]> www.ginac.de Git - ginac.git/blobdiff - ginac/add.cpp
* Some minor optimization glitches.
[ginac.git] / ginac / add.cpp
index d999a1004f39735ccd80eeba03a04016c01519df..b9eca995affd6d9cc295118062f67d79d74f89e2 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's sums of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2001 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 "add.h"
 #include "mul.h"
+#include "matrix.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(add, expairseq)
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
-// public
-
 add::add()
 {
-       debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
 }
 
-add::~add()
-{
-       debugmsg("add destructor",LOGLEVEL_DESTRUCT);
-       destroy(false);
-}
-
-add::add(const add & other)
-{
-       debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
-       copy(other);
-}
-
-const add & add::operator=(const add & other)
-{
-       debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
-       if (this != &other) {
-               destroy(true);
-               copy(other);
-       }
-       return *this;
-}
-
-// protected
-
-void add::copy(const add & other)
-{
-       inherited::copy(other);
-}
-
-void add::destroy(bool call_parent)
-{
-       if (call_parent) inherited::destroy(call_parent);
-}
+DEFAULT_COPY(add)
+DEFAULT_DESTROY(add)
 
 //////////
 // other constructors
@@ -89,51 +53,30 @@ void add::destroy(bool call_parent)
 
 add::add(const ex & lh, const ex & rh)
 {
-       debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
-       overall_coeff = _ex0();
+       overall_coeff = _ex0;
        construct_from_2_ex(lh,rh);
        GINAC_ASSERT(is_canonical());
 }
 
 add::add(const exvector & v)
 {
-       debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
-       overall_coeff = _ex0();
+       overall_coeff = _ex0;
        construct_from_exvector(v);
        GINAC_ASSERT(is_canonical());
 }
 
-/*
-add::add(const epvector & v, bool do_not_canonicalize)
-{
-       debugmsg("add constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_add;
-       if (do_not_canonicalize) {
-               seq=v;
-#ifdef EXPAIRSEQ_USE_HASHTAB
-               combine_same_terms(); // to build hashtab
-#endif // def EXPAIRSEQ_USE_HASHTAB
-       } else {
-               construct_from_epvector(v);
-       }
-       GINAC_ASSERT(is_canonical());
-}
-*/
-
 add::add(const epvector & v)
 {
-       debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
-       overall_coeff = _ex0();
+       overall_coeff = _ex0;
        construct_from_epvector(v);
        GINAC_ASSERT(is_canonical());
 }
 
 add::add(const epvector & v, const ex & oc)
 {
-       debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
        overall_coeff = oc;
        construct_from_epvector(v);
@@ -142,7 +85,6 @@ add::add(const epvector & v, const ex & oc)
 
 add::add(epvector * vp, const ex & oc)
 {
-       debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
        tinfo_key = TINFO_add;
        GINAC_ASSERT(vp!=0);
        overall_coeff = oc;
@@ -155,137 +97,125 @@ add::add(epvector * vp, const ex & oc)
 // archiving
 //////////
 
-/** Construct object from archive_node. */
-add::add(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
-       debugmsg("add constructor from archive_node", LOGLEVEL_CONSTRUCT);
-}
-
-/** Unarchive the object. */
-ex add::unarchive(const archive_node &n, const lst &sym_lst)
-{
-       return (new add(n, sym_lst))->setflag(status_flags::dynallocated);
-}
-
-/** Archive the object. */
-void add::archive(archive_node &n) const
-{
-       inherited::archive(n);
-}
+DEFAULT_ARCHIVING(add)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-basic * add::duplicate() const
+void add::print(const print_context & c, unsigned level) const
 {
-       debugmsg("add duplicate",LOGLEVEL_DUPLICATE);
-       return new add(*this);
-}
+       if (is_a<print_tree>(c)) {
 
-void add::print(std::ostream & os, unsigned upper_precedence) const
-{
-       debugmsg("add print",LOGLEVEL_PRINT);
-       if (precedence<=upper_precedence) os << "(";
-       numeric coeff;
-       bool first = true;
-       // first print the overall numeric coefficient, if present:
-       if (!overall_coeff.is_zero()) {
-               os << overall_coeff;
-               first = false;
-       }
-       // then proceed with the remaining factors:
-       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               coeff = ex_to_numeric(cit->coeff);
-               if (!first) {
-                       if (coeff.csgn()==-1) os << '-'; else os << '+';
-               } else {
-                       if (coeff.csgn()==-1) os << '-';
-                       first = false;
-               }
-               if (!coeff.is_equal(_num1()) &&
-                   !coeff.is_equal(_num_1())) {
-                       if (coeff.is_rational()) {
-                               if (coeff.is_negative())
-                                       os << -coeff;
-                               else
-                                       os << coeff;
+               inherited::print(c, level);
+
+       } else if (is_a<print_csrc>(c)) {
+
+               if (precedence() <= level)
+                       c.s << "(";
+       
+               // Print arguments, separated by "+"
+               epvector::const_iterator it = seq.begin(), itend = seq.end();
+               while (it != itend) {
+               
+                       // If the coefficient is -1, it is replaced by a single minus sign
+                       if (it->coeff.compare(_num1) == 0) {
+                               it->rest.print(c, precedence());
+                       } else if (it->coeff.compare(_num_1) == 0) {
+                               c.s << "-";
+                               it->rest.print(c, precedence());
+                       } else if (ex_to<numeric>(it->coeff).numer().compare(_num1) == 0) {
+                               it->rest.print(c, precedence());
+                               c.s << "/";
+                               ex_to<numeric>(it->coeff).denom().print(c, precedence());
+                       } else if (ex_to<numeric>(it->coeff).numer().compare(_num_1) == 0) {
+                               c.s << "-";
+                               it->rest.print(c, precedence());
+                               c.s << "/";
+                               ex_to<numeric>(it->coeff).denom().print(c, precedence());
                        } else {
-                               if (coeff.csgn()==-1)
-                                       (-coeff).print(os, precedence);
-                               else
-                                       coeff.print(os, precedence);
+                               it->coeff.print(c, precedence());
+                               c.s << "*";
+                               it->rest.print(c, precedence());
                        }
-                       os << '*';
+               
+                       // Separator is "+", except if the following expression would have a leading minus sign
+                       ++it;
+                       if (it != itend && !(it->coeff.compare(_num0) < 0 || (it->coeff.compare(_num1) == 0 && is_exactly_a<numeric>(it->rest) && it->rest.compare(_num0) < 0)))
+                               c.s << "+";
                }
-               cit->rest.print(os, precedence);
-       }
-       if (precedence<=upper_precedence) os << ")";
-}
+       
+               if (!overall_coeff.is_zero()) {
+                       if (overall_coeff.info(info_flags::positive))
+                               c.s << '+';
+                       overall_coeff.print(c, precedence());
+               }
+       
+               if (precedence() <= level)
+                       c.s << ")";
 
-void add::printraw(std::ostream & os) const
-{
-       debugmsg("add printraw",LOGLEVEL_PRINT);
-
-       os << "+(";
-       for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-               os << "(";
-               (*it).rest.bp->printraw(os);
-               os << ",";
-               (*it).coeff.bp->printraw(os);        
-               os << "),";
-       }
-       os << ",hash=" << hashvalue << ",flags=" << flags;
-       os << ")";
-}
+       } else {
 
-void add::printcsrc(std::ostream & os, unsigned type, unsigned upper_precedence) const
-{
-       debugmsg("add print csrc", LOGLEVEL_PRINT);
-       if (precedence <= upper_precedence)
-               os << "(";
+               if (precedence() <= level) {
+                       if (is_a<print_latex>(c))
+                               c.s << "{(";
+                       else
+                               c.s << "(";
+               }
 
-       // Print arguments, separated by "+"
-       epvector::const_iterator it = seq.begin();
-       epvector::const_iterator itend = seq.end();
-       while (it != itend) {
+               numeric coeff;
+               bool first = true;
 
-               // If the coefficient is -1, it is replaced by a single minus sign
-               if (it->coeff.compare(_num1()) == 0) {
-                       it->rest.bp->printcsrc(os, type, precedence);
-               } else if (it->coeff.compare(_num_1()) == 0) {
-                       os << "-";
-                       it->rest.bp->printcsrc(os, type, precedence);
-               } else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
-                       it->rest.bp->printcsrc(os, type, precedence);
-                       os << "/";
-                       ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
-               } else if (ex_to_numeric(it->coeff).numer().compare(_num_1()) == 0) {
-                       os << "-";
-                       it->rest.bp->printcsrc(os, type, precedence);
-                       os << "/";
-                       ex_to_numeric(it->coeff).denom().printcsrc(os, type, precedence);
-               } else {
-                       it->coeff.bp->printcsrc(os, type, precedence);
-                       os << "*";
-                       it->rest.bp->printcsrc(os, type, precedence);
+               // First print the overall numeric coefficient, if present
+               if (!overall_coeff.is_zero()) {
+                       if (!is_a<print_tree>(c))
+                               overall_coeff.print(c, 0);
+                       else
+                               overall_coeff.print(c, precedence());
+                       first = false;
                }
 
