]> www.ginac.de Git - ginac.git/blobdiff - ginac/expairseq.cpp
- do something about the mad cast disease.
[ginac.git] / ginac / expairseq.cpp
index 09a38af5931c14922e42761e2e1b016e6e5ef193..86f687de42879f3ba9c08238b1c16e51d8b904b0 100644 (file)
@@ -26,6 +26,8 @@
 
 #include "expairseq.h"
 #include "lst.h"
+#include "relational.h"
+#include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
 #include "utils.h"
@@ -186,102 +188,89 @@ basic *expairseq::duplicate() const
        return new expairseq(*this);
 }
 
-void expairseq::print(std::ostream &os, unsigned upper_precedence) const
+void expairseq::print(const print_context & c, unsigned level) const
 {
        debugmsg("expairseq print",LOGLEVEL_PRINT);
-       os << "[[";
-       printseq(os,',',precedence,upper_precedence);
-       os << "]]";
-}
 
-void expairseq::printraw(std::ostream &os) const
-{
-       debugmsg("expairseq printraw",LOGLEVEL_PRINT);
-       os << class_name() << "(";
-       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               os << "(";
-               (*cit).rest.printraw(os);
-               os << ",";
-               (*cit).coeff.printraw(os);
-               os << "),";
-       }
-       os << ")";
-}
+       if (is_of_type(c, print_tree)) {
 
-void expairseq::printtree(std::ostream &os, unsigned indent) const
-{
-       debugmsg("expairseq printtree",LOGLEVEL_PRINT);
+               unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
 
