fixed operator precedence
[ginac.git] / ginac / ncmul.cpp
index d7d97b957fa7d517abd10804c4bdb74e44df53c3..ccc91c490d4be13f853739e61b8d423c076e6fe4 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's non-commutative products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 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"
 
-#ifndef NO_GINAC_NAMESPACE
 namespace GiNaC {
-#endif // ndef NO_GINAC_NAMESPACE
 
-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
 //////////
 
-// public
-
 ncmul::ncmul()
 {
-    debugmsg("ncmul default constructor",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
-}
-
-ncmul::~ncmul()
-{
-    debugmsg("ncmul destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
-}
-
-ncmul::ncmul(ncmul const & other)
-{
-    debugmsg("ncmul copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
-}
-
-ncmul const & ncmul::operator=(ncmul const & other)
-{
-    debugmsg("ncmul operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
-}
-
-// protected
-
-void ncmul::copy(ncmul const & other)
-{
-    inherited::copy(other);
-}
-
-void ncmul::destroy(bool call_parent)
-{
-    if (call_parent) inherited::destroy(call_parent);
+       tinfo_key = TINFO_ncmul;
 }
 
 //////////
@@ -90,505 +56,504 @@ void ncmul::destroy(bool call_parent)
 
 // public
 
-ncmul::ncmul(ex const & lh, ex const & rh) :
-    inherited(lh,rh)
+ncmul::ncmul(const ex & lh, const ex & rh) : inherited(lh,rh)
 {
-    debugmsg("ncmul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+       tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3) :
-    inherited(f1,f2,f3)
+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;
+       tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4) : inherited(f1,f2,f3,f4)
+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;
+       tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4, ex const & f5) : inherited(f1,f2,f3,f4,f5)
+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;
+       tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(ex const & f1, ex const & f2, ex const & f3,
-      ex const & f4, ex const & f5, ex const & f6) :
-    inherited(f1,f2,f3,f4,f5,f6)
+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;
+       tinfo_key = TINFO_ncmul;
 }
 
-ncmul::ncmul(exvector const & v, bool discardable) : inherited(v,discardable)
+ncmul::ncmul(const exvector & v, bool discardable) : inherited(v,discardable)
 {
-    debugmsg("ncmul constructor from exvector,bool",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_ncmul;
+       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;
+       tinfo_key = TINFO_ncmul;
 }
 
 //////////
 // 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
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-basic * ncmul::duplicate() const
+void ncmul::do_print(const print_context & c, unsigned level) const
 {
-    debugmsg("ncmul duplicate",LOGLEVEL_ASSIGNMENT);
-    return new ncmul(*this);
+       printseq(c, '(', '*', ')', precedence(), level);
 }
 