-               // Separator is "+", except if the following expression would have a leading minus sign
-               it++;
-               if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_ex_exactly_of_type(it->rest, numeric) && it->rest.compare(_num0()) < 0)))
-                       os << "+";
-       }
-       
-       if (!overall_coeff.is_equal(_ex0())) {
-               if (overall_coeff.info(info_flags::positive)) os << '+';
-               overall_coeff.bp->printcsrc(os,type,precedence);
+               // Then proceed with the remaining factors
+               epvector::const_iterator it = seq.begin(), itend = seq.end();
+               while (it != itend) {
+                       coeff = ex_to<numeric>(it->coeff);
+                       if (!first) {
+                               if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
+                       } else {
+                               if (coeff.csgn() == -1) c.s << '-';
+                               first = false;
+                       }
+                       if (!coeff.is_equal(_num1) &&
+                           !coeff.is_equal(_num_1)) {
+                               if (coeff.is_rational()) {
+                                       if (coeff.is_negative())
+                                               (-coeff).print(c);
+                                       else
+                                               coeff.print(c);
+                               } else {
+                                       if (coeff.csgn() == -1)
+                                               (-coeff).print(c, precedence());
+                                       else
+                                               coeff.print(c, precedence());
+                               }
+                               if (is_a<print_latex>(c))
+                                       c.s << ' ';
+                               else
+                                       c.s << '*';
+                       }
+                       it->rest.print(c, precedence());
+                       ++it;
+               }
+
+               if (precedence() <= level) {
+                       if (is_a<print_latex>(c))
+                               c.s << ")}";
+                       else
+                               c.s << ")";
+               }
        }
-       
-       if (precedence <= upper_precedence)
-               os << ")";
 }
 
 bool add::info(unsigned inf) const
@@ -297,16 +227,20 @@ bool add::info(unsigned inf) const
                case info_flags::rational_polynomial:
                case info_flags::crational_polynomial:
                case info_flags::rational_function: {
-                       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+                       epvector::const_iterator i = seq.begin(), end = seq.end();
+                       while (i != end) {
                                if (!(recombine_pair_to_ex(*i).info(inf)))
                                        return false;
+                               ++i;
                        }
                        return overall_coeff.info(inf);
                }
                case info_flags::algebraic: {
-                       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+                       epvector::const_iterator i = seq.begin(), end = seq.end();
+                       while (i != end) {
                                if ((recombine_pair_to_ex(*i).info(inf)))
                                        return true;
+                               ++i;
                        }
                        return false;
                }
@@ -314,119 +248,161 @@ bool add::info(unsigned inf) const
        return inherited::info(inf);
 }
 
-int add::degree(const symbol & s) const
+int add::degree(const ex & s) const
 {
        int deg = INT_MIN;
-       if (!overall_coeff.is_equal(_ex0())) {
+       if (!overall_coeff.is_zero())
                deg = 0;
-       }
-       int cur_deg;
-       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               cur_deg=(*cit).rest.degree(s);
-               if (cur_deg>deg) deg=cur_deg;
+       
+       // Find maximum of degrees of individual terms
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               int cur_deg = i->rest.degree(s);
+               if (cur_deg > deg)
+                       deg = cur_deg;
+               ++i;
        }
        return deg;
 }
 
-int add::ldegree(const symbol & s) const
+int add::ldegree(const ex & s) const
 {
        int deg = INT_MAX;
-       if (!overall_coeff.is_equal(_ex0())) {
+       if (!overall_coeff.is_zero())
                deg = 0;
-       }
-       int cur_deg;
-       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               cur_deg = (*cit).rest.ldegree(s);
-               if (cur_deg<deg) deg=cur_deg;
+       
+       // Find minimum of degrees of individual terms
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               int cur_deg = i->rest.ldegree(s);
+               if (cur_deg < deg)
+                       deg = cur_deg;
+               ++i;
        }
        return deg;
 }
 
-ex add::coeff(const symbol & s, int n) const
+ex add::coeff(const ex & s, int n) const
 {
-       epvector coeffseq;
-       coeffseq.reserve(seq.size());
+       epvector *coeffseq = new epvector();
 
-       epvector::const_iterator it=seq.begin();
-       while (it!=seq.end()) {
-               coeffseq.push_back(combine_ex_with_coeff_to_pair((*it).rest.coeff(s,n),
-                                                                (*it).coeff));
-               ++it;
+       // Calculate sum of coefficients in each term
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               ex restcoeff = i->rest.coeff(s, n);
+               if (!restcoeff.is_zero())
+                       coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
+               ++i;
        }
-       if (n==0) {
-               return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
-       }
-       return (new add(coeffseq))->setflag(status_flags::dynallocated);
+
+       return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 }
 
