]> www.ginac.de Git - ginac.git/blobdiff - ginac/expairseq.cpp
Index renaming issues, sped up simplify_indexed, used defined NC-objects
[ginac.git] / ginac / expairseq.cpp
index 96da57c272ae403f8312536324a6c1731141d704..9f580d9e768ff4ac58c5fcaaa0865124ad7069fd 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of sequences of expression pairs. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2005 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
+#include <iostream>
 #include <algorithm>
 #include <string>
 #include <stdexcept>
 
 #include "expairseq.h"
 #include "lst.h"
+#include "mul.h"
+#include "power.h"
 #include "relational.h"
-#include "print.h"
+#include "wildcard.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "operators.h"
 #include "utils.h"
+#include "indexed.h"
 
 #if EXPAIRSEQ_USE_HASHTAB
 #include <cmath>
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS_NO_CTORS(expairseq, basic)
+       
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(expairseq, basic,
+  print_func<print_context>(&expairseq::do_print).
+  print_func<print_tree>(&expairseq::do_print_tree))
+
 
 //////////
 // helper classes
@@ -54,33 +62,23 @@ public:
 };
 
 //////////
-// default ctor, dtor, copy ctor assignment operator and helpers
+// default constructor
 //////////
 
 // public
 
-expairseq::expairseq(const expairseq &other)
-{
-       debugmsg("expairseq copy ctor",LOGLEVEL_CONSTRUCT);
-       copy(other);
-}
-
-const expairseq &expairseq::operator=(const expairseq &other)
-{
-       debugmsg("expairseq operator=",LOGLEVEL_ASSIGNMENT);
-       if (this != &other) {
-               destroy(true);
-               copy(other);
-       }
-       return *this;
-}
+expairseq::expairseq() : inherited(TINFO_expairseq)
+#if EXPAIRSEQ_USE_HASHTAB
+                                                   , hashtabsize(0)
+#endif // EXPAIRSEQ_USE_HASHTAB
+{}
 
 // protected
 
+#if 0
 /** For use by copy ctor and assignment operator. */
 void expairseq::copy(const expairseq &other)
 {
-       inherited::copy(other);
        seq = other.seq;
        overall_coeff = other.overall_coeff;
 #if EXPAIRSEQ_USE_HASHTAB
@@ -102,23 +100,20 @@ void expairseq::copy(const expairseq &other)
        }
 #endif // EXPAIRSEQ_USE_HASHTAB
 }
-
-DEFAULT_DESTROY(expairseq)
+#endif
 
 //////////
-// other ctors
+// other constructors
 //////////
 
 expairseq::expairseq(const ex &lh, const ex &rh) : inherited(TINFO_expairseq)
 {
-       debugmsg("expairseq ctor from ex,ex",LOGLEVEL_CONSTRUCT);
        construct_from_2_ex(lh,rh);
        GINAC_ASSERT(is_canonical());
 }
 
 expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 {
-       debugmsg("expairseq ctor from exvector",LOGLEVEL_CONSTRUCT);
        construct_from_exvector(v);
        GINAC_ASSERT(is_canonical());
 }
@@ -126,18 +121,17 @@ expairseq::expairseq(const exvector &v) : inherited(TINFO_expairseq)
 expairseq::expairseq(const epvector &v, const ex &oc)
   : inherited(TINFO_expairseq), overall_coeff(oc)
 {
-       debugmsg("expairseq ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
+       GINAC_ASSERT(is_a<numeric>(oc));
        construct_from_epvector(v);
        GINAC_ASSERT(is_canonical());
 }
 
-expairseq::expairseq(epvector *vp, const ex &oc)
+expairseq::expairseq(std::auto_ptr<epvector> vp, const ex &oc)
   : inherited(TINFO_expairseq), overall_coeff(oc)
 {
-       debugmsg("expairseq ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-       GINAC_ASSERT(vp!=0);
+       GINAC_ASSERT(vp.get()!=0);
+       GINAC_ASSERT(is_a<numeric>(oc));
        construct_from_epvector(*vp);
-       delete vp;
        GINAC_ASSERT(is_canonical());
 }
 
@@ -145,12 +139,11 @@ expairseq::expairseq(epvector *vp, const ex &oc)
 // archiving
 //////////
 
-expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+expairseq::expairseq(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
 #if EXPAIRSEQ_USE_HASHTAB
        , hashtabsize(0)
 #endif
 {
-       debugmsg("expairseq ctor from archive_node", LOGLEVEL_CONSTRUCT);
        for (unsigned int i=0; true; i++) {
                ex rest;
                ex coeff;
@@ -159,7 +152,11 @@ expairseq::expairseq(const archive_node &n, const lst &sym_lst) : inherited(n, s
                else
                        break;
        }
+
        n.find_ex("overall_coeff", overall_coeff, sym_lst);
+
+       canonicalize();
+       GINAC_ASSERT(is_canonical());
 }
 
 void expairseq::archive(archive_node &n) const
@@ -177,101 +174,90 @@ void expairseq::archive(archive_node &n) const
 DEFAULT_UNARCHIVE(expairseq)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-basic *expairseq::duplicate() const
+void expairseq::do_print(const print_context & c, unsigned level) const
 {
-       debugmsg("expairseq duplicate",LOGLEVEL_DUPLICATE);
-       return new expairseq(*this);
+       c.s << "[[";
+       printseq(c, ',', precedence(), level);
+       c.s << "]]";
 }
 
