- non-integer powers are treated as 0 by (l)degree() and coeff()
[ginac.git] / ginac / mul.cpp
index 860fb10aaeb5430d0e432076474630a4869a47ae..ad7aa13e3d5e5568241398f18ab55788241e94ad 100644 (file)
@@ -44,42 +44,42 @@ GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
 
 mul::mul()
 {
-    debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
+       debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
 }
 
 mul::~mul()
 {
-    debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
+       debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
+       destroy(false);
 }
 
 mul::mul(const mul & other)
 {
-    debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
-    copy(other);
+       debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
+       copy(other);
 }
 
 const mul & mul::operator=(const mul & other)
 {
-    debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
-    if (this != &other) {
-        destroy(1);
-        copy(other);
-    }
-    return *this;
+       debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
+       if (this != &other) {
+               destroy(true);
+               copy(other);
+       }
+       return *this;
 }
 
 // protected
 
 void mul::copy(const mul & other)
 {
-    inherited::copy(other);
+       inherited::copy(other);
 }
 
 void mul::destroy(bool call_parent)
 {
-    if (call_parent) inherited::destroy(call_parent);
+       if (call_parent) inherited::destroy(call_parent);
 }
 
 //////////
@@ -90,63 +90,63 @@ void mul::destroy(bool call_parent)
 
 mul::mul(const ex & lh, const ex & rh)
 {
-    debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    overall_coeff = _ex1();
-    construct_from_2_ex(lh,rh);
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       overall_coeff = _ex1();
+       construct_from_2_ex(lh,rh);
+       GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const exvector & v)
 {
-    debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    overall_coeff = _ex1();
-    construct_from_exvector(v);
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       overall_coeff = _ex1();
+       construct_from_exvector(v);
+       GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const epvector & v)
 {
-    debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    overall_coeff = _ex1();
-    construct_from_epvector(v);
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       overall_coeff = _ex1();
+       construct_from_epvector(v);
+       GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const epvector & v, const ex & oc)
 {
-    debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    overall_coeff = oc;
-    construct_from_epvector(v);
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       overall_coeff = oc;
+       construct_from_epvector(v);
+       GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(epvector * vp, const ex & oc)
 {
-    debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    GINAC_ASSERT(vp!=0);
-    overall_coeff = oc;
-    construct_from_epvector(*vp);
-    delete vp;
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       GINAC_ASSERT(vp!=0);
+       overall_coeff = oc;
+       construct_from_epvector(*vp);
+       delete vp;
+       GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 {
-    debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-    exvector factors;
-    factors.reserve(3);
-    factors.push_back(lh);
-    factors.push_back(mh);
-    factors.push_back(rh);
-    overall_coeff = _ex1();
-    construct_from_exvector(factors);
-    GINAC_ASSERT(is_canonical());
+       debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
+       tinfo_key = TINFO_mul;
+       exvector factors;
+       factors.reserve(3);
+       factors.push_back(lh);
+       factors.push_back(mh);
+       factors.push_back(rh);
+       overall_coeff = _ex1();
+       construct_from_exvector(factors);
+       GINAC_ASSERT(is_canonical());
 }
 
 //////////
@@ -156,19 +156,19 @@ mul::mul(const ex & lh, const ex & mh, const ex & rh)
 /** 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);
+       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);
+       return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
 }
 
 /** Archive the object. */
 void mul::archive(archive_node &n) const
 {
-    inherited::archive(n);
+       inherited::archive(n);
 }
 
 //////////
@@ -179,557 +179,552 @@ void mul::archive(archive_node &n) const
 
 basic * mul::duplicate() const
 {
-    debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
-    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 << ")";
+       debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
+       return new mul(*this);
+}
+
+void mul::print(std::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(std::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(std::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::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 overall_coeff.info(inf);
-    } else {
-        return inherited::info(inf);
-    }
-}
-
-typedef vector<int> intvector;
+       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: {
+                       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+                               if (!(recombine_pair_to_ex(*i).info(inf)))
+                                       return false;
+                       }
+                       return overall_coeff.info(inf);
+               }
+               case info_flags::algebraic: {
+                       for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+                               if ((recombine_pair_to_ex(*i).info(inf)))
+                                       return true;
+                       }
+                       return false;
+               }
+       }
+       return inherited::info(inf);
+}
+
+typedef std::vector<int> intvector;
 
