X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fexpairseq.cpp;h=5f3dd2904b2bbb10d1dc596ec3beadedfbb0af51;hp=09a38af5931c14922e42761e2e1b016e6e5ef193;hb=6bff4f32e5cbe9f7e51837f392a2d0bf0d5b721d;hpb=50dc516836ac5e91f4f60a60b9a307b375247e7c

diff --git a/ginac/expairseq.cpp b/ginac/expairseq.cpp
index 09a38af5..5f3dd290 100644
--- a/ginac/expairseq.cpp
+++ b/ginac/expairseq.cpp
@@ -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"
@@ -175,7 +177,7 @@ 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
@@ -186,102 +188,90 @@ 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);
-
-	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;
+		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;
 #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;
+				}
+				c.s << 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 +300,24 @@ 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;
+	}
+
+	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))
@@ -322,40 +330,95 @@ ex expairseq::eval(int level) const
 	return (new expairseq(vp,overall_coeff))->setflag(status_flags::dynallocated | status_flags::evaluated);
 }
 
-ex expairseq::evalf(int level) const
+bool expairseq::match(const ex & pattern, lst & repl_lst) const
 {
-	return thisexpairseq(evalfchildren(level),overall_coeff.evalf(level-1));
-}
+	// 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
 
-ex expairseq::normal(lst &sym_lst, lst &repl_lst, int level) const
-{
-	ex n = thisexpairseq(normalchildren(level),overall_coeff);
-	return n.bp->basic::normal(sym_lst,repl_lst,level);
+	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)
+			unsigned num = ops.size();
+			epvector *vp = new epvector();
+			vp->reserve(num);
+			for (unsigned 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);
+			}
+			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) const
+ex expairseq::subs(const lst &ls, const lst &lr, bool no_pattern) const
 {
-	epvector *vp = subschildren(ls,lr);
-	if (vp==0)
-		return inherited::subs(ls, lr);
-	
-	return thisexpairseq(vp,overall_coeff);
+	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
 
-/** Implementation of ex::diff() for an expairseq.
- *  It differentiates all elements of the sequence.
- *  @see ex::diff */
-ex expairseq::derivative(const symbol &s) const
-{
-	return thisexpairseq(diffchildren(s),overall_coeff);
-}
-
 int expairseq::compare_same_type(const basic &other) const
 {
 	GINAC_ASSERT(is_of_type(other, expairseq));
-	const expairseq &o = static_cast<const expairseq &>(const_cast<basic &>(other));
+	const expairseq &o = static_cast<const expairseq &>(other);
 	
 	int cmpval;
 	
@@ -420,7 +483,7 @@ 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 +497,9 @@ 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);
@@ -490,15 +553,17 @@ unsigned expairseq::return_type(void) const
 unsigned expairseq::calchash(void) const
 {
 	unsigned v = golden_ratio_hash(tinfo());
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
 #if !EXPAIRSEQ_USE_HASHTAB
 		v = rotate_left_31(v); // rotation would spoil commutativity
 #endif // EXPAIRSEQ_USE_HASHTAB
-		v ^= cit->rest.gethash();
+		v ^= i->rest.gethash();
 #if !EXPAIRSEQ_USE_HASHTAB
 		v = rotate_left_31(v);
-		v ^= cit->coeff.gethash();
+		v ^= i->coeff.gethash();
 #endif // EXPAIRSEQ_USE_HASHTAB
+		++i;
 	}
 	
 	v ^= overall_coeff.gethash();
@@ -516,13 +581,11 @@ unsigned expairseq::calchash(void) const
 ex expairseq::expand(unsigned options) const
 {
 	epvector *vp = expandchildren(options);
-	if (vp==0) {
-		// the terms have not changed, so it is safe to declare this expanded
-		setflag(status_flags::expanded);
-		return *this;
-	}
-	
-	return thisexpairseq(vp,overall_coeff);
+	if (vp == NULL) {
+		// The terms have not changed, so it is safe to declare this expanded
+		return (options == 0) ? setflag(status_flags::expanded) : *this;
+	} else
+		return thisexpairseq(vp, overall_coeff);
 }
 
