under certain conditions, power::expand_add_2() could produce non-canonical
[ginac.git] / ginac / add.cpp
index 6f5380cce2393042caff5f8def7e00f967ff239a..1c995aa7f74d9f36f0b98bba4d9173789aa6b1d8 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's sums of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2002 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 "debugmsg.h"
+#include "matrix.h"
+#include "archive.h"
+#include "utils.h"
 
 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(0);
-}
-
-add::add(add const & other)
-{
-    debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
-}
-
-add const & add::operator=(add const & other)
-{
-    debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
+       tinfo_key = TINFO_add;
 }
 
-// protected
-
-void add::copy(add const & other)
-{
-    expairseq::copy(other);
-}
-
-void add::destroy(bool call_parent)
-{
-    if (call_parent) expairseq::destroy(call_parent);
-}
+DEFAULT_COPY(add)
+DEFAULT_DESTROY(add)
 
 //////////
 // other constructors
@@ -81,576 +51,481 @@ void add::destroy(bool call_parent)
 
 // public
 
-add::add(ex const & lh, ex const & rh)
+add::add(const ex & lh, const ex & rh)
 {
-    debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_add;
-    overall_coeff=exZERO();
-    construct_from_2_ex(lh,rh);
-    GINAC_ASSERT(is_canonical());
+       tinfo_key = TINFO_add;
+       overall_coeff = _ex0;
+       construct_from_2_ex(lh,rh);
+       GINAC_ASSERT(is_canonical());
 }
 
-add::add(exvector const & v)
+add::add(const exvector & v)
 {
-    debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_add;
-    overall_coeff=exZERO();
-    construct_from_exvector(v);
-    GINAC_ASSERT(is_canonical());
+       tinfo_key = TINFO_add;
+       overall_coeff = _ex0;
+       construct_from_exvector(v);
+       GINAC_ASSERT(is_canonical());
 }
 
-/*
-add::add(epvector const & v, bool do_not_canonicalize)
+add::add(const epvector & v)
 {
-    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());
+       tinfo_key = TINFO_add;
+       overall_coeff = _ex0;
+       construct_from_epvector(v);
+       GINAC_ASSERT(is_canonical());
 }
-*/
 
-add::add(epvector const & v)
+add::add(const epvector & v, const ex & oc)
 {
-    debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_add;
-    overall_coeff=exZERO();
-    construct_from_epvector(v);
-    GINAC_ASSERT(is_canonical());
+       tinfo_key = TINFO_add;
+       overall_coeff = oc;
+       construct_from_epvector(v);
+       GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector const & v, ex const & oc)
+add::add(epvector * vp, 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());
+       tinfo_key = TINFO_add;
+       GINAC_ASSERT(vp!=0);
+       overall_coeff = oc;
+       construct_from_epvector(*vp);
+       delete vp;
+       GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector * vp, ex const & oc)
-{
-    debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_add;
-    GINAC_ASSERT(vp!=0);
-    overall_coeff=oc;
-    construct_from_epvector(*vp);
-    delete vp;
-    GINAC_ASSERT(is_canonical());
-}
+//////////
+// archiving
+//////////
+
+DEFAULT_ARCHIVING(add)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-basic * add::duplicate() const
-{
-    debugmsg("add duplicate",LOGLEVEL_DUPLICATE);
-    return new add(*this);
+void add::print(const print_context & c, unsigned level) const
+{
+       if (is_a<print_tree>(c)) {
+
+               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.is_equal(_ex1)) {
+                               it->rest.print(c, precedence());
+                       } else if (it->coeff.is_equal(_ex_1)) {
+                               c.s << "-";
+                               it->rest.print(c, precedence());
+                       } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num1)) {
+                               it->rest.print(c, precedence());
+                               c.s << "/";
+                               ex_to<numeric>(it->coeff).denom().print(c, precedence());
+                       } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num_1)) {
+                               c.s << "-";
+                               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());
+                       }
+               
+                       // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
+                       ++it;
+                       if (it != itend
+                        && (is_a<print_csrc_cl_N>(c)  // sign inside ctor arguments
+                         || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
+                               c.s << "+";
+               }
+       
+               if (!overall_coeff.is_zero()) {
+                       if (overall_coeff.info(info_flags::positive)
+                        || is_a<print_csrc_cl_N>(c))  // sign inside ctor argument
+                               c.s << '+';
+                       overall_coeff.print(c, precedence());
+               }
+               
+               if (precedence() <= level)
+                       c.s << ")";
+
+       } else if (is_a<print_python_repr>(c)) {
+
+               c.s << class_name() << '(';
+               op(0).print(c);
+               for (unsigned i=1; i<nops(); ++i) {
+                       c.s << ',';
+                       op(i).print(c);
+               }
+               c.s << ')';
+
+       } else {
+
+               if (precedence() <= level) {
+                       if (is_a<print_latex>(c))
+                               c.s << "{(";
+                       else
+                               c.s << "(";
+               }
+
+               numeric coeff;
+               bool first = true;
+
+               // 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;
+               }
+
+               // 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 << ")";
+               }
+       }
 }
 