-       os << std::string(indent,' ') << "type=" << class_name()
-          << ", hash=" << hashvalue
-          << " (0x" << std::hex << hashvalue << std::dec << ")"
-          << ", flags=" << flags
-          << ", nops=" << nops() << std::endl;
-       for (unsigned i=0; i<seq.size(); ++i) {
-               seq[i].rest.printtree(os,indent+delta_indent);
-               seq[i].coeff.printtree(os,indent+delta_indent);
-               if (i!=seq.size()-1)
-                       os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
-       }
-       if (!overall_coeff.is_equal(default_overall_coeff())) {
-               os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
-               os << std::string(indent+delta_indent,' ') << "overall_coeff" << std::endl;
-               overall_coeff.printtree(os,indent+delta_indent);
-       }
-       os << std::string(indent+delta_indent,' ') << "=====" << std::endl;
+               c.s << std::string(level, ' ') << class_name()
+                   << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+                   << ", nops=" << nops()
+                   << std::endl;
+               for (unsigned i=0; i<seq.size(); ++i) {
+                       seq[i].rest.print(c, level + delta_indent);
+                       seq[i].coeff.print(c, level + delta_indent);
+                       if (i != seq.size()-1)
+                               c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
+               }
+               if (!overall_coeff.is_equal(default_overall_coeff())) {
+                       c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl
+                           << std::string(level + delta_indent, ' ') << "overall_coeff" << std::endl;
+                       overall_coeff.print(c, level + delta_indent);
+               }
+               c.s << std::string(level + delta_indent,' ') << "=====" << std::endl;
 #if EXPAIRSEQ_USE_HASHTAB
-       os << std::string(indent+delta_indent,' ')
-          << "hashtab size " << hashtabsize << std::endl;
-       if (hashtabsize==0) return;
+               c.s << std::string(level + delta_indent,' ')
+                   << "hashtab size " << hashtabsize << std::endl;
+               if (hashtabsize == 0) return;
 #define MAXCOUNT 5
-       unsigned count[MAXCOUNT+1];
-       for (int i=0; i<MAXCOUNT+1; ++i)
-               count[i] = 0;
-       unsigned this_bin_fill;
-       unsigned cum_fill_sq = 0;
-       unsigned cum_fill = 0;
-       for (unsigned i=0; i<hashtabsize; ++i) {
-               this_bin_fill = 0;
-               if (hashtab[i].size()>0) {
-                       os << std::string(indent+delta_indent,' ') 
-                          << "bin " << i << " with entries ";
-                       for (epplist::const_iterator it=hashtab[i].begin();
-                            it!=hashtab[i].end(); ++it) {
-                               os << *it-seq.begin() << " ";
-                               ++this_bin_fill;
+               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;
                        }
-                       os << std::endl;
-                       cum_fill += this_bin_fill;
-                       cum_fill_sq += this_bin_fill*this_bin_fill;
+                       if (this_bin_fill<MAXCOUNT)
+                               ++count[this_bin_fill];
+                       else
+                               ++count[MAXCOUNT];
                }
-               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;
-               os << std::string(indent+delta_indent,' ') << "bins with " << k << " entries: "
-                  << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
-                  << int(prob*1000)/10.0 << ")" << std::endl;
-       }
-       os << std::string(indent+delta_indent,' ') << "bins with more entries: "
-          << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
-          << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
-       
-       os << std::string(indent+delta_indent,' ') << "variance: "
-          << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
-          << std::endl;
-       os << std::string(indent+delta_indent,' ') << "average fill: "
-          << (1.0*cum_fill)/hashtabsize
-          << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
+               unsigned fact = 1;
+               double cum_prob = 0;
+               double lambda = (1.0*seq.size()) / hashtabsize;
+               for (int k=0; k<MAXCOUNT; ++k) {
+                       if (k>0)
+                               fact *= k;
+                       double prob = std::pow(lambda,k)/fact * std::exp(-lambda);
+                       cum_prob += prob;
+                       c.s << std::string(level + delta_indent, ' ') << "bins with " << k << " entries: "
+                           << int(1000.0*count[k]/hashtabsize)/10.0 << "% (expected: "
+                           << int(prob*1000)/10.0 << ")" << std::endl;
+               }
+               c.s << std::string(level + delta_indent, ' ') << "bins with more entries: "
+                   << int(1000.0*count[MAXCOUNT]/hashtabsize)/10.0 << "% (expected: "
+                   << int((1-cum_prob)*1000)/10.0 << ")" << std::endl;
+       
+               c.s << std::string(level + delta_indent, ' ') << "variance: "
+                   << 1.0/hashtabsize*cum_fill_sq-(1.0/hashtabsize*cum_fill)*(1.0/hashtabsize*cum_fill)
+                   << std::endl;
+               c.s << std::string(level + delta_indent, ' ') << "average fill: "
+                   << (1.0*cum_fill)/hashtabsize
+                   << " (should be equal to " << (1.0*seq.size())/hashtabsize << ")" << std::endl;
 #endif // EXPAIRSEQ_USE_HASHTAB
+
+       } else {
+               c.s << "[[";
+               printseq(c, ',', precedence(), level);
+               c.s << "]]";
+       }
 }
 
 bool expairseq::info(unsigned inf) const
@@ -310,6 +299,20 @@ ex &expairseq::let_op(int i)
        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;
+       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++;
+       }
+
+       return thisexpairseq(v, f(overall_coeff));
+}
+
 ex expairseq::eval(int level) const
 {
        if ((level==1) && (flags &status_flags::evaluated))
@@ -333,13 +336,86 @@ ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
        return n.bp->basic::normal(sym_lst,repl_lst,level);
 }
 