-void expairseq::print(const print_context & c, unsigned level) const
+void expairseq::do_print_tree(const print_tree & c, unsigned level) const
 {
-       debugmsg("expairseq print",LOGLEVEL_PRINT);
-
-       if (is_of_type(c, print_tree)) {
-
-               unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
-
-               c.s << std::string(level, ' ') << class_name()
-                   << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
-                   << ", nops=" << nops()
-                   << std::endl;
-               unsigned num = seq.size();
-               for (unsigned i=0; i<num; ++i) {
-                       seq[i].rest.print(c, level + delta_indent);
-                       seq[i].coeff.print(c, level + delta_indent);
-                       if (i != num - 1)
-                               c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
-               }
-               if (!overall_coeff.is_equal(default_overall_coeff())) {
-                       c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
-                           << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
-                       overall_coeff.print(c, level + delta_indent);
-               }
-               c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
+       c.s << std::string(level, ' ') << class_name() << " @" << this
+           << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+           << ", nops=" << nops()
+           << std::endl;
+       size_t num = seq.size();
+       for (size_t i=0; i<num; ++i) {
+               seq[i].rest.print(c, level + c.delta_indent);
+               seq[i].coeff.print(c, level + c.delta_indent);
+               if (i != num - 1)
+                       c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
+       }
+       if (!overall_coeff.is_equal(default_overall_coeff())) {
+               c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl
+                   << std::string(level + c.delta_indent, ' ') << "overall_coeff" << std::endl;
+               overall_coeff.print(c, level + c.delta_indent);
+       }
+       c.s << std::string(level + c.delta_indent,' ') << "=====" << std::endl;
 #if EXPAIRSEQ_USE_HASHTAB
-               c.s << std::string(level + delta_indent,' ')
-                   << "hashtab size " << hashtabsize << std::endl;
-               if (hashtabsize == 0) return;
+       c.s << std::string(level + c.delta_indent,' ')
+           << "hashtab size " << hashtabsize << std::endl;
+       if (hashtabsize == 0) return;
 #define MAXCOUNT 5
-               unsigned count[MAXCOUNT+1];
-               for (int i=0; i<MAXCOUNT+1; ++i)
-                       count[i] = 0;
-               unsigned this_bin_fill;
-               unsigned cum_fill_sq = 0;
-               unsigned cum_fill = 0;
-               for (unsigned i=0; i<hashtabsize; ++i) {
-                       this_bin_fill = 0;
-                       if (hashtab[i].size() > 0) {
-                               c.s << std::string(level + delta_indent, ' ')
-                                   << "bin " << i << " with entries ";
-                               for (epplist::const_iterator it=hashtab[i].begin();
-                                    it!=hashtab[i].end(); ++it) {
-                                       c.s << *it-seq.begin() << " ";
-                                       ++this_bin_fill;
-                               }
-                               os << std::endl;
-                               cum_fill += this_bin_fill;
-                               cum_fill_sq += this_bin_fill*this_bin_fill;
+       unsigned count[MAXCOUNT+1];
+       for (int i=0; i<MAXCOUNT+1; ++i)
+               count[i] = 0;
+       unsigned this_bin_fill;
+       unsigned cum_fill_sq = 0;
+       unsigned cum_fill = 0;
+       for (unsigned i=0; i<hashtabsize; ++i) {
+               this_bin_fill = 0;
+               if (hashtab[i].size() > 0) {
+                       c.s << std::string(level + c.delta_indent, ' ')
+                           << "bin " << i << " with entries ";
+                       for (epplist::const_iterator it=hashtab[i].begin();
+                            it!=hashtab[i].end(); ++it) {
+                               c.s << *it-seq.begin() << " ";
+                               ++this_bin_fill;
                        }
-                       if (this_bin_fill<MAXCOUNT)
-                               ++count[this_bin_fill];
-                       else
-                               ++count[MAXCOUNT];
-               }
-               unsigned fact = 1;
-               double cum_prob = 0;
-               double lambda = (1.0*seq.size()) / hashtabsize;
-               for (int k=0; k<MAXCOUNT; ++k) {
-                       if (k>0)
-                               fact *= k;
-                       double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
-                       cum_prob += prob;
-                       c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
-                           << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
-                           << int(prob*1000)/10.0 << ")" << std::endl;
+                       c.s << std::endl;
+                       cum_fill += this_bin_fill;
+                       cum_fill_sq += this_bin_fill*this_bin_fill;
                }
-               c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
-                   << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
-                   << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
-       
-               c.s << std::string(level + delta_indent, ' ') << "variance: "
-                   << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
-                   << std::endl;
-               c.s << std::string(level + delta_indent, ' ') << "average fill: "
-                   << (1.0*cum_fill)/hashtabsize
-                   << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
-#endif // EXPAIRSEQ_USE_HASHTAB
-
-       } else {
-               c.s << "[[";
-               printseq(c, ',', precedence(), level);
-               c.s << "]]";
+               if (this_bin_fill<MAXCOUNT)
+                       ++count[this_bin_fill];
+               else
+                       ++count[MAXCOUNT];
+       }
+       unsigned fact = 1;
+       double cum_prob = 0;
+       double lambda = (1.0*seq.size()) / hashtabsize;
+       for (int k=0; k<MAXCOUNT; ++k) {
+               if (k>0)
+                       fact *= k;
+               double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
+               cum_prob += prob;
+               c.s << std::string(level + c.delta_indent, ' ') << "bins with " << k << " entries: "
+                   << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
+                   << int(prob*1000)/10.0 << ")" << std::endl;
        }
+       c.s << std::string(level + c.delta_indent, ' ') << "bins with more entries: "
+           << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
+           << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
+
+       c.s << std::string(level + c.delta_indent, ' ') << "variance: "
+           << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
+           << std::endl;
+       c.s << std::string(level + c.delta_indent, ' ') << "average fill: "
+           << (1.0*cum_fill)/hashtabsize
+           << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
+#endif // EXPAIRSEQ_USE_HASHTAB
 }
 
 bool expairseq::info(unsigned inf) const
@@ -279,7 +265,7 @@ bool expairseq::info(unsigned inf) const
        return inherited::info(inf);
 }
 
-unsigned expairseq::nops() const
+size_t expairseq::nops() const
 {
        if (overall_coeff.is_equal(default_overall_coeff()))
                return seq.size();
@@ -287,43 +273,78 @@ unsigned expairseq::nops() const
                return seq.size()+1;
 }
 
-ex expairseq::op(int i) const
+ex expairseq::op(size_t i) const
 {
-       if (unsigned(i)<seq.size())
+       if (i < seq.size())
                return recombine_pair_to_ex(seq[i]);
        GINAC_ASSERT(!overall_coeff.is_equal(default_overall_coeff()));
        return overall_coeff;
 }
 
-ex &expairseq::let_op(int i)
+ex expairseq::map(map_function &f) const
 {
-       throw(std::logic_error("let_op not defined for expairseq and derived classes (add,mul,...)"));
-}
-
-ex expairseq::map(map_function & f) const
-{
-       epvector *v = new epvector;
+       std::auto_ptr<epvector> v(new epvector);
        v->reserve(seq.size());
 
        epvector::const_iterator cit = seq.begin(), last = seq.end();
        while (cit != last) {
                v->push_back(split_ex_to_pair(f(recombine_pair_to_ex(*cit))));
-               cit++;
+               ++cit;
        }
 
-       return thisexpairseq(v, f(overall_coeff));
+       if (overall_coeff.is_equal(default_overall_coeff()))
+               return thisexpairseq(v, default_overall_coeff());
+       else
+               return thisexpairseq(v, f(overall_coeff));
 }
 
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
 ex expairseq::eval(int level) const
 {
        if ((level==1) && (flags &status_flags::evaluated))
                return *this;
        
-       epvector *vp = evalchildren(level);
-       if (vp==0)
+       std::auto_ptr<epvector> vp = evalchildren(level);
+       if (vp.get() == 0)
                return this->hold();
        
