]> www.ginac.de Git - ginac.git/blobdiff - ginac/add.cpp
- Doxygen'ed a bunch of comments.
[ginac.git] / ginac / add.cpp
index 6f5380cce2393042caff5f8def7e00f967ff239a..aa8ff64f2785d40ff64e739f2562b98367d44837 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) 1999-2000 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 "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
@@ -47,13 +53,13 @@ add::~add()
     destroy(0);
 }
 
-add::add(add const & other)
+add::add(const add & other)
 {
     debugmsg("add copy constructor",LOGLEVEL_CONSTRUCT);
     copy(other);
 }
 
-add const & add::operator=(add const & other)
+const add & add::operator=(const add & other)
 {
     debugmsg("add operator=",LOGLEVEL_ASSIGNMENT);
     if (this != &other) {
@@ -65,14 +71,14 @@ add const & add::operator=(add const & other)
 
 // protected
 
-void add::copy(add const & other)
+void add::copy(const add & other)
 {
-    expairseq::copy(other);
+    inherited::copy(other);
 }
 
 void add::destroy(bool call_parent)
 {
-    if (call_parent) expairseq::destroy(call_parent);
+    if (call_parent) inherited::destroy(call_parent);
 }
 
 //////////
@@ -81,26 +87,26 @@ 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();
+    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();
+    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, bool do_not_canonicalize)
 {
     debugmsg("add constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_add;
@@ -116,35 +122,57 @@ add::add(epvector const & v, bool do_not_canonicalize)
 }
 */
 
-add::add(epvector const & v)
+add::add(const epvector & v)
 {
     debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_add;
-    overall_coeff=exZERO();
+    overall_coeff = _ex0();
     construct_from_epvector(v);
     GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector const & v, ex const & oc)
+add::add(const epvector & v, const ex & oc)
 {
     debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_add;
-    overall_coeff=oc;
+    overall_coeff = oc;
     construct_from_epvector(v);
     GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector * vp, ex const & 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;
+    overall_coeff = oc;
     construct_from_epvector(*vp);
     delete vp;
     GINAC_ASSERT(is_canonical());
 }
 
+//////////
+// 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);
+}
+
 //////////
 // functions overriding virtual functions from bases classes
 //////////
@@ -157,25 +185,133 @@ basic * add::duplicate() const
     return new add(*this);
 }
 
+void add::print(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;
+            } else {
+                if (coeff.csgn()==-1)
+                    (-coeff).print(os, precedence);
+                else
+                    coeff.print(os, precedence);
+            }
+            os << '*';
+        }
+        os << cit->rest;
+    }
+    if (precedence<=upper_precedence) os << ")";
+}
+
+void add::printraw(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 << ")";
+}
+
+void add::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
+{
+    debugmsg("add print csrc", LOGLEVEL_PRINT);
+    if (precedence <= upper_precedence)
+        os << "(";
+
+    // Print arguments, separated by "+"
+    epvector::const_iterator it = seq.begin();
+    epvector::const_iterator 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->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);
+        }
+
+        // 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);
+    }
+    
+    if (precedence <= upper_precedence)
+        os << ")";
+}
+
 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) {
+    if (inf==info_flags::polynomial ||
+        inf==info_flags::integer_polynomial ||
+        inf==info_flags::cinteger_polynomial ||
+        inf==info_flags::rational_polynomial ||
+        inf==info_flags::crational_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;
+        return overall_coeff.info(inf);
     } else {
-        return expairseq::info(inf);
+        return inherited::info(inf);
     }
 }
 
-int add::degree(symbol const & s) const
+int add::degree(const symbol & s) const
 {
-    int deg=INT_MIN;
-    if (!overall_coeff.is_equal(exZERO())) {
-        deg=0;
+    int deg = INT_MIN;
+    if (!overall_coeff.is_equal(_ex0())) {
+        deg = 0;
     }
     int cur_deg;
     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
@@ -185,21 +321,21 @@ int add::degree(symbol const & s) const
     return deg;
 }
 