-ex expairseq::subs(const lst &ls, const lst &lr) const
+bool expairseq::match(const ex & pattern, lst & repl_lst) const
 {
-       epvector *vp = subschildren(ls,lr);
-       if (vp==0)
-               return inherited::subs(ls, lr);
-       
-       return thisexpairseq(vp,overall_coeff);
+       // This differs from basic::match() because we want "a+b+c+d" to
+       // match "d+*+b" with "*" being "a+c", and we want to honor commutativity
+
+       if (tinfo() == pattern.bp->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)) {
+                               has_global_wildcard = true;
+                               global_wildcard = pattern.op(i);
+                               break;
+                       }
+               }
+
+               // Unfortunately, this is an O(N^2) operation because we can't
+               // sort the pattern in a useful way...
+
+               // Chop into terms
+               exvector ops;
+               ops.reserve(nops());
+               for (unsigned 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++) {
+                       ex p = pattern.op(i);
+                       if (has_global_wildcard && p.is_equal(global_wildcard))
+                               continue;
+                       exvector::iterator it = ops.begin(), itend = ops.end();
+                       while (it != itend) {
+                               if (it->match(p, repl_lst)) {
+                                       ops.erase(it);
+                                       goto found;
+                               }
+                               it++;
+                       }
+                       return false; // no match found
+found:         ;
+               }
+
+               if (has_global_wildcard) {
+
+                       // Assign all the remaining terms to the global wildcard (unless
+                       // it has already been matched before, in which case the matches
+                       // must be equal)
+                       epvector *vp = new epvector();
+                       vp->reserve(ops.size());
+                       for (unsigned i=0; i<ops.size(); 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);
+                       }
+                       repl_lst.append(global_wildcard == rest);
+                       return true;
+
+               } else {
+
+                       // No global wildcard, then the match fails if there are any
+                       // unmatched terms left
+                       return ops.empty();
+               }
+       }
+       return inherited::match(pattern, repl_lst);
+}
+
+ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
+{
+       epvector *vp = subschildren(ls, lr, no_pattern);
+       if (vp)
+               return thisexpairseq(vp, overall_coeff).bp->basic::subs(ls, lr, no_pattern);
+       else
+               return basic::subs(ls, lr, no_pattern);
 }
 
 // protected
@@ -355,7 +431,7 @@ ex expairseq::derivative(const symbol &s) const
 int expairseq::compare_same_type(const basic &other) const
 {
        GINAC_ASSERT(is_of_type(other, expairseq));
-       const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
+       const expairseq &o = static_cast<const expairseq &>(other);
        
        int cmpval;
        
@@ -420,7 +496,7 @@ int expairseq::compare_same_type(const basic &other) const
 
 bool expairseq::is_equal_same_type(const basic &other) const
 {
-       const expairseq &o = dynamic_cast<const expairseq &>(const_cast<basic &>(other));
+       const expairseq &o = static_cast<const expairseq &>(other);
        
        // compare number of elements
        if (seq.size()!=o.seq.size())
@@ -434,9 +510,9 @@ bool expairseq::is_equal_same_type(const basic &other) const
        // compare number of elements in each hashtab entry
        if (hashtabsize!=o.hashtabsize) {
                std::cout << "this:" << std::endl;
-               printtree(std::cout,0);
+               print(print_tree(std::cout));
                std::cout << "other:" << std::endl;
-               other.printtree(std::cout,0);
+               other.print(print_tree(std::cout));
        }
                
        GINAC_ASSERT(hashtabsize==o.hashtabsize);
@@ -549,34 +625,34 @@ ex expairseq::thisexpairseq(epvector *vp, const ex &oc) const
        return expairseq(vp,oc);
 }
 
-void expairseq::printpair(std::ostream &os, const expair &p, unsigned upper_precedence) const
+void expairseq::printpair(const print_context & c, const expair & p, unsigned upper_precedence) const
 {
-       os << "[[";
-       p.rest.bp->print(os,precedence);
-       os << ",";
-       p.coeff.bp->print(os,precedence);
-       os << "]]";
+       c.s << "[[";
+       p.rest.bp->print(c, precedence());
+       c.s << ",";
+       p.coeff.bp->print(c, precedence());
+       c.s << "]]";
 }
 