-       return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
+       return (new expairseq(vp, overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
+}
+
+epvector* conjugateepvector(const epvector&epv)
+{
+       epvector *newepv = 0;
+       for (epvector::const_iterator i=epv.begin(); i!=epv.end(); ++i) {
+               if(newepv) {
+                       newepv->push_back(i->conjugate());
+                       continue;
+               }
+               expair x = i->conjugate();
+               if (x.is_equal(*i)) {
+                       continue;
+               }
+               newepv = new epvector;
+               newepv->reserve(epv.size());
+               for (epvector::const_iterator j=epv.begin(); j!=i; ++j) {
+                       newepv->push_back(*j);
+               }
+               newepv->push_back(x);
+       }
+       return newepv;
+}
+
+ex expairseq::conjugate() const
+{
+       epvector* newepv = conjugateepvector(seq);
+       ex x = overall_coeff.conjugate();
+       if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
+               return *this;
+       }
+       ex result = thisexpairseq(newepv ? *newepv : seq, x);
+       if (newepv) {
+               delete newepv;
+       }
+       return result;
 }
 
 bool expairseq::match(const ex & pattern, lst & repl_lst) const
@@ -331,14 +352,14 @@ bool expairseq::match(const ex & pattern, lst & repl_lst) const
        // This differs from basic::match() because we want "a+b+c+d" to
        // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
 
-       if (tinfo() == pattern.bp->tinfo()) {
+       if (this->tinfo() == ex_to<basic>(pattern).tinfo()) {
 
                // Check whether global wildcard (one that matches the "rest of the
                // expression", like "*" above) is present
                bool has_global_wildcard = false;
                ex global_wildcard;
-               for (unsigned int i=0; i<pattern.nops(); i++) {
-                       if (is_ex_exactly_of_type(pattern.op(i), wildcard)) {
+               for (size_t i=0; i<pattern.nops(); i++) {
+                       if (is_exactly_a<wildcard>(pattern.op(i))) {
                                has_global_wildcard = true;
                                global_wildcard = pattern.op(i);
                                break;
@@ -351,12 +372,12 @@ bool expairseq::match(const ex & pattern, lst & repl_lst) const
                // Chop into terms
                exvector ops;
                ops.reserve(nops());
-               for (unsigned i=0; i<nops(); i++)
+               for (size_t i=0; i<nops(); i++)
                        ops.push_back(op(i));
 
                // Now, for every term of the pattern, look for a matching term in
                // the expression and remove the match
-               for (unsigned i=0; i<pattern.nops(); i++) {
+               for (size_t i=0; i<pattern.nops(); i++) {
                        ex p = pattern.op(i);
                        if (has_global_wildcard && p.is_equal(global_wildcard))
                                continue;
@@ -377,15 +398,15 @@ found:            ;
                        // Assign all the remaining terms to the global wildcard (unless
                        // it has already been matched before, in which case the matches
                        // must be equal)
-                       unsigned num = ops.size();
-                       epvector *vp = new epvector();
+                       size_t num = ops.size();
+                       std::auto_ptr<epvector> vp(new epvector);
                        vp->reserve(num);
-                       for (unsigned i=0; i<num; i++)
+                       for (size_t i=0; i<num; i++)
                                vp->push_back(split_ex_to_pair(ops[i]));
                        ex rest = thisexpairseq(vp, default_overall_coeff());
-                       for (unsigned i=0; i<repl_lst.nops(); i++) {
-                               if (repl_lst.op(i).op(0).is_equal(global_wildcard))
-                                       return rest.is_equal(*repl_lst.op(i).op(1).bp);
+                       for (lst::const_iterator it = repl_lst.begin(); it != repl_lst.end(); ++it) {
+                               if (it->op(0).is_equal(global_wildcard))
+                                       return rest.is_equal(it->op(1));
                        }
                        repl_lst.append(global_wildcard == rest);
                        return true;
@@ -400,20 +421,22 @@ found:            ;
        return inherited::match(pattern, repl_lst);
 }
 
-ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
+ex expairseq::subs(const exmap & m, unsigned options) const
 {
-       epvector *vp = subschildren(ls, lr, no_pattern);
-       if (vp)
-               return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
+       std::auto_ptr<epvector> vp = subschildren(m, options);
+       if (vp.get())
+               return ex_to<basic>(thisexpairseq(vp, overall_coeff));
+       else if ((options & subs_options::algebraic) && is_exactly_a<mul>(*this))
+               return static_cast<const mul *>(this)->algebraic_subs_mul(m, options);
        else
-               return basic::subs(ls, lr, no_pattern);
+               return subs_one_level(m, options);
 }
 
 // protected
 
 int expairseq::compare_same_type(const basic &other) const
 {
-       GINAC_ASSERT(is_of_type(other, expairseq));
+       GINAC_ASSERT(is_a<expairseq>(other));
        const expairseq &o = static_cast<const expairseq &>(other);
        
        int cmpval;
@@ -541,30 +564,28 @@ bool expairseq::is_equal_same_type(const basic &other) const
 #endif // EXPAIRSEQ_USE_HASHTAB
 }
 
-unsigned expairseq::return_type(void) const
+unsigned expairseq::return_type() const
 {
        return return_types::noncommutative_composite;
 }
 
-unsigned expairseq::calchash(void) const
+unsigned expairseq::calchash() const
 {
-       unsigned v = golden_ratio_hash(tinfo());
-       epvector::const_iterator i = seq.begin(), end = seq.end();
+       unsigned v = golden_ratio_hash(this->tinfo());
+       epvector::const_iterator i = seq.begin();
+       const epvector::const_iterator end = seq.end();
        while (i != end) {
-#if !EXPAIRSEQ_USE_HASHTAB
-               v = rotate_left_31(v); // rotation would spoil commutativity
-#endif // EXPAIRSEQ_USE_HASHTAB
                v ^= i->rest.gethash();
 #if !EXPAIRSEQ_USE_HASHTAB
-               v = rotate_left_31(v);
+               // rotation spoils commutativity!
+               v = rotate_left(v);
                v ^= i->coeff.gethash();
-#endif // EXPAIRSEQ_USE_HASHTAB
+#endif // !EXPAIRSEQ_USE_HASHTAB
                ++i;
        }
-       
+
        v ^= overall_coeff.gethash();
-       v &= 0x7FFFFFFFU;
-       
+
        // store calculated hash value only if object is already evaluated
        if (flags &status_flags::evaluated) {
                setflag(status_flags::hash_calculated);
@@ -576,12 +597,13 @@ unsigned expairseq::calchash(void) const
 
 ex expairseq::expand(unsigned options) const
 {
-       epvector *vp = expandchildren(options);
-       if (vp == NULL) {
-               // The terms have not changed, so it is safe to declare this expanded
-               return this->setflag(status_flags::expanded);
-       } else
+       std::auto_ptr<epvector> vp = expandchildren(options);
+       if (vp.get())
                return thisexpairseq(vp, overall_coeff);
+       else {
+               // The terms have not changed, so it is safe to declare this expanded
+               return (options == 0) ? setflag(status_flags::expanded) : *this;
+       }
 }
 