 bool add::info(unsigned inf) const
 {
-    // TODO: optimize
-    if (inf==info_flags::polynomial || inf==info_flags::integer_polynomial || inf==info_flags::rational_polynomial || inf==info_flags::rational_function) {
-        for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-            if (!(recombine_pair_to_ex(*it).info(inf)))
-                return false;
-        }
-        return true;
-    } else {
-        return expairseq::info(inf);
-    }
-}
-
-int add::degree(symbol const & s) const
-{
-    int deg=INT_MIN;
-    if (!overall_coeff.is_equal(exZERO())) {
-        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;
-    }
-    return deg;
-}
-
-int add::ldegree(symbol const & s) const
-{
-    int deg=INT_MAX;
-    if (!overall_coeff.is_equal(exZERO())) {
-        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;
-    }
-    return deg;
-}
-
-ex add::coeff(symbol const & s, int const 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);
-    }
-    return (new add(coeffseq))->setflag(status_flags::dynallocated);
-}
-
-/*
-ex add::eval(int level) const
-{
-    // simplifications: +(...,x,c1,c2) -> +(...,x,c1+c2) (c1, c2 numeric())
-    //                  +(...,(c1,c2)) -> (...,(c1*c2,1)) (normalize)
-    //                  +(...,x,0) -> +(...,x)
-    //                  +(x) -> x
-    //                  +() -> 0
-
-    debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    epvector newseq=seq;
-    epvector::iterator it1,it2;
-    
-    // +(...,x,c1,c2) -> +(...,x,c1+c2) (c1, c2 numeric())
-    it2=newseq.end()-1;
-    it1=it2-1;
-    while ((newseq.size()>=2)&&is_exactly_of_type(*(*it1).rest.bp,numeric)&&
-                               is_exactly_of_type(*(*it2).rest.bp,numeric)) {
-        *it1=expair(ex_to_numeric((*it1).rest).mul(ex_to_numeric((*it1).coeff))
-                    .add(ex_to_numeric((*it2).rest).mul(ex_to_numeric((*it2).coeff))),exONE());
-        newseq.pop_back();
-        it2=newseq.end()-1;
-        it1=it2-1;
-    }
-
-    if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
-        // +(...,(c1,c2)) -> (...,(c1*c2,1)) (normalize)
-        *it2=expair(ex_to_numeric((*it2).rest).mul(ex_to_numeric((*it2).coeff)),exONE());
-        // +(...,x,0) -> +(...,x)
-        if (ex_to_numeric((*it2).rest).compare(0)==0) {
-            newseq.pop_back();
-        }
-    }
-
-    if (newseq.size()==0) {
-        // +() -> 0
-        return exZERO();
-    } else if (newseq.size()==1) {
-        // +(x) -> x
-        return recombine_pair_to_ex(*(newseq.begin()));
-    }
-
-    return (new add(newseq,1))->setflag(status_flags::dynallocated  |
-                                        status_flags::evaluated );
-}
-*/
-
-/*
+       switch (inf) {
+               case info_flags::polynomial:
+               case info_flags::integer_polynomial:
+               case info_flags::cinteger_polynomial:
+               case info_flags::rational_polynomial:
+               case info_flags::crational_polynomial:
+               case info_flags::rational_function: {
+                       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: {
+                       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;
+               }
+       }
+       return inherited::info(inf);
+}
+
+int add::degree(const ex & s) const
+{
+       int deg = INT_MIN;
+       if (!overall_coeff.is_zero())
+               deg = 0;
+       
+       // 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_zero())
+               deg = 0;
+       
+       // 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 = new epvector();
+
+       // 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;
+       }
+
+       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: +(...,x,c1,c2) -> +(...,x,c1+c2) (c1, c2 numeric())
-    //                  +(...,(c1,c2)) -> (...,(c1*c2,1)) (normalize)
-    //                  +(...,x,0) -> +(...,x)
-    //                  +(x) -> x
-    //                  +() -> 0
-
-    debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    if ((level==1)&&(flags & status_flags::evaluated)) {
+       epvector *evaled_seqp = evalchildren(level);
+       if (evaled_seqp) {
+               // do more evaluation later
+               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));
-            GINAC_ASSERT(!(is_ex_exactly_of_type((*cit).rest,numeric)&&
-                     (ex_to_numeric((*cit).coeff).compare(numONE())!=0)));
-        }
-#endif // def DO_GINAC_ASSERT
-        return *this;
-    }
-
-    epvector newseq;
-    epvector::iterator it1,it2;
-    bool seq_copied=false;
-
-    epvector * evaled_seqp=evalchildren(level);
-    if (evaled_seqp!=0) {
-        // do more evaluation later
-        return (new add(evaled_seqp))->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));
-        GINAC_ASSERT(!(is_ex_exactly_of_type((*cit).rest,numeric)&&
-                 (ex_to_numeric((*cit).coeff).compare(numONE())!=0)));
-    }
+       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_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_zero());
+               return *this;
+       }
+       
+       int seq_size = seq.size();
+       if (seq_size == 0) {
+               // +(;c) -> c
+               return overall_coeff;
+       } 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();
+}
+
+ex add::evalm(void) const
+{
+       // 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;
+       }
+
+       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.empty())
+               return inherited::simplify_ncmul(v);
+       else
+               return seq.begin()->rest.simplify_ncmul(v);
+}    
 