-void expairseq::printseq(std::ostream &os, char delim,
+void expairseq::printseq(const print_context & c, char delim,
                          unsigned this_precedence,
                          unsigned upper_precedence) const
 {
-       if (this_precedence<=upper_precedence)
-               os << "(";
-       epvector::const_iterator it,it_last;
-       it_last=seq.end();
-       --it_last;
+       if (this_precedence <= upper_precedence)
+               c.s << "(";
+       epvector::const_iterator it, it_last = seq.end() - 1;
        for (it=seq.begin(); it!=it_last; ++it) {
-               printpair(os,*it,this_precedence);
-               os << delim;
+               printpair(c, *it, this_precedence);
+               c.s << delim;
+       }
+       printpair(c, *it, this_precedence);
+       if (!overall_coeff.is_equal(default_overall_coeff())) {
+               c.s << delim;
+               overall_coeff.print(c, this_precedence);
        }
-       printpair(os,*it,this_precedence);
-       if (!overall_coeff.is_equal(default_overall_coeff()))
-               os << delim << overall_coeff;
        
-       if (this_precedence<=upper_precedence)
-               os << ")";
+       if (this_precedence <= upper_precedence)
+               c.s << ")";
 }
 
 
@@ -603,7 +679,7 @@ expair expairseq::combine_pair_with_coeff_to_pair(const expair &p,
        GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
        GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
        
-       return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
+       return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 }
 
 
@@ -631,7 +707,7 @@ void expairseq::combine_overall_coeff(const ex &c)
 {
        GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
        GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
-       overall_coeff = ex_to_numeric(overall_coeff).add_dyn(ex_to_numeric(c));
+       overall_coeff = ex_to<numeric>(overall_coeff).add_dyn(ex_to<numeric>(c));
 }
 
 void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
@@ -639,8 +715,8 @@ void expairseq::combine_overall_coeff(const ex &c1, const ex &c2)
        GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
        GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
        GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
-       overall_coeff = ex_to_numeric(overall_coeff).
-                       add_dyn(ex_to_numeric(c1).mul(ex_to_numeric(c2)));
+       overall_coeff = ex_to<numeric>(overall_coeff).
+                       add_dyn(ex_to<numeric>(c1).mul(ex_to<numeric>(c2)));
 }
 
 bool expairseq::can_make_flat(const expair &p) const
@@ -671,26 +747,26 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
        if (lh.bp->tinfo()==tinfo()) {
                if (rh.bp->tinfo()==tinfo()) {
 #if EXPAIRSEQ_USE_HASHTAB
-                       unsigned totalsize = ex_to_expairseq(lh).seq.size() +
-                                            ex_to_expairseq(rh).seq.size();
+                       unsigned totalsize = ex_to<expairseq>(lh).seq.size() +
+                                            ex_to<expairseq>(rh).seq.size();
                        if (calc_hashtabsize(totalsize)!=0) {
                                construct_from_2_ex_via_exvector(lh,rh);
                        } else {
 #endif // EXPAIRSEQ_USE_HASHTAB
-                               construct_from_2_expairseq(ex_to_expairseq(lh),
-                                                          ex_to_expairseq(rh));
+                               construct_from_2_expairseq(ex_to<expairseq>(lh),
+                                                          ex_to<expairseq>(rh));
 #if EXPAIRSEQ_USE_HASHTAB
                        }
 #endif // EXPAIRSEQ_USE_HASHTAB
                        return;
                } else {
 #if EXPAIRSEQ_USE_HASHTAB
-                       unsigned totalsize = ex_to_expairseq(lh).seq.size()+1;
+                       unsigned totalsize = ex_to<expairseq>(lh).seq.size()+1;
                        if (calc_hashtabsize(totalsize)!=0) {
                                construct_from_2_ex_via_exvector(lh, rh);
                        } else {
 #endif // EXPAIRSEQ_USE_HASHTAB
-                               construct_from_expairseq_ex(ex_to_expairseq(lh), rh);
+                               construct_from_expairseq_ex(ex_to<expairseq>(lh), rh);
 #if EXPAIRSEQ_USE_HASHTAB
                        }
 #endif // EXPAIRSEQ_USE_HASHTAB
@@ -698,12 +774,12 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
                }
        } else if (rh.bp->tinfo()==tinfo()) {
 #if EXPAIRSEQ_USE_HASHTAB
-               unsigned totalsize=ex_to_expairseq(rh).seq.size()+1;
+               unsigned totalsize=ex_to<expairseq>(rh).seq.size()+1;
                if (calc_hashtabsize(totalsize)!=0) {
                        construct_from_2_ex_via_exvector(lh,rh);
                } else {
 #endif // EXPAIRSEQ_USE_HASHTAB
-                       construct_from_expairseq_ex(ex_to_expairseq(rh),lh);
+                       construct_from_expairseq_ex(ex_to<expairseq>(rh),lh);
 #if EXPAIRSEQ_USE_HASHTAB
                }
 #endif // EXPAIRSEQ_USE_HASHTAB
@@ -736,8 +812,8 @@ void expairseq::construct_from_2_ex(const ex &lh, const ex &rh)
                        