-void ncmul::print(ostream & os, unsigned upper_precedence) const
+void ncmul::do_print_csrc(const print_context & c, unsigned level) const
 {
-    debugmsg("ncmul print",LOGLEVEL_PRINT);
-    printseq(os,'(','%',')',precedence,upper_precedence);
-}
-
-void ncmul::printraw(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 << ")";
-}
-
-void ncmul::printcsrc(ostream & os, 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 << ")";
+       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 vector<int> intvector;
+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());
-
-    int number_of_adds=0;
-    int number_of_expanded_terms=1;
-
-    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;
-            add const & 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);
-    }
-
-    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;
-    }
-
-    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));
-            add const & 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));
-
-        // increment k[]
-        l=number_of_adds-1;
-        while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
-            k[l]=0;    
-            l--;
-        }
-        if (l<0) break;
-    }
-
-    return (new add(distrseq))->setflag(status_flags::dynallocated |
-                                        status_flags::expanded);
-}
-
-int ncmul::degree(symbol const & s) const
+       // 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());
+
+       size_t number_of_adds = 0;
+       size_t number_of_expanded_terms = 1;
+
+       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_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;
+       }
+
+       // 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(number_of_adds);
+
+       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[]
+               int l = number_of_adds-1;
+               while ((l>=0) && ((++k[l]) >= number_of_add_operands[l])) {
+                       k[l] = 0;
+                       l--;
+               }
+               if (l<0)
+                       break;
+       }
+
+       return (new add(distrseq))->
+               setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+}
+
+int ncmul::degree(const ex & s) const
+{
+       // 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
+{
+       // 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 ex & s, int n) const
+{
+       exvector coeffseq;
+       coeffseq.reserve(seq.size());
+
+       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();
+               while (it!=seq.end()) {
+                       coeffseq.push_back((*it).coeff(s,n));
+                       ++it;
+               }
+               return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+       }
+                
+       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(c);
+                       coeff_found = true;
+               }
+               ++i;
+       }
+
+       if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
+       
+       return _ex0;
+}
+
+size_t ncmul::count_factors(const ex & e) const
+{
+       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;
+       }
+       return 1;
+}
+               
+void ncmul::append_factors(exvector & v, const ex & e) const
+{
+       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
 {
-    int deg_sum=0;
-    for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        deg_sum+=(*cit).degree(s);
-    }
-    return deg_sum;
+       // 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,...) ->
+       //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
+       //                      (X noncommutative_composite)
+
+       if ((level==1) && (flags & status_flags::evaluated)) {
+               return *this;
+       }
+
+       exvector evaledseq=evalchildren(level);
+
+       // ncmul(...,*(x1,x2),...,ncmul(x3,x4),...) ->
+       //     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);
+       cit = evaledseq.begin();
+       while (cit != citend)
+               append_factors(assocseq, *cit++);
+       
+       // ncmul(x) -> x
+       if (assocseq.size()==1) return *(seq.begin());
+
+       // ncmul() -> 1
+       if (assocseq.empty()) return _ex1;
+
+       // determine return types
+       unsignedvector rettypes;
+       rettypes.reserve(assocseq.size());
+       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;
+               case return_types::noncommutative:
+                       count_noncommutative++;
+                       break;
+               case return_types::noncommutative_composite:
+                       count_noncommutative_composite++;
+                       break;
+               default:
+                       throw(std::logic_error("ncmul::eval(): invalid return type"));
+               }
+               ++i; ++cit;
+       }
+       GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
+
+       // ncmul(...,c1,...,c2,...) ->
+       //     *(c1,c2,ncmul(...)) (pull out commutative elements)
+       if (count_commutative!=0) {
+               exvector commutativeseq;
+               commutativeseq.reserve(count_commutative+1);
+               exvector noncommutativeseq;
+               noncommutativeseq.reserve(assocseq.size()-count_commutative);
+               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
+                               noncommutativeseq.push_back(assocseq[i]);
+               }
+               commutativeseq.push_back((new ncmul(noncommutativeseq,1))->setflag(status_flags::dynallocated));
+               return (new mul(commutativeseq))->setflag(status_flags::dynallocated);
+       }
+               
+       // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
+       //     (collect elements of same type)
+
+       if (count_noncommutative_composite==0) {
+               // there are neither commutative nor noncommutative_composite
+               // elements in assocseq
+               GINAC_ASSERT(count_commutative==0);
+
+               size_t assoc_num = assocseq.size();
+               exvectorvector evv;
+               unsignedvector rttinfos;
+               evv.reserve(assoc_num);
+               rttinfos.reserve(assoc_num);
+
+               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<rtt_num; ++i) {
+                               if (ti == rttinfos[i]) {
+                                       evv[i].push_back(*cit);
+                                       break;
+                               }
+                       }
+                       if (i >= rtt_num) {
+                               // new type
+                               rttinfos.push_back(ti);
+                               evv.push_back(exvector());
+                               (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_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 == assoc_num);
+#endif // def DO_GINAC_ASSERT
+               
+               // if all elements are of same type, simplify the string
+               if (evv_num == 1)
+                       return evv[0][0].eval_ncmul(evv[0]);
+               
+               exvector splitseq;
+               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);
+       }
+       
+       return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
+                                                                                 status_flags::evaluated);
 }
 
-int ncmul::ldegree(symbol const & s) const
+ex ncmul::evalm() const
 {
-    int deg_sum=0;
-    for (exvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        deg_sum+=(*cit).ldegree(s);
-    }
-    return deg_sum;
-}
+       // 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++;
+       }
 
-ex ncmul::coeff(symbol const & s, int const n) const
-{
-    exvector coeffseq;
-    coeffseq.reserve(seq.size());
-
-    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();
-        while (it!=seq.end()) {
-            coeffseq.push_back((*it).coeff(s,n));
-            ++it;
-        }
-        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;
-        } else {
-            coeffseq.push_back(*it);
-        }
-        ++it;
-    }
-
-    if (coeff_found) return (new ncmul(coeffseq,1))->setflag(status_flags::dynallocated);
-    
-    return _ex0();
-}
+       // 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;
+       }
 
