(const vecteur & v,const gen & elem){
    vecteur::const_iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it)
      if (contains(*it,elem))
	return true;
    return false;
  }

  bool contains(const gen & e,const gen & elem){
    if (e==elem)
      return true;
    if (e.type==_VECT){
      return contains(*e._VECTptr,elem);
    }
    if (e.type==_SYMB){
      return contains(e._SYMBptr->feuille,elem);
    }
    if (e.type==_FRAC)
      return contains(e._FRACptr->num,elem) || contains(e._FRACptr->den,elem);
#if defined HAVE_LIBMPFI && !defined NO_RTTI
    if (e.type==_REAL){
      if (real_interval * ptr=dynamic_cast<real_interval *>(e._REALptr)){
	mpfr_t tmp; mpfr_init2(tmp,mpfi_get_prec(ptr->infsup));
	mpfi_get_left(tmp,ptr->infsup);
	gen einf=real_object(tmp);
	mpfi_get_right(tmp,ptr->infsup);
	gen esup=real_object(tmp);
	gen eleminf,elemsup;
	if (elem.type!=_REAL)
	  ptr=0;
	else
	  ptr=dynamic_cast<real_interval *>(elem._REALptr);
	if (ptr){
	  mpfi_get_left(tmp,ptr->infsup);
	  eleminf=real_object(tmp);
	  mpfi_get_right(tmp,ptr->infsup);
	  elemsup=real_object(tmp);
	}
	else {
	  eleminf=elem; elemsup=elem;
	}	  
	mpfr_clear(tmp);
	return is_greater(esup,elemsup,context0) && is_greater(eleminf,einf,context0);
      }
    }
#endif
    return false;
  }
  
  vecteur lvarx(const gen &e,const gen & x,bool test){
    vecteur v(lvar(e));
    vecteur res;
    vecteur::const_iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it){
      // remove at_of if the function of of is x
      vecteur l=lop(*it,at_of);
      int i;
      for (i=0;i<l.size();++i){
	if (contains(l[i]._SYMBptr->feuille[0],x))
	  break;
      }
      if (i<l.size())
	continue;
      // remove ^ if exponent does not depend on x
      if ( (it->type==_SYMB) 
	   && ( (it->_SYMBptr->sommet==at_pow && !contains((*(it->_SYMBptr->feuille._VECTptr))[1],x)) ||
		(it->_SYMBptr->sommet==at_NTHROOT && !contains((*(it->_SYMBptr->feuille._VECTptr))[0],x)) )
	   ){
	vecteur tmp(lvarx((*(it->_SYMBptr->feuille._VECTptr))[(it->_SYMBptr->sommet==at_pow)?0:1],x));
	const_iterateur it=tmp.begin(),itend=tmp.end();
	for (;it!=itend;++it){
	  if (!equalposcomp(res,*it))
	    res.push_back(*it);
	}
      }
      else {
	if ( (!test || res.empty() || *it!=x ) && contains(*it,x) && !equalposcomp(res,*it))
	  res.push_back(*it);
      }
    }
    return res;
  }

  void rlvarx(const gen &e,const gen & xgen,vecteur & res){
    const vecteur & v=lvar(e);
    vecteur::const_iterator it=v.begin(),itend=v.end();
    for (;it!=itend;++it){
      if (!contains(*it,xgen) || equalposcomp(res,*it))
	continue;
      // recursive call
      res.push_back(*it);
      if (it->is_symb_of_sommet(at_derive) && it->_SYMBptr->feuille.type==_VECT && it->_SYMBptr->feuille._VECTptr->size()==3 && it->_SYMBptr->feuille._VECTptr->back().type==_INT_){
	int n=it->_SYMBptr->feuille._VECTptr->back().val;
	for (--n;n>1;--n){
	  res.push_back(symbolic(at_derive,makesequence(it->_SYMBptr->feuille._VECTptr->front(),(*it->_SYMBptr->feuille._VECTptr)[1],n)));
	}
	res.push_back(symbolic(at_derive,makesequence(it->_SYMBptr->feuille._VECTptr->front(),(*it->_SYMBptr->feuille._VECTptr)[1])));
      }
      if (it->type==_SYMB) {
	rlvarx(it->_SYMBptr->feuille,xgen,res);
	if ( (it->_SYMBptr->sommet==at_pow) 
	     && contains((*(it->_SYMBptr->feuille._VECTptr))[1],xgen) )
	  rlvarx(symbolic(at_ln,(*(it->_SYMBptr->feuille._VECTptr))[0]),xgen,res);
      }
    }
  }

  void tri_rlvarx(vecteur & v){
    int s=v.size();
    for (;;){
      bool ok=true;
      for (int i=0;i<s-1;++i){
	if (symb_size_less(v[i+1],v[i])){
	  ok=false;
	  swapgen(v[i],v[i+1]);
	}
      }
      if (ok)
	return;
    }
  }

  vecteur rlvarx(const gen &e,const gen & x){
    vecteur res;
    rlvarx(e,x,res);
#ifdef FXCG
    tri_rlvarx(res);
#else
    gen_sort_f(res.begin(),res.end(),symb_size_less);
#endif
    return res;
  }

  static void upscale(gen & e,const identificateur & x,GIAC_CONTEXT){
    vecteur a_remplacer,remplacer_par;
    a_remplacer.push_back(ln(x,contextptr));
    remplacer_par.push_back(x);
    a_remplacer.push_back(x);
    remplacer_par.push_back(exp(x,contextptr));
    e=subst(e,a_remplacer,remplacer_par,false,contextptr);
  }

  static void downscale(gen & e,const identificateur & x,GIAC_CONTEXT){
    vecteur a_remplacer,remplacer_par;
    a_remplacer.push_back(exp(x,contextptr));
    remplacer_par.push_back(x);
    a_remplacer.push_back(x);
    remplacer_par.push_back(ln(x,contextptr));
    e=subst(e,a_remplacer,remplacer_par,false,contextptr);
  }
  
  /*
  gen pow2exp(const gen & e,const identificateur & x){
    if (e.type==_VECT){
      const_iterateur it=e._VECTptr->begin(),itend=e._VECTptr->end();
      vecteur v;
      v.reserve(itend-it);
      for (;it!=itend;++it)
	v.push_back(pow2exp(*it,x));
      return v;
    }
    if (e.type!=_SYMB)
      return e;
    if ( e._SYMBptr->sommet==at_pow && contains((*(e._SYMBptr->feuille._VECTptr))[1],x))
      return exp(pow2exp((*(e._SYMBptr->feuille._VECTptr))[1],x)*pow2exp(ln((*(e._SYMBptr->feuille._VECTptr))[0]),x));
    if ( e._SYMBptr->sommet==at_tan && contains (e._SYMBptr->feuille,x))
      return symbolic(at_sin,pow2exp(e._SYMBptr->feuille,x))/symbolic(at_cos,pow2exp(e._SYMBptr->feuille,x));
    return e._SYMBptr->sommet(pow2exp(e._SYMBptr->feuille,x),contextptr); 
  }
  */

  static int check_bounded(const gen & g,GIAC_CONTEXT){
    vecteur v=loptab(g,sincostan_tab);
    int vs=int(v.size());
    vecteur w;
    for (int i=0;i<vs;++i){
      if (v[i].type==_SYMB && v[i]._SYMBptr->feuille.type==_SPOL1)
	w.push_back(v[i]);
    }
    if (w.empty())
      return 0;
    for (unsigned i=0;i<w.size();++i){
      vecteur lv=lvarxwithinv(g,w[i],contextptr);
      if (lv.empty())
	continue;
      if (lv.size()>=2 || lv[0]!=w[i]){
	//gensizeerr("Limit probably undefined, algorithm unable to handle "+g.print(contextptr));
	return -1;
      }
    }
    return 1;
  }

  // specialization 
  static int equalposcomp(const std::vector<const unary_function_ptr *> & v,unary_function_ptr * w){
    int n=1;
    for (std::vector<const unary_function_ptr *>::const_iterator it=v.begin();it!=v.end();++it){
      if (*(*it)==*w)
	return n;
      else
	n++;
    }
    return 0;
  }

  static gen ln_expand0_(const gen & e,GIAC_CONTEXT){
    if (e.type!=_SYMB)
      return ln(e,contextptr);
    if (e._SYMBptr->sommet==at_exp)
      return e._SYMBptr->feuille;
    if (e._SYMBptr->sommet==at_prod)
      return symbolic(at_plus,apply(e._SYMBptr->feuille,ln_expand0_,contextptr));
    if (e._SYMBptr->sommet==at_inv)
      return -ln_expand0_(e._SYMBptr->feuille,contextptr);
    if (e._SYMBptr->sommet==at_pow){
      gen & tmp=e._SYMBptr->feuille;
      if (tmp.type==_VECT && tmp._VECTptr->size()==2)
	return tmp._VECTptr->back()*ln_expand0_(tmp._VECTptr->front(),contextptr);
    }
    return ln(e,contextptr);
  }

  static gen ln_expand_(const gen & e0,GIAC_CONTEXT){
    gen e(factor(e0,false,contextptr));
    return ln_expand0_(e,contextptr);
  }