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x stands for a symbolic variables of type ex and c stands for such
+ *  an expression that contain a plain number.
+ *  - +(;c) -> c
+ *  - +(x;1) -> x
+ *
+ *  @param level cut-off in recursive evaluation */
 ex add::eval(int level) const
 {
-       // simplifications: +(;c) -> c
-       //                  +(x;1) -> x
-
-       debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
-
-       epvector * evaled_seqp=evalchildren(level);
-       if (evaled_seqp!=0) {
+       epvector *evaled_seqp = evalchildren(level);
+       if (evaled_seqp) {
                // do more evaluation later
-               return (new add(evaled_seqp,overall_coeff))->
+               return (new add(evaled_seqp, overall_coeff))->
                       setflag(status_flags::dynallocated);
        }
        
 #ifdef DO_GINAC_ASSERT
-       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-               GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
-               if (is_ex_exactly_of_type((*cit).rest,numeric)) {
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               GINAC_ASSERT(!is_exactly_a<add>(i->rest));
+               if (is_ex_exactly_of_type(i->rest,numeric))
                        dbgprint();
-               }
-               GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
+               GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
+               ++i;
        }
 #endif // def DO_GINAC_ASSERT
        
        if (flags & status_flags::evaluated) {
                GINAC_ASSERT(seq.size()>0);
-               GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex0()));
+               GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
                return *this;
        }
        
-       int seq_size=seq.size();
-       if (seq_size==0) {
+       int seq_size = seq.size();
+       if (seq_size == 0) {
                // +(;c) -> c
                return overall_coeff;
-       } else if ((seq_size==1)&&overall_coeff.is_equal(_ex0())) {
+       } else if (seq_size == 1 && overall_coeff.is_zero()) {
                // +(x;0) -> x
                return recombine_pair_to_ex(*(seq.begin()));
+       } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
+               throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
        }
        return this->hold();
 }
 
-exvector add::get_indices(void) const
+ex add::evalm(void) const
 {
-       // FIXME: all terms in the sum should have the same indices (compatible
-       // tensors) however this is not checked, since there is no function yet
-       // which compares indices (idxvector can be unsorted)
-       if (seq.size()==0) {
-               return exvector();
+       // Evaluate children first and add up all matrices. Stop if there's one
+       // term that is not a matrix.
+       epvector *s = new epvector;
+       s->reserve(seq.size());
+
+       bool all_matrices = true;
+       bool first_term = true;
+       matrix sum;
+
+       epvector::const_iterator it = seq.begin(), itend = seq.end();
+       while (it != itend) {
+               const ex &m = recombine_pair_to_ex(*it).evalm();
+               s->push_back(split_ex_to_pair(m));
+               if (is_ex_of_type(m, matrix)) {
+                       if (first_term) {
+                               sum = ex_to<matrix>(m);
+                               first_term = false;
+                       } else
+                               sum = sum.add(ex_to<matrix>(m));
+               } else
+                       all_matrices = false;
+               ++it;
        }
-       return (seq.begin())->rest.get_indices();
-}    
+
+       if (all_matrices) {
+               delete s;
+               return sum + overall_coeff;
+       } else
+               return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
+}
 
 ex add::simplify_ncmul(const exvector & v) const
 {
-       if (seq.size()==0) {
+       if (seq.empty())
                return inherited::simplify_ncmul(v);
-       }
-       return (*seq.begin()).rest.simplify_ncmul(v);
+       else
+               return seq.begin()->rest.simplify_ncmul(v);
 }    
 
 // protected
 
 /** Implementation of ex::diff() for a sum. It differentiates each term.
  *  @see ex::diff */
-ex add::derivative(const symbol & s) const
+ex add::derivative(const symbol & y) const
 {
-       // D(a+b+c)=D(a)+D(b)+D(c)
-       return (new add(diffchildren(s)))->setflag(status_flags::dynallocated);
+       epvector *s = new epvector();
+       s->reserve(seq.size());
+       
+       // Only differentiate the "rest" parts of the expairs. This is faster
+       // than the default implementation in basic::derivative() although
+       // if performs the same function (differentiate each term).
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
+               ++i;
+       }
+       return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 }
 
 int add::compare_same_type(const basic & other) const
@@ -441,18 +417,18 @@ bool add::is_equal_same_type(const basic & other) const
 
 unsigned add::return_type(void) const
 {
-       if (seq.size()==0) {
+       if (seq.empty())
                return return_types::commutative;
-       }
-       return (*seq.begin()).rest.return_type();
+       else
+               return seq.begin()->rest.return_type();
 }
    