                        int cmpval = p1.rest.compare(p2.rest);
                        if (cmpval==0) {
-                               p1.coeff=ex_to_numeric(p1.coeff).add_dyn(ex_to_numeric(p2.coeff));
-                               if (!ex_to_numeric(p1.coeff).is_zero()) {
+                               p1.coeff=ex_to<numeric>(p1.coeff).add_dyn(ex_to<numeric>(p2.coeff));
+                               if (!ex_to<numeric>(p1.coeff).is_zero()) {
                                        // no further processing is necessary, since this
                                        // one element will usually be recombined in eval()
                                        seq.push_back(p1);
@@ -775,8 +851,8 @@ 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));
                                if (expair_needs_further_processing(seq.end()-1)) {
@@ -834,8 +910,8 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
                int cmpval=(*first).rest.compare(p.rest);
                if (cmpval==0) {
                        // combine terms
-                       const numeric &newcoeff = ex_to_numeric((*first).coeff).
-                                                  add(ex_to_numeric(p.coeff));
+                       const numeric &newcoeff = ex_to<numeric>((*first).coeff).
+                                                  add(ex_to<numeric>(p.coeff));
                        if (!newcoeff.is_zero()) {
                                seq.push_back(expair((*first).rest,newcoeff));
                                if (expair_needs_further_processing(seq.end()-1)) {
@@ -922,7 +998,7 @@ void expairseq::make_flat(const exvector &v)
        while (cit!=v.end()) {
                if (cit->bp->tinfo()==this->tinfo()) {
                        ++nexpairseqs;
-                       noperands += ex_to_expairseq(*cit).seq.size();
+                       noperands += ex_to<expairseq>(*cit).seq.size();
                }
                ++cit;
        }
@@ -934,7 +1010,7 @@ void expairseq::make_flat(const exvector &v)
        cit = v.begin();
        while (cit!=v.end()) {
                if (cit->bp->tinfo()==this->tinfo()) {
-                       const expairseq &subseqref = ex_to_expairseq(*cit);
+                       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()) {
@@ -968,7 +1044,7 @@ void expairseq::make_flat(const epvector &v)
        while (cit!=v.end()) {
                if (cit->rest.bp->tinfo()==this->tinfo()) {
                        ++nexpairseqs;
-                       noperands += ex_to_expairseq((*cit).rest).seq.size();
+                       noperands += ex_to<expairseq>((*cit).rest).seq.size();
                }
                ++cit;
        }
@@ -981,13 +1057,13 @@ void expairseq::make_flat(const epvector &v)
        while (cit!=v.end()) {
                if (cit->rest.bp->tinfo()==this->tinfo() &&
                    this->can_make_flat(*cit)) {
-                       const expairseq &subseqref = ex_to_expairseq((*cit).rest);
-                       combine_overall_coeff(ex_to_numeric(subseqref.overall_coeff),
-                                                           ex_to_numeric((*cit).coeff));
+                       const expairseq &subseqref = ex_to<expairseq>((*cit).rest);
+                       combine_overall_coeff(ex_to<numeric>(subseqref.overall_coeff),
+                                                           ex_to<numeric>((*cit).coeff));
                        epvector::const_iterator cit_s = subseqref.seq.begin();
                        while (cit_s!=subseqref.seq.end()) {
                                seq.push_back(expair((*cit_s).rest,
-                                                    ex_to_numeric((*cit_s).coeff).mul_dyn(ex_to_numeric((*cit).coeff))));
+                                                    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;
@@ -1003,7 +1079,6 @@ void expairseq::make_flat(const epvector &v)
        return;
 }
 
