fixed operator precedence
[ginac.git] / ginac / ncmul.cpp
index 12c1d5e41fcf799eae4485967196222989a282a1..ccc91c490d4be13f853739e61b8d423c076e6fe4 100644 (file)
@@ -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
 #include "ex.h"
 #include "add.h"
 #include "mul.h"
+#include "matrix.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
 //////////
@@ -57,46 +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;
 }
 
@@ -107,141 +101,123 @@ 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(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("ncmul print",LOGLEVEL_PRINT);
-       printseq(os,'(','*',')',precedence,upper_precedence);
-}
-
-void ncmul::printraw(std::ostream & os) const
+void ncmul::do_print(const print_context & c, unsigned level) const
 {
-       debugmsg("ncmul printraw",LOGLEVEL_PRINT);
-       os << "ncmul(";
-       for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-               (*it).bp->printraw(os);
-               os << ",";
-       }
-       os << ",hash=" << hashvalue << ",flags=" << flags;
-       os << ")";
+       printseq(c, '(', '*', ')', precedence(), level);
 }
 
-void ncmul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
+void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 {
-       debugmsg("ncmul print csrc",LOGLEVEL_PRINT);
-       exvector::const_iterator it;
-       exvector::const_iterator itend = seq.end()-1;
-       os << "ncmul(";
-       for (it=seq.begin(); it!=itend; ++it) {
-               (*it).bp->printcsrc(os,precedence);
-               os << ",";
-       }
-       (*it).bp->printcsrc(os,precedence);
-       os << ")";
+       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 symbol & s) const
+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 symbol & s) const
+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;
 }
 
-ex ncmul::coeff(const symbol & s, int n) const
+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();
@@ -252,30 +228,30 @@ ex ncmul::coeff(const symbol & 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;
@@ -285,31 +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,...) ->
@@ -323,31 +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;
@@ -360,7 +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());
 
@@ -371,7 +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
@@ -389,48 +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);
        }
@@ -439,28 +422,84 @@ ex ncmul::eval(int level) const
                                                                                  status_flags::evaluated);
 }
 
-ex ncmul::subs(const lst & ls, const lst & lr) const
+ex ncmul::evalm() const
 {
-       return ncmul(subschildren(ls, lr));
+       // Evaluate children first
+       std::auto_ptr<exvector> s(new exvector);
+       s->reserve(seq.size());
+       exvector::const_iterator it = seq.begin(), itend = seq.end();
+       while (it != itend) {
+               s->push_back(it->evalm());
+               it++;
+       }
+
+       // If there are only matrices, simply multiply them
+       it = s->begin(); itend = s->end();
+       if (is_a<matrix>(*it)) {
+               matrix prod(ex_to<matrix>(*it));
+               it++;
+               while (it != itend) {
+                       if (!is_a<matrix>(*it))
+                               goto no_matrix;
+                       prod = prod.mul(ex_to<matrix>(*it));
+                       it++;
+               }
+               return prod;
+       }
+
+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
@@ -468,50 +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;
 }
@@ -526,48 +566,59 @@ 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());
+       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;
+                       }
 
-       for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-               s.push_back((*it).expand(options));
+                       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;
 }
 
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned ncmul::precedence = 50;
-
 //////////
 // 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