 //////////
@@ -600,20 +622,20 @@ ex expairseq::expand(unsigned options) const
  *  definition. */
 ex expairseq::thisexpairseq(const epvector &v, const ex &oc) const
 {
-       return expairseq(v,oc);
+       return expairseq(v, oc);
 }
 
-ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
+ex expairseq::thisexpairseq(std::auto_ptr<epvector> vp, const ex &oc) const
 {
-       return expairseq(vp,oc);
+       return expairseq(vp, oc);
 }
 
 void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 {
        c.s << "[[";
-       p.rest.bp->print(c, precedence());
+       p.rest.print(c, precedence());
        c.s << ",";
-       p.coeff.bp->print(c, precedence());
+       p.coeff.print(c, precedence());
        c.s << "]]";
 }
 
@@ -643,14 +665,14 @@ void expairseq::printseq(const print_context & c, char delim,
  *  @see expairseq::recombine_pair_to_ex() */
 expair expairseq::split_ex_to_pair(const ex &e) const
 {
-       return expair(e,_ex1());
+       return expair(e,_ex1);
 }
 
 
 expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
                                                 const ex &c) const
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
        
        return expair(e,c);
 }
@@ -659,8 +681,8 @@ expair expairseq::combine_ex_with_coeff_to_pair(const ex &e,
 expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
                                                   const ex &c) const
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
-       GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+       GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
        
        return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 }
@@ -681,23 +703,23 @@ bool expairseq::expair_needs_further_processing(epp it)
        return false;
 }
 
-ex expairseq::default_overall_coeff(void) const
+ex expairseq::default_overall_coeff() const
 {
-       return _ex0();
+       return _ex0;
 }
 
 void expairseq::combine_overall_coeff(const ex &c)
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-       GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+       GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
        overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 }
 
 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-       GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
-       GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
+       GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c1));
+       GINAC_ASSERT(is_exactly_a<numeric>(c2));
        overall_coeff = ex_to<numeric>(overall_coeff).
                        add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 }
@@ -727,8 +749,8 @@ void expairseq::construct_from_2_ex_via_exvector(const ex &lh, const ex &rh)
 
 void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 {
-       if (lh.bp->tinfo()==tinfo()) {
-               if (rh.bp->tinfo()==tinfo()) {
+       if (ex_to<basic>(lh).tinfo()==this->tinfo()) {
+               if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 #if EXPAIRSEQ_USE_HASHTAB
                        unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
                                             ex_to<expairseq>(rh).seq.size();
@@ -736,8 +758,15 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
                                construct_from_2_ex_via_exvector(lh,rh);
                        } else {
 #endif // EXPAIRSEQ_USE_HASHTAB
-                               construct_from_2_expairseq(ex_to<expairseq>(lh),
-                                                          ex_to<expairseq>(rh));
+                               if(is_a<mul>(lh))
+                               {       
+                                       ex newrh=rename_dummy_indices_uniquely(lh, rh);
+                                       construct_from_2_expairseq(ex_to<expairseq>(lh),
+                                                                  ex_to<expairseq>(newrh));
+                               }
+                               else
+                                       construct_from_2_expairseq(ex_to<expairseq>(lh),
+                                                                  ex_to<expairseq>(rh));
 #if EXPAIRSEQ_USE_HASHTAB
                        }
 #endif // EXPAIRSEQ_USE_HASHTAB
@@ -755,7 +784,7 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
 #endif // EXPAIRSEQ_USE_HASHTAB
                        return;
                }
-       } else if (rh.bp->tinfo()==tinfo()) {
+       } else if (ex_to<basic>(rh).tinfo()==this->tinfo()) {
 #if EXPAIRSEQ_USE_HASHTAB
                unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
                if (calc_hashtabsize(totalsize)!=0) {
@@ -777,8 +806,8 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
        hashtabsize = 0;
 #endif // EXPAIRSEQ_USE_HASHTAB
        
-       if (is_ex_exactly_of_type(lh,numeric)) {
-               if (is_ex_exactly_of_type(rh,numeric)) {
+       if (is_exactly_a<numeric>(lh)) {
+               if (is_exactly_a<numeric>(rh)) {
                        combine_overall_coeff(lh);
                        combine_overall_coeff(rh);
                } else {
@@ -786,7 +815,7 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
                        seq.push_back(split_ex_to_pair(rh));
                }
        } else {
-               if (is_ex_exactly_of_type(rh,numeric)) {
+               if (is_exactly_a<numeric>(rh)) {
                        combine_overall_coeff(rh);
                        seq.push_back(split_ex_to_pair(lh));
                } else {
@@ -795,7 +824,7 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
                        
                        int cmpval = p1.rest.compare(p2.rest);
                        if (cmpval==0) {
-                               p1.coeff=ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
+                               p1.coeff = ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
                                if (!ex_to<numeric>(p1.coeff).is_zero()) {
                                        // no further processing is necessary, since this
                                        // one element will usually be recombined in eval()
@@ -834,10 +863,10 @@ void expairseq::construct_from_2_expairseq(const expairseq &s1,
                int cmpval = (*first1).rest.compare((*first2).rest);
                if (cmpval==0) {
                        // combine terms
-                       const numeric &newcoeff = ex_to<numeric>((*first1).coeff).
-                                                  add(ex_to<numeric>((*first2).coeff));
+                       const numeric &newcoeff = ex_to<numeric>(first1->coeff).
+                                                  add(ex_to<numeric>(first2->coeff));
                        if (!newcoeff.is_zero()) {
-                               seq.push_back(expair((*first1).rest,newcoeff));
+                               seq.push_back(expair(first1->rest,newcoeff));
                                if (expair_needs_further_processing(seq.end()-1)) {
                                        needs_further_processing = true;
                                }
@@ -873,7 +902,7 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
                                                                                        const ex &e)
 {
        combine_overall_coeff(s.overall_coeff);
-       if (is_ex_exactly_of_type(e,numeric)) {
+       if (is_exactly_a<numeric>(e)) {
                combine_overall_coeff(e);
                seq = s.seq;
                return;
@@ -890,16 +919,15 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
        
        // merge p into s.seq
        while (first!=last) {
-               int cmpval=(*first).rest.compare(p.rest);
+               int cmpval = (*first).rest.compare(p.rest);
                if (cmpval==0) {
                        // combine terms
-                       const numeric &newcoeff = ex_to<numeric>((*first).coeff).
+                       const numeric &newcoeff = ex_to<numeric>(first->coeff).
                                                   add(ex_to<numeric>(p.coeff));
                        if (!newcoeff.is_zero()) {
-                               seq.push_back(expair((*first).rest,newcoeff));
-                               if (expair_needs_further_processing(seq.end()-1)) {
+                               seq.push_back(expair(first->rest,newcoeff));
+                               if (expair_needs_further_processing(seq.end()-1))
                                        needs_further_processing = true;
-                               }
                        }
                        ++first;
                        p_pushed = true;
@@ -977,7 +1005,7 @@ void expairseq::make_flat(const exvector &v)
        
        cit = v.begin();
        while (cit!=v.end()) {
-               if (cit->bp->tinfo()==this->tinfo()) {
+               if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
                        ++nexpairseqs;
                        noperands += ex_to<expairseq>(*cit).seq.size();
                }
@@ -988,18 +1016,32 @@ void expairseq::make_flat(const exvector &v)
        seq.reserve(v.size()+noperands-nexpairseqs);
        