-
 /** Brings this expairseq into a sorted (canonical) form. */
 void expairseq::canonicalize(void)
 {
@@ -1030,13 +1105,13 @@ void expairseq::combine_same_terms_sorted_seq(void)
                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));
+                               (*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 (!ex_to<numeric>((*itin1).coeff).is_zero()) {
                                        if (must_copy)
                                                *itout = *itin1;
                                        ++itout;
@@ -1045,7 +1120,7 @@ void expairseq::combine_same_terms_sorted_seq(void)
                        }
                        ++itin2;
                }
-               if (!ex_to_numeric((*itin1).coeff).is_zero()) {
+               if (!ex_to<numeric>((*itin1).coeff).is_zero()) {
                        if (must_copy)
                                *itout = *itin1;
                        ++itout;
@@ -1195,7 +1270,7 @@ void expairseq::sorted_insert(epplist &eppl, epp elem)
 
 void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
                                           epvector::iterator &last_non_zero,
-                                          vector<bool> &touched,
+                                          std::vector<bool> &touched,
                                           unsigned &number_of_zeroes)
 {
        epp current=seq.begin();
@@ -1222,8 +1297,8 @@ 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 
@@ -1241,7 +1316,7 @@ void expairseq::build_hashtab_and_combine(epvector::iterator &first_numeric,
 
 void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
                                    epvector::iterator &last_non_zero,
-                                   vector<bool> &touched,
+                                   std::vector<bool> &touched,
                                    unsigned &number_of_zeroes)
 {
        // move terms with coeff 0 to end and remove them from hashtab
@@ -1252,7 +1327,7 @@ void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
                if (!touched[i]) {
                        ++current;
                        ++i;
-               } else if (!ex_to_numeric((*current).coeff).is_zero()) {
+               } else if (!ex_to<numeric>((*current).coeff).is_zero()) {
                        ++current;
                        ++i;
                } else {
@@ -1341,7 +1416,7 @@ void expairseq::combine_same_terms(void)
        epvector::iterator first_numeric = seq.end();
        epvector::iterator last_non_zero = seq.end()-1;
        
-       vector<bool> touched;
+       std::vector<bool> touched;
        touched.reserve(seq.size());
        for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
        
@@ -1399,32 +1474,32 @@ void expairseq::combine_same_terms(void)
  *  debugging or in assertions since being sorted is an invariance. */
 bool expairseq::is_canonical() const
 {
-       if (seq.size()<=1)
+       if (seq.size() <= 1)
                return 1;
        
 #if EXPAIRSEQ_USE_HASHTAB
-       if (hashtabsize>0) return 1; // not canoncalized
+       if (hashtabsize > 0) return 1; // not canoncalized
 #endif // EXPAIRSEQ_USE_HASHTAB
        