-int add::ldegree(symbol const & s) const
+int add::ldegree(const symbol & s) const
 {
-    int deg=INT_MAX;
-    if (!overall_coeff.is_equal(exZERO())) {
-        deg=0;
+    int deg = INT_MAX;
+    if (!overall_coeff.is_equal(_ex0())) {
+        deg = 0;
     }
     int cur_deg;
     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        cur_deg=(*cit).rest.ldegree(s);
+        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
+ex add::coeff(const symbol & s, int n) const
 {
     epvector coeffseq;
     coeffseq.reserve(seq.size());
@@ -216,170 +352,6 @@ ex add::coeff(symbol const & s, int const n) const
     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 );
-}
-*/
-
-/*
-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)) {
-#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)));
-    }
-#endif // def DO_GINAC_ASSERT
-
-    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 );
-}
-*/
-
 ex add::eval(int level) const
 {
     // simplifications: +(;c) -> c
@@ -393,7 +365,7 @@ ex add::eval(int level) const
         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));
@@ -403,18 +375,18 @@ ex add::eval(int level) const
         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()));
+        GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex0()));
         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())) {
+    } else if ((seq_size==1)&&overall_coeff.is_equal(_ex0())) {
         // +(x;0) -> x
         return recombine_pair_to_ex(*(seq.begin()));
     }
@@ -432,24 +404,32 @@ exvector add::get_indices(void) const
     return (seq.begin())->rest.get_indices();
 }    
 
-ex add::simplify_ncmul(exvector const & v) const
+ex add::simplify_ncmul(const exvector & v) const
 {
     if (seq.size()==0) {
-        return expairseq::simplify_ncmul(v);
+        return inherited::simplify_ncmul(v);
     }
     return (*seq.begin()).rest.simplify_ncmul(v);
 }    
 
 // protected
 
-int add::compare_same_type(basic const & other) const
+/** Implementation of ex::diff() for a sum. It differentiates each term.
+ *  @see ex::diff */
+ex add::derivative(const symbol & s) const
+{
+    // D(a+b+c)=D(a)+D(b)+D(c)
+    return (new add(diffchildren(s)))->setflag(status_flags::dynallocated);
+}
+
+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
@@ -468,148 +448,78 @@ unsigned add::return_type_tinfo(void) const
     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);
 }
 
-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);
 }
 
-/*
-expair add::split_ex_to_pair(ex const & 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());
-}
-*/
-
-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);
+        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=exONE();
+        mulcopyp->overall_coeff=_ex1();
         mulcopyp->clearflag(status_flags::evaluated);
         mulcopyp->clearflag(status_flags::hash_calculated);
         return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
     }
-    return expair(e,exONE());
+    return expair(e,_ex1());
 }
 
-/*
-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);
-        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);
-}
-*/
-
-expair add::combine_ex_with_coeff_to_pair(ex const & e,
-                                          ex const & c) const
+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)) {
-        mul const & mulref=ex_to_mul(e);
+        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=exONE();
+        mulcopyp->overall_coeff=_ex1();
         mulcopyp->clearflag(status_flags::evaluated);
         mulcopyp->clearflag(status_flags::hash_calculated);
-        if (are_ex_trivially_equal(c,exONE())) {
+        if (are_ex_trivially_equal(c,_ex1())) {
             return expair(mulcopyp->setflag(status_flags::dynallocated),numfactor);
-        } else if (are_ex_trivially_equal(numfactor,exONE())) {
+        } else if (are_ex_trivially_equal(numfactor,_ex1())) {
             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());
+        if (are_ex_trivially_equal(c,_ex1())) {
+            return expair(e,_ex1());
         }
-        return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)),exONE());
+        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(expair const & p,
-                                            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(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(numONE())); // should be normalized
-        return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),exONE());
+        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)));
 }
     
-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())) {
+    //if (p.coeff.compare(_ex1())==0) {
+    //if (are_ex_trivially_equal(p.coeff,_ex1())) {
+    if (ex_to_numeric(p.coeff).is_equal(_num1())) {
         return p.rest;
     } else {
         return p.rest*p.coeff;
@@ -618,7 +528,7 @@ ex add::recombine_pair_to_ex(expair const & p) const
 
 ex add::expand(unsigned options) const
 {
-    epvector * vp=expandchildren(options);
+    epvector * vp = expandchildren(options);
     if (vp==0) {
         return *this;
     }
@@ -644,13 +554,15 @@ ex add::expand(unsigned options) const
 
 // protected
 
-unsigned add::precedence=40;
+unsigned add::precedence = 40;
 
 //////////
 // global constants
 //////////
 
 const add some_add;
-type_info const & typeid_add=typeid(some_add);
+const type_info & typeid_add = typeid(some_add);
 
+#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
+#endif // ndef NO_NAMESPACE_GINAC