        // copy elements and split off numerical part
+       exvector dummy_indices;
        cit = v.begin();
        while (cit!=v.end()) {
-               if (cit->bp->tinfo()==this->tinfo()) {
-                       const expairseq &subseqref = ex_to<expairseq>(*cit);
-                       combine_overall_coeff(subseqref.overall_coeff);
-                       epvector::const_iterator cit_s = subseqref.seq.begin();
-                       while (cit_s!=subseqref.seq.end()) {
+               if (ex_to<basic>(*cit).tinfo()==this->tinfo()) {
+                       const expairseq *subseqref;
+                       ex newfactor;
+                       if(is_a<mul>(*cit))
+                       {
+                               exvector dummies_of_factor = get_all_dummy_indices(*cit);
+                               sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
+                               newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, *cit);
+                               subseqref = &(ex_to<expairseq>(newfactor));
+                               exvector new_dummy_indices;
+                               set_union(dummy_indices.begin(), dummy_indices.end(), dummies_of_factor.begin(), dummies_of_factor.end(), std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
+                               dummy_indices.swap(new_dummy_indices);
+                       }
+                       else
+                               subseqref = &ex_to<expairseq>(*cit);
+                       combine_overall_coeff(subseqref->overall_coeff);
+                       epvector::const_iterator cit_s = subseqref->seq.begin();
+                       while (cit_s!=subseqref->seq.end()) {
                                seq.push_back(*cit_s);
                                ++cit_s;
                        }
                } else {
-                       if (is_ex_exactly_of_type(*cit,numeric))
+                       if (is_exactly_a<numeric>(*cit))
                                combine_overall_coeff(*cit);
                        else
                                seq.push_back(split_ex_to_pair(*cit));
@@ -1021,9 +1063,9 @@ void expairseq::make_flat(const epvector &v)
        
        cit = v.begin();
        while (cit!=v.end()) {
-               if (cit->rest.bp->tinfo()==this->tinfo()) {
+               if (ex_to<basic>(cit->rest).tinfo()==this->tinfo()) {
                        ++nexpairseqs;
-                       noperands += ex_to<expairseq>((*cit).rest).seq.size();
+                       noperands += ex_to<expairseq>(cit->rest).seq.size();
                }
                ++cit;
        }
@@ -1034,15 +1076,15 @@ void expairseq::make_flat(const epvector &v)
        // copy elements and split off numerical part
        cit = v.begin();
        while (cit!=v.end()) {
-               if (cit->rest.bp->tinfo()==this->tinfo() &&
+               if (ex_to<basic>(cit->rest).tinfo()==this->tinfo() &&
                    this->can_make_flat(*cit)) {
-                       const expairseq &subseqref = ex_to<expairseq>((*cit).rest);
+                       const expairseq &subseqref = ex_to<expairseq>(cit->rest);
                        combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
-                                                           ex_to<numeric>((*cit).coeff));
+                                                           ex_to<numeric>(cit->coeff));
                        epvector::const_iterator cit_s = subseqref.seq.begin();
                        while (cit_s!=subseqref.seq.end()) {
-                               seq.push_back(expair((*cit_s).rest,
-                                                    ex_to<numeric>((*cit_s).coeff).mul_dyn(ex_to<numeric>((*cit).coeff))));
+                               seq.push_back(expair(cit_s->rest,
+                                                    ex_to<numeric>(cit_s->coeff).mul_dyn(ex_to<numeric>(cit->coeff))));
                                //seq.push_back(combine_pair_with_coeff_to_pair(*cit_s,
                                //                                              (*cit).coeff));
                                ++cit_s;
@@ -1058,53 +1100,54 @@ void expairseq::make_flat(const epvector &v)
 }
 
 /** Brings this expairseq into a sorted (canonical) form. */
-void expairseq::canonicalize(void)
+void expairseq::canonicalize()
 {
-       sort(seq.begin(), seq.end(), expair_is_less());
+       std::sort(seq.begin(), seq.end(), expair_rest_is_less());
 }
 
 
 /** Compact a presorted expairseq by combining all matching expairs to one
  *  each.  On an add object, this is responsible for 2*x+3*x+y -> 5*x+y, for
  *  instance. */
-void expairseq::combine_same_terms_sorted_seq(void)
+void expairseq::combine_same_terms_sorted_seq()
 {
+       if (seq.size()<2)
+               return;
+
        bool needs_further_processing = false;
-       
-       if (seq.size()>1) {
-               epvector::iterator itin1 = seq.begin();
-               epvector::iterator itin2 = itin1+1;
-               epvector::iterator itout = itin1;
-               epvector::iterator last = seq.end();
-               // must_copy will be set to true the first time some combination is 
-               // possible from then on the sequence has changed and must be compacted
-               bool must_copy = false;
-               while (itin2!=last) {
-                       if ((*itin1).rest.compare((*itin2).rest)==0) {
-                               (*itin1).coeff = ex_to<numeric>((*itin1).coeff).
-                                                add_dyn(ex_to<numeric>((*itin2).coeff));
-                               if (expair_needs_further_processing(itin1))
-                                       needs_further_processing = true;
-                               must_copy = true;
-                       } else {
-                               if (!ex_to<numeric>((*itin1).coeff).is_zero()) {
-                                       if (must_copy)
-                                               *itout = *itin1;
-                                       ++itout;
-                               }
-                               itin1 = itin2;
+
+       epvector::iterator itin1 = seq.begin();
+       epvector::iterator itin2 = itin1+1;
+       epvector::iterator itout = itin1;
+       epvector::iterator last = seq.end();
+       // must_copy will be set to true the first time some combination is 
+       // possible from then on the sequence has changed and must be compacted
+       bool must_copy = false;
+       while (itin2!=last) {
+               if (itin1->rest.compare(itin2->rest)==0) {
+                       itin1->coeff = ex_to<numeric>(itin1->coeff).
+                                      add_dyn(ex_to<numeric>(itin2->coeff));
+                       if (expair_needs_further_processing(itin1))
+                               needs_further_processing = true;
+                       must_copy = true;
+               } else {
+                       if (!ex_to<numeric>(itin1->coeff).is_zero()) {
+                               if (must_copy)
+                                       *itout = *itin1;
+                               ++itout;
                        }
-                       ++itin2;
+                       itin1 = itin2;
                }
-               if (!ex_to<numeric>((*itin1).coeff).is_zero()) {
-                       if (must_copy)
-                               *itout = *itin1;
-                       ++itout;
-               }
-               if (itout!=last)
-                       seq.erase(itout,last);
+               ++itin2;
        }
-       
+       if (!ex_to<numeric>(itin1->coeff).is_zero()) {
+               if (must_copy)
+                       *itout = *itin1;
+               ++itout;
+       }
+       if (itout!=last)
+               seq.erase(itout,last);
+
        if (needs_further_processing) {
                epvector v = seq;
                seq.clear();
@@ -1123,7 +1166,7 @@ unsigned expairseq::calc_hashtabsize(unsigned sz) const
        size = nearest_power_of_2/hashtabfactor;
        if (size<minhashtabsize)
                return 0;
-       GINAC_ASSERT(hashtabsize<=0x8000000U); // really max size due to 31 bit hashing
+
        // hashtabsize must be a power of 2
        GINAC_ASSERT((1U << log2(size))==size);
        return size;
@@ -1132,21 +1175,19 @@ unsigned expairseq::calc_hashtabsize(unsigned sz) const
 unsigned expairseq::calc_hashindex(const ex &e) const
 {
        // calculate hashindex
-       unsigned hash = e.gethash();
        unsigned hashindex;
-       if (is_a_numeric_hash(hash)) {
+       if (is_a<numeric>(e)) {
                hashindex = hashmask;
        } else {
-               hashindex = hash &hashmask;
+               hashindex = e.gethash() & hashmask;
                // last hashtab entry is reserved for numerics
                if (hashindex==hashmask) hashindex = 0;
        }
-       GINAC_ASSERT(hashindex>=0);
        GINAC_ASSERT((hashindex<hashtabsize)||(hashtabsize==0));
        return hashindex;
 }
 