 int mul::degree(const symbol & s) const
 {
-    int deg_sum = 0;
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
-    }
-    return deg_sum;
+       int deg_sum = 0;
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               if (ex_to_numeric(cit->coeff).is_integer())
+                       deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
+       }
+       return deg_sum;
 }
 
 int mul::ldegree(const symbol & s) const
 {
-    int deg_sum = 0;
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
-    }
-    return deg_sum;
+       int deg_sum = 0;
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               if (ex_to_numeric(cit->coeff).is_integer())
+                       deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
+       }
+       return deg_sum;
 }
 
 ex mul::coeff(const symbol & s, int n) const
 {
-    exvector coeffseq;
-    coeffseq.reserve(seq.size()+1);
-    
-    if (n==0) {
-        // product of individual coeffs
-        // if a non-zero power of s is found, the resulting product will be 0
-        epvector::const_iterator it=seq.begin();
-        while (it!=seq.end()) {
-            coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
-            ++it;
-        }
-        coeffseq.push_back(overall_coeff);
-        return (new mul(coeffseq))->setflag(status_flags::dynallocated);
-    }
-         
-    epvector::const_iterator it=seq.begin();
-    bool coeff_found=0;
-    while (it!=seq.end()) {
-        ex t=recombine_pair_to_ex(*it);
-        ex c=t.coeff(s,n);
-        if (!c.is_zero()) {
-            coeffseq.push_back(c);
-            coeff_found=1;
-        } else {
-            coeffseq.push_back(t);
-        }
-        ++it;
-    }
-    if (coeff_found) {
-        coeffseq.push_back(overall_coeff);
-        return (new mul(coeffseq))->setflag(status_flags::dynallocated);
-    }
-    
-    return _ex0();
+       exvector coeffseq;
+       coeffseq.reserve(seq.size()+1);
+       
+       if (n==0) {
+               // product of individual coeffs
+               // if a non-zero power of s is found, the resulting product will be 0
+               epvector::const_iterator it=seq.begin();
+               while (it!=seq.end()) {
+                       coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
+                       ++it;
+               }
+               coeffseq.push_back(overall_coeff);
+               return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+       }
+                
+       epvector::const_iterator it=seq.begin();
+       bool coeff_found=0;
+       while (it!=seq.end()) {
+               ex t=recombine_pair_to_ex(*it);
+               ex c=t.coeff(s,n);
+               if (!c.is_zero()) {
+                       coeffseq.push_back(c);
+                       coeff_found=1;
+               } else {
+                       coeffseq.push_back(t);
+               }
+               ++it;
+       }
+       if (coeff_found) {
+               coeffseq.push_back(overall_coeff);
+               return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+       }
+       
+       return _ex0();
 }
 
 ex mul::eval(int level) const
 {
-    // simplifications  *(...,x;0) -> 0
-    //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
-    //                  *(x;1) -> x
-    //                  *(;c) -> c
+       // simplifications  *(...,x;0) -> 0
+       //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
+       //                  *(x;1) -> x
+       //                  *(;c) -> c
 
-    debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
+       debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 
-    epvector * evaled_seqp=evalchildren(level);
-    if (evaled_seqp!=0) {
-        // do more evaluation later
-        return (new mul(evaled_seqp,overall_coeff))->
-                   setflag(status_flags::dynallocated);
-    }
+       epvector * evaled_seqp=evalchildren(level);
+       if (evaled_seqp!=0) {
+               // do more evaluation later
+               return (new mul(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,mul))||
-               (!(ex_to_numeric((*cit).coeff).is_integer())));
-        GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
-        if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
-            printtree(cerr,0);
-        }
-        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));
-        GINAC_ASSERT(p.rest.is_equal((*cit).rest));
-        GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
-        /* end paranoia */
-    }
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
+                          (!(ex_to_numeric((*cit).coeff).is_integer())));
+               GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
+               if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
+                       printtree(cerr,0);
+               }
+               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));
+               GINAC_ASSERT(p.rest.is_equal((*cit).rest));
+               GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
+               /* end paranoia */
+       }
 #endif // def DO_GINAC_ASSERT
 
-    if (flags & status_flags::evaluated) {
-        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(_ex0())) {
-        // *(...,x;0) -> 0
-        return _ex0();
-    } else if (seq_size==0) {
-        // *(;c) -> c
-        return overall_coeff;
-    } 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(_num1())) {
-        // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
-        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) {
-            distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
-                                   overall_coeff));
-        }
-        return (new add(distrseq,
-                        ex_to_numeric(addref.overall_coeff).
-                        mul_dyn(ex_to_numeric(overall_coeff))))
-            ->setflag(status_flags::dynallocated |
-                      status_flags::evaluated );
-    }
-    return this->hold();
+       if (flags & status_flags::evaluated) {
+               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(_ex0())) {
+               // *(...,x;0) -> 0
+               return _ex0();
+       } else if (seq_size==0) {
+               // *(;c) -> c
+               return overall_coeff;
+       } 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(_num1())) {
+               // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
+               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) {
+                       distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
+               }
+               return (new add(distrseq,
+                               ex_to_numeric(addref.overall_coeff).
+                               mul_dyn(ex_to_numeric(overall_coeff))))
+                     ->setflag(status_flags::dynallocated | status_flags::evaluated);
+       }
+       return this->hold();
 }
 
 ex mul::evalf(int level) const
 {
-    if (level==1)
-        return mul(seq,overall_coeff);
-    
-    if (level==-max_recursion_level)
-        throw(std::runtime_error("max recursion level reached"));
-    
-    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 mul(s,overall_coeff.evalf(level));
+       if (level==1)
+               return mul(seq,overall_coeff);
+       
+       if (level==-max_recursion_level)
+               throw(std::runtime_error("max recursion level reached"));
+       
+       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 mul(s,overall_coeff.evalf(level));
 }
 
 exvector mul::get_indices(void) const
 {
-    // return union of indices of factors
-    exvector iv;
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        exvector subiv=(*cit).rest.get_indices();
-        iv.reserve(iv.size()+subiv.size());
-        for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
-            iv.push_back(*cit2);
-        }
-    }
-    return iv;
+       // return union of indices of factors
+       exvector iv;
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               exvector subiv=(*cit).rest.get_indices();
+               iv.reserve(iv.size()+subiv.size());
+               for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
+                       iv.push_back(*cit2);
+               }
+       }
+       return iv;
 }
 
 ex mul::simplify_ncmul(const exvector & v) const
 {
-    throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
+       throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 }
 
 // protected
 
-/** Implementation of ex::diff() for a product. It applies the product rule.
+/** 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);
+       exvector addseq;
+       addseq.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 mulseq = seq;
+               mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
+                                            seq[i].rest.diff(s));
+               addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
+       }
+       return (new add(addseq))->setflag(status_flags::dynallocated);
 }
 
 int mul::compare_same_type(const basic & other) const
 {
-    return inherited::compare_same_type(other);
+       return inherited::compare_same_type(other);
 }
 
 bool mul::is_equal_same_type(const basic & other) const
 {
-    return inherited::is_equal_same_type(other);
+       return inherited::is_equal_same_type(other);
 }
 
 unsigned mul::return_type(void) const
 {
-    if (seq.size()==0) {
-        // mul without factors: should not happen, but commutes
-        return return_types::commutative;
-    }
-
-    bool all_commutative = 1;
-    unsigned rt;
-    epvector::const_iterator cit_noncommutative_element; // point to first found nc element
-
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        rt=(*cit).rest.return_type();
-        if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
-        if ((rt==return_types::noncommutative)&&(all_commutative)) {
-            // first nc element found, remember position
-            cit_noncommutative_element = cit;
-            all_commutative = 0;
-        }
-        if ((rt==return_types::noncommutative)&&(!all_commutative)) {
-            // 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;
-            }
-        }
-    }
-    // all factors checked
-    return all_commutative ? return_types::commutative : return_types::noncommutative;
+       if (seq.size()==0) {
+               // mul without factors: should not happen, but commutes
+               return return_types::commutative;
+       }
+
+       bool all_commutative = 1;
+       unsigned rt;
+       epvector::const_iterator cit_noncommutative_element; // point to first found nc element
+
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               rt=(*cit).rest.return_type();
+               if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
+               if ((rt==return_types::noncommutative)&&(all_commutative)) {
+                       // first nc element found, remember position
+                       cit_noncommutative_element = cit;
+                       all_commutative = 0;
+               }
+               if ((rt==return_types::noncommutative)&&(!all_commutative)) {
+                       // 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;
+                       }
+               }
+       }
+       // all factors checked
+       return all_commutative ? return_types::commutative : return_types::noncommutative;
 }
    