 //////////
@@ -549,34 +612,34 @@ 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 +666,7 @@ 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 +694,7 @@ 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 +702,8 @@ 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 +734,26 @@ 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 +761,12 @@ 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 +799,8 @@ 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 +838,8 @@ 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)) {
@@ -831,16 +894,15 @@ void expairseq::construct_from_expairseq_ex(const expairseq &s,
 	
 	// merge p into s.seq
 	while (first!=last) {
-		int cmpval=(*first).rest.compare(p.rest);
+		int cmpval = (*first).rest.compare(p.rest);
 		if (cmpval==0) {
 			// combine terms
-			const numeric &newcoeff = ex_to_numeric((*first).coeff).
-			                           add(ex_to_numeric(p.coeff));
+			const numeric &newcoeff = ex_to<numeric>(first->coeff).
+			                           add(ex_to<numeric>(p.coeff));
 			if (!newcoeff.is_zero()) {
-				seq.push_back(expair((*first).rest,newcoeff));
-				if (expair_needs_further_processing(seq.end()-1)) {
+				seq.push_back(expair(first->rest,newcoeff));
+				if (expair_needs_further_processing(seq.end()-1))
 					needs_further_processing = true;
-				}
 			}
 			++first;
 			p_pushed = true;
@@ -887,7 +949,6 @@ void expairseq::construct_from_exvector(const exvector &v)
 	canonicalize();
 	combine_same_terms_sorted_seq();
 #endif // EXPAIRSEQ_USE_HASHTAB
-	return;
 }
 
 void expairseq::construct_from_epvector(const epvector &v)
@@ -904,7 +965,6 @@ void expairseq::construct_from_epvector(const epvector &v)
 	canonicalize();
 	combine_same_terms_sorted_seq();
 #endif // EXPAIRSEQ_USE_HASHTAB
-	return;
 }
 
 /** Combine this expairseq with argument exvector.
@@ -922,7 +982,7 @@ 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 +994,7 @@ 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()) {
@@ -949,8 +1009,6 @@ void expairseq::make_flat(const exvector &v)
 		}
 		++cit;
 	}
-	
-	return;
 }
 
 /** Combine this expairseq with argument epvector.
@@ -968,7 +1026,7 @@ 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 +1039,13 @@ 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))));
+				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;
@@ -1000,16 +1058,12 @@ void expairseq::make_flat(const epvector &v)
 		}
 		++cit;
 	}
-	return;
 }
 
-
 /** Brings this expairseq into a sorted (canonical) form. */
 void expairseq::canonicalize(void)
 {
-	// canonicalize
-	sort(seq.begin(),seq.end(),expair_is_less());
-	return;
+	sort(seq.begin(), seq.end(), expair_is_less());
 }
 
 
@@ -1029,14 +1083,14 @@ void expairseq::combine_same_terms_sorted_seq(void)
 		// 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 (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 (!ex_to<numeric>(itin1->coeff).is_zero()) {
 					if (must_copy)
 						*itout = *itin1;
 					++itout;
@@ -1045,7 +1099,7 @@ 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;
@@ -1059,7 +1113,6 @@ void expairseq::combine_same_terms_sorted_seq(void)
 		seq.clear();
 		construct_from_epvector(v);
 	}
-	return;
 }
 
 #if EXPAIRSEQ_USE_HASHTAB
@@ -1142,14 +1195,13 @@ 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);
@@ -1184,10 +1236,10 @@ 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::iterator current = eppl.begin();
-	while ((current!=eppl.end())&&((*(*current)).is_less(*elem))) {
+	epplist::const_iterator current = eppl.begin();
+	while ((current!=eppl.end()) && ((*current)->is_less(*elem))) {
 		++current;
 	}
 	eppl.insert(current,elem);
@@ -1195,24 +1247,24 @@ 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();
+	epp current = seq.begin();
 