-void expairseq::shrink_hashtab(void)
+void expairseq::shrink_hashtab()
 {
        unsigned new_hashtabsize;
        while (hashtabsize!=(new_hashtabsize=calc_hashtabsize(seq.size()))) {
@@ -1192,14 +1233,13 @@ void expairseq::remove_hashtab_entry(epvector::const_iterator element)
                ++epplit;
        }
        if (!erased) {
-               printtree(cout,0);
-               cout << "tried to erase " << element-seq.begin() << std::endl;
-               cout << "size " << seq.end()-seq.begin() << std::endl;
+               std::cout << "tried to erase " << element-seq.begin() << std::endl;
+               std::cout << "size " << seq.end()-seq.begin() << std::endl;
 
-               unsigned hashindex = calc_hashindex((*element).rest);
+               unsigned hashindex = calc_hashindex(element->rest);
                epplist &eppl = hashtab[hashindex];
-               epplist::iterator epplit=eppl.begin();
-               bool erased=false;
+               epplist::iterator epplit = eppl.begin();
+               bool erased = false;
                while (epplit!=eppl.end()) {
                        if (*epplit == element) {
                                eppl.erase(epplit);
@@ -1234,10 +1274,10 @@ void expairseq::move_hashtab_entry(epvector::const_iterator oldpos,
        GINAC_ASSERT(epplit!=eppl.end());
 }
 
-void expairseq::sorted_insert(epplist &eppl, epp elem)
+void expairseq::sorted_insert(epplist &eppl, epvector::const_iterator elem)
 {
        epplist::const_iterator current = eppl.begin();
-       while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
+       while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
                ++current;
        }
        eppl.insert(current,elem);
@@ -1248,21 +1288,21 @@ void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
                                           std::vector<bool> &touched,
                                           unsigned &number_of_zeroes)
 {
-       epp current=seq.begin();
+       epp current = seq.begin();
 
        while (current!=first_numeric) {
-               if (is_ex_exactly_of_type((*current).rest,numeric)) {
+               if (is_exactly_a<numeric>(current->rest)) {
                        --first_numeric;
                        iter_swap(current,first_numeric);
                } else {
                        // calculate hashindex
-                       unsigned currenthashindex = calc_hashindex((*current).rest);
+                       unsigned currenthashindex = calc_hashindex(current->rest);
 
                        // test if there is already a matching expair in the hashtab-list
                        epplist &eppl=hashtab[currenthashindex];
                        epplist::iterator epplit = eppl.begin();
                        while (epplit!=eppl.end()) {
-                               if ((*current).rest.is_equal((*(*epplit)).rest))
+                               if (current->rest.is_equal((*epplit)->rest))
                                        break;
                                ++epplit;
                        }
@@ -1272,8 +1312,8 @@ void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
                                ++current;
                        } else {
                                // epplit points to a matching expair, combine it with current
-                               (*(*epplit)).coeff = ex_to<numeric>((*(*epplit)).coeff).
-                                                    add_dyn(ex_to<numeric>((*current).coeff));
+                               (*epplit)->coeff = ex_to<numeric>((*epplit)->coeff).
+                                                  add_dyn(ex_to<numeric>(current->coeff));
                                
                                // move obsolete current expair to end by swapping with last_non_zero element
                                // if this was a numeric, it is swapped with the expair before first_numeric 
@@ -1283,7 +1323,7 @@ void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
                                --last_non_zero;
                                ++number_of_zeroes;
                                // test if combined term has coeff 0 and can be removed is done later
-                               touched[(*epplit)-seq.begin()]=true;
+                               touched[(*epplit)-seq.begin()] = true;
                        }
                }
        }
@@ -1297,7 +1337,7 @@ void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
        // move terms with coeff 0 to end and remove them from hashtab
        // check only those elements which have been touched
        epp current = seq.begin();
-       unsigned i = 0;
+       size_t i = 0;
        while (current!=first_numeric) {
                if (!touched[i]) {
                        ++current;
@@ -1312,8 +1352,9 @@ void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
                        if (current!=last_non_zero) {
                                iter_swap(current,last_non_zero);
                                --first_numeric;
-                               bool numeric_swapped=first_numeric!=last_non_zero;
-                               if (numeric_swapped) iter_swap(first_numeric,current);
+                               bool numeric_swapped = first_numeric!=last_non_zero;
+                               if (numeric_swapped)
+                                       iter_swap(first_numeric,current);
                                epvector::iterator changed_entry;
 
                                if (numeric_swapped)
@@ -1343,7 +1384,7 @@ void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
 /** True if one of the coeffs vanishes, otherwise false.
  *  This would be an invariant violation, so this should only be used for
  *  debugging purposes. */
-bool expairseq::has_coeff_0(void) const
+bool expairseq::has_coeff_0() const
 {
        epvector::const_iterator i = seq.begin(), end = seq.end();
        while (i != end) {
@@ -1366,7 +1407,7 @@ void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
        }
 }
 
