some more comments and cleanups to mul::expand() and ncmul::expand()
[ginac.git] / ginac / ncmul.cpp
index 8964d6b7ddf2f946fa417be53ab5c7587f8ffb48..c4cfe69cb2a93fd3b8afe03f2e571c9a1ba0e34e 100644 (file)
 #include "ex.h"
 #include "add.h"
 #include "mul.h"
+#include "matrix.h"
+#include "print.h"
 #include "archive.h"
 #include "debugmsg.h"
 #include "utils.h"
 
-#ifndef NO_NAMESPACE_GINAC
 namespace GiNaC {
-#endif // ndef NO_NAMESPACE_GINAC
 
 GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
 
@@ -42,47 +42,14 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(ncmul, exprseq)
 // default constructor, destructor, copy constructor assignment operator and helpers
 //////////
 
-// public
-
 ncmul::ncmul()
 {
        debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_ncmul;
 }
 
-ncmul::~ncmul()
-{
-       debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
-       destroy(false);
-}
-
-ncmul::ncmul(const ncmul & other)
-{
-       debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
-       copy(other);
-}
-
-const ncmul & ncmul::operator=(const ncmul & other)
-{
-       debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
-       if (this != &other) {
-               destroy(true);
-               copy(other);
-       }
-       return *this;
-}
-
-// protected
-
-void ncmul::copy(const ncmul & other)
-{
-       inherited::copy(other);
-}
-
-void ncmul::destroy(bool call_parent)
-{
-       if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_COPY(ncmul)
+DEFAULT_DESTROY(ncmul)
 
 //////////
 // other constructors
@@ -139,24 +106,7 @@ ncmul::ncmul(exvector * vp) : inherited(vp)
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-ncmul::ncmul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
-       debugmsg("ncmul constructor from archive_node", LOGLEVEL_CONSTRUCT);
-}
-
-/** Unarchive the object. */
-ex ncmul::unarchive(const archive_node &n, const lst &sym_lst)
-{
-       return (new ncmul(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
-void ncmul::archive(archive_node &n) const
-{
-       inherited::archive(n);
-}
-
+DEFAULT_ARCHIVING(ncmul)
        
 //////////
 // functions overriding virtual functions from bases classes
@@ -164,42 +114,28 @@ void ncmul::archive(archive_node &n) const
 
 // public
 
-basic * ncmul::duplicate() const
+void ncmul::print(const print_context & c, unsigned level) const
 {
-       debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
-       return new ncmul(*this);
-}
+       debugmsg("ncmul print", LOGLEVEL_PRINT);
 
-void ncmul::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("ncmul print",LOGLEVEL_PRINT);
-       printseq(os,'(','%',')',precedence,upper_precedence);
-}
+       if (is_of_type(c, print_tree)) {
 
-void ncmul::printraw(std::ostream & os) const
-{
-       debugmsg("ncmul printraw",LOGLEVEL_PRINT);
-       os << "%(";
-       for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-               (*it).bp->printraw(os);
-               os << ",";
-       }
-       os << ",hash=" << hashvalue << ",flags=" << flags;
-       os << ")";
-}
+               inherited::print(c, level);
 
-void ncmul::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) 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 << ")";
+       } 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 << ")";
+
+       } else
+               printseq(c, '(', '*', ')', precedence(), level);
 }
 
 bool ncmul::info(unsigned inf) const
@@ -211,95 +147,101 @@ 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);
+       // First, expand the children
+       exvector expanded_seq = expandchildren(options);
 
-       positions_of_adds.resize(expanded_seq.size());
-       number_of_add_operands.resize(expanded_seq.size());
+       // Now, look for all the factors that are sums and remember their
+       // position and number of terms. One remark is in order here: we do not
+       // take into account the overall_coeff of the add objects. This is
+       // because in GiNaC, all terms of a sum must be of the same type, so
+       // a non-zero overall_coeff (which can only be numeric) would imply that
+       // the sum only has commutative terms. But then it would never appear
+       // as a factor of an ncmul.
+       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;
+       int number_of_adds = 0;
+       int number_of_expanded_terms = 1;
 
-       unsigned current_position=0;
-       exvector::const_iterator last=expanded_seq.end();
+       unsigned 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();
+               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();
                        number_of_adds++;
                }
                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)
+               return (new ncmul(expanded_seq, true))->
+                       setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 
+       // 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]]);
+       while (true) {
+               exvector term = expanded_seq;
+               for (int i=0; i<number_of_adds; i++) {
+                       GINAC_ASSERT(is_ex_exactly_of_type(expanded_seq[positions_of_adds[i]], add));
+                       const add & addref = ex_to<add>(expanded_seq[positions_of_adds[i]]);
+                       term[positions_of_adds[i]] = addref.recombine_pair_to_ex(addref.seq[k[i]]);
                }
-               distrseq.push_back((new ncmul(term,1))->setflag(status_flags::dynallocated |
-                                                                                                               status_flags::expanded));
+               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();
@@ -310,17 +252,17 @@ 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);
@@ -347,10 +289,8 @@ void ncmul::append_factors(exvector & v, const ex & e) const
                (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);
+       } else 
+               v.push_back(e);
 }
 
 typedef std::vector<unsigned> unsignedvector;
@@ -366,7 +306,7 @@ ex ncmul::eval(int level) const
        //                      *(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,...)
+       //                  ncmul(x1,x2,x3,...) -> x::simplify_ncmul(x1,x2,x3,...)
        // the following 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...)
@@ -374,7 +314,7 @@ ex ncmul::eval(int level) const
        //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
        //                      (X noncommutative_composite)
 
-       if ((level==1)&&(flags & status_flags::evaluated)) {
+       if ((level==1) && (flags & status_flags::evaluated)) {
                return *this;
        }
 
@@ -382,32 +322,33 @@ ex ncmul::eval(int level) const
 
        // 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);
-       }
-
+       unsigned 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 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()) {
+       cit = assocseq.begin(); citend = assocseq.end();
+       while (cit != citend) {
+               switch (rettypes[i] = cit->return_type()) {
                case return_types::commutative:
                        count_commutative++;
                        break;
@@ -420,7 +361,7 @@ 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());
 
@@ -431,12 +372,12 @@ 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) {
-                       if (rettypes[i]==return_types::commutative) {
+               unsigned num = assocseq.size();
+               for (unsigned i=0; i<num; ++i) {
+                       if (rettypes[i]==return_types::commutative)
                                commutativeseq.push_back(assocseq[i]);
-                       } else {
+                       else
                                noncommutativeseq.push_back(assocseq[i]);
-                       }
                }
                commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
                return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
@@ -450,50 +391,52 @@ ex ncmul::eval(int level) const
                // elements in assocseq
                GINAC_ASSERT(count_commutative==0);
 
+               unsigned 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();
+                       unsigned 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;
                }
 
+               unsigned evv_num = evv.size();
 #ifdef DO_GINAC_ASSERT
-               GINAC_ASSERT(evv.size()==rttinfos.size());
-               GINAC_ASSERT(evv.size()>0);
+               GINAC_ASSERT(evv_num == rttinfos.size());
+               GINAC_ASSERT(evv_num > 0);
                unsigned s=0;
-               for (i=0; i<evv.size(); ++i) {
+               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) {
+               if (evv_num == 1)
                        return evv[0][0].simplify_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);
        }
        
@@ -501,23 +444,34 @@ ex ncmul::eval(int level) const
                                                                                  status_flags::evaluated);
 }
 
-exvector ncmul::get_indices(void) const
+ex ncmul::evalm(void) const
 {
-       // return union of indices of factors
-       exvector iv;
-       for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               exvector subiv=(*cit).get_indices();
-               iv.reserve(iv.size()+subiv.size());
-               for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
-                       iv.push_back(*cit2);
+       // Evaluate children first
+       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_ex_of_type(*it, matrix)) {
+               matrix prod(ex_to<matrix>(*it));
+               it++;
+               while (it != itend) {
+                       if (!is_ex_of_type(*it, matrix))
+                               goto no_matrix;
+                       prod = prod.mul(ex_to<matrix>(*it));
+                       it++;
                }
+               delete s;
+               return prod;
        }
-       return iv;
-}
 
-ex ncmul::subs(const lst & ls, const lst & lr) const
-{
-       return ncmul(subschildren(ls, lr));
+no_matrix:
+       return (new ncmul(s))->setflag(status_flags::dynallocated);
 }
 
 ex ncmul::thisexprseq(const exvector & v) const
@@ -532,11 +486,24 @@ ex ncmul::thisexprseq(exvector * vp) const
 
 // 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();
+       unsigned 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 (unsigned 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
@@ -546,30 +513,30 @@ int ncmul::compare_same_type(const basic & other) const
 
 unsigned ncmul::return_type(void) 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();
@@ -578,16 +545,17 @@ unsigned ncmul::return_type(void) const
    
 unsigned ncmul::return_type_tinfo(void) 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;
 }
@@ -606,9 +574,10 @@ exvector ncmul::expandchildren(unsigned options) const
 {
        exvector s;
        s.reserve(seq.size());
-
-       for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-               s.push_back((*it).expand(options));
+       exvector::const_iterator it = seq.begin(), itend = seq.end();
+       while (it != itend) {
+               s.push_back(it->expand(options));
+               it++;
        }
        return s;
 }
@@ -618,14 +587,6 @@ const exvector & ncmul::get_factors(void) const
        return seq;
 }
 
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned ncmul::precedence=50;
-
 //////////
 // friend functions
 //////////
@@ -637,15 +598,13 @@ ex nonsimplified_ncmul(const exvector & v)
 
 ex simplified_ncmul(const exvector & v)
 {
-       if (v.size()==0) {
+       if (v.empty())
                return _ex1();
-       } else if (v.size()==1) {
+       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);
 }
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC