- Doxygen'ed a bunch of comments.
[ginac.git] / ginac / mul.cpp
index e3cbd78..b0caa52 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products 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 "mul.h"
 #include "add.h"
 #include "power.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(mul, expairseq)
 
 //////////
 // default constructor, destructor, copy constructor assignment operator and helpers
@@ -45,13 +54,13 @@ mul::~mul()
     destroy(0);
 }
 
-mul::mul(mul const & other)
+mul::mul(const mul & other)
 {
     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
     copy(other);
 }
 
-mul const & mul::operator=(mul const & other)
+const mul & mul::operator=(const mul & other)
 {
     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
     if (this != &other) {
@@ -63,14 +72,14 @@ mul const & mul::operator=(mul const & other)
 
 // protected
 
-void mul::copy(mul const & other)
+void mul::copy(const mul & other)
 {
-    expairseq::copy(other);
+    inherited::copy(other);
 }
 
 void mul::destroy(bool call_parent)
 {
-    if (call_parent) expairseq::destroy(call_parent);
+    if (call_parent) inherited::destroy(call_parent);
 }
 
 //////////
@@ -79,71 +88,54 @@ void mul::destroy(bool call_parent)
 
 // public
 
-mul::mul(ex const & lh, ex const & rh)
+mul::mul(const ex & lh, const ex & rh)
 {
     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
-    overall_coeff=exONE();
+    overall_coeff = _ex1();
     construct_from_2_ex(lh,rh);
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(exvector const & v)
+mul::mul(const exvector & v)
 {
     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
-    overall_coeff=exONE();
+    overall_coeff = _ex1();
     construct_from_exvector(v);
-    ASSERT(is_canonical());
-}
-
-/*
-mul::mul(epvector const & v, bool do_not_canonicalize)
-{
-    debugmsg("mul constructor from epvector,bool",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    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);
-    }
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
 }
-*/
 
-mul::mul(epvector const & v)
+mul::mul(const epvector & v)
 {
     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
-    overall_coeff=exONE();
+    overall_coeff = _ex1();
     construct_from_epvector(v);
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(epvector const & v, ex const & oc)
+mul::mul(const epvector & v, const ex & oc)
 {
     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
-    overall_coeff=oc;
+    overall_coeff = oc;
     construct_from_epvector(v);
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(epvector * vp, ex const & oc)
+mul::mul(epvector * vp, const ex & oc)
 {
     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
-    ASSERT(vp!=0);
-    overall_coeff=oc;
+    GINAC_ASSERT(vp!=0);
+    overall_coeff = oc;
     construct_from_epvector(*vp);
     delete vp;
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(ex const & lh, ex const & mh, ex const & rh)
+mul::mul(const ex & lh, const ex & mh, const ex & rh)
 {
     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
     tinfo_key = TINFO_mul;
@@ -152,9 +144,31 @@ mul::mul(ex const & lh, ex const & mh, ex const & rh)
     factors.push_back(lh);
     factors.push_back(mh);
     factors.push_back(rh);
-    overall_coeff=exONE();
+    overall_coeff = _ex1();
     construct_from_exvector(factors);
-    ASSERT(is_canonical());
+    GINAC_ASSERT(is_canonical());
+}
+
+//////////
+// archiving
+//////////
+
+/** Construct object from archive_node. */
+mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+{
+    debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
+}
+
+/** Unarchive the object. */
+ex mul::unarchive(const archive_node &n, const lst &sym_lst)
+{
+    return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
+}
+
+/** Archive the object. */
+void mul::archive(archive_node &n) const
+{
+    inherited::archive(n);
 }
 
 //////////
@@ -169,23 +183,123 @@ basic * mul::duplicate() const
     return new mul(*this);
 }
 
+void mul::print(ostream & os, unsigned upper_precedence) const
+{
+    debugmsg("mul print",LOGLEVEL_PRINT);
+    if (precedence<=upper_precedence) os << "(";
+    bool first=true;
+    // first print the overall numeric coefficient:
+    numeric coeff = ex_to_numeric(overall_coeff);
+    if (coeff.csgn()==-1) os << '-';
+    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 << '*';
+    }
+    // then proceed with the remaining factors:
+    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+        if (!first) {
+            os << '*';
+        } else {
+            first=false;
+        }
+        recombine_pair_to_ex(*cit).print(os,precedence);
+    }
+    if (precedence<=upper_precedence) os << ")";
+}
+
+void mul::printraw(ostream & os) const
+{
+    debugmsg("mul 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 mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
+{
+    debugmsg("mul print csrc", LOGLEVEL_PRINT);
+    if (precedence <= upper_precedence)
+        os << "(";
+
+    if (!overall_coeff.is_equal(_ex1())) {
+        overall_coeff.bp->printcsrc(os,type,precedence);
+        os << "*";
+    }
+    
+    // Print arguments, separated by "*" or "/"
+    epvector::const_iterator it = seq.begin();
+    epvector::const_iterator itend = seq.end();
+    while (it != itend) {
+
+        // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
+        if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
+            if (type == csrc_types::ctype_cl_N)
+                os << "recip(";
+            else
+                os << "1.0/";
+        }
+
+        // If the exponent is 1 or -1, it is left out
+        if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
+            it->rest.bp->printcsrc(os, type, precedence);
+        else
+            // outer parens around ex needed for broken gcc-2.95 parser:
+            (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
+
+        // Separator is "/" for negative integer powers, "*" otherwise
+        it++;
+        if (it != itend) {
+            if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
+                os << "/";
+            else
+                os << "*";
+        }
+    }
+    if (precedence <= upper_precedence)
+        os << ")";
+}
+
 bool mul::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);
     }
 }
 
 typedef vector<int> intvector;
 
-int mul::degree(symbol const & s) const
+int mul::degree(const symbol & s) const
 {
     int deg_sum=0;
     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
@@ -194,7 +308,7 @@ int mul::degree(symbol const & s) const
     return deg_sum;
 }
 
-int mul::ldegree(symbol const & s) const
+int mul::ldegree(const symbol & s) const
 {
     int deg_sum=0;
     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
@@ -203,7 +317,7 @@ int mul::ldegree(symbol const & s) const
     return deg_sum;
 }
 
-ex mul::coeff(symbol const & s, int const n) const
+ex mul::coeff(const symbol & s, int n) const
 {
     exvector coeffseq;
     coeffseq.reserve(seq.size()+1);
@@ -238,229 +352,8 @@ ex mul::coeff(symbol const & s, int const n) const
         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
     }
     
-    return exZERO();
-}
-
-/*
-ex mul::eval(int level) const
-{
-    // simplifications: *(...,x,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric(), move pairs to end first)
-    //                  *(...,x,1) -> *(...,x)
-    //                  *(...,x,0) -> 0
-    //                  *(+(x,y,...),(c,1)) -> *(+(*(x,c),*(y,c),...)) (c numeric())
-    //                  *(x) -> x
-    //                  *() -> 1
-
-    debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    if ((level==1)&&(flags & status_flags::evaluated)) {
-#ifdef DOASSERT
-        for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-            ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
-                   (!(ex_to_numeric((*cit).coeff).is_integer())));
-        }
-
-        // test if all numerics were moved to the end and
-        // all numerics with coeff 1 to the very end
-        if (seq.size()!=0) {
-            epvector::const_iterator cit=seq.end();
-            bool all_coeff_1=true;
-            bool all_numeric=true;
-            do {
-                cit--;
-                if (is_ex_exactly_of_type((*cit).rest,numeric)) {
-                    ASSERT(all_numeric);
-                    if ((*cit).coeff.is_equal(exONE())) {
-                        ASSERT(all_coeff_1);
-                    } else {
-                        all_coeff_1=false;
-                    }
-                } else {
-                    all_numeric=false;
-                }
-            } while (cit!=seq.begin());
-        }
-#endif // def DOASSERT    
-        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 mul(evaled_seqp))->setflag(status_flags::dynallocated);
-    }
-
-    // combine pairs with coeff 1 (all numerics should be at end, assert below)
-    if (seq.size()>1) {
-        // count number of pairs with coeff 1
-        unsigned num_coeff_1=0;
-        bool still_numeric=true;
-        epvector::const_iterator cit=seq.end();
-        unsigned first_pos;
-        unsigned second_pos;
-        do {
-            cit--;
-            if (is_ex_exactly_of_type((*cit).rest,numeric)) {
-                if ((*cit).coeff.is_equal(exONE())) {
-                    num_coeff_1++;
-                }
-            } else {
-                still_numeric=false;
-            }
-        } while ((cit!=seq.begin())&&still_numeric);
-        if (num_coeff_1>1) {
-            newseq=seq;
-            
-    }
-    
-    
-#ifdef DOASSERT
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
-               (!(ex_to_numeric((*cit).coeff).is_integer())));
-    }
-
-    // test if all numerics were moved to the end and
-    // all numerics with coeff 1 to the very end
-    if (seq.size()!=0) {
-        epvector::const_iterator cit=seq.end();
-        bool all_coeff_1=true;
-        bool all_numeric=true;
-        do {
-            cit--;
-            if (is_ex_exactly_of_type((*cit).rest,numeric)) {
-                ASSERT(all_numeric);
-                if ((*cit).coeff.is_equal(exONE())) {
-                    ASSERT(all_coeff_1);
-                } else {
-                    all_coeff_1=false;
-                }
-            } else {
-                all_numeric=false;
-            }
-        } while (cit!=seq.begin());
-    }
-#endif // def DOASSERT
-    
-    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,(c1,1),(c2,1)) -> *(...,x,(c1*c2,1)) (c1, c2 numeric())
-    if ((!seq_copied) && (seq_size>=2) &&
-        is_ex_exactly_of_type(last_expair.rest,numeric) &&
-        ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
-        is_ex_exactly_of_type(next_to_last_expair.rest,numeric) &&
-        ex_to_numeric(next_to_last_expair.coeff).is_equal(numONE()) ) {
-        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) &&
-           ex_to_numeric((*it1).coeff).is_equal(numONE()) &&
-           is_ex_exactly_of_type((*it2).rest,numeric) &&
-           ex_to_numeric((*it2).coeff).is_equal(numONE()) ) {
-        *it1=expair(ex_to_numeric((*it1).rest).mul_dyn(ex_to_numeric((*it2).rest)),exONE());
-        newseq.pop_back();
-        it2=newseq.end()-1;
-        it1=it2-1;
-    }
-
-    // *(...,x,1) -> *(...,x)
-    if ((!seq_copied) && (seq_size>=1) &&
-        (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
-        (ex_to_numeric(last_expair.rest).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).rest).compare(numONE())==0)) {
-        newseq.pop_back();
-        it2=newseq.end()-1;
-    }
-
-    // *(...,x,0) -> 0
-    if ((!seq_copied) && (seq_size>=1) &&
-        (is_ex_exactly_of_type(last_expair.rest,numeric)) &&
-        (ex_to_numeric(last_expair.rest).is_zero())) {
-        return exZERO();
-    }
-    if (seq_copied && (newseq.size()>=1) &&
-        (is_ex_exactly_of_type((*it2).rest,numeric)) &&
-        (ex_to_numeric((*it2).rest).is_zero())) {
-        return exZERO();
-    }
-
-    // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
-    if ((!seq_copied) && (seq_size==2) &&
-        is_ex_exactly_of_type(next_to_last_expair.rest,add) &&
-        is_ex_exactly_of_type(last_expair.rest,numeric) &&
-        ex_to_numeric(last_expair.coeff).is_equal(numONE()) &&
-        (ex_to_numeric(next_to_last_expair.coeff).compare(numONE())==0)) {
-        add const & addref=ex_to_add(next_to_last_expair.rest);
-        epvector distrseq;
-        distrseq.reserve(addref.seq.size());
-        for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
-            distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
-                                   last_expair.rest));
-        }
-        // special treatment for the last element if it is numeric (to
-        // avoid terms like (2/3)*(3/2)) is no longer necessary, this
-        // is handled in add::combine_pair_with_coeff_to_pair()
-        return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
-                                              status_flags::evaluated );
-    }
-    if (seq_copied && (newseq.size()==2) &&
-        is_ex_exactly_of_type(newseq[0].rest,add) &&
-        is_ex_exactly_of_type(newseq[1].rest,numeric) &&
-        ex_to_numeric(newseq[1].coeff).is_equal(numONE()) &&
-        (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
-        add const & addref=ex_to_add(newseq[0].rest);
-        epvector distrseq;
-        distrseq.reserve(addref.seq.size());
-        for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
-            distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
-                                   newseq[1].rest));
-        }
-        // special treatment for the last element if it is numeric (to
-        // avoid terms like (2/3)*(3/2)) is no longer necessary, this
-        // is handled in add::combine_pair_with_coeff_to_pair()
-        return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
-                                              status_flags::evaluated );
-    }
-    
-    // *() -> 1
-    if ((!seq_copied) && (seq_size==0)) {
-        return exONE();
-    } else if (seq_copied && (newseq.size()==0)) {
-        return exONE();
-    }
-
-    // *(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 mul(newseq,1))->setflag(status_flags::dynallocated  |
-                                        status_flags::evaluated );
+    return _ex0();
 }
-*/
 
 ex mul::eval(int level) const
 {
@@ -478,44 +371,44 @@ ex mul::eval(int level) const
                    setflag(status_flags::dynallocated);
     }
 
-#ifdef DOASSERT
+#ifdef DO_GINAC_ASSERT
     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
+        GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
                (!(ex_to_numeric((*cit).coeff).is_integer())));
-        ASSERT(!((*cit).is_numeric_with_coeff_1()));
+        GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
             printtree(cerr,0);
         }
-        ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
+        GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
         /* for paranoia */
         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
-        ASSERT(p.rest.is_equal((*cit).rest));
-        ASSERT(p.coeff.is_equal((*cit).coeff));
+        GINAC_ASSERT(p.rest.is_equal((*cit).rest));
+        GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
         /* end paranoia */
     }
-#endif // def DOASSERT
+#endif // def DO_GINAC_ASSERT
 
     if (flags & status_flags::evaluated) {
-        ASSERT(seq.size()>0);
-        ASSERT((seq.size()>1)||!overall_coeff.is_equal(exONE()));
+        GINAC_ASSERT(seq.size()>0);
+        GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
         return *this;
     }
 
     int seq_size=seq.size();
-    if (overall_coeff.is_equal(exZERO())) {
+    if (overall_coeff.is_equal(_ex0())) {
         // *(...,x;0) -> 0
-        return exZERO();
+        return _ex0();
     } else if (seq_size==0) {
         // *(;c) -> c
         return overall_coeff;
-    } else if ((seq_size==1)&&overall_coeff.is_equal(exONE())) {
+    } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
         // *(x;1) -> x
         return recombine_pair_to_ex(*(seq.begin()));
     } else if ((seq_size==1) &&
                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
-               ex_to_numeric((*seq.begin()).coeff).is_equal(numONE())) {
+               ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
-        add const & addref=ex_to_add((*seq.begin()).rest);
+        const add & addref=ex_to_add((*seq.begin()).rest);
         epvector distrseq;
         distrseq.reserve(addref.seq.size());
         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
@@ -531,78 +424,24 @@ ex mul::eval(int level) const
     return this->hold();
 }
 
-/*
-ex mul::eval(int level) const
+ex mul::evalf(int level) const
 {
-    // simplifications: *(...,x,c1,c2) -> *(...,x,c1*c2) (c1, c2 numeric())
-    //                  *(...,(c1,c2)) -> (...,(c1^c2,1)) (normalize)
-    //                  *(...,x,1) -> +(...,x)
-    //                  *(...,x,0) -> 0
-    //                  *(+(x,y,...),c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
-    //                  *(x) -> x
-    //                  *() -> 1
-
-    debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
-
-    epvector newseq=seq;
-    epvector::iterator it1,it2;
+    if (level==1)
+        return mul(seq,overall_coeff);
     
-    // *(...,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).power(ex_to_numeric((*it1).coeff))
-                    .mul(ex_to_numeric((*it2).rest).power(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).power(ex_to_numeric((*it2).coeff)),exONE());
-        // *(...,x,1) -> *(...,x)
-        if (static_cast<numeric &>(*(*it2).rest.bp).compare(numONE())==0) {
-            newseq.pop_back();
-            it2=newseq.end()-1;
-        }
-    }
-
-    // *(...,x,0) -> 0
-    if ((newseq.size()>=1)&&is_exactly_of_type(*(*it2).rest.bp,numeric)) {
-        if (static_cast<numeric &>(*(*it2).rest.bp).is_zero()==0) {
-            return exZERO();
-        }
-    }
-
-    // *(+(x,y,...),c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
-    if ((newseq.size()==2)&&is_ex_exactly_of_type(newseq[0].rest,add)&&
-        is_ex_exactly_of_type(newseq[1].rest,numeric)&&
-        (ex_to_numeric(newseq[0].coeff).compare(numONE())==0)) {
-        add const & addref=ex_to_add(newseq[0].rest);
-        numeric const & numref=ex_to_numeric(newseq[1].rest);
-        epvector distrseq;
-        distrseq.reserve(addref.seq.size());
-        for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
-            distrseq.push_back(expair((*cit).rest,ex_to_numeric((*cit).coeff).mul(numref)));
-        }
-        return (new add(distrseq,1))->setflag(status_flags::dynallocated  |
-                                              status_flags::evaluated );
-    }
+    if (level==-max_recursion_level)
+        throw(std::runtime_error("max recursion level reached"));
     
-    if (newseq.size()==0) {
-        // *() -> 1
-        return exONE();
-    } else if (newseq.size()==1) {
-        // *(x) -> x
-        return recombine_pair_to_ex(*newseq.begin());
+    epvector s;
+    s.reserve(seq.size());
+    
+    --level;
+    for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
+        s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
+                                                  (*it).coeff));
     }
-
-    return (new mul(newseq,1))->setflag(status_flags::dynallocated  |
-                                        status_flags::evaluated );
+    return mul(s,overall_coeff.evalf(level));
 }
-*/
 
 exvector mul::get_indices(void) const
 {
@@ -618,21 +457,39 @@ exvector mul::get_indices(void) const
     return iv;
 }
 
-ex mul::simplify_ncmul(exvector const & v) const
+ex mul::simplify_ncmul(const exvector & v) const
 {
     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 }
 
 // protected
 
-int mul::compare_same_type(basic const & other) const
+/** Implementation of ex::diff() for a product. It applies the product rule.
+ *  @see ex::diff */
+ex mul::derivative(const symbol & s) const
+{
+    exvector new_seq;
+    new_seq.reserve(seq.size());
+
+    // D(a*b*c)=D(a)*b*c+a*D(b)*c+a*b*D(c)
+    for (unsigned i=0; i!=seq.size(); i++) {
+        epvector sub_seq=seq;
+        sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff*
+                                      power(sub_seq[i].rest,sub_seq[i].coeff-1)*
+                                      sub_seq[i].rest.diff(s));
+        new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated));
+    }
+    return (new add(new_seq))->setflag(status_flags::dynallocated);
+}
+
+int mul::compare_same_type(const basic & other) const
 {
-    return expairseq::compare_same_type(other);
+    return inherited::compare_same_type(other);
 }
 
-bool mul::is_equal_same_type(basic const & other) const
+bool mul::is_equal_same_type(const basic & other) const
 {
-    return expairseq::is_equal_same_type(other);
+    return inherited::is_equal_same_type(other);
 }
 
 unsigned mul::return_type(void) const
@@ -655,10 +512,10 @@ unsigned mul::return_type(void) const
             all_commutative=0;
         }
         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
-               // another nc element found, compare type_infos
+            // another nc element found, compare type_infos
             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
-               // diffent types -> mul is ncc
-               return return_types::noncommutative_composite;
+                // diffent types -> mul is ncc
+                return return_types::noncommutative_composite;
             }
         }
     }
@@ -682,58 +539,58 @@ unsigned mul::return_type_tinfo(void) const
     return tinfo_key;
 }
 
-ex mul::thisexpairseq(epvector const & v, ex const & oc) const
+ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 {
     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 }
 
-ex mul::thisexpairseq(epvector * vp, ex const & oc) const
+ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 {
     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 }
 
-expair mul::split_ex_to_pair(ex const & e) const
+expair mul::split_ex_to_pair(const ex & e) const
 {
     if (is_ex_exactly_of_type(e,power)) {
-        power const & powerref=ex_to_power(e);
+        const power & powerref=ex_to_power(e);
         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
             return expair(powerref.basis,powerref.exponent);
         }
     }
-    return expair(e,exONE());
+    return expair(e,_ex1());
 }
     
-expair mul::combine_ex_with_coeff_to_pair(ex const & e,
-                                          ex const & c) const
+expair mul::combine_ex_with_coeff_to_pair(const ex & e,
+                                          const ex & c) const
 {
     // to avoid duplication of power simplification rules,
     // we create a temporary power object
     // otherwise it would be hard to correctly simplify
     // expression like (4^(1/3))^(3/2)
-    if (are_ex_trivially_equal(c,exONE())) {
+    if (are_ex_trivially_equal(c,_ex1())) {
         return split_ex_to_pair(e);
     }
     return split_ex_to_pair(power(e,c));
 }
     
-expair mul::combine_pair_with_coeff_to_pair(expair const & p,
-                                            ex const & c) const
+expair mul::combine_pair_with_coeff_to_pair(const expair & p,
+                                            const ex & c) const
 {
     // to avoid duplication of power simplification rules,
     // we create a temporary power object
     // otherwise it would be hard to correctly simplify
     // expression like (4^(1/3))^(3/2)
-    if (are_ex_trivially_equal(c,exONE())) {
+    if (are_ex_trivially_equal(c,_ex1())) {
         return p;
     }
     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 }
     
-ex mul::recombine_pair_to_ex(expair const & p) const
+ex mul::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 power(p.rest,p.coeff);
@@ -755,7 +612,7 @@ bool mul::expair_needs_further_processing(epp it)
             *it=ep;
             return true;
         }
-        if (ex_to_numeric((*it).coeff).is_equal(numONE())) {
+        if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
             // combined pair has coeff 1 and must be moved to the end
             return true;
         }
@@ -765,32 +622,32 @@ bool mul::expair_needs_further_processing(epp it)
 
 ex mul::default_overall_coeff(void) const
 {
-    return exONE();
+    return _ex1();
 }
 
-void mul::combine_overall_coeff(ex const & c)
+void mul::combine_overall_coeff(const ex & c)
 {
-    ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-    ASSERT(is_ex_exactly_of_type(c,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 }
 
-void mul::combine_overall_coeff(ex const & c1, ex const & c2)
+void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 {
-    ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-    ASSERT(is_ex_exactly_of_type(c1,numeric));
-    ASSERT(is_ex_exactly_of_type(c2,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
     overall_coeff = ex_to_numeric(overall_coeff).
                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 }
 
-bool mul::can_make_flat(expair const & p) const
+bool mul::can_make_flat(const expair & p) const
 {
-    ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
+    GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
     // this assertion will probably fail somewhere
     // it would require a more careful make_flat, obeying the power laws
     // probably should return true only if p.coeff is integer
-    return ex_to_numeric(p.coeff).is_equal(numONE());
+    return ex_to_numeric(p.coeff).is_equal(_num1());
 }
 
 ex mul::expand(unsigned options) const
@@ -799,25 +656,25 @@ ex mul::expand(unsigned options) const
     intvector positions_of_adds;
     intvector number_of_add_operands;
 
-    epvector * expanded_seqp=expandchildren(options);
+    epvector * expanded_seqp = expandchildren(options);
 
-    epvector const & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
+    const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 
     positions_of_adds.resize(expanded_seq.size());
     number_of_add_operands.resize(expanded_seq.size());
 
-    int number_of_adds=0;
-    int number_of_expanded_terms=1;
+    int number_of_adds = 0;
+    int number_of_expanded_terms = 1;
 
-    unsigned current_position=0;
-    epvector::const_iterator last=expanded_seq.end();
+    unsigned current_position = 0;
+    epvector::const_iterator last = expanded_seq.end();
     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
         if (is_ex_exactly_of_type((*cit).rest,add)&&
-            (ex_to_numeric((*cit).coeff).is_equal(numONE()))) {
-            positions_of_adds[number_of_adds]=current_position;
-            add const & expanded_addref=ex_to_add((*cit).rest);
-            int addref_nops=expanded_addref.nops();
-            number_of_add_operands[number_of_adds]=addref_nops;
+            (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
+            positions_of_adds[number_of_adds] = current_position;
+            const add & expanded_addref = ex_to_add((*cit).rest);
+            unsigned addref_nops = expanded_addref.nops();
+            number_of_add_operands[number_of_adds] = addref_nops;
             number_of_expanded_terms *= addref_nops;
             number_of_adds++;
         }
@@ -848,8 +705,8 @@ ex mul::expand(unsigned options) const
         epvector term;
         term=expanded_seq;
         for (l=0; l<number_of_adds; l++) {
-            add const & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
-            ASSERT(term[positions_of_adds[l]].coeff.compare(exONE())==0);
+            const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
+            GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
         }
         /*
@@ -890,66 +747,6 @@ ex mul::expand(unsigned options) const
                                         status_flags::expanded);
 }
 
-/*
-ex mul::expand(unsigned options) const
-{
-    exvector sub_expanded_seq;
-    intvector positions_of_adds;
-    intvector number_of_add_operands;
-
-    sub_expanded_seq.resize(seq.size());
-    positions_of_adds.resize(seq.size());
-    number_of_add_operands.reserve(seq.size());
-
-    int number_of_adds=0;
-    int number_of_expanded_terms=1;
-    for (unsigned current_position=0; current_position<seq.size(); current_position++) {
-        ex const & expanded_ex=recombine_pair_to_ex(seq[current_position]).expand(options);
-        if (is_ex_exactly_of_type(expanded_ex,add)) {
-            positions_of_adds[number_of_adds]=current_position;
-            add const & expanded_addref=ex_to_add(expanded_ex);
-            number_of_add_operands[number_of_adds]=expanded_addref.seq.size();
-            number_of_expanded_terms *= expanded_addref.seq.size();
-            number_of_adds++;
-        }
-        sub_expanded_seq.push_back(expanded_ex);
-    }
-
-    exvector distrseq;
-    distrseq.reserve(number_of_expanded_terms);
-
-    intvector k;
-    k.resize(number_of_adds);
-    
-    int l;
-    for (l=0; l<number_of_adds; l++) {
-        k[l]=0;
-    }
-
-    while (1) {
-        exvector term;
-        term=sub_expanded_seq;
-        for (l=0; l<number_of_adds; l++) {
-            add const & addref=ex_to_add(sub_expanded_seq[positions_of_adds[l]]);
-            term[positions_of_adds[l]]=addref.recombine_pair_to_ex(addref.seq[k[l]]);
-        }
-        distrseq.push_back((new mul(term))->setflag(status_flags::dynallocated |
-                                                    status_flags::expanded));
-
-        // increment k[]
-        l=number_of_adds-1;
-        while ((l>=0)&&((++k[l])>=number_of_add_operands[l])) {
-            k[l]=0;    
-            l--;
-        }
-        if (l<0) break;
-    }
-
-    return (new add(distrseq))->setflag(status_flags::dynallocated |
-                                        status_flags::expanded);
-}
-*/
-
 //////////
 // new virtual functions which can be overridden by derived classes
 //////////
@@ -962,11 +759,11 @@ ex mul::expand(unsigned options) const
 
 epvector * mul::expandchildren(unsigned options) const
 {
-    epvector::const_iterator last=seq.end();
-    epvector::const_iterator cit=seq.begin();
+    epvector::const_iterator last = seq.end();
+    epvector::const_iterator cit = seq.begin();
     while (cit!=last) {
-        ex const & factor=recombine_pair_to_ex(*cit);
-        ex const & expanded_factor=factor.expand(options);
+        const ex & factor = recombine_pair_to_ex(*cit);
+        const ex & expanded_factor = factor.expand(options);
         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 
             // something changed, copy seq, eval and return it
@@ -974,7 +771,7 @@ epvector * mul::expandchildren(unsigned options) const
             s->reserve(seq.size());
 
             // copy parts of seq which are known not to have changed
-            epvector::const_iterator cit2=seq.begin();
+            epvector::const_iterator cit2 = seq.begin();
             while (cit2!=cit) {
                 s->push_back(*cit2);
                 ++cit2;
@@ -1001,7 +798,7 @@ epvector * mul::expandchildren(unsigned options) const
 
 // protected
 
-unsigned mul::precedence=50;
+unsigned mul::precedence = 50;
 
 
 //////////
@@ -1009,6 +806,8 @@ unsigned mul::precedence=50;
 //////////
 
 const mul some_mul;
-type_info const & typeid_mul=typeid(some_mul);
-
+const type_info & typeid_mul = typeid(some_mul);
 
+#ifndef NO_NAMESPACE_GINAC
+} // namespace GiNaC
+#endif // ndef NO_NAMESPACE_GINAC