 unsigned mul::return_type_tinfo(void) const
 {
-    if (seq.size()==0) {
-        // mul without factors: should not happen
-        return tinfo_key;
-    }
-    // return type_info of first noncommutative element
-    for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-        if ((*cit).rest.return_type()==return_types::noncommutative) {
-            return (*cit).rest.return_type_tinfo();
-        }
-    }
-    // no noncommutative element found, should not happen
-    return tinfo_key;
+       if (seq.size()==0) {
+               // mul without factors: should not happen
+               return tinfo_key;
+       }
+       // return type_info of first noncommutative element
+       for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
+               if ((*cit).rest.return_type()==return_types::noncommutative) {
+                       return (*cit).rest.return_type_tinfo();
+               }
+       }
+       // no noncommutative element found, should not happen
+       return tinfo_key;
 }
 
 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 {
-    return (new mul(v,oc))->setflag(status_flags::dynallocated);
+       return (new mul(v,oc))->setflag(status_flags::dynallocated);
 }
 
 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 {
-    return (new mul(vp,oc))->setflag(status_flags::dynallocated);
+       return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 }
 
 expair mul::split_ex_to_pair(const ex & e) const
 {
-    if (is_ex_exactly_of_type(e,power)) {
-        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,_ex1());
+       if (is_ex_exactly_of_type(e,power)) {
+               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,_ex1());
 }
-    
+       
 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,_ex1())) {
-        return split_ex_to_pair(e);
-    }
-    return split_ex_to_pair(power(e,c));
+       // 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,_ex1()))
+               return split_ex_to_pair(e);
+       
+       return split_ex_to_pair(power(e,c));
 }
-    
+       
 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,_ex1())) {
-        return p;
-    }
-    return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
+       // 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,_ex1()))
+               return p;
+       
+       return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 }
-    
+       
 ex mul::recombine_pair_to_ex(const expair & p) const
 {
-    // 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);
-    }
+       if (ex_to_numeric(p.coeff).is_equal(_num1())) 
+               return p.rest;
+       else
+               return power(p.rest,p.coeff);
 }
 
 bool mul::expair_needs_further_processing(epp it)
 {
-    if (is_ex_exactly_of_type((*it).rest,mul) &&
-        ex_to_numeric((*it).coeff).is_integer()) {
-        // combined pair is product with integer power -> expand it
-        *it=split_ex_to_pair(recombine_pair_to_ex(*it));
-        return true;
-    }
-    if (is_ex_exactly_of_type((*it).rest,numeric)) {
-        expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
-        if (!ep.is_equal(*it)) {
-            // combined pair is a numeric power which can be simplified
-            *it=ep;
-            return true;
-        }
-        if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
-            // combined pair has coeff 1 and must be moved to the end
-            return true;
-        }
-    }
-    return false;
+       if (is_ex_exactly_of_type((*it).rest,mul) &&
+               ex_to_numeric((*it).coeff).is_integer()) {
+               // combined pair is product with integer power -> expand it
+               *it=split_ex_to_pair(recombine_pair_to_ex(*it));
+               return true;
+       }
+       if (is_ex_exactly_of_type((*it).rest,numeric)) {
+               expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
+               if (!ep.is_equal(*it)) {
+                       // combined pair is a numeric power which can be simplified
+                       *it=ep;
+                       return true;
+               }
+               if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
+                       // combined pair has coeff 1 and must be moved to the end
+                       return true;
+               }
+       }
+       return false;
 }       
 
 ex mul::default_overall_coeff(void) const
 {
-    return _ex1();
+       return _ex1();
 }
 
 void mul::combine_overall_coeff(const ex & c)
 {
-    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));
+       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(const ex & c1, const ex & c2)
 {
-    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)));
+       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(const expair & p) const
 {
-    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(_num1());
+       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(_num1());
 }
 
