Update copyright statements.
[ginac.git] / ginac / add.cpp
index 1b7b271..81a4f2f 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's sums of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2014 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
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <iostream>
-#include <stdexcept>
-
 #include "add.h"
 #include "mul.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "operators.h"
+#include "matrix.h"
 #include "utils.h"
+#include "clifford.h"
+#include "ncmul.h"
+#include "compiler.h"
+
+#include <iostream>
+#include <limits>
+#include <stdexcept>
+#include <string>
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
+  print_func<print_context>(&add::do_print).
+  print_func<print_latex>(&add::do_print_latex).
+  print_func<print_csrc>(&add::do_print_csrc).
+  print_func<print_tree>(&add::do_print_tree).
+  print_func<print_python_repr>(&add::do_print_python_repr))
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
 //////////
 
 add::add()
 {
-       debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_add;
 }
 
-DEFAULT_COPY(add)
-DEFAULT_DESTROY(add)
-
 //////////
 // other constructors
 //////////
@@ -54,48 +60,37 @@ DEFAULT_DESTROY(add)
 
 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)
 {
-       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);
        GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector * vp, const ex & oc)
+add::add(std::auto_ptr<epvector> vp, const ex & oc)
 {
-       debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-       tinfo_key = TINFO_add;
-       GINAC_ASSERT(vp!=0);
+       GINAC_ASSERT(vp.get()!=0);
        overall_coeff = oc;
        construct_from_epvector(*vp);
-       delete vp;
        GINAC_ASSERT(is_canonical());
 }
 
@@ -103,127 +98,124 @@ add::add(epvector * vp, const ex & oc)
 // archiving
 //////////
 
-DEFAULT_ARCHIVING(add)
+GINAC_BIND_UNARCHIVER(add);
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-void add::print(const print_context & c, unsigned level) const
+void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 {
-       debugmsg("add print", LOGLEVEL_PRINT);
-
-       if (is_of_type(c, print_tree)) {
+       if (precedence() <= level)
+               c.s << openbrace << '(';
 
-               inherited::print(c, level);
+       numeric coeff;
+       bool first = true;
 
-       } else if (is_of_type(c, print_csrc)) {
+       // First print the overall numeric coefficient, if present
+       if (!overall_coeff.is_zero()) {
+               overall_coeff.print(c, 0);
+               first = false;
+       }
 
-               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.bp->print(c, precedence);
-                       } else if (it->coeff.compare(_num_1()) == 0) {
-                               c.s << "-";
-                               it->rest.bp->print(c, precedence);
-                       } else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
-                               it->rest.bp->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.bp->print(c, precedence);
-                               c.s << "/";
-                               ex_to_numeric(it->coeff).denom().print(c, 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_p) &&
+                   !coeff.is_equal(*_num_1_p)) {
+                       if (coeff.is_rational()) {
+                               if (coeff.is_negative())
+                                       (-coeff).print(c);
+                               else
+                                       coeff.print(c);
                        } else {
-                               it->coeff.bp->print(c, precedence);
-                               c.s << "*";
-                               it->rest.bp->print(c, precedence);
+                               if (coeff.csgn() == -1)
+                                       (-coeff).print(c, precedence());
+                               else
+                                       coeff.print(c, precedence());
                        }
-               
-                       // 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)))
-                               c.s << "+";
-               }
-       
-               if (!overall_coeff.is_zero()) {
-                       if (overall_coeff.info(info_flags::positive))
-                               c.s << '+';
-                       overall_coeff.bp->print(c, precedence);
+                       c.s << mul_sym;
                }
-       
-               if (precedence <= level)
-                       c.s << ")";
-
-       } else {
+               it->rest.print(c, precedence());
+               ++it;
+       }
 
-               if (precedence <= level) {
-                       if (is_of_type(c, print_latex))
-                               c.s << "{(";
-                       else
-                               c.s << "(";
-               }
+       if (precedence() <= level)
+               c.s << ')' << closebrace;
+}
 
-               numeric coeff;
-               bool first = true;
+void add::do_print(const print_context & c, unsigned level) const
+{
+       print_add(c, "", "", "*", level);
+}
 
-               // First print the overall numeric coefficient, if present
-               if (!overall_coeff.is_zero()) {
-                       if (!is_of_type(c, print_tree))
-                               overall_coeff.print(c, 0);
-                       else
-                               overall_coeff.print(c, precedence);
-                       first = false;
-               }
+void add::do_print_latex(const print_latex & c, unsigned level) const
+{
+       print_add(c, "{", "}", " ", level);
+}
 
-               // 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_of_type(c, print_latex))
-                                       c.s << ' ';
-                               else
-                                       c.s << '*';
-                       }
-                       it->rest.print(c, precedence);
-                       it++;
+void add::do_print_csrc(const print_csrc & c, unsigned level) const
+{
+       if (precedence() <= level)
+               c.s << "(";
+       
+       // Print arguments, separated by "+" or "-"
+       epvector::const_iterator it = seq.begin(), itend = seq.end();
+       char separator = ' ';
+       while (it != itend) {
+               
+               // If the coefficient is negative, separator is "-"
+               if (it->coeff.is_equal(_ex_1) || 
+                       ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
+                       separator = '-';
+               c.s << separator;
+               if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
+                       it->rest.print(c, precedence());
+               } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
+                                ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
+               {
+                       it->rest.print(c, precedence());
+                       c.s << '/';
+                       ex_to<numeric>(it->coeff).denom().print(c, precedence());
+               } else {
+                       it->coeff.print(c, precedence());
+                       c.s << '*';
+                       it->rest.print(c, precedence());
                }
+               
+               ++it;
+               separator = '+';
+       }
+       
+       if (!overall_coeff.is_zero()) {
+               if (overall_coeff.info(info_flags::positive)
+                || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
+                       c.s << '+';
+               overall_coeff.print(c, precedence());
+       }
+               
+       if (precedence() <= level)
+               c.s << ")";
+}
 
-               if (precedence <= level) {
-                       if (is_of_type(c, print_latex))
-                               c.s << ")}";
-                       else
-                               c.s << ")";
-               }
+void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+       c.s << class_name() << '(';
+       op(0).print(c);
+       for (size_t i=1; i<nops(); ++i) {
+               c.s << ',';
+               op(i).print(c);
        }
+       c.s << ')';
 }
 
 bool add::info(unsigned inf) const
@@ -233,18 +225,34 @@ bool add::info(unsigned inf) const
                case info_flags::integer_polynomial:
                case info_flags::cinteger_polynomial:
                case info_flags::rational_polynomial:
+               case info_flags::real:
+               case info_flags::rational:
+               case info_flags::integer:
+               case info_flags::crational:
+               case info_flags::cinteger:
+               case info_flags::positive:
+               case info_flags::nonnegative:
+               case info_flags::posint:
+               case info_flags::nonnegint:
+               case info_flags::even:
                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;
                        }
+                       if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
+                               return true;
                        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;
                }
@@ -252,72 +260,101 @@ bool add::info(unsigned inf) const
        return inherited::info(inf);
 }
 
+bool add::is_polynomial(const ex & var) const
+{
+       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+               if (!(i->rest).is_polynomial(var)) {
+                       return false;
+               }
+       }
+       return true;
+}
+
 int add::degree(const ex & s) const
 {
-       int deg = INT_MIN;
-       if (!overall_coeff.is_equal(_ex0()))
+       int deg = std::numeric_limits<int>::min();
+       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)
+       // 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 ex & s) const
 {
-       int deg = INT_MAX;
-       if (!overall_coeff.is_equal(_ex0()))
+       int deg = std::numeric_limits<int>::max();
+       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 ex & s, int n) const
 {
-       epvector coeffseq;
-       coeffseq.reserve(seq.size());
-
-       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;
-       }
-       if (n==0) {
-               return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
+       std::auto_ptr<epvector> coeffseq(new epvector);
+       std::auto_ptr<epvector> coeffseq_cliff(new epvector);
+       int rl = clifford_max_label(s);
+       bool do_clifford = (rl != -1);
+       bool nonscalar = false;
+
+       // 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()) {
+                       if (do_clifford) {
+                               if (clifford_max_label(restcoeff) == -1) {
+                                       coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
+                               } else {
+                                       coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
+                                       nonscalar = true;
+                               }
+                       }
+                       coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
+               }
+               ++i;
        }
-       return (new add(coeffseq))->setflag(status_flags::dynallocated);
+
+       return (new add(nonscalar ? coeffseq_cliff : 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;0) -> 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) {
+       std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
+       if (evaled_seqp.get()) {
                // 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))
-                       dbgprint();
-               GINAC_ASSERT(!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));
+               ++i;
        }
 #endif // def DO_GINAC_ASSERT
        