-    if (flags & status_flags::evaluated) {
-        return *this;
-    }
-    
-    expair const & last_expair=*(seq.end()-1);
-    expair const & next_to_last_expair=*(seq.end()-2);
-    int seq_size = seq.size();
-
-    // +(...,x,c1,c2) -> +(...,x,c1+c2) (c1, c2 numeric())
-    if ((!seq_copied)&&(seq_size>=2)&&
-        is_ex_exactly_of_type(last_expair.rest,numeric)&&
-        is_ex_exactly_of_type(next_to_last_expair.rest,numeric)) {
-        newseq=seq;
-        seq_copied=true;
-        it2=newseq.end()-1;
-        it1=it2-1;
-    }
-    while (seq_copied&&(newseq.size()>=2)&&
-           is_ex_exactly_of_type((*it1).rest,numeric)&&
-           is_ex_exactly_of_type((*it2).rest,numeric)) {
-        *it1=expair(ex_to_numeric((*it1).rest).mul(ex_to_numeric((*it1).coeff))
-                    .add_dyn(ex_to_numeric((*it2).rest).mul(ex_to_numeric((*it2).coeff))),exONE());
-        newseq.pop_back();
-        it2=newseq.end()-1;
-        it1=it2-1;
-    }
-
-    // +(...,(c1,c2)) -> (...,(c1*c2,1)) (normalize)
-    if ((!seq_copied)&&(seq_size>=1)&&
-        (is_ex_exactly_of_type(last_expair.rest,numeric))&&
-        (ex_to_numeric(last_expair.coeff).compare(numONE())!=0)) {
-        newseq=seq;
-        seq_copied=true;
-        it2=newseq.end()-1;
-    }
-    if (seq_copied&&(newseq.size()>=1)&&
-        (is_ex_exactly_of_type((*it2).rest,numeric))&&
-        (ex_to_numeric((*it2).coeff).compare(numONE())!=0)) {
-        *it2=expair(ex_to_numeric((*it2).rest).mul_dyn(ex_to_numeric((*it2).coeff)),exONE());
-    }
-        
-    // +(...,x,0) -> +(...,x)
-    if ((!seq_copied)&&(seq_size>=1)&&
-        (is_ex_exactly_of_type(last_expair.rest,numeric))&&
-        (ex_to_numeric(last_expair.rest).is_zero())) {
-        newseq=seq;
-        seq_copied=true;
-        it2=newseq.end()-1;
-    }
-    if (seq_copied&&(newseq.size()>=1)&&
-        (is_ex_exactly_of_type((*it2).rest,numeric))&&
-        (ex_to_numeric((*it2).rest).is_zero())) {
-        newseq.pop_back();
-    }
-
-    // +() -> 0
-    if ((!seq_copied)&&(seq_size==0)) {
-        return exZERO();
-    } else if (seq_copied&&(newseq.size()==0)) {
-        return exZERO();
-    }
-
-    // +(x) -> x
-    if ((!seq_copied)&&(seq_size==1)) {
-        return recombine_pair_to_ex(*(seq.begin()));
-    } else if (seq_copied&&(newseq.size()==1)) {
-        return recombine_pair_to_ex(*(newseq.begin()));
-    }
-
-    if (!seq_copied) return this->hold();
-
-    return (new add(newseq,1))->setflag(status_flags::dynallocated  |
-                                        status_flags::evaluated );
-}
-*/
+// protected
 