  static gen exp_series_(const gen & e0,GIAC_CONTEXT){
    vecteur v=lop(e0,at_ln);
    if (v.size()==1 && is_integer(v.front()._SYMBptr->feuille)){
      gen a,b;
      if (is_linear_wrt(e0,v.front(),a,b,contextptr))
	return exp(b,contextptr)*pow(v.front()._SYMBptr->feuille,a,contextptr);
    }
    return exp(e0,contextptr);
  }

  static gen remove_lnexp(const gen & e,GIAC_CONTEXT){
    vector<const unary_function_ptr *> v(1,at_ln);
    v.push_back(at_exp);
    vector< gen_op_context > w(1,&ln_expand_);
    w.push_back(&exp_series_);
    return subst(e,v,w,false,contextptr);
  }

  gen limit_symbolic_preprocess(const gen & e0,const identificateur & x,const gen & lim_point,int direction,GIAC_CONTEXT){
    // FIXME: add support for int and sum
    gen e=factorial2gamma(e0,contextptr);
    int trigs=loptab(e,sincostan_tab).size();
    if (trigs>=2){
      gen tmp=trigcos(e,contextptr);
      int trigtmps=loptab(tmp,sincostan_tab).size();
      if (trigtmps<trigs){
	e=ratnormal(tmp);
	trigs=loptab(e,sincostan_tab).size();
      }
      tmp=trigsin(e,contextptr);
      trigtmps=loptab(tmp,sincostan_tab).size();
      if (trigtmps<trigs){
	e=ratnormal(tmp);
	trigs=loptab(e,sincostan_tab).size();
      }
      tmp=trigtan(e,contextptr);
      trigtmps=loptab(tmp,sincostan_tab).size();
      if (trigtmps<trigs){
	e=ratnormal(tmp);
      }
    }
    gen first_try=subst(e,x,lim_point,false,contextptr);
    first_try=simplifier(first_try,contextptr);
    if (!contains(lidnt(first_try),unsigned_inf)){
      gen chknum;
      bool hasnum=has_evalf(first_try,chknum,1,contextptr);
      first_try=recursive_ratnormal(first_try,contextptr);
      gen chk=recursive_normal(first_try,contextptr);
      if (hasnum && !is_undef(chk) && abs(chk-chknum,contextptr)>1e-10 && abs(1-chk/chknum,contextptr)>1e-10)
	e=_simplify(e,contextptr);
    }
    // Find functions depending of x in e which are in the list
    // If their argument tends to +/-infinity, replace these functions
    vecteur v=rlvarx(e,x);
    int vs=int(v.size()),pos1,pos2=0;
    vecteur v1,v2;
    for (int i=0;i<vs;++i){
      if (v[i].type==_SYMB){
	if (v[i].is_symb_of_sommet(at_ln)){
 	  gen g=limit(v[i]._SYMBptr->feuille,x,lim_point,direction,contextptr);
	  if (is_inf(g) && g!=plus_inf)
	    return gensizeerr(gettext("ln of unsigned or minus infinity"));
	}
	if (v[i].is_symb_of_sommet(at_sinh) || v[i].is_symb_of_sommet(at_cosh) || v[i].is_symb_of_sommet(at_tanh)){
	  gen g=limit(v[i]._SYMBptr->feuille,x,lim_point,direction,contextptr);
	  if (is_inf(g)){
	    v1.push_back(v[i]);
	    v2.push_back(hyp2exp(v[i],contextptr));
	    continue;
	  }
	}
	if (v[i].is_symb_of_sommet(at_sum)){
	  gen tmp;
	  if (v[i]._SYMBptr->feuille.type==_VECT && v[i]._SYMBptr->feuille._VECTptr->size()==4){
	    vecteur & vv=*v[i]._SYMBptr->feuille._VECTptr;
	    if (derive(vv[2],x,contextptr)==0 && derive(vv[3],x,contextptr)==0)
	      continue;
	  }
	  if (!convert_to_euler_mac_laurin(v[i],x,tmp,contextptr))
	    return gensizeerr(gettext("Unable to convert sum to Euler Mac-Laurin ")+v[i].print(contextptr));
	  v1.push_back(v[i]);
	  v2.push_back(tmp);
	}
	if ( ( (pos1=equalposcomp(limit_tab,v[i]._SYMBptr->sommet)) || (pos2=equalposcomp(limit_tractable_functions(),&v[i]._SYMBptr->sommet)) ) ){
	  gen g=limit(v[i]._SYMBptr->feuille,x,lim_point,direction,contextptr);
	  if ( is_inf(g) || (g.type==_VECT && !g._VECTptr->empty() && is_inf(g._VECTptr->back())) ){
	    v1.push_back(v[i]);
	    v2.push_back(pos1?limit_replace[pos1-1](v[i]._SYMBptr->feuille,contextptr):limit_tractable_replace()[pos2-1](v[i]._SYMBptr->feuille,contextptr));
	  }
	  if (is_zero(g)){
	    if (v[i]._SYMBptr->sommet==at_Ci){
	      v1.push_back(v[i]);
	      v2.push_back(Ci_replace0(v[i]._SYMBptr->feuille,contextptr));
	    }
	    if (v[i]._SYMBptr->sommet==at_Ei){
	      v1.push_back(v[i]);
	      v2.push_back(Ei_replace0(v[i]._SYMBptr->feuille,contextptr));
	    }
	  }
	}
      }
    }
    if (!v1.empty()){
      v2=subst(v2,v1,v2,false,contextptr);
      e=remove_lnexp(subst(e,v1,v2,false,contextptr),contextptr);
    }
    v=rlvarx(e,x);
    vs=int(v.size());
    v1.clear(); v2.clear();
    for (int i=0;i<vs;++i){
#if 1
      if (v[i].is_symb_of_sommet(at_sign)){
	gen g=v[i]._SYMBptr->feuille,tmp;
	unsigned j=0;
	for (;j<5;++j){
	  tmp=simplify(limit(g,x,lim_point,direction,contextptr),contextptr);
	  if (!is_zero(tmp)){
	    break;
	  }
	  g=derive(g,x,contextptr);
	}
	if (direction==0 && j!=0) {
	  continue;
	}
	if (j!=5){
	  // sign( x^j*tmp)
	  tmp=sign(tmp,contextptr);
	  if (direction==-1 && j%2)
	    tmp=-tmp;
	  v1.push_back(v[i]);
	  v2.push_back(tmp);	  
	}
      }
#else
      if (v[i].is_symb_of_sommet(at_sign) && v[i]!=e){
	gen g;
#ifndef NO_STDEXCEPT
	try {
#endif
	  g=limit(v[i],x,lim_point,direction,contextptr);
	  v1.push_back(v[i]);
	  v2.push_back(g);
#ifndef NO_STDEXCEPT
	} catch (std::runtime_error & ) {
	}
#endif
      }
#endif
    }
    e=subst(e,v1,v2,false,contextptr);
    return e;
  }

  bool is_analytic(const gen & g){
    if (g.type==_VECT){
      const_iterateur it=g._VECTptr->begin(),itend=g._VECTptr->end();
      for (;it!=itend;++it){
	if (!is_analytic(*it))
	  return false;
      }
    }
    if (g.type!=_SYMB)
      return true;
    if (equalposcomp(analytic_sommets,g._SYMBptr->sommet))
      return is_analytic(g._SYMBptr->feuille);
    return false;
  }

  static gen unidirectional_limit(const gen & e0,const identificateur & x,const gen & lim_point,int direction,GIAC_CONTEXT){
    gen e_copy=e0;
    // Unidirectional limit, rewrite first (if needed)
    if (is_inf(lim_point)){
      if (lim_point==minus_inf)
	e_copy=subst(e_copy,x,-x,false,contextptr);
    }
    else {
      if (direction>0)
	e_copy=subst(e_copy,x,lim_point+inv(x,contextptr),false,contextptr);
      else
	e_copy=subst(e_copy,x,lim_point-inv(x,contextptr),false,contextptr);
    }
    gen coeff,mrv_var,exponent;
    sparse_poly1 p;
    if (!mrv_lead_term(e_copy,x,coeff,mrv_var,exponent,p,mrv_begin_order,contextptr,false) || is_undef(coeff)){
      gensizeerr("Limit: Max order reached or unable to make series expansion");
      return undef;
    }
    // check added for limit((tan(x)-x)/x^3,x=inf)
    for (unsigned i=0;i<p.size();++i){
      if (check_bounded(p[i].coeff,contextptr)==-1)
	return gensizeerr("Limit probably undefined, algorithm unable to handle "+p[i].coeff.print(contextptr));
    }
    if (ck_is_strictly_positive(exponent,contextptr))
      return 0;
    if (is_zero(exponent)){
      int l=check_bounded(coeff,contextptr);
      if (l==-1)
	return gensizeerr("Limit probably undefined, algorithm unable to handle "+coeff.print(contextptr));
      return l==1?bounded_function(contextptr):coeff;
    }
    // check sign of coeff, if coeff depends on x first find equivalent
    gen essai=subst(coeff,x,plus_inf,false,contextptr);
    if (is_undef(essai) || is_zero(essai) || (essai==unsigned_inf)){
      while (contains(coeff,x)){
	e_copy=coeff;
	if (!mrv_lead_term(e_copy,x,coeff,mrv_var,exponent,p,mrv_begin_order,contextptr,false))
	  return gensizeerr(contextptr);
      }
      essai=coeff;
    }
    gen s=0;
    if (calc_mode(contextptr)!=1 || !has_i(p)) // should do it only up to order 0 terms
      s=sign(essai,contextptr); 
    if (s==plus_one)
      return plus_inf;
    if (s==minus_one)
      return minus_inf;
    // ? FIXME: if essai=cos(<pi,-1>)+i*sin(<pi,-1>) unsigned_inf better
    // limit((-2)^n,n,inf)
    int l=check_bounded(essai,contextptr);
    if (l==-1)
      return gensizeerr("Limit probably undefined, algorithm unable to handle "+essai.print(contextptr));
    return l==1?undef:unsigned_inf;
    /* 
    essai=eval(subst(essai,sincosinf,vecteur(sincosinf.size(),undef)));
    if (is_undef(essai))
      return undef;
    else
      return unsigned_inf;
    */
  }