 	while (current!=first_numeric) {
-		if (is_ex_exactly_of_type((*current).rest,numeric)) {
+		if (is_ex_exactly_of_type(current->rest,numeric)) {
 			--first_numeric;
 			iter_swap(current,first_numeric);
 		} else {
 			// calculate hashindex
-			unsigned currenthashindex = calc_hashindex((*current).rest);
+			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;
 			}
@@ -1222,8 +1274,8 @@ 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 
@@ -1233,7 +1285,7 @@ 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;
 			}
 		}
 	}
@@ -1241,7 +1293,7 @@ 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 +1304,7 @@ 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 {
@@ -1262,8 +1314,9 @@ 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)
@@ -1295,9 +1348,11 @@ void expairseq::drop_coeff_0_terms(epvector::iterator &first_numeric,
  *  debugging purposes. */
 bool expairseq::has_coeff_0(void) const
 {
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if ((*cit).coeff.is_zero())
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		if (i->coeff.is_zero())
 			return true;
+		++i;
 	}
 	return false;
 }
@@ -1305,12 +1360,11 @@ bool expairseq::has_coeff_0(void) const
 void expairseq::add_numerics_to_hashtab(epvector::iterator first_numeric,
 										epvector::const_iterator last_non_zero)
 {
-	if (first_numeric==seq.end()) return; // no numerics    
+	if (first_numeric == seq.end()) return; // no numerics
 	
-	epvector::iterator current = first_numeric;
-	epvector::const_iterator last = last_non_zero+1;
-	while (current!=last) {
-		sorted_insert(hashtab[hashmask],current);
+	epvector::const_iterator current = first_numeric, last = last_non_zero + 1;
+	while (current != last) {
+		sorted_insert(hashtab[hashmask], current);
 		++current;
 	}
 }
@@ -1341,41 +1395,18 @@ void expairseq::combine_same_terms(void)
 	epvector::iterator first_numeric = seq.end();
 	epvector::iterator last_non_zero = seq.end()-1;
 	
-	vector<bool> touched;
-	touched.reserve(seq.size());
-	for (unsigned i=0; i<seq.size(); ++i) touched[i]=false;
+	unsigned num = seq.size();
+	std::vector<bool> touched(num);
 	
 	unsigned number_of_zeroes = 0;
 	
 	GINAC_ASSERT(!has_coeff_0());
 	build_hashtab_and_combine(first_numeric,last_non_zero,touched,number_of_zeroes);
-	/*
-	cout << "in combine:" << std::endl;
-	printtree(cout,0);
-	cout << "size=" << seq.end() - seq.begin() << std::endl;
-	cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
-	cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
-	for (unsigned i=0; i<seq.size(); ++i) {
-		if (touched[i]) cout << i << " is touched" << std::endl;
-	}
-	cout << "end in combine" << std::endl;
-	*/
 	
 	// there should not be any terms with coeff 0 from the beginning,
 	// so it should be safe to skip this step
 	if (number_of_zeroes!=0) {
 		drop_coeff_0_terms(first_numeric,last_non_zero,touched,number_of_zeroes);
-		/*
-		cout << "in combine after drop:" << std::endl;
-		printtree(cout,0);
-		cout << "size=" << seq.end() - seq.begin() << std::endl;
-		cout << "first_numeric=" << first_numeric - seq.begin() << std::endl;
-		cout << "last_non_zero=" << last_non_zero - seq.begin() << std::endl;
-		for (unsigned i=0; i<seq.size(); ++i) {
-			if (touched[i]) cout << i << " is touched" << std::endl;
-		}
-		cout << "end in combine after drop" << std::endl;
-		*/
 	}
 	
 	add_numerics_to_hashtab(first_numeric,last_non_zero);
@@ -1399,32 +1430,32 @@ 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 = seq.begin(), itend = seq.end();
 	epvector::const_iterator it_last = it;
-	for (++it; it!=seq.end(); it_last=it, ++it) {
-		if (!((*it_last).is_less(*it)||(*it_last).is_equal(*it))) {
-			if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
-				!is_ex_exactly_of_type((*it).rest,numeric)) {
+	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)) {
 				// double test makes it easier to set a breakpoint...
-				if (!is_ex_exactly_of_type((*it_last).rest,numeric)||
-					!is_ex_exactly_of_type((*it).rest,numeric)) {
-					printpair(std::clog,*it_last,0);
+				if (!is_ex_exactly_of_type(it_last->rest,numeric) ||
+					!is_ex_exactly_of_type(it->rest,numeric)) {
+					printpair(std::clog, *it_last, 0);
 					std::clog << ">";
-					printpair(std::clog,*it,0);
+					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;
 				}
 			}
@@ -1444,8 +1475,8 @@ epvector * expairseq::expandchildren(unsigned options) const
 	epvector::const_iterator last = seq.end();
 	epvector::const_iterator cit = seq.begin();
 	while (cit!=last) {
-		const ex &expanded_ex = (*cit).rest.expand(options);
-		if (!are_ex_trivially_equal((*cit).rest,expanded_ex)) {
+		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;
@@ -1459,12 +1490,12 @@ epvector * expairseq::expandchildren(unsigned options) const
 			}
 			// 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;
@@ -1494,11 +1525,11 @@ epvector * expairseq::evalchildren(int level) const
 		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;
@@ -1512,12 +1543,12 @@ epvector * expairseq::evalchildren(int level) const
 			}
 			// 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;
@@ -1529,125 +1560,98 @@ epvector * expairseq::evalchildren(int level) const
 }
 
 
-/** Member-wise evaluate numerically all expairs in this sequence.
+/** Member-wise substitute in this sequence.
  *
- *  @see expairseq::evalf()
- *  @return epvector with all entries evaluated numerically. */
-epvector expairseq::evalfchildren(int level) const
+ *  @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
 {
-	if (level==1)
-		return seq;
-	
-	if (level==-max_recursion_level)
-		throw(std::runtime_error("max recursion level reached"));
-	
-	epvector s;
-	s.reserve(seq.size());
-	
-	--level;
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
-		                                          (*it).coeff.evalf(level)));
-	}
-	return s;
-}
+	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;
+		}
 
-/** Member-wise normalize all expairs in this sequence.
- *
- *  @see expairseq::normal()
- *  @return epvector with all entries normalized. */
-epvector expairseq::normalchildren(int level) const
-{
-	if (level==1)
-		return seq;
-	
-	if (level==-max_recursion_level)
-		throw(std::runtime_error("max recursion level reached"));
-	
-	epvector s;
-	s.reserve(seq.size());
-	
-	--level;
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.normal(level),
-		                                          (*it).coeff));
-	}
-	return s;
-}
+	if (complex_subs) {
 
+		// Substitute in the recombined pairs
+		epvector::const_iterator cit = seq.begin(), last = seq.end();
+		while (cit != last) {
 
-/** Member-wise differentiate all expairs in this sequence.
- *
- *  @see expairseq::diff()
- *  @return epvector with all entries differentiated. */
-epvector expairseq::diffchildren(const symbol &y) const
-{
-	epvector s;
-	s.reserve(seq.size());
-	
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
-		                                          (*it).coeff));
-	}
-	return s;
-}
+			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());
 
-/** Member-wise substitute in this sequence.
- *
- *  @see expairseq::subs()
- *  @return pointer to epvector containing pairs after application of subs or zero
- *  pointer, if no members were changed. */
-epvector * expairseq::subschildren(const lst &ls, const lst &lr) const
-{
-	// returns a NULL pointer if nothing had to be substituted
-	// returns a pointer to a newly created epvector otherwise
-	// (which has to be deleted somewhere else)
-	GINAC_ASSERT(ls.nops()==lr.nops());
-	
-	epvector::const_iterator last = seq.end();
-	epvector::const_iterator cit = seq.begin();
-	while (cit!=last) {
-		const ex &subsed_ex=(*cit).rest.subs(ls,lr);
-		if (!are_ex_trivially_equal((*cit).rest,subsed_ex)) {
+				// Copy 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;