-void expairseq::combine_same_terms(void)
+void expairseq::combine_same_terms()
 {
        // combine same terms, drop term with coeff 0, move numerics to end
        
@@ -1392,7 +1433,7 @@ void expairseq::combine_same_terms(void)
        epvector::iterator first_numeric = seq.end();
        epvector::iterator last_non_zero = seq.end()-1;
        
-       unsigned num = seq.size();
+       size_t num = seq.size();
        std::vector<bool> touched(num);
        
        unsigned number_of_zeroes = 0;
@@ -1437,22 +1478,22 @@ bool expairseq::is_canonical() const
        epvector::const_iterator it = seq.begin(), itend = seq.end();
        epvector::const_iterator it_last = it;
        for (++it; it!=itend; it_last=it, ++it) {
-               if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
-                       if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
-                               !is_ex_exactly_of_type((*it).rest,numeric)) {
+               if (!(it_last->is_less(*it) || it_last->is_equal(*it))) {
+                       if (!is_exactly_a<numeric>(it_last->rest) ||
+                               !is_exactly_a<numeric>(it->rest)) {
                                // double test makes it easier to set a breakpoint...
-                               if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
-                                       !is_ex_exactly_of_type((*it).rest,numeric)) {
+                               if (!is_exactly_a<numeric>(it_last->rest) ||
+                                       !is_exactly_a<numeric>(it->rest)) {
                                        printpair(std::clog, *it_last, 0);
                                        std::clog << ">";
                                        printpair(std::clog, *it, 0);
                                        std::clog << "\n";
                                        std::clog << "pair1:" << std::endl;
-                                       (*it_last).rest.print(print_tree(std::clog));
-                                       (*it_last).coeff.print(print_tree(std::clog));
+                                       it_last->rest.print(print_tree(std::clog));
+                                       it_last->coeff.print(print_tree(std::clog));
                                        std::clog << "pair2:" << std::endl;
-                                       (*it).rest.print(print_tree(std::clog));
-                                       (*it).coeff.print(print_tree(std::clog));
+                                       it->rest.print(print_tree(std::clog));
+                                       it->coeff.print(print_tree(std::clog));
                                        return 0;
                                }
                        }
@@ -1467,16 +1508,16 @@ bool expairseq::is_canonical() const
  *  @see expairseq::expand()
  *  @return pointer to epvector containing expanded pairs or zero pointer,
  *  if no members were changed. */
-epvector * expairseq::expandchildren(unsigned options) const
+std::auto_ptr<epvector> expairseq::expandchildren(unsigned options) const
 {
-       epvector::const_iterator last = seq.end();
+       const epvector::const_iterator last = seq.end();
        epvector::const_iterator cit = seq.begin();
        while (cit!=last) {
-               const ex &expanded_ex = (*cit).rest.expand(options);
-               if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
+               const ex &expanded_ex = cit->rest.expand(options);
+               if (!are_ex_trivially_equal(cit->rest,expanded_ex)) {
                        
                        // something changed, copy seq, eval and return it
-                       epvector *s = new epvector;
+                       std::auto_ptr<epvector> s(new epvector);
                        s->reserve(seq.size());
                        
                        // copy parts of seq which are known not to have changed
@@ -1485,14 +1526,16 @@ epvector * expairseq::expandchildren(unsigned options) const
                                s->push_back(*cit2);
                                ++cit2;
                        }
+
                        // copy first changed element
                        s->push_back(combine_ex_with_coeff_to_pair(expanded_ex,
-                                                                  (*cit2).coeff));
+                                                                  cit2->coeff));
                        ++cit2;
+
                        // copy rest
                        while (cit2!=last) {
-                               s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.expand(options),
-                                                                          (*cit2).coeff));
+                               s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.expand(options),
+                                                                          cit2->coeff));
                                ++cit2;
                        }
                        return s;
@@ -1500,7 +1543,7 @@ epvector * expairseq::expandchildren(unsigned options) const
                ++cit;
        }
        
-       return 0; // signalling nothing has changed
+       return std::auto_ptr<epvector>(0); // signalling nothing has changed
 }
 
 
@@ -1509,27 +1552,27 @@ epvector * expairseq::expandchildren(unsigned options) const
  *  @see expairseq::eval()
  *  @return pointer to epvector containing evaluated pairs or zero pointer,
  *  if no members were changed. */
-epvector * expairseq::evalchildren(int level) const
+std::auto_ptr<epvector> expairseq::evalchildren(int level) const
 {
        // returns a NULL pointer if nothing had to be evaluated
        // returns a pointer to a newly created epvector otherwise
        // (which has to be deleted somewhere else)
 
        if (level==1)
-               return 0;
+               return std::auto_ptr<epvector>(0);
        
        if (level == -max_recursion_level)
                throw(std::runtime_error("max recursion level reached"));
        
        --level;
-       epvector::const_iterator last=seq.end();
-       epvector::const_iterator cit=seq.begin();
+       epvector::const_iterator last = seq.end();
+       epvector::const_iterator cit = seq.begin();
        while (cit!=last) {
-               const ex &evaled_ex = (*cit).rest.eval(level);
-               if (!are_ex_trivially_equal((*cit).rest,evaled_ex)) {
+               const ex &evaled_ex = cit->rest.eval(level);
+               if (!are_ex_trivially_equal(cit->rest,evaled_ex)) {
                        
                        // something changed, copy seq, eval and return it
-                       epvector *s = new epvector;
+                       std::auto_ptr<epvector> s(new epvector);
                        s->reserve(seq.size());
                        
                        // copy parts of seq which are known not to have changed
@@ -1538,14 +1581,16 @@ epvector * expairseq::evalchildren(int level) const
                                s->push_back(*cit2);
                                ++cit2;
                        }
+
                        // copy first changed element
                        s->push_back(combine_ex_with_coeff_to_pair(evaled_ex,
-                                                                  (*cit2).coeff));
+                                                                  cit2->coeff));
                        ++cit2;
+
                        // copy rest
                        while (cit2!=last) {
-                               s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.eval(level),
-                                                                          (*cit2).coeff));
+                               s->push_back(combine_ex_with_coeff_to_pair(cit2->rest.eval(level),
+                                                                          cit2->coeff));
                                ++cit2;
                        }
                        return s;
@@ -1553,56 +1598,126 @@ epvector * expairseq::evalchildren(int level) const
                ++cit;
        }
        