  static gen in_limit(const gen & e0,const identificateur & x,const gen & lim_point,int direction,GIAC_CONTEXT){
    if (direction==-2)
      return gensizeerr(contextptr);
    vecteur vint=lop(rlvarx(e0,x),at_integrate);
    for (unsigned i=0;i<vint.size();++i){
      gen f=vint[i]._SYMBptr->feuille;
      if (f.type!=_VECT || f._VECTptr->size()!=4)
	return gensizeerr(gettext("Undefined integral"));
      if ((*f._VECTptr)[1]==x)
	return gensizeerr(gettext("Integration variable and limit variable are the same"));	
      if (!is_zero(derive(f._VECTptr->front(),x,contextptr)))
	return gensizeerr(gettext("Integral in limit not implemented yet"));
    }
    if (e0.type==_VECT){
      const_iterateur it=e0._VECTptr->begin(),itend=e0._VECTptr->end();
      vecteur res;
      res.reserve(itend-it);
      for (;it!=itend;++it){
	res.push_back(in_limit(*it,x,lim_point,direction,contextptr));
      }
      return gen(res,e0.subtype);
    }
    if (_about(x,contextptr)!=x){
      vecteur l(lvar(e0));
      for (int i=0;;++i){
	gen X("x"+print_INT_(i),contextptr);
	if (X.type!=_IDNT || equalposcomp(l,X))
	  continue;
	if (_about(X,contextptr)!=X)
	  continue;
	return in_limit(quotesubst(e0,x,X,contextptr),*X._IDNTptr,lim_point,direction,contextptr);
      }
      // never reached
      gen xprime("x"+print_INT_(giac_rand(contextptr)),contextptr);
      return in_limit(quotesubst(e0,x,xprime,contextptr),*xprime._IDNTptr,lim_point,direction,contextptr);
    }
    gen e=Heavisidetosign(when2sign(piecewise2when(e0,contextptr),contextptr),contextptr);
    // Adjust direction for +/- inf limits
    if (lim_point==plus_inf)
      direction=1;
    if (lim_point==minus_inf)
      direction=-1;    
    // First try substitution
    if (has_i(lop(e,at_ln)))
      e=recursive_normal(expln2trig(e,contextptr),contextptr);
    vecteur vsign(loptab(e,sign_floor_ceil_round_tab));
    if (//0 && 
	direction && !vsign.empty() && !equalposcomp(sign_floor_ceil_round_tab,e._SYMBptr->sommet)){
      // evaluate vsign first
      vecteur res(vsign.size());
      for (int i=0;i<int(vsign.size());++i){
	res[i]=in_limit(vsign[i],x,lim_point,direction,contextptr);
      }
      e=subst(e,vsign,res,false,contextptr);
      vsign.clear();
    }
    if (vsign.empty()){
      gen first_try=subst(e,x,lim_point,false,contextptr);
      first_try=eval(first_try,1,contextptr);
      first_try=simplifier(first_try,contextptr);
      // if (first_try==plus_inf || first_try==minus_inf) return first_try;
      if (!contains(lidnt(first_try),unsigned_inf)){
	if (has_num_coeff(first_try))
	  return first_try;
	gen chknum;
	bool hasnum=has_evalf(first_try,chknum,1,contextptr);
	first_try=recursive_ratnormal(first_try,contextptr);
	gen chk;
	if (has_evalf(first_try,chk,1,contextptr) && !is_zero(chk) && !is_undef(chk) && !is_inf(chk))
	  return first_try; // avoid 0 because it might be 0/almost 0
	chk=recursive_normal(first_try,contextptr);
	if (hasnum && !is_undef(chk) && abs(chk-chknum,contextptr)>1e-10 && abs(1-chk/chknum,contextptr)>1e-10){
	  chk=undef;
	  e=_simplify(e,contextptr);
	}
	if (!is_undef(chk)){
	  /*
	    if (!lop(chk,at_rootof).empty())
	    chk=ratnormal(first_try);
	  */
	  if (!is_undef(chk) && !contains(lidnt(chk),unsigned_inf)){
	    chk=first_try;
	    return taille(chk,100)<taille(first_try,100)?chk:first_try;
	  }
	}
      }
      if (lim_point==unsigned_inf){
	*logptr(contextptr) << gettext("Warning, infinity is unsigned, perhaps you meant +infinity")<< '\n';
	first_try = subst(partfrac(e,false,contextptr),x,lim_point,false,contextptr);
	// first_try = subst(ratnormal(e,contextptr),x,lim_point,false,contextptr);
      }
      else {
	//bool b=assume_t_in_ab(x,direction==1?lim_point:lim_point-1,direction==-1?lim_point:lim_point+1,true,true,contextptr);
	first_try = quotesubst(partfrac(e,false,contextptr),x,lim_point,contextptr);
	// if (b) purgenoassume(x,contextptr);
	// first_try = quotesubst(ratnormal(e,contextptr),x,lim_point,contextptr);
      }
      gen numtry=evalf(first_try,1,contextptr);
      bool absb=eval_abs(contextptr);
      first_try=eval(first_try,eval_level(contextptr),contextptr); // moved before eval_abs(false,contextptr), must be before simplifier below
      first_try=simplifier(first_try,contextptr); // for assume(a>0); limit((sqrt(2*a^3*x-x^4)-a*root(3,a^2*x))/(a-root(4,a*x^3)),x=a);
      eval_abs(false,contextptr);
      first_try = recursive_normal(first_try,contextptr);
      //first_try=eval(first_try,1,contextptr);
      eval_abs(absb,contextptr);
      if (is_undef(first_try) && first_try.type==_STRNG)
	return first_try;
      if (!is_undef(first_try) && !is_undef(numtry)){
	// if (!direction) return first_try;
	if (first_try!=unsigned_inf && numtry!=unsigned_inf)
	  return first_try;
      }
    } // end if vsign.empty()
    if (has_op(e,*at_surd) || has_op(e,*at_NTHROOT)){
      // FIXME: adjust using limit/direction information
      vecteur subst1,subst2;
      surd2pow(e,subst1,subst2,contextptr);
      gen g=subst(e,subst1,subst2,false,contextptr);
      g=limit(g,x,lim_point,direction,contextptr);
      return subst(g,subst2,subst1,false,contextptr);
    }
    e=limit_symbolic_preprocess(e,x,lim_point,direction,contextptr);
    if (is_undef(e)) return e;
    gen errcode=checkanglemode(contextptr);
    if (is_undef(errcode))
      return errcode;
    if (e.type!=_SYMB) // e might be an _IDNT equal to x (limit(x*sign(x),x,0,1))
      return subst(e,x,lim_point,false,contextptr);
    if (e._SYMBptr->sommet==at_exp)
      return exp(in_limit(e._SYMBptr->feuille,x,lim_point,direction,contextptr),contextptr);
    if (e._SYMBptr->sommet==at_ln){
      gen tmp=in_limit(e._SYMBptr->feuille,x,lim_point,direction,contextptr);
      if (is_undef(tmp)) return tmp;
      if (!is_positive(-tmp,contextptr))
	return ln(tmp,contextptr);
    }
    gen e_copy;
    // Rewrite non rational ^ and tan 
    e_copy=_pow2exp(tan2sincos(exact(e,contextptr),contextptr),contextptr);
    // FIXME: this translate exp(i*...) to sin/cos without bugging for
    // exp(exp(exp(x)/(1-1/x)))-exp(exp(exp(x)/(1-1/x-exp((-(ln(x)))*ln(ln(x))))))
    if (has_i(e_copy)) {
      e_copy=subst(e_copy,tan_tab,tan2sincos_tab,true,contextptr);
      e_copy=subst(e_copy,exp_tab,exp2sincos_tab,true,contextptr);
      if (has_i(lop(e_copy,at_erfs)))
	return gensizeerr(gettext("erf/erfc/erfs with complex argument not yet implemented in limit"));
    }
    // Rewrite constants
    vecteur rv=rlvar(e_copy,false),cv;
    for (int i=0;i<rv.size();++i){
      if (evalf(rv[i],1,contextptr).type<_CPLX)
	cv.push_back(rv[i]);
    }
    if (!cv.empty()){
      gen cvg=tsimplify(cv,contextptr);
      if (!has_i(cvg) && cvg.type==_VECT && cvg._VECTptr->size()==cv.size())
	e_copy=subst(e_copy,cv,*cvg._VECTptr,false,contextptr);
    }
    if (!direction) { 
      if (!is_analytic(e_copy) || has_op(e_copy,*at_acos) || has_op(e_copy,*at_asin)){
	gen g1=unidirectional_limit(e_copy,x,lim_point,1,contextptr);
	if (is_undef(g1))
	  return g1;
	gen g2=unidirectional_limit(e_copy,x,lim_point,-1,contextptr);
	if (is_undef(g2))
	  return g2;
	if (g1==g2 || is_zero(ratnormal(g1-g2,contextptr)))
	  return g1;
	return gensizeerr("Unidirectional limits are distinct "+g2.print(contextptr)+","+g1.print(contextptr));
      }
      // supposed to be analytic, try first series expansion 
      sparse_poly1 p;
      p.push_back(monome(undef,0));
      double ordre=mrv_begin_order;
      for ( ; !p.empty() && is_undef(p.front().coeff) && (ordre<mrv_begin_order*4);ordre=1.5*ordre+1) {
	p=series__SPOL1(e_copy,x,lim_point,int(ordre),0,contextptr);
	if (!p.empty() && !is_undef(p.front().coeff)){
	  if (p.front().coeff.type==_FRAC && is_strictly_positive(-p.front().coeff._FRACptr->den,contextptr))
	    p.front().coeff=fraction(-p.front().coeff._FRACptr->num,-p.front().coeff._FRACptr->den);
	  break;
	}
      }
      // COUT << p << '\n';
      if (ordre>=mrv_begin_order*4){
	gen g1=unidirectional_limit(e_copy,x,lim_point,1,contextptr);
	if (is_undef(g1))
	  return g1;
	gen g2=unidirectional_limit(e_copy,x,lim_point,-1,contextptr);
	if (is_undef(g2))
	  return g2;
	if (is_zero(ratnormal(g1-g2,contextptr)))
	  return g1;
	return gensizeerr("Unidirectional limits are distincts "+g2.print(contextptr)+","+g1.print(contextptr));
      }
      if (p.empty() || ck_is_strictly_positive(p.front().exponent,contextptr) ){
	if (check_bounded(p.front().coeff,contextptr)==-1)
	  return gensizeerr("Unable to bound coefficient");
	return 0;
      }
      if (ck_is_strictly_positive(-p.front().exponent,contextptr)){
	if (p.front().exponent.type==_INT_ && p.front().exponent.val%2==0){
	  int s=fastsign(p.front().coeff,contextptr);
	  if (s==1)
	    return plus_inf;
	  if (s==-1)
	    return minus_inf;
	}
	return unsigned_inf;
      }
      if (is_zero(p.front().exponent)){
	if (contains(p.front().coeff,x)){
	  return gensizeerr(gettext("Try unidirectional series"));
	}
	int l=check_bounded(p.front().coeff,contextptr);
	if (l==-1)
	  return gensizeerr("Limit probably undefined, algorithm unable to handle "+p.front().coeff.print(contextptr));
	return l==1?bounded_function(contextptr):p.front().coeff;
      }
      return gensizeerr(gettext("Series internal bug"));
    }
    return unidirectional_limit(e_copy,x,lim_point,direction,contextptr);
  }
  