-ex add::eval(int level) const
+/** Implementation of ex::diff() for a sum. It differentiates each term.
+ *  @see ex::diff */
+ex add::derivative(const symbol & y) const
 {
-    // simplifications: +(;c) -> c
-    //                  +(x;1) -> x
-
-    debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    epvector * evaled_seqp=evalchildren(level);
-    if (evaled_seqp!=0) {
-        // do more evaluation later
-        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));
-    }
-#endif // def DO_GINAC_ASSERT
-
-    if (flags & status_flags::evaluated) {
-        GINAC_ASSERT(seq.size()>0);
-        GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(exZERO()));
-        return *this;
-    }
-
-    int seq_size=seq.size();
-    if (seq_size==0) {
-        // +(;c) -> c
-        return overall_coeff;
-    } else if ((seq_size==1)&&overall_coeff.is_equal(exZERO())) {
-        // +(x;0) -> x
-        return recombine_pair_to_ex(*(seq.begin()));
-    }
-    return this->hold();
+       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);
 }
 
-exvector add::get_indices(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();
-    }
-    return (seq.begin())->rest.get_indices();
-}    
-
-ex add::simplify_ncmul(exvector const & v) const
-{
-    if (seq.size()==0) {
-        return expairseq::simplify_ncmul(v);
-    }
-    return (*seq.begin()).rest.simplify_ncmul(v);
-}    
-
-// protected
-
-int add::compare_same_type(basic const & other) const
+int add::compare_same_type(const basic & other) const
 {
-    return expairseq::compare_same_type(other);
+       return inherited::compare_same_type(other);
 }
 
-bool add::is_equal_same_type(basic const & other) const
+bool add::is_equal_same_type(const basic & other) const
 {
-    return expairseq::is_equal_same_type(other);
+       return inherited::is_equal_same_type(other);
 }
 
 unsigned add::return_type(void) const
 {
-    if (seq.size()==0) {
-        return return_types::commutative;
-    }
-    return (*seq.begin()).rest.return_type();
+       if (seq.empty())
+               return return_types::commutative;
+       else
+               return seq.begin()->rest.return_type();
 }
    
 unsigned add::return_type_tinfo(void) const
 {
-    if (seq.size()==0) {
-        return tinfo_key;
-    }
-    return (*seq.begin()).rest.return_type_tinfo();
+       if (seq.empty())
+               return tinfo_key;
+       else
+               return seq.begin()->rest.return_type_tinfo();
 }
 