        epvector::const_iterator it = seq.begin();
        epvector::const_iterator it_last = it;
        for (++it; it!=seq.end(); it_last=it, ++it) {
-               if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
-                       if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
+               if (!((*it_last).is_less(*it) || (*it_last).is_equal(*it))) {
+                       if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
                                !is_ex_exactly_of_type((*it).rest,numeric)) {
                                // double test makes it easier to set a breakpoint...
-                               if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
+                               if (!is_ex_exactly_of_type((*it_last).rest,numeric) ||
                                        !is_ex_exactly_of_type((*it).rest,numeric)) {
-                                       printpair(std::clog,*it_last,0);
+                                       printpair(std::clog, *it_last, 0);
                                        std::clog << ">";
-                                       printpair(std::clog,*it,0);
+                                       printpair(std::clog, *it, 0);
                                        std::clog << "\n";
                                        std::clog << "pair1:" << std::endl;
-                                       (*it_last).rest.printtree(std::clog);
-                                       (*it_last).coeff.printtree(std::clog);
+                                       (*it_last).rest.print(print_tree(std::clog));
+                                       (*it_last).coeff.print(print_tree(std::clog));
                                        std::clog << "pair2:" << std::endl;
-                                       (*it).rest.printtree(std::clog);
-                                       (*it).coeff.printtree(std::clog);
+                                       (*it).rest.print(print_tree(std::clog));
+                                       (*it).coeff.print(print_tree(std::clog));
                                        return 0;
                                }
                        }
@@ -1597,57 +1672,95 @@ epvector expairseq::diffchildren(const symbol &y) const
 /** Member-wise substitute in this sequence.
  *
  *  @see expairseq::subs()
- *  @return pointer to epvector containing pairs after application of subs or zero
- *  pointer, if no members were changed. */
-epvector * expairseq::subschildren(const lst &ls, const lst &lr) const
+ *  @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
 {
-       // returns a NULL pointer if nothing had to be substituted
-       // returns a pointer to a newly created epvector otherwise
-       // (which has to be deleted somewhere else)
        GINAC_ASSERT(ls.nops()==lr.nops());
-       
-       epvector::const_iterator last = seq.end();
-       epvector::const_iterator cit = seq.begin();
-       while (cit!=last) {
-               const ex &subsed_ex=(*cit).rest.subs(ls,lr);
-               if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
+
+       // 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;
+               }
+
+       if (complex_subs) {
+
+               // 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);
+                       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());
+
+                               // Copy parts of seq which are known not to have changed
+                               s->insert(s->begin(), seq.begin(), cit);
+
+                               // Copy first changed element
+                               s->push_back(split_ex_to_pair(subsed_ex));
+                               ++cit;
+
+                               // Copy rest
+                               while (cit != last) {
+                                       s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit).subs(ls, lr, no_pattern)));
+                                       ++cit;
+                               }
+                               return s;
+                       }
+
+                       ++cit;
+               }
+
+       } else {
+
+               // Substitute only in the "rest" part of the pairs
+               epvector::const_iterator cit = seq.begin(), last = seq.end();
+               while (cit != last) {
+
+                       const ex &subsed_ex = cit->rest.subs(ls, lr, no_pattern);
+                       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());
+                               // Something changed, copy seq, subs and return it
+                               epvector *s = new epvector;
+                               s->reserve(seq.size());
+
+                               // Copy parts of seq which are known not to have changed
+                               s->insert(s->begin(), seq.begin(), cit);
                        
-                       // copy parts of seq which are known not to have changed
-                       epvector::const_iterator cit2 = seq.begin();
-                       while (cit2!=cit) {
-                               s->push_back(*cit2);
-                               ++cit2;
-                       }
-                       // copy first changed element
-                       s->push_back(combine_ex_with_coeff_to_pair(subsed_ex,
-                                                                  (*cit2).coeff));
-                       ++cit2;
-                       // copy rest
-                       while (cit2!=last) {
-                               s->push_back(combine_ex_with_coeff_to_pair((*cit2).rest.subs(ls,lr),
-                                                                          (*cit2).coeff));
-                               ++cit2;
+                               // Copy first changed element
+                               s->push_back(combine_ex_with_coeff_to_pair(subsed_ex, cit->coeff));
+                               ++cit;
+
+                               // Copy rest
+                               while (cit != last) {
+                                       s->push_back(combine_ex_with_coeff_to_pair(cit->rest.subs(ls, lr, no_pattern),
+                                                                                  cit->coeff));
+                                       ++cit;
+                               }
+                               return s;
                        }
-                       return s;
+
+                       ++cit;
                }
-               ++cit;
        }
        
-       return 0; // signalling nothing has changed
+       // Nothing has changed
+       return NULL;
 }
 
 //////////
 // static member variables
 //////////
 
-// protected
-
-unsigned expairseq::precedence = 10;
-
 #if EXPAIRSEQ_USE_HASHTAB
 unsigned expairseq::maxhashtabsize = 0x4000000U;
 unsigned expairseq::minhashtabsize = 0x1000U;