-       return 0; // signalling nothing has changed
+       return std::auto_ptr<epvector>(0); // signalling nothing has changed
+}
+
+class safe_inserter
+{
+       public:
+               safe_inserter(const ex&, const bool disable_renaming=false);
+               std::auto_ptr<epvector> getseq(){return epv;}
+               void insert_old_pair(const expair &p)
+               {
+                       epv->push_back(p);
+               }
+               void insert_new_pair(const expair &p, const ex &orig_ex);
+       private:
+               std::auto_ptr<epvector> epv;
+               bool dodummies;
+               exvector dummy_indices;
+               void update_dummy_indices(const exvector&);
+};
+
+safe_inserter::safe_inserter(const ex&e, const bool disable_renaming)
+               :epv(new epvector)
+{
+       epv->reserve(e.nops());
+       dodummies=is_a<mul>(e);
+       if(disable_renaming)
+               dodummies=false;
+       if(dodummies) {
+               dummy_indices = get_all_dummy_indices(e);
+               sort(dummy_indices.begin(), dummy_indices.end(), ex_is_less());
+       }
 }
 
+void safe_inserter::update_dummy_indices(const exvector &v)
+{
+       exvector new_dummy_indices;
+       set_union(dummy_indices.begin(), dummy_indices.end(), v.begin(), v.end(),
+               std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
+       dummy_indices.swap(new_dummy_indices);
+}
+
+void safe_inserter::insert_new_pair(const expair &p, const ex &orig_ex)
+{
+       if(!dodummies) {
+               epv->push_back(p);
+               return;
+       }
+       exvector dummies_of_factor = get_all_dummy_indices(p.rest);
+       if(dummies_of_factor.size() == 0) {
+               epv->push_back(p);
+               return;
+       }
+       sort(dummies_of_factor.begin(), dummies_of_factor.end(), ex_is_less());
+       exvector dummies_of_orig_ex = get_all_dummy_indices(orig_ex);
+       sort(dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(), ex_is_less());
+       exvector new_dummy_indices;
+       new_dummy_indices.reserve(dummy_indices.size());
+       set_difference(dummy_indices.begin(), dummy_indices.end(), dummies_of_orig_ex.begin(), dummies_of_orig_ex.end(),
+               std::back_insert_iterator<exvector>(new_dummy_indices), ex_is_less());
+       dummy_indices.swap(new_dummy_indices);
+       ex newfactor = rename_dummy_indices_uniquely(dummy_indices, dummies_of_factor, p.rest);
+       update_dummy_indices(dummies_of_factor);
+       epv -> push_back(expair(newfactor, p.coeff));
+}
 
 /** Member-wise substitute in this sequence.
  *
  *  @see expairseq::subs()
  *  @return pointer to epvector containing pairs after application of subs,
  *    or NULL pointer if no members were changed. */
-epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern) const
+std::auto_ptr<epvector> expairseq::subschildren(const exmap & m, unsigned options) const
 {
-       GINAC_ASSERT(ls.nops()==lr.nops());
-
-       // The substitution is "complex" when any of the objects to be substituted
-       // is a product or power. In this case we have to recombine the pairs
-       // because the numeric coefficients may be part of the search pattern.
-       bool complex_subs = false;
-       for (unsigned i=0; i<ls.nops(); i++)
-               if (is_ex_exactly_of_type(ls.op(i), mul) || is_ex_exactly_of_type(ls.op(i), power)) {
-                       complex_subs = true;
-                       break;
+       // When any of the objects to be substituted is a product or power
+       // we have to recombine the pairs because the numeric coefficients may
+       // be part of the search pattern.
+       if (!(options & (subs_options::pattern_is_product | subs_options::pattern_is_not_product))) {
+
+               // Search the list of substitutions and cache our findings
+               for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+                       if (is_exactly_a<mul>(it->first) || is_exactly_a<power>(it->first)) {
+                               options |= subs_options::pattern_is_product;
+                               break;
+                       }
                }
+               if (!(options & subs_options::pattern_is_product))
+                       options |= subs_options::pattern_is_not_product;
+       }
 
-       if (complex_subs) {
+       if (options & subs_options::pattern_is_product) {
 
                // Substitute in the recombined pairs
                epvector::const_iterator cit = seq.begin(), last = seq.end();
                while (cit != last) {
 
                        const ex &orig_ex = recombine_pair_to_ex(*cit);
-                       const ex &subsed_ex = orig_ex.subs(ls, lr, no_pattern);
+                       const ex &subsed_ex = orig_ex.subs(m, options);
                        if (!are_ex_trivially_equal(orig_ex, subsed_ex)) {
 
                                // Something changed, copy seq, subs and return it
-                               epvector *s = new epvector;
-                               s->reserve(seq.size());
+                               safe_inserter s(*this, options & subs_options::no_index_renaming);
 
                                // Copy parts of seq which are known not to have changed
-                               s->insert(s->begin(), seq.begin(), cit);
+                               for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
+                                       s.insert_old_pair(*i);
 
                                // Copy first changed element
-                               s->push_back(split_ex_to_pair(subsed_ex));
+                               s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
                                ++cit;
 
                                // Copy rest
                                while (cit != last) {
-                                       s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
+                                       ex orig_ex = recombine_pair_to_ex(*cit);
+                                       ex subsed_ex = orig_ex.subs(m, options);
+                                       if(are_ex_trivially_equal(orig_ex, subsed_ex))
+                                               s.insert_old_pair(*cit);
+                                       else
+                                               s.insert_new_pair(split_ex_to_pair(subsed_ex), orig_ex);
                                        ++cit;
                                }
-                               return s;
+                               return s.getseq();
                        }
 
                        ++cit;
@@ -1614,27 +1729,31 @@ epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern
                epvector::const_iterator cit = seq.begin(), last = seq.end();
                while (cit != last) {
 
-                       const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
+                       const ex &subsed_ex = cit->rest.subs(m, options);
                        if (!are_ex_trivially_equal(cit->rest, subsed_ex)) {
                        
                                // Something changed, copy seq, subs and return it
-                               epvector *s = new epvector;
-                               s->reserve(seq.size());
+                               safe_inserter s(*this, options & subs_options::no_index_renaming);
 
                                // Copy parts of seq which are known not to have changed
-                               s->insert(s->begin(), seq.begin(), cit);
+                               for(epvector::const_iterator i=seq.begin(); i!=cit; ++i)
+                                       s.insert_old_pair(*i);
                        
                                // Copy first changed element
-                               s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
+                               s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), cit->rest);
                                ++cit;
 
                                // Copy rest
                                while (cit != last) {
-                                       s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
-                                                                                  cit->coeff));
+                                       const ex &orig_ex = cit->rest;
+                                       const ex &subsed_ex = cit->rest.subs(m, options);
+                                       if(are_ex_trivially_equal(orig_ex, subsed_ex))
+                                               s.insert_old_pair(*cit);
+                                       else
+                                               s.insert_new_pair(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff), orig_ex);
                                        ++cit;
                                }
-                               return s;
+                               return s.getseq();
                        }
 
                        ++cit;
@@ -1642,7 +1761,7 @@ epvector * expairseq::subschildren(const lst &ls, const lst &lr, bool no_pattern
        }
        
        // Nothing has changed
-       return NULL;
+       return std::auto_ptr<epvector>(0);
 }
 
 //////////