-ex add::thisexpairseq(epvector const & v, ex const & oc) const
+ex add::thisexpairseq(const epvector & v, const ex & oc) const
 {
-    return (new add(v,oc))->setflag(status_flags::dynallocated);
+       return (new add(v,oc))->setflag(status_flags::dynallocated);
 }
 
-ex add::thisexpairseq(epvector * vp, ex const & oc) const
+ex add::thisexpairseq(epvector * vp, const ex & oc) const
 {
-    return (new add(vp,oc))->setflag(status_flags::dynallocated);
+       return (new add(vp,oc))->setflag(status_flags::dynallocated);
 }
 
-/*
-expair add::split_ex_to_pair(ex const & e) const
+expair add::split_ex_to_pair(const ex & e) const
 {
-    if (is_ex_exactly_of_type(e,mul)) {
-        mul const & mulref=ex_to_mul(e);
-        GINAC_ASSERT(mulref.seq.size()>1);
-        ex const & lastfactor_rest=(*(mulref.seq.end()-1)).rest;
-        ex const & lastfactor_coeff=(*(mulref.seq.end()-1)).coeff;
-        if (is_ex_exactly_of_type(lastfactor_rest,numeric) &&
-            ex_to_numeric(lastfactor_coeff).is_equal(numONE())) {
-            epvector s=mulref.seq;
-            //s.pop_back();
-            //return expair((new mul(s,1))->setflag(status_flags::dynallocated),
-            //              lastfactor);
-            mul * mulp=static_cast<mul *>(mulref.duplicate());
-#ifdef EXPAIRSEQ_USE_HASHTAB
-            mulp->remove_hashtab_entry(mulp->seq.end()-1);
-#endif // def EXPAIRSEQ_USE_HASHTAB
-            mulp->seq.pop_back();
-#ifdef EXPAIRSEQ_USE_HASHTAB
-            mulp->shrink_hashtab();
-#endif // def EXPAIRSEQ_USE_HASHTAB
-            mulp->clearflag(status_flags::evaluated);
-            mulp->clearflag(status_flags::hash_calculated);
-            return expair(mulp->setflag(status_flags::dynallocated),lastfactor_rest);
-        }
-    }
-    return expair(e,exONE());
+       if (is_ex_exactly_of_type(e,mul)) {
+               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);
+               mulcopyp->setflag(status_flags::dynallocated);
+               return expair(*mulcopyp,numfactor);
+       }
+       return expair(e,_ex1);
 }
-*/
 
-expair add::split_ex_to_pair(ex const & e) const
+expair add::combine_ex_with_coeff_to_pair(const ex & e,
+                                                                                 const ex & c) const
 {
-    if (is_ex_exactly_of_type(e,mul)) {
-        mul const & 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=exONE();
-        mulcopyp->clearflag(status_flags::evaluated);
-        mulcopyp->clearflag(status_flags::hash_calculated);
-        return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
-    }
-    return expair(e,exONE());
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
+       if (is_ex_exactly_of_type(e, mul)) {
+               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);
+               mulcopyp->setflag(status_flags::dynallocated);
+               if (are_ex_trivially_equal(c, _ex1))
+                       return expair(*mulcopyp, numfactor);
+               else if (are_ex_trivially_equal(numfactor, _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(e, c);
 }
 