@@ -328,32 +365,165 @@ ex add::eval(int level) const
        }
        
        int seq_size = seq.size();
-       if (seq_size==0) {
+       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"));
        }
+       
+       // if any terms in the sum still are purely numeric, then they are more
+       // appropriately collected into the overall coefficient
+       epvector::const_iterator last = seq.end();
+       epvector::const_iterator j = seq.begin();
+       int terms_to_collect = 0;
+       while (j != last) {
+               if (unlikely(is_a<numeric>(j->rest)))
+                       ++terms_to_collect;
+               ++j;
+       }
+       if (terms_to_collect) {
+               std::auto_ptr<epvector> s(new epvector);
+               s->reserve(seq_size - terms_to_collect);
+               numeric oc = *_num1_p;
+               j = seq.begin();
+               while (j != last) {
+                       if (unlikely(is_a<numeric>(j->rest)))
+                               oc = oc.mul(ex_to<numeric>(j->rest)).mul(ex_to<numeric>(j->coeff));
+                       else
+                               s->push_back(*j);
+                       ++j;
+               }
+               return (new add(s, ex_to<numeric>(overall_coeff).add_dyn(oc)))
+                       ->setflag(status_flags::dynallocated);
+       }
+       
        return this->hold();
 }
 
-ex add::simplify_ncmul(const exvector & v) const
+ex add::evalm() const
 {
-       if (seq.size()==0) {
-               return inherited::simplify_ncmul(v);
+       // Evaluate children first and add up all matrices. Stop if there's one
+       // term that is not a matrix.
+       std::auto_ptr<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_a<matrix>(m)) {
+                       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.simplify_ncmul(v);
+
+       if (all_matrices)
+               return sum + overall_coeff;
+       else
+               return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
+}
+
+ex add::conjugate() const
+{
+       exvector *v = 0;
+       for (size_t i=0; i<nops(); ++i) {
+               if (v) {
+                       v->push_back(op(i).conjugate());
+                       continue;
+               }
+               ex term = op(i);
+               ex ccterm = term.conjugate();
+               if (are_ex_trivially_equal(term, ccterm))
+                       continue;
+               v = new exvector;
+               v->reserve(nops());
+               for (size_t j=0; j<i; ++j)
+                       v->push_back(op(j));
+               v->push_back(ccterm);
+       }
+       if (v) {
+               ex result = add(*v);
+               delete v;
+               return result;
+       }
+       return *this;
+}
+
+ex add::real_part() const
+{
+       epvector v;
+       v.reserve(seq.size());
+       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+               if ((i->coeff).info(info_flags::real)) {
+                       ex rp = (i->rest).real_part();
+                       if (!rp.is_zero())
+                               v.push_back(expair(rp, i->coeff));
+               } else {
+                       ex rp=recombine_pair_to_ex(*i).real_part();
+                       if (!rp.is_zero())
+                               v.push_back(split_ex_to_pair(rp));
+               }
+       return (new add(v, overall_coeff.real_part()))
+               -> setflag(status_flags::dynallocated);
+}
+
+ex add::imag_part() const
+{
+       epvector v;
+       v.reserve(seq.size());
+       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+               if ((i->coeff).info(info_flags::real)) {
+                       ex ip = (i->rest).imag_part();
+                       if (!ip.is_zero())
+                               v.push_back(expair(ip, i->coeff));
+               } else {
+                       ex ip=recombine_pair_to_ex(*i).imag_part();
+                       if (!ip.is_zero())
+                               v.push_back(split_ex_to_pair(ip));
+               }
+       return (new add(v, overall_coeff.imag_part()))
+               -> setflag(status_flags::dynallocated);
+}
+
+ex add::eval_ncmul(const exvector & v) const
+{
+       if (seq.empty())
+               return inherited::eval_ncmul(v);
+       else
+               return seq.begin()->rest.eval_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);
+       std::auto_ptr<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
@@ -361,74 +531,71 @@ int add::compare_same_type(const basic & other) const
        return inherited::compare_same_type(other);
 }
 
-bool add::is_equal_same_type(const basic & other) const
+unsigned add::return_type() const
 {
-       return inherited::is_equal_same_type(other);
-}
-
-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
+
+return_type_t add::return_type_tinfo() const
 {
-       if (seq.size()==0) {
-               return tinfo_key;
-       }
-       return (*seq.begin()).rest.return_type_tinfo();
+       if (seq.empty())
+               return make_return_type_t<add>();
+       else
+               return seq.begin()->rest.return_type_tinfo();
 }
 
-ex add::thisexpairseq(const epvector & v, const ex & oc) const
+// Note: do_index_renaming is ignored because it makes no sense for an add.
+ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 {
        return (new add(v,oc))->setflag(status_flags::dynallocated);
 }
 
-ex add::thisexpairseq(epvector * vp, const ex & oc) const
+// Note: do_index_renaming is ignored because it makes no sense for an add.
+ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 {
        return (new add(vp,oc))->setflag(status_flags::dynallocated);
 }
 
 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;
+       if (is_exactly_a<mul>(e)) {
+               const mul &mulref(ex_to<mul>(e));
+               const ex &numfactor = mulref.overall_coeff;
                mul *mulcopyp = new mul(mulref);
-               mulcopyp->overall_coeff = _ex1();
+               mulcopyp->overall_coeff = _ex1;
                mulcopyp->clearflag(status_flags::evaluated);
                mulcopyp->clearflag(status_flags::hash_calculated);
                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));
-       if (is_ex_exactly_of_type(e, mul)) {
-               const mul &mulref = ex_to_mul(e);
-               ex numfactor = mulref.overall_coeff;
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
+       if (is_exactly_a<mul>(e)) {
+               const mul &mulref(ex_to<mul>(e));
+               const ex &numfactor = mulref.overall_coeff;
                mul *mulcopyp = new mul(mulref);
-               mulcopyp->overall_coeff = _ex1();
+               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, _ex1()))
+               if (c.is_equal(_ex1))
                        return expair(*mulcopyp, numfactor);
-               else if (are_ex_trivially_equal(numfactor, _ex1()))
+               else if (numfactor.is_equal(_ex1))
                        return expair(*mulcopyp, 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, _ex1()))
-                       return expair(e, _ex1());
-               return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)), _ex1());
+                       return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
+       } else if (is_exactly_a<numeric>(e)) {
+               if (c.is_equal(_ex1))
+                       return expair(e, _ex1);
+               return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
        }
        return expair(e, c);
 }
@@ -436,46 +603,34 @@ expair add::combine_ex_with_coeff_to_pair(const ex & e,
 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());
+       if (is_exactly_a<numeric>(p.rest)) {
+               GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // 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_p))
                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) {
+       std::auto_ptr<epvector> vp = expandchildren(options);
+       if (vp.get() == 0) {
                // the terms have not changed, so it is safe to declare this expanded
-               setflag(status_flags::expanded);
-               return *this;
+               return (options == 0) ? setflag(status_flags::expanded) : *this;
        }
-       
-       return (new add(vp,overall_coeff))->setflag(status_flags::expanded | status_flags::dynallocated);
-}
-
-//////////
-// static member variables
-//////////
 
-// protected
-
-unsigned add::precedence = 40;
+       return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+}
 
 } // namespace GiNaC