-unsigned ncmul::count_factors(ex const & 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++)
-            factors += count_factors(e.op(i));
-        
-        return factors;
-    }
-    return 1;
-}
-        
-void ncmul::append_factors(exvector & v, ex const & 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);
+no_matrix:
+       return (new ncmul(s))->setflag(status_flags::dynallocated);
 }
 
-typedef vector<unsigned> unsignedvector;
-typedef vector<exvector> exvectorvector;
-
-ex ncmul::eval(int level) const
+ex ncmul::thiscontainer(const exvector & v) 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::eval_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...)
-    //                  ncmul(x1,x2,...,X,y1,y2,...) ->
-    //                      ncmul(ncmul(x1,x2,...),X,ncmul(y1,y2,...)
-    //                      (X noncommutative_composite)
-
-    if ((level==1)&&(flags & status_flags::evaluated)) {
-        return *this;
-    }
-
-    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);
-    }
-
-    exvector assocseq;
-    assocseq.reserve(factors);
-    for (exvector::const_iterator cit=evaledseq.begin(); cit!=evaledseq.end(); ++cit) {
-        append_factors(assocseq,*cit);
-    }
-
-    // ncmul(x) -> x
-    if (assocseq.size()==1) return *(seq.begin());
-
-    // ncmul() -> 1
-    if (assocseq.size()==0) 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()) {
-        case return_types::commutative:
-            count_commutative++;
-            break;
-        case return_types::noncommutative:
-            count_noncommutative++;
-            break;
-        case return_types::noncommutative_composite:
-            count_noncommutative_composite++;
-            break;
-        default:
-            throw(std::logic_error("ncmul::eval(): invalid return type"));
-        }
-        ++i;
-    }
-    GINAC_ASSERT(count_commutative+count_noncommutative+count_noncommutative_composite==assocseq.size());
-
-    // ncmul(...,c1,...,c2,...) ->
-    //     *(c1,c2,ncmul(...)) (pull out commutative elements)
-    if (count_commutative!=0) {
-        exvector commutativeseq;
-        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) {
-                commutativeseq.push_back(assocseq[i]);
-            } 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);
-    }
-        
-    // ncmul(x1,y1,x2,y2) -> *(ncmul(x1,x2),ncmul(y1,y2))
-    //     (collect elements of same type)
-
-    if (count_noncommutative_composite==0) {
-        // there are neither commutative nor noncommutative_composite
-        // elements in assocseq
-        GINAC_ASSERT(count_commutative==0);
-
-        exvectorvector evv;
-        unsignedvector rttinfos;
-        evv.reserve(assocseq.size());
-        rttinfos.reserve(assocseq.size());
-
-        for (exvector::const_iterator cit=assocseq.begin(); cit!=assocseq.end(); ++cit) {
-            unsigned ti=(*cit).return_type_tinfo();
-            // search type in vector of known types
-            for (i=0; i<rttinfos.size(); ++i) {
-                if (ti==rttinfos[i]) {
-                    evv[i].push_back(*cit);
-                    break;
-                }
-            }
-            if (i>=rttinfos.size()) {
-                // new type
-                rttinfos.push_back(ti);
-                evv.push_back(exvector());
-                (*(evv.end()-1)).reserve(assocseq.size());
-                (*(evv.end()-1)).push_back(*cit);
-            }
-        }
-
-#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) {
-            s += evv[i].size();
-        }
-        GINAC_ASSERT(s==assocseq.size());
-#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]);
-        }
-        
-        exvector splitseq;
-        splitseq.reserve(evv.size());
-        for (i=0; i<evv.size(); ++i) {
-            splitseq.push_back((new ncmul(evv[i]))->
-                               setflag(status_flags::dynallocated));
-        }
-
-        return (new mul(splitseq))->setflag(status_flags::dynallocated);
-    }
-    
-    return (new ncmul(assocseq))->setflag(status_flags::dynallocated |
-                                          status_flags::evaluated);
+       return (new ncmul(v))->setflag(status_flags::dynallocated);
 }
 
-exvector ncmul::get_indices(void) const
+ex ncmul::thiscontainer(std::auto_ptr<exvector> vp) 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);
-        }
-    }
-    return iv;
+       return (new ncmul(vp))->setflag(status_flags::dynallocated);
 }
 