  // return plus_inf if a > b (at x=+infinity), !0 if a#b, 0 if a < b
  static gen mrv_compare(const gen & a,const gen & b,const identificateur & x,GIAC_CONTEXT){
    if ((a.type!=_SYMB) && (b.type!=_SYMB))
      return 1;
    gen lna,lnb,l;
    if ((a.type==_SYMB) && (a._SYMBptr->sommet==at_exp))
      lna=a._SYMBptr->feuille;
    else
      lna=ln(a,contextptr);
    if ((b.type==_SYMB) && (b._SYMBptr->sommet==at_exp))
      lnb=b._SYMBptr->feuille;
    else
      lnb=ln(b,contextptr);
    gen coeff,mrv_var,exponent;
    sparse_poly1 p;
    if (!mrv_lead_term(rdiv(lna,lnb,contextptr),x,coeff,mrv_var,exponent,p,mrv_begin_order,contextptr,false))
      return gensizeerr(contextptr);
    if (ck_is_strictly_positive(exponent,contextptr))
      return 0;
    if (is_zero(exponent))
      return coeff;
    return plus_inf;
  }

  static bool mrv_max(const vecteur & a_faster_var, const vecteur & a_coeff_ln, const vecteur & a_slower_var, const vecteur & b_faster_var,const vecteur & b_coeff_ln, const vecteur & b_slower_var,const identificateur & x, vecteur & faster_var, vecteur & coeff_ln, vecteur & slower_var,GIAC_CONTEXT){
    int pos_a,pos_b;
    gen s;
    if (intersect(a_faster_var,b_faster_var,pos_a,pos_b))
      s=normal(rdiv(a_faster_var[pos_a],b_faster_var[pos_b],contextptr),contextptr);
    else {
      if (a_faster_var.empty() || intersect(a_faster_var,b_slower_var,pos_a,pos_b))
	s=0;
      else {
	if (b_faster_var.empty() || intersect(b_faster_var,a_slower_var,pos_a,pos_b) )
	  s=plus_inf;
	else
	  s=mrv_compare(a_faster_var.front(),b_faster_var.front(),x,contextptr);
      }
      if (is_undef(s))
	return false;
      if (s==plus_inf){
	slower_var=mergevecteur(a_slower_var,b_slower_var);
	slower_var=mergevecteur(b_faster_var,slower_var);      
	faster_var=a_faster_var;
	coeff_ln=a_coeff_ln;
	return true;
      }
      if (is_zero(s)){
	slower_var=mergevecteur(a_slower_var,b_slower_var);
	slower_var=mergevecteur(a_faster_var,slower_var);
	faster_var=b_faster_var;
	coeff_ln=b_coeff_ln;
	return true;
      }
    }
    // s!=0 && s!=plus_inf
    // size test used to get w or inv(w) at the front()
    if (a_faster_var.front().symb_size()>b_faster_var.front().symb_size()){
      coeff_ln=mergevecteur(b_coeff_ln,multvecteur(s,a_coeff_ln));
      faster_var=mergevecteur(b_faster_var,a_faster_var);
      slower_var=mergevecteur(b_slower_var,a_slower_var);
    }
    else {
      coeff_ln=mergevecteur(a_coeff_ln,multvecteur(inv(s,contextptr),b_coeff_ln));
      faster_var=mergevecteur(a_faster_var,b_faster_var);
      slower_var=mergevecteur(a_slower_var,b_slower_var);
    }
    return true;
  }
  
  // Find most rapidly varying subexpression of e and res
  static bool mrv(const gen & e,const identificateur & x,vecteur & faster_var,vecteur & coeff_ln, vecteur & slower_var,GIAC_CONTEXT){
    // Find all var of e depending on x
    vecteur v0(lvarx(e,x));
    // Find mrv of these vars
    vecteur::const_iterator it=v0.begin(),itend=v0.end();
    for (;it!=itend;++it){
      if (equalposcomp(faster_var,*it) || equalposcomp(slower_var,*it))
	continue;
      if (it->type!=_SYMB){
	if (!mrv_max(faster_var,coeff_ln,slower_var,
		     vecteur(1,*it),vecteur(1,plus_one),vecteur(0),
		     x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      gen temp=*it;
      if (temp._SYMBptr->sommet==at_ln){
	if (!mrv(temp._SYMBptr->feuille,x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      if (temp._SYMBptr->sommet==at_Psi && temp._SYMBptr->feuille.type==_VECT){
	if (!mrv(temp._SYMBptr->feuille[0],x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      if (temp._SYMBptr->sommet==at_lower_incomplete_gamma || temp._SYMBptr->sommet==at_igamma_exp){
	gen & f = temp._SYMBptr->feuille;
	if (depend(f[0],x))
	  return false;
	if (!mrv(f[1],x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      if (temp._SYMBptr->sommet==at_pow)
	temp=symbolic(at_exp,(*(temp._SYMBptr->feuille._VECTptr))[1]*ln((*(temp._SYMBptr->feuille._VECTptr))[0],contextptr));
      if (temp._SYMBptr->sommet==at_euler_mac_laurin){
	gen & f = temp._SYMBptr->feuille;
	if (f.type==_VECT && f._VECTptr->size()==5){
	  if (!mrv(f[0],x,faster_var,coeff_ln,slower_var,contextptr) ||
	      !mrv(f[3],x,faster_var,coeff_ln,slower_var,contextptr) ||
	      !mrv(f[4],x,faster_var,coeff_ln,slower_var,contextptr))
	    return false;
	  continue;
	}
      }
      if (temp._SYMBptr->sommet==at_integrate){
	gen & f = temp._SYMBptr->feuille;
	if (f.type==_VECT && f._VECTptr->size()==4){
	  if (!mrv(f[0],x,faster_var,coeff_ln,slower_var,contextptr) ||
	      !mrv(f[2],x,faster_var,coeff_ln,slower_var,contextptr) ||
	      !mrv(f[3],x,faster_var,coeff_ln,slower_var,contextptr))
	    return false;
	  continue;
	}
      }
      if (temp._SYMBptr->feuille.type==_VECT){
	*logptr(contextptr) << gettext("Limit probably undefined, algorithm unable to handle ")+temp.print(contextptr) << '\n';
	return false;
      }
      gen l=in_limit(temp._SYMBptr->feuille,x,plus_inf,0,contextptr);
      if (is_undef(l) || (l==unsigned_inf && temp._SYMBptr->sommet!=at_cos && temp._SYMBptr->sommet!=at_sin && temp._SYMBptr->sommet!=at_erfs)){
	*logptr(contextptr) << gettext("Undef/Unsigned Inf encountered in limit") << '\n';
	return false;
      }
      if (!is_inf(l)){
	if (!mrv(temp._SYMBptr->feuille,x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      if (temp._SYMBptr->sommet==at_exp){
	if (!mrv(temp._SYMBptr->feuille,x,faster_var,coeff_ln,slower_var,contextptr) ||
	    !mrv_max(faster_var,coeff_ln,slower_var,
		    vecteur(1,temp),vecteur(1,plus_one),vecteur(0),
		     x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      // (semi-)tractable functions?
      gen shift_coeff;
      if (!temp._SYMBptr->sommet.ptr()->series_expansion){
	invalidserieserr(string(gettext("no taylor method for "))+temp._SYMBptr->sommet.ptr()->print(contextptr));
	return false;
      }
      gen test=temp._SYMBptr->sommet.ptr()->series_expansion(l,0,temp._SYMBptr->sommet,0,shift_coeff,contextptr); // fixme: 0 should be image_of_direction 
      if (!is_undef(test)){
	if (!mrv(temp._SYMBptr->feuille,x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
	continue;
      }
      // fixme: add support for integrals and sums
      if (temp._SYMBptr->sommet!=at_exp)
	return false; // setsizeerr(gettext("series.cc/mrv"));
    }
    return true;
  }

  bool pnormal(sparse_poly1 & v,GIAC_CONTEXT){
    sparse_poly1::const_iterator it=v.begin(),itend=v.end();
    sparse_poly1 p;
    gen e;
    for (;it!=itend;++it){
      e=recursive_normal(it->coeff,contextptr);
      if (!is_zero(e))
	p.push_back(monome(e,it->exponent));
    }
    swap(p,v);
    return true;
  }

  // find asymptotic equivalent of e in terms of the mrv var of e
  static bool mrv_lead_term(const gen & e,const identificateur & x,gen & coeff, gen & mrv_var, gen & exponent,sparse_poly1 & q,int begin_ordre,GIAC_CONTEXT,bool series){
    if (!contains(e,x)){
      coeff=ratnormal(e,contextptr);
      mrv_var=x;
      exponent=0;
      q.clear();
      q.push_back(monome(coeff,0));
      return true;
    }
    vecteur faster_var,coeff_ln,slower_var;
    gen ecopy(e);
    if (!mrv(ecopy,x,faster_var,coeff_ln,slower_var,contextptr))
      return false;
    int rescaling=0; // number of ln(x) -> x substitution
    // if the mrv contains x, we must change scale ln(x) -> x and x -> e^x
    for (;equalposcomp(faster_var,x);++rescaling){
      upscale(ecopy,x,contextptr);
      // next test needed to avoid infinite recursion
      // if there is an e^x inside the new mrv is m rescaled
      if (contains(ecopy,exp(x,contextptr))){
	gen temp(faster_var);
	upscale(temp,x,contextptr);
	faster_var=*temp._VECTptr;
      }
      else {
	faster_var.clear();
	slower_var.clear();
	coeff_ln.clear();
	if (!mrv(ecopy,x,faster_var,coeff_ln,slower_var,contextptr))
	  return false;
      }
    }
    if (faster_var.empty()){
      coeff=ratnormal(ecopy,contextptr);
      mrv_var=x;
      exponent=0;
      q.clear();
      q.push_back(monome(coeff,0));
      return true;
    }
    // now find w, the mrv element -> 0 and express other elements of the mrv
    // algo: sort faster_var by symb_size
    // w is the shortest one, set g=ln(w)
    // replace the next shortest at position pos
    // by w^coeff_ln[pos]* exp(ln(faster_var[pos])-coeff_ln[pos]*g)
    // then replace faster_var[0] by w above
    // go on, the replace operation should be done with 
    // previous ordered_faster by their expression in terms of w
    // At the end replace w by 1/w if w -> plus_inf
    bool dont_invert=is_zero(in_limit(faster_var.front(),x,plus_inf,0,contextptr));
    vecteur faster_var_tmp(faster_var);
#if 1 // FXCG
    tri_rlvarx(faster_var); 
#else
    stable_sort(faster_var.begin(),faster_var.end(),symb_size_less_t());
#endif
    vecteur ecopyv(lidnt(ecopy));
    string ws("w");
    identificateur w(ws); 
    // create free identifier, not present in ecopy
    while (equalposcomp(ecopyv,w)){
      ws+='_';
      w=identificateur(ws);
    }
    vecteur faster_var_subst(1,w);
    gen g=faster_var.front()._SYMBptr->feuille;
    iterateur it=faster_var.begin()+1,itend=faster_var.end();
    gen c,f;
    for (;it!=itend;++it){
      int p=equalposcomp(faster_var_tmp,*it);
      // assert(p);
      c=coeff_ln[p-1];
      f=subst(it->_SYMBptr->feuille,faster_var,faster_var_subst,false,contextptr);
      faster_var_subst.push_back(pow(w,c,contextptr)*exp(normal(f-c*g,contextptr),contextptr));
    }
    // add original variable in faster_var/faster_var_subst
    // otherwise we might miss replacements
    if (faster_var.front().is_symb_of_sommet(at_exp) && faster_var.front()._SYMBptr->feuille==x){
      faster_var.push_back(x);
      faster_var_subst.push_back(ln(faster_var_subst.front(),contextptr));
    }
    // subst in original expression and make the asymptotic expansion
    double ordre=begin_ordre;
    f=subst(ecopy,faster_var,faster_var_subst,false,contextptr);
    if (!dont_invert)
      f=subst(f,w,inv(w,contextptr),false,contextptr);
    if (faster_var.front().is_symb_of_sommet(at_exp)){
      // replace ln(exp(g)^k*...) by k*g+ln(...)
      // where g=ln(w)
      gen effg(g); // symbolic(at_ln,w)); does not work
      vecteur lf(lop(f,at_ln)),lf1,lf2;
      iterateur it=lf.begin(),itend=lf.end();
      for (;it!=itend;++it){
	gen argln=it->_SYMBptr->feuille;
	sparse_poly1 p=series__SPOL1(argln,w,0,int(ordre),1,contextptr);
	if (!p.empty() && !is_undef(p.front().coeff) ){
	  if (!is_zero(p.front().exponent))
	    argln=argln*symbolic(at_pow,gen(makevecteur(w,-p.front().exponent),_SEQ__VECT));
	  lf1.push_back(*it);
	  lf2.push_back(p.front().exponent*(dont_invert?effg:-effg)+symbolic(at_ln,argln));
	}
      }
      if (!lf1.empty())
	f=subst(f,lf1,lf2,false,contextptr);
    }
    sparse_poly1 p;
    p.push_back(monome(undef,0));
    // FIXME: if ordre>max_series it might return a wrong answer here
    for (unsigned count=0; (ordre<max_series_expansion_order) && !p.empty() && 
	   (p.size()>=1) && is_undef(p.front().coeff) ;++count,ordre=ordre*1.5+1){
      bool inv=false;
      p=series__SPOL1(f,w,0,int(ordre),1,contextptr);
      // if (count==2 && p.size()==1 && is_undef(p.front().coeff)){ f=ratnormal(f,contextptr); p=series__SPOL1(f,w,0,int(ordre),1,contextptr); }
#ifdef TIMEOUT
      control_c();
#endif
      if (ctrl_c || interrupted || (!p.empty() &&  is_undef(p.front().exponent))) 
	return false;
      if (!p.empty() && !is_undef(p.front().coeff) ){
	// substitution of ln(w) by +-g should not be useful anymore
	gen tmp=ratnormal(subst(p.front().coeff,ln(w,contextptr),(dont_invert?g:-g),false,contextptr),contextptr);
	if (is_undef(tmp) ){
	  inv=true;
	  p=spdiv(sparse_poly1(1,monome(1,0)),p,contextptr);
	  if (is_undef(p))
	    return false;
	  pnormal(p,contextptr);
	}
      }
      // cerr << p << '\n';
      // replace ln( w) in coeff by g or -g
      if (dont_invert)
	p=subst(p,ln(w,contextptr),g,false,contextptr);
      else
	p=subst(p,ln(w,contextptr),-g,false,contextptr);
      if (inv){
	p=spdiv(sparse_poly1(1,monome(1,0)),p,contextptr);
	if (is_undef(p))
	  return false;
	pnormal(p,contextptr);
      }
    }
    if (!p.empty())
      p.front().exponent=simplify(p.front().exponent,contextptr);
    q=p;
    if (!p.empty()){
      bool done=false;
      // check for exponent 0 at front()
      if (is_zero(p.front().exponent) && contains(p.front().coeff,x) && !is_zero(derive(p.front().coeff,x,contextptr))){
	// if p is uniquely composed of this coeff, expand
	if (!mrv_lead_term(p.front().coeff,x,coeff,mrv_var,exponent,p,mrv_begin_order,contextptr,false))
	  return false;
	if (p.empty()
	    // test below allow expanding series(ln(x+1),x=inf)
	    // the boolean series was added 
	    // otherwise testlimit would not work correctly
	    || (series && p.size()==1 && q.size()>1 &&!is_undef(p.front().coeff)) 
	    ){
	  done=false;
	  p=q;
	}
	else {
	  if (q.size()>1 && !is_undef(p.back().coeff))
	    p.push_back(monome(undef,p.back().exponent+begin_ordre));
	  q=p;
	  done=true;
	}
      }
      if (!done) {
	if (dont_invert)
	  mrv_var=faster_var.front();
	else
	  mrv_var=inv(faster_var.front(),contextptr);
	coeff = p.front().coeff;
	exponent = p.front().exponent;
      }
    }
    // mrv_var is w as function of x, rescaled using the int variable rescaling
    // coeff must be rescaled as well
    sparse_poly1::iterator it0=q.begin(),it1=q.end();
    for (;rescaling;--rescaling){
      downscale(mrv_var,x,contextptr);
      downscale(coeff,x,contextptr);
      for (sparse_poly1::iterator it=it0;it!=it1;++it)
	downscale(it->coeff,x,contextptr);
    }
    return true;
  }