 unsigned add::return_type_tinfo(void) const
 {
-       if (seq.size()==0) {
+       if (seq.empty())
                return tinfo_key;
-       }
-       return (*seq.begin()).rest.return_type_tinfo();
+       else
+               return seq.begin()->rest.return_type_tinfo();
 }
 
 ex add::thisexpairseq(const epvector & v, const ex & oc) const
@@ -468,107 +444,75 @@ ex add::thisexpairseq(epvector * vp, const ex & oc) const
 expair add::split_ex_to_pair(const ex & e) const
 {
        if (is_ex_exactly_of_type(e,mul)) {
-               const mul & mulref=ex_to_mul(e);
-               ex numfactor=mulref.overall_coeff;
-               // mul * mulcopyp=static_cast<mul *>(mulref.duplicate());
-               mul * mulcopyp=new mul(mulref);
-               mulcopyp->overall_coeff=_ex1();
+               const mul &mulref(ex_to<mul>(e));
+               const ex &numfactor = mulref.overall_coeff;
+               mul *mulcopyp = new mul(mulref);
+               mulcopyp->overall_coeff = _ex1;
                mulcopyp->clearflag(status_flags::evaluated);
                mulcopyp->clearflag(status_flags::hash_calculated);
-               return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
+               mulcopyp->setflag(status_flags::dynallocated);
+               return expair(*mulcopyp,numfactor);
        }
-       return expair(e,_ex1());
+       return expair(e,_ex1);
 }
 
 expair add::combine_ex_with_coeff_to_pair(const ex & e,
                                                                                  const ex & c) const
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
-       ex one = _ex1();
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
        if (is_ex_exactly_of_type(e, mul)) {
-               const mul &mulref = ex_to_mul(e);
-               ex numfactor = mulref.overall_coeff;
+               const mul &mulref(ex_to<mul>(e));
+               const ex &numfactor = mulref.overall_coeff;
                mul *mulcopyp = new mul(mulref);
-               mulcopyp->overall_coeff = one;
+               mulcopyp->overall_coeff = _ex1;
                mulcopyp->clearflag(status_flags::evaluated);
                mulcopyp->clearflag(status_flags::hash_calculated);
                mulcopyp->setflag(status_flags::dynallocated);
-               if (are_ex_trivially_equal(c, one)) {
+               if (are_ex_trivially_equal(c, _ex1))
                        return expair(*mulcopyp, numfactor);
-               } else if (are_ex_trivially_equal(numfactor, one)) {
+               else if (are_ex_trivially_equal(numfactor, _ex1))
                        return expair(*mulcopyp, c);
-               }
-               return expair(*mulcopyp, ex_to_numeric(numfactor).mul_dyn(ex_to_numeric(c)));
+               else
+                       return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
        } else if (is_ex_exactly_of_type(e, numeric)) {
-               if (are_ex_trivially_equal(c, one)) {
-                       return expair(e, one);
-               }
-               return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)), one);
+               if (are_ex_trivially_equal(c, _ex1))
+                       return expair(e, _ex1);
+               return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
        }
        return expair(e, c);
 }
-       
+
 expair add::combine_pair_with_coeff_to_pair(const expair & p,
                                                                                        const ex & c) const
 {
-       GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
-       GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+       GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
 
        if (is_ex_exactly_of_type(p.rest,numeric)) {
-               GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(_num1())); // should be normalized
-               return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),_ex1());
+               GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
+               return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
        }
 
-       return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
+       return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 }
        
 ex add::recombine_pair_to_ex(const expair & p) const
 {
-       if (ex_to_numeric(p.coeff).is_equal(_num1()))
+       if (ex_to<numeric>(p.coeff).is_equal(_num1))
                return p.rest;
        else
-               return p.rest*p.coeff;
+               return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 }
 
 ex add::expand(unsigned options) const
 {
-       if (flags & status_flags::expanded)
-               return *this;
-       
-       epvector * vp = expandchildren(options);
-       if (vp==0)
-               return *this;
+       epvector *vp = expandchildren(options);
+       if (vp == NULL) {
+               // the terms have not changed, so it is safe to declare this expanded
+               return (options == 0) ? setflag(status_flags::expanded) : *this;
+       }
        
-       return (new add(vp,overall_coeff))->setflag(status_flags::expanded | status_flags::dynallocated);
+       return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 }
 
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
-
-// none
-
-//////////
-// non-virtual functions in this class
-//////////
-
-// none
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned add::precedence = 40;
-
-//////////
-// global constants
-//////////
-
-const add some_add;
-const std::type_info & typeid_add = typeid(some_add);
-
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC