X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fncmul.cpp;h=ccc91c490d4be13f853739e61b8d423c076e6fe4;hp=e4a9186aa87b2d7620a1b0781f0b124fcb62f3b7;hb=948071fb79e925111799128dacff49296c69f2ca;hpb=591b85b0697370f2f5f25a29a1e94ff831a02c12;ds=sidebyside

diff --git a/ginac/ncmul.cpp b/ginac/ncmul.cpp
index e4a9186a..ccc91c49 100644
--- a/ginac/ncmul.cpp
+++ b/ginac/ncmul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's non-commutative products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2004 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
@@ -29,28 +29,27 @@
 #include "add.h"
 #include "mul.h"
 #include "matrix.h"
-#include "print.h"
 #include "archive.h"
-#include "debugmsg.h"
 #include "utils.h"
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(ncmul, exprseq,
+  print_func<print_context>(&ncmul::do_print).
+  print_func<print_tree>(&ncmul::do_print_tree).
+  print_func<print_csrc>(&ncmul::do_print_csrc).
+  print_func<print_python_repr>(&ncmul::do_print_csrc))
+
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
 //////////
 
 ncmul::ncmul()
 {
-	debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
-DEFAULT_COPY(ncmul)
-DEFAULT_DESTROY(ncmul)
-
 //////////
 // other constructors
 //////////
@@ -59,46 +58,39 @@ DEFAULT_DESTROY(ncmul)
 
 ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
 {
-	debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3) : inherited(f1,f2,f3)
 {
-	debugmsg("ncmul constructor from 3 ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
              const ex & f4) : inherited(f1,f2,f3,f4)
 {
-	debugmsg("ncmul constructor from 4 ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
              const ex & f4, const ex & f5) : inherited(f1,f2,f3,f4,f5)
 {
-	debugmsg("ncmul constructor from 5 ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
 ncmul::ncmul(const ex & f1, const ex & f2, const ex & f3,
              const ex & f4, const ex & f5, const ex & f6) : inherited(f1,f2,f3,f4,f5,f6)
 {
-	debugmsg("ncmul constructor from 6 ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
 ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
 {
-	debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(exvector * vp) : inherited(vp)
+ncmul::ncmul(std::auto_ptr<exvector> vp) : inherited(vp)
 {
-	debugmsg("ncmul constructor from exvector *",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_ncmul;
 }
 
@@ -109,123 +101,113 @@ ncmul::ncmul(exvector * vp) : inherited(vp)
 DEFAULT_ARCHIVING(ncmul)
 	
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-void ncmul::print(const print_context & c, unsigned level) const
+void ncmul::do_print(const print_context & c, unsigned level) const
 {
-	debugmsg("ncmul print", LOGLEVEL_PRINT);
-
-	if (is_of_type(c, print_tree)) {
-
-		inherited::print(c, level);
-
-	} else if (is_of_type(c, print_csrc)) {
-
-		c.s << "ncmul(";
-		exvector::const_iterator it = seq.begin(), itend = seq.end()-1;
-		while (it != itend) {
-			it->print(c, precedence());
-			c.s << ",";
-			it++;
-		}
-		it->print(c, precedence());
-		c.s << ")";
+	printseq(c, '(', '*', ')', precedence(), level);
+}
 
-	} else
-		printseq(c, '(', '*', ')', precedence(), level);
+void ncmul::do_print_csrc(const print_context & c, unsigned level) const
+{
+	c.s << class_name();
+	printseq(c, '(', ',', ')', precedence(), precedence());
 }
 
 bool ncmul::info(unsigned inf) const
 {
-	throw(std::logic_error("which flags have to be implemented in ncmul::info()?"));
+	return inherited::info(inf);
 }
 
 typedef std::vector<int> intvector;
 
 ex ncmul::expand(unsigned options) const
 {
-	exvector sub_expanded_seq;
-	intvector positions_of_adds;
-	intvector number_of_add_operands;
-
-	exvector expanded_seq=expandchildren(options);
-
-	positions_of_adds.resize(expanded_seq.size());
-	number_of_add_operands.resize(expanded_seq.size());
+	// First, expand the children
+	std::auto_ptr<exvector> vp = expandchildren(options);
+	const exvector &expanded_seq = vp.get() ? *vp : this->seq;
+	
+	// Now, look for all the factors that are sums and remember their
+	// position and number of terms.
+	intvector positions_of_adds(expanded_seq.size());
+	intvector number_of_add_operands(expanded_seq.size());
 
-	int number_of_adds=0;
-	int number_of_expanded_terms=1;
+	size_t number_of_adds = 0;
+	size_t number_of_expanded_terms = 1;
 
-	unsigned current_position=0;
-	exvector::const_iterator last=expanded_seq.end();
+	size_t current_position = 0;
+	exvector::const_iterator last = expanded_seq.end();
 	for (exvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
-		if (is_ex_exactly_of_type((*cit),add)) {
-			positions_of_adds[number_of_adds]=current_position;
-			const add & expanded_addref=ex_to<add>(*cit);
-			number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
-			number_of_expanded_terms *= expanded_addref.seq.size();
+		if (is_exactly_a<add>(*cit)) {
+			positions_of_adds[number_of_adds] = current_position;
+			size_t num_ops = cit->nops();
+			number_of_add_operands[number_of_adds] = num_ops;
+			number_of_expanded_terms *= num_ops;
 			number_of_adds++;
 		}
-		current_position++;
+		++current_position;
 	}
 
-	if (number_of_adds==0) {
-		return (new ncmul(expanded_seq,1))->setflag(status_flags::dynallocated ||
-													status_flags::expanded);
+	// If there are no sums, we are done
+	if (number_of_adds == 0) {
+		if (vp.get())
+			return (new ncmul(vp))->
+			        setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+		else
+			return *this;
 	}
 
+	// Now, form all possible products of the terms of the sums with the
+	// remaining factors, and add them together
 	exvector distrseq;
 	distrseq.reserve(number_of_expanded_terms);
 
-	intvector k;
-	k.resize(number_of_adds);
-	
-	int l;
-	for (l=0; l<number_of_adds; l++) {
-		k[l]=0;
-	}
+	intvector k(number_of_adds);
 
-	while (1) {
-		exvector term;
-		term=expanded_seq;
-		for (l=0; l<number_of_adds; l++) {
-			GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[l]],add));
-			const add & addref=ex_to<add>(expanded_seq[positions_of_adds[l]]);
-			term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
-		}
-		distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
-														status_flags::expanded));
+	while (true) {
+		exvector term = expanded_seq;
+		for (size_t i=0; i<number_of_adds; i++)
+			term[positions_of_adds[i]] = expanded_seq[positions_of_adds[i]].op(k[i]);
+		distrseq.push_back((new ncmul(term, true))->
+		                    setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 
 		// increment k[]
-		l=number_of_adds-1;
-		while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
-			k[l]=0;    
+		int l = number_of_adds-1;
+		while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+			k[l] = 0;
 			l--;
 		}
-		if (l<0) break;
+		if (l<0)
+			break;
 	}
 
-	return (new add(distrseq))->setflag(status_flags::dynallocated |
-										status_flags::expanded);
+	return (new add(distrseq))->
+	        setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 }
 
 int ncmul::degree(const ex & s) const
 {
-	int deg_sum=0;
-	for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		deg_sum+=(*cit).degree(s);
+	// Sum up degrees of factors
+	int deg_sum = 0;
+	exvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		deg_sum += i->degree(s);
+		++i;
 	}
 	return deg_sum;
 }
 
 int ncmul::ldegree(const ex & s) const
 {
-	int deg_sum=0;
-	for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		deg_sum+=(*cit).ldegree(s);
+	// Sum up degrees of factors
+	int deg_sum = 0;
+	exvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		deg_sum += i->degree(s);
+		++i;
 	}
 	return deg_sum;
 }
@@ -235,7 +217,7 @@ ex ncmul::coeff(const ex & s, int n) const
 	exvector coeffseq;
 	coeffseq.reserve(seq.size());
 
-	if (n==0) {
+	if (n == 0) {
 		// product of individual coeffs
 		// if a non-zero power of s is found, the resulting product will be 0
 		exvector::const_iterator it=seq.begin();
@@ -246,30 +228,30 @@ ex ncmul::coeff(const ex & s, int n) const
 		return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 	}
 		 
-	exvector::const_iterator it=seq.begin();
-	bool coeff_found=0;
-	while (it!=seq.end()) {
-		ex c=(*it).coeff(s,n);
-		if (!c.is_zero()) {
-			coeffseq.push_back(c);
-			coeff_found=1;
+	exvector::const_iterator i = seq.begin(), end = seq.end();
+	bool coeff_found = false;
+	while (i != end) {
+		ex c = i->coeff(s,n);
+		if (c.is_zero()) {
+			coeffseq.push_back(*i);
 		} else {
-			coeffseq.push_back(*it);
+			coeffseq.push_back(c);
+			coeff_found = true;
 		}
-		++it;
+		++i;
 	}
 
 	if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
 	
-	return _ex0();
+	return _ex0;
 }
 
-unsigned ncmul::count_factors(const ex & e) const
+size_t ncmul::count_factors(const ex & e) const
 {
-	if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
-		(is_ex_exactly_of_type(e,ncmul))) {
-		unsigned factors=0;
-		for (unsigned i=0; i<e.nops(); i++)
+	if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+		(is_exactly_a<ncmul>(e))) {
+		size_t factors=0;
+		for (size_t i=0; i<e.nops(); i++)
 			factors += count_factors(e.op(i));
 		
 		return factors;
@@ -279,31 +261,31 @@ unsigned ncmul::count_factors(const ex & e) const
 		
 void ncmul::append_factors(exvector & v, const ex & e) const
 {
-	if ((is_ex_exactly_of_type(e,mul)&&(e.return_type()!=return_types::commutative))||
-		(is_ex_exactly_of_type(e,ncmul))) {
-		for (unsigned i=0; i<e.nops(); i++)
-			append_factors(v,e.op(i));
-		
-		return;
-	}
-	v.push_back(e);
+	if ((is_exactly_a<mul>(e)&&(e.return_type()!=return_types::commutative))||
+		(is_exactly_a<ncmul>(e))) {
+		for (size_t i=0; i<e.nops(); i++)
+			append_factors(v, e.op(i));
+	} else 
+		v.push_back(e);
 }
 
 typedef std::vector<unsigned> unsignedvector;
 typedef std::vector<exvector> exvectorvector;
 
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ *  stand for such expressions that contain a plain number.
+ *  - ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) -> ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
+ *  - ncmul(x) -> x
+ *  - ncmul() -> 1
+ *  - ncmul(...,c1,...,c2,...) -> *(c1,c2,ncmul(...))  (pull out commutative elements)
+ *  - ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))  (collect elements of same type)
+ *  - ncmul(x1,x2,x3,...) -> x::eval_ncmul(x1,x2,x3,...)
+ *
+ *  @param level cut-off in recursive evaluation */
 ex ncmul::eval(int level) const
 {
-	// simplifications: ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
-	//                      ncmul(...,x1,x2,...,x3,x4,...) (associativity)
-	//                  ncmul(x) -> x
-	//                  ncmul() -> 1
-	//                  ncmul(...,c1,...,c2,...)
-	//                      *(c1,c2,ncmul(...)) (pull out commutative elements)
-	//                  ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
-	//                      (collect elements of same type)
-	//                  ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
-	// the following rule would be nice, but produces a recursion,
+	// The following additional rule would be nice, but produces a recursion,
 	// which must be trapped by introducing a flag that the sub-ncmuls()
 	// are already evaluated (maybe later...)
 	//                  ncmul(x1,x2,...,X,y1,y2,...) ->
@@ -317,31 +299,34 @@ ex ncmul::eval(int level) const
 	exvector evaledseq=evalchildren(level);
 
 	// ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
-	//     ncmul(...,x1,x2,...,x3,x4,...) (associativity)
-	unsigned factors=0;
-	for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
-		factors += count_factors(*cit);
+	//     ncmul(...,x1,x2,...,x3,x4,...)  (associativity)
+	size_t factors = 0;
+	exvector::const_iterator cit = evaledseq.begin(), citend = evaledseq.end();
+	while (cit != citend)
+		factors += count_factors(*cit++);
 	
 	exvector assocseq;
 	assocseq.reserve(factors);
-	for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit)
-		append_factors(assocseq,*cit);
+	cit = evaledseq.begin();
+	while (cit != citend)
+		append_factors(assocseq, *cit++);
 	