-ex ncmul::subs(lst const & ls, lst const & lr) const
+ex ncmul::conjugate() const
 {
-    return ncmul(subschildren(ls, lr));
-}
+       if (return_type() != return_types::noncommutative) {
+               return exprseq::conjugate();
+       }
 
-ex ncmul::thisexprseq(exvector const & v) const
-{
-    return (new ncmul(v))->setflag(status_flags::dynallocated);
-}
+       if ((return_type_tinfo() & 0xffffff00U) != TINFO_clifford) {
+               return exprseq::conjugate();
+       }
 
-ex ncmul::thisexprseq(exvector * vp) const
-{
-    return (new ncmul(vp))->setflag(status_flags::dynallocated);
+       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
 
-int ncmul::compare_same_type(basic const & other) const
-{
-    return inherited::compare_same_type(other);
-}
-
-unsigned ncmul::return_type(void) const
-{
-    if (seq.size()==0) {
-        // ncmul without factors: should not happen, but commutes
-        return return_types::commutative;
-    }
-
-    bool all_commutative=1;
-    unsigned rt;
-    exvector::const_iterator cit_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)) {
-            // first nc element found, remember position
-            cit_noncommutative_element=cit;
-            all_commutative=0;
-        }
-        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()) {
-               // diffent types -> mul is ncc
-               return return_types::noncommutative_composite;
-            }
-        }
-    }
-    // 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;
+/** Implementation of ex::diff() for a non-commutative product. It applies
+ *  the product rule.
+ *  @see ex::diff */
+ex ncmul::derivative(const symbol & s) const
+{
+       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
+{
+       return inherited::compare_same_type(other);
+}
+
+unsigned ncmul::return_type() const
+{
+       if (seq.empty())
+               return return_types::commutative;
+
+       bool all_commutative = true;
+       exvector::const_iterator noncommutative_element; // point to first found nc element
+
+       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
+                       noncommutative_element = i;
+                       all_commutative = false;
+               }
+               if ((rt == return_types::noncommutative) && (!all_commutative)) {
+                       // another nc element found, compare type_infos
+                       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
-        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();
-        }
-    }
-    // no noncommutative element found, should not happen
-    return tinfo_key;
+       if (seq.empty())
+               return tinfo_key;
+
+       // return type_info of first noncommutative element
+       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;
 }
 
 //////////
@@ -601,58 +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());
-
-    for (exvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-        s.push_back((*it).expand(options));
-    }
-    return s;
-}
+       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)) {
 
-exvector const & ncmul::get_factors(void) const
-{
-    return seq;
-}
+                       // 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());
 
-//////////
-// static member variables
-//////////
+                       // insert changed element
+                       s->push_back(expanded_ex);
+                       ++cit;
 
-// protected
+                       // copy rest
+                       while (cit != end) {
+                               s->push_back(cit->expand(options));
+                               ++cit;
+                       }
 
-unsigned ncmul::precedence=50;
+                       return s;
+               }
 
+               ++cit;
+       }
 
-//////////
-// global constants
-//////////
+       return std::auto_ptr<exvector>(0); // nothing has changed
+}
 
-const ncmul some_ncmul;
-type_info const & typeid_ncmul=typeid(some_ncmul);
+const exvector & ncmul::get_factors() const
+{
+       return seq;
+}
 
 //////////
 // friend functions
 //////////
 
-ex nonsimplified_ncmul(exvector const & v)
+ex reeval_ncmul(const exvector & v)
 {
-    return (new ncmul(v))->setflag(status_flags::dynallocated);
+       return (new ncmul(v))->setflag(status_flags::dynallocated);
 }
 
-ex simplified_ncmul(exvector const & v)
+ex hold_ncmul(const exvector & v)
 {
-    if (v.size()==0) {
-        return _ex1();
-    } else if (v.size()==1) {
-        return v[0];
-    }
-    return (new ncmul(v))->setflag(status_flags::dynallocated |
-                                   status_flags::evaluated);
+       if (v.empty())
+               return _ex1;
+       else if (v.size() == 1)
+               return v[0];
+       else
+               return (new ncmul(v))->setflag(status_flags::dynallocated |
+                                              status_flags::evaluated);
 }
 
-#ifndef NO_GINAC_NAMESPACE
 } // namespace GiNaC
-#endif // ndef NO_GINAC_NAMESPACE