-/*
-expair add::combine_ex_with_coeff_to_pair(ex const & e,
-                                          ex const & c) const
+expair add::combine_pair_with_coeff_to_pair(const expair & p,
+                                                                                       const ex & c) const
 {
-    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
-    if (is_ex_exactly_of_type(e,mul)) {
-        mul const & mulref=ex_to_mul(e);
-        GINAC_ASSERT(mulref.seq.size()>1);
-        ex const & lastfactor_rest=(*(mulref.seq.end()-1)).rest;
-        ex const & lastfactor_coeff=(*(mulref.seq.end()-1)).coeff;
-        if (is_ex_exactly_of_type(lastfactor_rest,numeric) &&
-            ex_to_numeric(lastfactor_coeff).is_equal(numONE())) {
-            //epvector s=mulref.seq;
-            //s.pop_back();
-            //return expair((new mul(s,1))->setflag(status_flags::dynallocated),
-            //              ex_to_numeric(lastfactor).mul_dyn(ex_to_numeric(c)));
-            mul * mulp=static_cast<mul *>(mulref.duplicate());
-#ifdef EXPAIRSEQ_USE_HASHTAB
-            mulp->remove_hashtab_entry(mulp->seq.end()-1);
-#endif // def EXPAIRSEQ_USE_HASHTAB
-            mulp->seq.pop_back();
-#ifdef EXPAIRSEQ_USE_HASHTAB
-            mulp->shrink_hashtab();
-#endif // def EXPAIRSEQ_USE_HASHTAB
-            mulp->clearflag(status_flags::evaluated);
-            mulp->clearflag(status_flags::hash_calculated);
-            if (are_ex_trivially_equal(c,exONE())) {
-                return expair(mulp->setflag(status_flags::dynallocated),lastfactor_rest);
-            } else if (are_ex_trivially_equal(lastfactor_rest,exONE())) {
-                return expair(mulp->setflag(status_flags::dynallocated),c);
-            }                
-            return expair(mulp->setflag(status_flags::dynallocated),
-                          ex_to_numeric(lastfactor_rest).mul_dyn(ex_to_numeric(c)));
-        }
-    }
-    return expair(e,c);
-}
-*/
+       GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
 
-expair add::combine_ex_with_coeff_to_pair(ex const & e,
-                                          ex const & c) const
-{
-    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
-    if (is_ex_exactly_of_type(e,mul)) {
-        mul const & 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=exONE();
-        mulcopyp->clearflag(status_flags::evaluated);
-        mulcopyp->clearflag(status_flags::hash_calculated);
-        if (are_ex_trivially_equal(c,exONE())) {
-            return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
-        } else if (are_ex_trivially_equal(numfactor,exONE())) {
-            return expair(mulcopyp->setflag(status_flags::dynallocated),c);
-        }
-        return expair(mulcopyp->setflag(status_flags::dynallocated),
-                          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,exONE())) {
-            return expair(e,exONE());
-        }
-        return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)),exONE());
-    }
-    return expair(e,c);
-}
-    
-expair add::combine_pair_with_coeff_to_pair(expair const & p,
-                                            ex const & c) const
-{
-    GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
-    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+       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_ex_exactly_of_type(p.rest,numeric)) {
-        GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(numONE())); // should be normalized
-        return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),exONE());
-    }
-
-    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(expair const & p) const
+       
+ex add::recombine_pair_to_ex(const expair & p) const
 {
-    //if (p.coeff.compare(exONE())==0) {
-    //if (are_ex_trivially_equal(p.coeff,exONE())) {
-    if (ex_to_numeric(p.coeff).is_equal(numONE())) {
-        return p.rest;
-    } else {
-        return p.rest*p.coeff;
-    }
+       if (ex_to<numeric>(p.coeff).is_equal(_num1))
+               return p.rest;
+       else
+               return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 }
 
 ex add::expand(unsigned options) const
 {
-    epvector * vp=expandchildren(options);
-    if (vp==0) {
-        return *this;
-    }
-    return (new add(vp,overall_coeff))->setflag(status_flags::expanded    |
-                                                status_flags::dynallocated );
-}
-
-//////////
-// new virtual functions which can be overridden by derived classes
-//////////
-
-// none
-
-//////////
-// non-virtual functions in this class
-//////////
+       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;
+       }
 
-// none
-
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned add::precedence=40;
-
-//////////
-// global constants
-//////////
-
-const add some_add;
-type_info const & typeid_add=typeid(some_add);
+       return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+}
 
 } // namespace GiNaC