 	// ncmul(x) -> x
 	if (assocseq.size()==1) return *(seq.begin());
 
 	// ncmul() -> 1
-	if (assocseq.size()==0) return _ex1();
+	if (assocseq.empty()) return _ex1;
 
 	// determine return types
 	unsignedvector rettypes;
 	rettypes.reserve(assocseq.size());
-	unsigned i=0;
-	unsigned count_commutative=0;
-	unsigned count_noncommutative=0;
-	unsigned count_noncommutative_composite=0;
-	for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
-		switch (rettypes[i]=(*cit).return_type()) {
+	size_t i = 0;
+	size_t count_commutative=0;
+	size_t count_noncommutative=0;
+	size_t count_noncommutative_composite=0;
+	cit = assocseq.begin(); citend = assocseq.end();
+	while (cit != citend) {
+		switch (rettypes[i] = cit->return_type()) {
 		case return_types::commutative:
 			count_commutative++;
 			break;
@@ -354,7 +339,7 @@ ex ncmul::eval(int level) const
 		default:
 			throw(std::logic_error("ncmul::eval(): invalid return type"));
 		}
-		++i;
+		++i; ++cit;
 	}
 	GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
 
@@ -365,7 +350,8 @@ ex ncmul::eval(int level) const
 		commutativeseq.reserve(count_commutative+1);
 		exvector noncommutativeseq;
 		noncommutativeseq.reserve(assocseq.size()-count_commutative);
-		for (i=0; i<assocseq.size(); ++i) {
+		size_t num = assocseq.size();
+		for (size_t i=0; i<num; ++i) {
 			if (rettypes[i]==return_types::commutative)
 				commutativeseq.push_back(assocseq[i]);
 			else
@@ -383,48 +369,51 @@ ex ncmul::eval(int level) const
 		// elements in assocseq
 		GINAC_ASSERT(count_commutative==0);
 
+		size_t assoc_num = assocseq.size();
 		exvectorvector evv;
 		unsignedvector rttinfos;
-		evv.reserve(assocseq.size());
-		rttinfos.reserve(assocseq.size());
+		evv.reserve(assoc_num);
+		rttinfos.reserve(assoc_num);
 
-		for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
-			unsigned ti=(*cit).return_type_tinfo();
+		cit = assocseq.begin(), citend = assocseq.end();
+		while (cit != citend) {
+			unsigned ti = cit->return_type_tinfo();
+			size_t rtt_num = rttinfos.size();
 			// search type in vector of known types
-			for (i=0; i<rttinfos.size(); ++i) {
-				if (ti==rttinfos[i]) {
+			for (i=0; i<rtt_num; ++i) {
+				if (ti == rttinfos[i]) {
 					evv[i].push_back(*cit);
 					break;
 				}
 			}
-			if (i>=rttinfos.size()) {
+			if (i >= rtt_num) {
 				// new type
 				rttinfos.push_back(ti);
 				evv.push_back(exvector());
-				(*(evv.end()-1)).reserve(assocseq.size());
-				(*(evv.end()-1)).push_back(*cit);
+				(evv.end()-1)->reserve(assoc_num);
+				(evv.end()-1)->push_back(*cit);
 			}
+			++cit;
 		}
 
+		size_t evv_num = evv.size();
 #ifdef DO_GINAC_ASSERT
-		GINAC_ASSERT(evv.size()==rttinfos.size());
-		GINAC_ASSERT(evv.size()>0);
-		unsigned s=0;
-		for (i=0; i<evv.size(); ++i) {
+		GINAC_ASSERT(evv_num == rttinfos.size());
+		GINAC_ASSERT(evv_num > 0);
+		size_t s=0;
+		for (i=0; i<evv_num; ++i)
 			s += evv[i].size();
-		}
-		GINAC_ASSERT(s==assocseq.size());
+		GINAC_ASSERT(s == assoc_num);
 #endif // def DO_GINAC_ASSERT
 		
 		// if all elements are of same type, simplify the string
-		if (evv.size()==1)
-			return evv[0][0].simplify_ncmul(evv[0]);
+		if (evv_num == 1)
+			return evv[0][0].eval_ncmul(evv[0]);
 		
 		exvector splitseq;
-		splitseq.reserve(evv.size());
-		for (i=0; i<evv.size(); ++i) {
+		splitseq.reserve(evv_num);
+		for (i=0; i<evv_num; ++i)
 			splitseq.push_back((new ncmul(evv[i]))->setflag(status_flags::dynallocated));
-		}
 		
 		return (new mul(splitseq))->setflag(status_flags::dynallocated);
 	}
@@ -433,10 +422,10 @@ ex ncmul::eval(int level) const
 										  status_flags::evaluated);
 }
 
-ex ncmul::evalm(void) const
+ex ncmul::evalm() const
 {
 	// Evaluate children first
-	exvector *s = new exvector;
+	std::auto_ptr<exvector> s(new exvector);
 	s->reserve(seq.size());
 	exvector::const_iterator it = seq.begin(), itend = seq.end();
 	while (it != itend) {
@@ -446,16 +435,15 @@ ex ncmul::evalm(void) const
 
 	// If there are only matrices, simply multiply them
 	it = s->begin(); itend = s->end();
-	if (is_ex_of_type(*it, matrix)) {
+	if (is_a<matrix>(*it)) {
 		matrix prod(ex_to<matrix>(*it));
 		it++;
 		while (it != itend) {
-			if (!is_ex_of_type(*it, matrix))
+			if (!is_a<matrix>(*it))
 				goto no_matrix;
 			prod = prod.mul(ex_to<matrix>(*it));
 			it++;
 		}
-		delete s;
 		return prod;
 	}
 
@@ -463,23 +451,55 @@ no_matrix:
 	return (new ncmul(s))->setflag(status_flags::dynallocated);
 }
 
-ex ncmul::thisexprseq(const exvector & v) const
+ex ncmul::thiscontainer(const exvector & v) const
 {
 	return (new ncmul(v))->setflag(status_flags::dynallocated);
 }
 
-ex ncmul::thisexprseq(exvector * vp) const
+ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) const
 {
 	return (new ncmul(vp))->setflag(status_flags::dynallocated);
 }
 
+ex ncmul::conjugate() const
+{
+	if (return_type() != return_types::noncommutative) {
+		return exprseq::conjugate();
+	}
+
+	if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
+		return exprseq::conjugate();
+	}
+
+	exvector ev;
+	ev.reserve(nops());
+	for (const_iterator i=end(); i!=begin();) {
+		--i;
+		ev.push_back(i->conjugate());
+	}
+	return (new ncmul(ev, true))->setflag(status_flags::dynallocated).eval();
+}
+
 // protected
 
-/** Implementation of ex::diff() for a non-commutative product. It always returns 0.
+/** Implementation of ex::diff() for a non-commutative product. It applies
+ *  the product rule.
  *  @see ex::diff */
 ex ncmul::derivative(const symbol & s) const
 {
-	return _ex0();
+	size_t num = seq.size();
+	exvector addseq;
+	addseq.reserve(num);
+	
+	// D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
+	exvector ncmulseq = seq;
+	for (size_t i=0; i<num; ++i) {
+		ex e = seq[i].diff(s);
+		e.swap(ncmulseq[i]);
+		addseq.push_back((new ncmul(ncmulseq))->setflag(status_flags::dynallocated));
+		e.swap(ncmulseq[i]);
+	}
+	return (new add(addseq))->setflag(status_flags::dynallocated);
 }
 
 int ncmul::compare_same_type(const basic & other) const
@@ -487,50 +507,51 @@ int ncmul::compare_same_type(const basic & other) const
 	return inherited::compare_same_type(other);
 }
 
-unsigned ncmul::return_type(void) const
+unsigned ncmul::return_type() const
 {
-	if (seq.size()==0) {
-		// ncmul without factors: should not happen, but commutes
+	if (seq.empty())
 		return return_types::commutative;
-	}
 
-	bool all_commutative=1;
-	unsigned rt;
-	exvector::const_iterator cit_noncommutative_element; // point to first found nc element
+	bool all_commutative = true;
+	exvector::const_iterator noncommutative_element; // point to first found nc element
 
-	for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		rt=(*cit).return_type();
-		if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
-		if ((rt==return_types::noncommutative)&&(all_commutative)) {
+	exvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		unsigned rt = i->return_type();
+		if (rt == return_types::noncommutative_composite)
+			return rt; // one ncc -> mul also ncc
+		if ((rt == return_types::noncommutative) && (all_commutative)) {
 			// first nc element found, remember position
-			cit_noncommutative_element=cit;
-			all_commutative=0;
+			noncommutative_element = i;
+			all_commutative = false;
 		}
-		if ((rt==return_types::noncommutative)&&(!all_commutative)) {
+		if ((rt == return_types::noncommutative) && (!all_commutative)) {
 			// another nc element found, compare type_infos
-			if ((*cit_noncommutative_element).return_type_tinfo()!=(*cit).return_type_tinfo()) {
+			if (noncommutative_element->return_type_tinfo() != i->return_type_tinfo()) {
 				// diffent types -> mul is ncc
 				return return_types::noncommutative_composite;
 			}
 		}
+		++i;
 	}
 	// all factors checked
 	GINAC_ASSERT(!all_commutative); // not all factors should commute, because this is a ncmul();
 	return all_commutative ? return_types::commutative : return_types::noncommutative;
 }
    
-unsigned ncmul::return_type_tinfo(void) const
+unsigned ncmul::return_type_tinfo() const
 {
-	if (seq.size()==0) {
-		// mul without factors: should not happen
+	if (seq.empty())
 		return tinfo_key;
-	}
+
 	// return type_info of first noncommutative element
-	for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if ((*cit).return_type()==return_types::noncommutative) {
-			return (*cit).return_type_tinfo();
-		}
+	exvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		if (i->return_type() == return_types::noncommutative)
+			return i->return_type_tinfo();
+		++i;
 	}
+
 	// no noncommutative element found, should not happen
 	return tinfo_key;
 }
@@ -545,19 +566,37 @@ unsigned ncmul::return_type_tinfo(void) const
 // non-virtual functions in this class
 //////////
 
-exvector ncmul::expandchildren(unsigned options) const
+std::auto_ptr<exvector> ncmul::expandchildren(unsigned options) const
 {
-	exvector s;
-	s.reserve(seq.size());
-	exvector::const_iterator it = seq.begin(), itend = seq.end();
-	while (it != itend) {
-		s.push_back(it->expand(options));
-		it++;
+	const_iterator cit = this->seq.begin(), end = this->seq.end();
+	while (cit != end) {
+		const ex & expanded_ex = cit->expand(options);
+		if (!are_ex_trivially_equal(*cit, expanded_ex)) {
+
+			// copy first part of seq which hasn't changed
+			std::auto_ptr<exvector> s(new exvector(this->seq.begin(), cit));
+			reserve(*s, this->seq.size());
+
+			// insert changed element
+			s->push_back(expanded_ex);
+			++cit;
+
+			// copy rest
+			while (cit != end) {
+				s->push_back(cit->expand(options));
+				++cit;
+			}
+
+			return s;
+		}
+
+		++cit;
 	}
-	return s;
+
+	return std::auto_ptr<exvector>(0); // nothing has changed
 }
 
-const exvector & ncmul::get_factors(void) const
+const exvector & ncmul::get_factors() const
 {
 	return seq;
 }
@@ -566,20 +605,20 @@ const exvector & ncmul::get_factors(void) const
 // friend functions
 //////////
 
-ex nonsimplified_ncmul(const exvector & v)
+ex reeval_ncmul(const exvector & v)
 {
 	return (new ncmul(v))->setflag(status_flags::dynallocated);
 }
 
-ex simplified_ncmul(const exvector & v)
+ex hold_ncmul(const exvector & v)
 {
-	if (v.size()==0) {
-		return _ex1();
-	} else if (v.size()==1) {
+	if (v.empty())
+		return _ex1;
+	else if (v.size() == 1)
 		return v[0];
-	}
-	return (new ncmul(v))->setflag(status_flags::dynallocated |
-	                               status_flags::evaluated);
+	else
+		return (new ncmul(v))->setflag(status_flags::dynallocated |
+		                               status_flags::evaluated);
 }
 
 } // namespace GiNaC