  bool intersect(const vecteur & a,const vecteur &b,int & pos_a,int & pos_b){
    vecteur res;
    if (a.empty() || b.empty())
      return false;
    vecteur::const_iterator it=a.begin(),itend=a.end();
    for (;it!=itend;++it)
      pos_b=equalposcomp(b,*it);
      if (pos_b){
	--pos_b;
	pos_a=int(it-a.begin());
	return true;
      }
    return false;
  }

  static int convert_to_direction(const gen & l){
    // addition by L.Marohnić: enable using left/right symbols for specifying a direction
    if (is_one(l) || l==at_plus || l==at_right)
      return 1;
    if (is_minus_one(l) || l==at_binary_minus || l==at_neg || l==at_left)
      return -1;
    if (is_zero(l))
      return 0;
    return -2;
  }

  // Main limit entry point
  gen limit(const gen & e,const identificateur & x,const gen & lim_point_,int direction,GIAC_CONTEXT){
    gen lim_point(eval(lim_point_,1,contextptr));
    if (is_undef(lim_point))
      return lim_point;
    if (lim_point.type==_DOUBLE_){
      double d=lim_point._DOUBLE_val;
      if (d==int(d))
	return limit(e,x,int(d),direction,contextptr);
    }
    if (has_num_coeff(lim_point)) // otherwise A:=conic(x^2/4+y^2/3=1); B:=element(A,1)+nop(-1.666-1.243*i) runs forever
      return subst(e,x,lim_point,false,contextptr);
    // Insert here code for cleaning limit remember
    int save_series_flags=series_flags(contextptr);
    series_flags(save_series_flags | 8,contextptr);
    // sincosinf.clear();
    gen e_exact=exact(e,contextptr);
    gen lim_point_exact=exact(lim_point,contextptr);
    gen l=in_limit(e_exact,x,lim_point_exact,direction,contextptr);
    if (e.is_approx() || lim_point.is_approx())
      l=evalf(l,1,contextptr);
    series_flags(save_series_flags,contextptr);
    // vecteur sincosinfsub(sincosinf.size(),undef);
    // l=eval(subst(l,sincosinf,sincosinfsub));
    return l;
  }

  gen quotedlimit(const gen & e,const identificateur & x,const gen & lim_point,int direction,GIAC_CONTEXT){
    vecteur v(1,exact(e,contextptr));
    v=quote_eval(v,vecteur(1,x),contextptr);
    return limit(v[0],x,lim_point,direction,contextptr);
  }
  
  // "unary" version
  static const char _limit_s []="limit";
  gen _limit(const gen & args,GIAC_CONTEXT){
    if ( args.type==_STRNG && args.subtype==-1) return  args;
    if (args.type!=_VECT)
      return quotedlimit(args,*vx_var._IDNTptr,0,0,contextptr);
    vecteur v =*args._VECTptr;
    int s=int(v.size());
    if (!s)
      toofewargs(_limit_s);
    gen G=v[0];
    if (s==1)
      return quotedlimit(G,*vx_var._IDNTptr,0,0,contextptr);
    gen e=v[1];
    if (s==2){
      if (calc_mode(contextptr)==1 && !v[1].is_symb_of_sommet(at_equal))
	return _limit(makesequence(G,ggb_var(G),e),contextptr);
      if (e.type==_IDNT)
	return quotedlimit(G,*e._IDNTptr,0,0,contextptr);
      if (e.type!=_SYMB)
	return gentypeerr(contextptr);
      if (!is_equal(e))
	return gensizeerr(contextptr);
      gen x=(*(e._SYMBptr->feuille._VECTptr))[0];
      if (x.type!=_IDNT)
	return gensizeerr(contextptr);
      return quotedlimit(G,*x._IDNTptr,(*(e._SYMBptr->feuille._VECTptr))[1],0,contextptr);
    }
    if (s>2)
      v[2]=eval(v[2],1,contextptr);
    if (s>3)
      v[3]=eval(v[3],1,contextptr);
    if (s==3){
      gen arg3=v[2];
      if (e.type==_IDNT)
	return quotedlimit(G,*e._IDNTptr,arg3,0,contextptr);
      if (e.type!=_SYMB){
  int dir=convert_to_direction(arg3);
	if (dir!=-2)
	  return quotedlimit(G,*ggb_var(G)._IDNTptr,e,dir,contextptr);
	return gentypeerr(contextptr);
      }
      if (!is_equal(e)){
  int dir=convert_to_direction(arg3);
	if (dir!=-2)
	  return quotedlimit(G,*ggb_var(G)._IDNTptr,e,dir,contextptr);
	return gensizeerr(contextptr);
      }
      gen x=(*(e._SYMBptr->feuille._VECTptr))[0];
      if (x.type!=_IDNT)
	return gensizeerr(contextptr);
      return quotedlimit(G,*x._IDNTptr,(*(e._SYMBptr->feuille._VECTptr))[1],convert_to_direction(v[2]),contextptr);
    }
    if (s>4)
      return gentoomanyargs(_limit_s);
    if (e.type!=_IDNT)
      return gentypeerr(contextptr);
    return quotedlimit(G,*e._IDNTptr,v[2],convert_to_direction(v[3]),contextptr);
  }
  static string texprintaslimit(const gen & g,const char * orig_s,GIAC_CONTEXT){
    string s("\\lim ");
    if (g.type!=_VECT)
      return s+gen2tex(g,contextptr);
    vecteur v(*g._VECTptr);
    int l(int(v.size()));
    if (!l)
      return s;
    if (l==1)
      return s+gen2tex(v[0],contextptr);
    if (l==2)
      return s+"_{"+gen2tex(v[1],contextptr)+"}"+gen2tex(v[0],contextptr);
    // directional limit
    if (l==3){
      if (is_one(v[2]))
	return s+"_{"+gen2tex(v[1],contextptr)+"^+}"+gen2tex(v[0],contextptr);
      if (is_minus_one(v[2]))
	return s+"_{"+gen2tex(v[1],contextptr)+"^-}"+gen2tex(v[0],contextptr);
      else return s+"_{"+gen2tex(v[1],contextptr)+"}"+gen2tex(v[0],contextptr);
    }
    return s;
  }
  static define_unary_function_eval4 (__limit,&_limit,_limit_s,0,&texprintaslimit);
  define_unary_function_ptr5( at_limit ,alias_at_limit,&__limit,_QUOTE_ARGUMENTS,true);

#if 0 // def NSPIRE_NEWLIB
  static const char _lim_s []="lim";
  static define_unary_function_eval4 (__lim,&_limit,_lim_s,0,&texprintaslimit);
  define_unary_function_ptr5( at_lim ,alias_at_lim,&__lim,_QUOTE_ARGUMENTS,true);
#endif

  // like sparse_poly12gen, but if there is only 1 term and no remainder
  // expand it, l.1976
  static gen sparse_poly12gen_expand(const sparse_poly1 & s,const identificateur & x,const gen & mrv_var,int ordre,gen & remains,bool with_order_size,GIAC_CONTEXT){
    if (s.size()!=1 || !contains(s.front().coeff,x) )
      return sparse_poly12gen(s,mrv_var,remains,with_order_size);
    gen afaire=s.front().coeff,mrv_fait(mrv_var),a,b,c,exponent(s.front().exponent);
    if (mrv_fait.is_symb_of_sommet(at_inv) && mrv_fait._SYMBptr->feuille.is_symb_of_sommet(at_exp))
      mrv_fait=symbolic(at_exp,symbolic(at_neg,mrv_fait._SYMBptr->feuille._SYMBptr->feuille));
    if (mrv_fait.is_symb_of_sommet(at_exp)){
      // search embedded ln if mrv_var is an exp var
      mrv_fait=mrv_fait._SYMBptr->feuille;
      vecteur l(lop(mrv_fait,at_ln));
      int ls=int(l.size());
      for (int i=0;i<ls;++i){
	identificateur tx(" x");
	gen tmpx(tx);
	gen mrv_temp=subst(mrv_fait,l[i],tmpx,true,contextptr);
	if (is_linear_wrt(mrv_temp,tmpx,a,b,contextptr)){
	  // extract constant part of a in c using decompose_plus
	  if (a.is_symb_of_sommet(at_plus) && a._SYMBptr->feuille.type==_VECT){
	    c=0;
	    vecteur non_constant;
	    decompose_plus(*a._SYMBptr->feuille._VECTptr,x,non_constant,c,contextptr);
	    a=_plus(non_constant,contextptr);
	    afaire=afaire*pow(l[i]._SYMBptr->feuille,c*exponent,contextptr);
	    mrv_fait=a*l[i]+b;
	  }
	}
      }
      mrv_fait=symbolic(at_exp,mrv_fait);
    }
    gen coeff2,mrv_var2,exponent2;
    sparse_poly1 s2;
    if (!mrv_lead_term(afaire,x,coeff2,mrv_var2,exponent2,s2,ordre,contextptr,true))
      return false;
    return sparse_poly12gen_expand(s2,x,mrv_var2,ordre,remains,with_order_size,contextptr)*pow(mrv_fait,exponent,contextptr);
  }

  static gen in_series(const gen & e0,const identificateur & x,const gen & lim_point,int ordre,int direction,GIAC_CONTEXT){
    gen e=limit_symbolic_preprocess(e0,x,lim_point,direction,contextptr);
    if (is_undef(e)) return e;
    gen errcode=checkanglemode(contextptr);
    if (is_undef(errcode)) return errcode;    
    if (lim_point==plus_inf){
      gen coeff,mrv_var,exponent,remains;
      sparse_poly1 s;
      if (!mrv_lead_term(e,x,coeff,mrv_var,exponent,s,ordre,contextptr,true)){
#ifdef EMCC
	return undef;
#else
	return gensizeerr(contextptr);
#endif
      }
      if (series_flags(contextptr) & (1<<4) ) 
	return s; // no back conversion if bit 4 is set
      return sparse_poly12gen_expand(s,x,mrv_var,ordre,remains,true,contextptr);
    }
    if (lim_point==minus_inf){
      gen coeff,mrv_var,exponent,remains;
      sparse_poly1 s;
      if (!mrv_lead_term(subst(e,x,-x,false,contextptr),x,coeff,mrv_var,exponent,s,ordre,contextptr,true))
	return gensizeerr(contextptr);
      if (series_flags(contextptr) & (1<<4) ) 
	return s; // no back conversion if bit 4 is set
      return subst(sparse_poly12gen_expand(s,x,mrv_var,ordre,remains,true,contextptr),x,-x,false,contextptr);
    }
    if (direction==1){
      gen ecopy=subst(e,x,lim_point+inv(x,contextptr),false,contextptr);
      gen coeff,mrv_var,exponent,remains;
      sparse_poly1 s;
      if (!mrv_lead_term(ecopy,x,coeff,mrv_var,exponent,s,ordre,contextptr,true))
	return gensizeerr(contextptr);
      if (series_flags(contextptr) & (1<<4) ) 
	return s; // no back conversion if bit 4 is set
      return subst(sparse_poly12gen_expand(s,x,mrv_var,ordre,remains,true,contextptr),x,inv(x-lim_point,contextptr),false,contextptr);
    }
    if (direction==-1){
      gen ecopy=subst(e,x,lim_point-inv(x,contextptr),false,contextptr);
      gen coeff,mrv_var,exponent,remains;
      sparse_poly1 s;
      if (!mrv_lead_term(ecopy,x,coeff,mrv_var,exponent,s,ordre,contextptr,true))
	return gensizeerr(contextptr);
      if (series_flags(contextptr) & (1<<4) ) 
	return s; // no back conversion if bit 4 is set
      return subst(sparse_poly12gen_expand(s,x,mrv_var,ordre,remains,true,contextptr),x,inv(lim_point-x,contextptr),false,contextptr);
    }
    gen remains;
    switch (e.type){
    case _INT_: case _ZINT: case _DOUBLE_: case _CPLX:
      return e;
    case _IDNT:
      if ( !ordre && (*e._IDNTptr==x) )
	return lim_point+(x-lim_point)*order_size(x-lim_point,contextptr);
      else
	return e;
    case _SYMB: {
      sparse_poly1 s;
      s=ck_series__SPOL1(e,x,lim_point,ordre,direction,contextptr);
      if (series_flags(contextptr) & (1<<4) ) 
	return s; // no back conversion if bit 4 is set
      return sparse_poly12gen(s,x-lim_point,remains,true);
    }
    default:
      return symbolic(at_series,makesequence(e,x,lim_point,ordre));
    }
  }

  // Main series entry point
  gen series(const gen & e_,const identificateur & x,const gen & lim_point,int ordre,int direction,GIAC_CONTEXT){
    gen e(e_);
    int save_series_flags=series_flags(contextptr);
    series_flags(save_series_flags | 8,contextptr);
    if (has_op(e,*at_surd) || has_op(e,*at_NTHROOT)){
      vecteur ls(lop(e,at_NTHROOT)),lsa,lsb;
      for (int i=0;i<ls.size();++i){
	vecteur v=*ls[i]._SYMBptr->feuille._VECTptr;
	if (v[0].type==_INT_ && v[0].val%2){
	  gen li=limit(v[1],x,lim_point,direction,contextptr);
	  if (!is_zero(li) && is_positive(-li,contextptr)){
	    lsa.push_back(ls[i]);
	    lsb.push_back(-symbolic(at_NTHROOT,makesequence(v[0],-v[1])));
	  }
	}
      }
      if (!lsa.empty())
	e=subst(e,lsa,lsb,false,contextptr);
      vecteur subst1,subst2;
      surd2pow(e,subst1,subst2,contextptr);
      gen g=subst(e,subst1,subst2,false,contextptr);
      g=series(g,x,lim_point,ordre,direction,contextptr);
      series_flags(save_series_flags,contextptr);
      return subst(g,subst2,subst1,false,contextptr);
    }
    if (e.type==_VECT){
      vecteur res = *e._VECTptr;
      int l=int(res.size());
      for (int i=0;i<l;++i){
	res[i]=in_series(_pow2exp(tan2sincos(res[i],contextptr),contextptr),x,lim_point,ordre,direction,contextptr);
      }
      series_flags(save_series_flags,contextptr);
      return res;
    }
    gen res=in_series(_pow2exp(tan2sincos(e,contextptr),contextptr),x,lim_point,ordre,direction,contextptr);
    series_flags(save_series_flags,contextptr);
    return res;
  }

  gen series(const gen & e,const gen & vars,const gen & lim_point,int ordre,int direction,GIAC_CONTEXT){
    gen x,l;
    if (is_equal(vars)){
      // vars= x==lim_point, overwrites lim_point definition
      // direction is given by lim_point (for interactive input)
      x = (*(vars._SYMBptr->feuille._VECTptr)) [0];
      l = (*(vars._SYMBptr->feuille._VECTptr)) [1];
      if (lim_point.type!=_INT_)
	return gensizeerr(contextptr);
      if (absint(lim_point.val)>0){
	if (!direction && absint(ordre)<2)
	  direction=ordre;
	ordre=absint(lim_point.val);
      }
      else
	direction = lim_point.val;
    }
    else {
      x=vars;
      l=lim_point;
    }
    if (x.type==_VECT && l.type==_VECT){
      vecteur &v=*x._VECTptr;
      gen h(identificateur(" h"));
      vecteur w=addvecteur(*l._VECTptr,multvecteur(h,v));
      gen newe=subst(e,v,w,false,contextptr);
      sparse_poly1 res=series__SPOL1(newe,*h._IDNTptr,zero,ordre,direction,contextptr);
      poly_truncate(res,ordre,contextptr);
      if (!res.empty() && is_undef(res.back().coeff))
	res.pop_back();
      // order term has been removed
      gen remains;
      gen r=sparse_poly12gen(res,1,remains,false);
      return subst(r,v,subvecteur(v,*l._VECTptr),false,contextptr);
    }
    if (x.type!=_IDNT){
      identificateur xx("x");
      gen res=series(subst(e,x,xx,false,contextptr),xx,l,ordre,direction,contextptr);
      return subst(res,xx,x,false,contextptr);
    }
    return series(e,*x._IDNTptr,l,ordre,direction,contextptr);
  }

  gen series(const gen & e,const gen & vars,const gen & lim_point,const gen & ordre0,GIAC_CONTEXT){
    gen ordre(ordre0);
    if (!is_integral(ordre))
      return gensizeerr(contextptr);
    return series(e,vars,lim_point,ordre.val,0,contextptr); // it's the direction
  }

  // "unary" version
  static const char _series_s []="series";
  gen _series(const gen & args,GIAC_CONTEXT){
    if ( args.type==_STRNG && args.subtype==-1) return  args;
    if (args.type==_SPOL1)
      return args;
    if (args.type==_VECT && args._VECTptr->size()==2 && args._VECTptr->front().type==_STRNG && args._VECTptr->back().type==_INT_){
      int n=args._VECTptr->back().val;
      if (n<=0 || n>1024)
	return gensizeerr("Default series order must be >0 and <=1024");
      series_default_order(n,contextptr);
      return _series(args._VECTptr->front(),contextptr);
    }
    if (args.type==_STRNG && args._STRNGptr->size()==1){
      char ch=(*args._STRNGptr)[0];
      gen h(*args._STRNGptr,contextptr);
      series_variable_name(ch,contextptr);
      sparse_poly1 s(1,monome(1,1));
      sto(s,h,contextptr);
      series_flags(contextptr) = series_flags(contextptr) | (1<<5);
      *logptr(contextptr) << "Setting " << ch << " as series variable name" << '\n';
      string Os=abs_calc_mode(contextptr)==38?"b":"O";
      gen O(Os,contextptr);
      if (eval(O,1,contextptr)!=O)
	*logptr(contextptr) << "Purge "<<Os<<" if you want to use "<<Os<<"("<< h <<"^...) notation"<< '\n';
      else {
	gen prog=symb_program(vx_var,0,vx_var*symbolic(at_order_size,h),contextptr);
	*logptr(contextptr) << "Assigning "<<Os<<" so that you can use use "<<Os<<"("<< h<<"^...) notation"<< '\n';
	sto(prog,O,contextptr);
	series_flags(contextptr)=series_flags(contextptr) | (1<<6) ;
      }
      return s;
    }
    if (args.type!=_VECT)
      return series(args,vx_var,0,series_default_order(contextptr),0,contextptr);
    vecteur v=*args._VECTptr;
    if (v.empty())
      return gensizeerr(contextptr);
    if (v.back().type==_INT_ && v.back().subtype==_INT_MAPLECONVERSION && v.back().val==_POLY1__VECT){
      gen p=v.back();
      v.pop_back();
      gen res=_series(gen(v,_SEQ__VECT),contextptr);
      res=_convert(makesequence(res,p),contextptr);
      return res;
    }
    v[0]=Heavisidetosign(when2sign(piecewise2when(v[0],contextptr),contextptr),contextptr);
    int s=int(v.size());
    if (!s)
      toofewargs(_series_s);
    if (s==1)
      return series( v[0],vx_var,0,series_default_order(contextptr),0,contextptr);
    if (s==2){
      if (v[1].type==_INT_)
	return series( v[0],vx_var,0,v[1],contextptr);	
      return series( v[0],v[1],0,series_default_order(contextptr),contextptr);
    }
    if (s==3){
      if ( (v[1].type==_VECT && v[2].type==_VECT) ||
	   ( v[1].type==_IDNT || ( v[1].type==_SYMB && (v[1]._SYMBptr->sommet==at_equal || v[1]._SYMBptr->sommet==at_equal2 || v[1]._SYMBptr->sommet==at_at ) ) )
	   )
	return series( v[0],v[1],v[2],series_default_order(contextptr),contextptr);
      if (v[1].type==_VECT){
	vecteur vars=*v[1]._VECTptr,vals(vars.size());
	for (int i=0;i<vars.size();++i){
	  if (vars[i].is_symb_of_sommet(at_equal)){
	    vals[i]=vars[i]._SYMBptr->feuille[1];
	    vars[i]=vars[i]._SYMBptr->feuille[0];
	  }
	}
	return series(v[0],vars,vals,v[2],contextptr);
      }
      return series( v[0],symbolic(at_equal,makesequence(vx_var,v[1])),v[2],series_default_order(contextptr),contextptr);
    }
    if (s==4)
      return series( v[0],v[1],v[2],v[3],contextptr);    
    if (s>5 || v[3].type!=_INT_ || v[4].type!=_INT_)
      return gentoomanyargs(_series_s);
    return series(v[0],v[1],v[2],v[3].val,v[4].val,contextptr);
  }
  static define_unary_function_eval (__series,&_series,_series_s);
  define_unary_function_ptr5( at_series ,alias_at_series,&__series,0,true);

  // "unary" version
  static const char _revert_s []="revert";
  gen _revert(const gen & args,GIAC_CONTEXT){
    if ( args.type==_STRNG && args.subtype==-1) return  args;
    if (args.type==_SPOL1){
      const sparse_poly1 & s=*args._SPOL1ptr;
      if (s.empty() || s.front().exponent==0)
	return gensizeerr("Not invertible for composition");
      sparse_poly1 res;
      if (!prevert(s,res,contextptr))
	return gensizeerr("Not invertible for composition");
      return res;
    }
    vecteur v=gen2vecteur(args);
    if (v.empty())
      return gensizeerr(contextptr);
    gen g=v[0],x;
    if (v.size()==1)
      x=vx_var;
    else
      x=v[1];
    if (x.type!=_IDNT){
      identificateur idx(" trevert");
      return _revert(subst(args,x,idx,false,contextptr),contextptr);
    }
    // find ordre
    int ordre=series_default_order(contextptr);
    if (v.size()>2 && v[2].type==_INT_)
      ordre=v[2].val;
    vecteur w=lop(g,at_order_size);
    if (w.size()==1){
      gen xn=derive(g,w.front(),contextptr);
      if (is_undef(xn)) return xn;
      if (xn.is_symb_of_sommet(at_pow)){
	gen & f=xn._SYMBptr->feuille;
	if (f.type==_VECT && f._VECTptr->size()==2 && f._VECTptr->back().type==_INT_){
	  ordre=f._VECTptr->back().val;
	  w.clear();
	  g=subst(g,w.front(),0,false,contextptr);
	} 
      }
    }
    if (!w.empty())
      return gensizeerr(contextptr);
    sparse_poly1 p=series__SPOL1(g,*x._IDNTptr,zero,ordre,0,contextptr),res;
    if (!prevert(p,res,contextptr))
      return gensizeerr(contextptr);
    gen remains;
    return sparse_poly12gen(res,x,remains,false);
  }
  static define_unary_function_eval (__revert,&_revert,_revert_s);
  define_unary_function_ptr5( at_revert ,alias_at_revert,&__revert,0,true);

  static const char _bounded_function_s []="bounded_function";
  gen _bounded_function(const gen & args,GIAC_CONTEXT){
    if ( args.type==_STRNG && args.subtype==-1) return  args;
    return symbolic(at_bounded_function,args);
  }
  gen bounded_function(GIAC_CONTEXT){
    int i=bounded_function_no(contextptr);
    ++i;
    bounded_function_no(i,contextptr);
    return symbolic(at_bounded_function,i);
  }
  static define_unary_function_eval (__bounded_function,&_bounded_function,_bounded_function_s);
  define_unary_function_ptr5( at_bounded_function ,alias_at_bounded_function,&__bounded_function,0,true);

  // internal function, used to replace sum for limit/series
  // args = expression, antiderivative, variable, lower_bound, upper_bound
  static const char _euler_mac_laurin_s []="euler_mac_laurin";
  gen _euler_mac_laurin(const gen & args,GIAC_CONTEXT){
    if ( args.type==_STRNG && args.subtype==-1) return  args;
    return symbolic(at_euler_mac_laurin,args);
  }
  static define_unary_function_eval (__euler_mac_laurin,&_euler_mac_laurin,_euler_mac_laurin_s);
  define_unary_function_ptr5( at_euler_mac_laurin ,alias_at_euler_mac_laurin,&__euler_mac_laurin,0,true);

  bool convert_to_euler_mac_laurin(const gen & g,const identificateur & n,gen & res,GIAC_CONTEXT){
    if (g.is_symb_of_sommet(at_sum)){
      gen & f = g._SYMBptr->feuille;
      if (f.type!=_VECT || f._VECTptr->size()!=4)
	return false;
      gen l=in_limit((f[3]-f[2])/n,n,plus_inf,1,contextptr);
      if (is_zero(l) || is_undef(l) || is_inf(l))
	return false;
      // check that the expression to be summed has a derivative
      // which is a o(expression) as n -> inf
      gen f0=f._VECTptr->front();
      gen x =f[1];
      if (x.type!=_IDNT){
	*logptr(contextptr) << gettext("Unable to convert to euler mac laurin") << ' ';
	return false;
      }
      gen f0prime=derive(f0,x,contextptr), f03=derive(f0prime,x,contextptr);
      f03=derive(f03,x,contextptr);
      if (is_undef(f03)) return false;
      l=in_limit(f03/f0prime,n,plus_inf,1,contextptr);
      if (!is_zero(l)) 
	return false;
      gen remains;
      gen F0=integrate_gen_rem(f0,x,remains,0,contextptr);
      if (!is_zero(remains) || is_undef(F0))
	return false;
      res=symbolic(at_euler_mac_laurin,gen(makevecteur(f0,F0,x,f[2],f[3]),_SEQ__VECT));
      return true;
    }
    vecteur v=lop(g,at_sum);
    vecteur w=v;
    int s=int(v.size());
    for (int i=0;i<s;++i){
      if (!convert_to_euler_mac_laurin(v[i],n,w[i],contextptr))
	return false;
    }
    res=subst(g,v,w,false,contextptr);
    return true;
  }

#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // ndef NO_NAMESPACE_GIAC