 ex mul::expand(unsigned options) const
 {
-    if (flags & status_flags::expanded)
-        return *this;
-    
-    exvector sub_expanded_seq;
-    intvector positions_of_adds;
-    intvector number_of_add_operands;
-    
-    epvector * expanded_seqp = expandchildren(options);
-    
-    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;
-    
-    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(_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++;
-        }
-        current_position++;
-    }
-    
-    if (number_of_adds==0) {
-        if (expanded_seqp==0) {
-            return this->setflag(status_flags::expanded);
-        }
-        return (new mul(expanded_seqp,overall_coeff))->
-            setflag(status_flags::dynallocated |
-                    status_flags::expanded);
-    }
-    
-    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) {
-        epvector term;
-        term = expanded_seq;
-        for (l=0; l<number_of_adds; l++) {
-            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]));
-        }
-        distrseq.push_back((new mul(term,overall_coeff))->
-                           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;
-    }
-    
-    if (expanded_seqp!=0)
-        delete expanded_seqp;
-    
-    return (new add(distrseq))->setflag(status_flags::dynallocated |
-                                        status_flags::expanded);
+       if (flags & status_flags::expanded)
+               return *this;
+       
+       exvector sub_expanded_seq;
+       intvector positions_of_adds;
+       intvector number_of_add_operands;
+       
+       epvector * expanded_seqp = expandchildren(options);
+       
+       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;
+       
+       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) &&
+                       ((*cit).coeff.is_equal(_ex1()))) {
+                       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;
+               }
+               ++current_position;
+       }
+       
+       if (number_of_adds==0) {
+               if (expanded_seqp==0)
+                       return this->setflag(status_flags::expanded);
+               else
+                       return ((new mul(expanded_seqp,overall_coeff))->
+                              setflag(status_flags::dynallocated | status_flags::expanded));
+       }
+       
+       exvector distrseq;
+       distrseq.reserve(number_of_expanded_terms);
+       
+       intvector k;
+       k.resize(number_of_adds, 0);
+       
+       for (;;) {
+               epvector term;
+               term = expanded_seq;
+               for (int l=0; l<number_of_adds; ++l) {
+                       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]));
+               }
+               distrseq.push_back((new mul(term,overall_coeff))->
+                                   setflag(status_flags::dynallocated | status_flags::expanded));
+               
+               // increment k[]
+               int l = number_of_adds-1;
+               while ((l>=0) && ((++k[l])>=number_of_add_operands[l])) {
+                       k[l] = 0;    
+                       --l;
+               }
+               if (l < 0) break;
+       }
+       
+       if (expanded_seqp!=0)
+               delete expanded_seqp;
+       
+       return (new add(distrseq))->setflag(status_flags::dynallocated |
+                                                                               status_flags::expanded);
 }
 
 //////////
@@ -744,37 +739,37 @@ ex mul::expand(unsigned options) const
 
 epvector * mul::expandchildren(unsigned options) const
 {
-    epvector::const_iterator last = seq.end();
-    epvector::const_iterator cit = seq.begin();
-    while (cit!=last) {
-        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
-            epvector *s=new epvector;
-            s->reserve(seq.size());
-            
-            // copy parts of seq which are known not to have changed
-            epvector::const_iterator cit2 = seq.begin();
-            while (cit2!=cit) {
-                s->push_back(*cit2);
-                ++cit2;
-            }
-            // copy first changed element
-            s->push_back(split_ex_to_pair(expanded_factor));
-            ++cit2;
-            // copy rest
-            while (cit2!=last) {
-                s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
-                ++cit2;
-            }
-            return s;
-        }
-        ++cit;
-    }
-    
-    return 0; // nothing has changed
+       epvector::const_iterator last = seq.end();
+       epvector::const_iterator cit = seq.begin();
+       while (cit!=last) {
+               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
+                       epvector *s=new epvector;
+                       s->reserve(seq.size());
+                       
+                       // copy parts of seq which are known not to have changed
+                       epvector::const_iterator cit2 = seq.begin();
+                       while (cit2!=cit) {
+                               s->push_back(*cit2);
+                               ++cit2;
+                       }
+                       // copy first changed element
+                       s->push_back(split_ex_to_pair(expanded_factor));
+                       ++cit2;
+                       // copy rest
+                       while (cit2!=last) {
+                               s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
+                               ++cit2;
+                       }
+                       return s;
+               }
+               ++cit;
+       }
+       
+       return 0; // nothing has changed
 }
    
 //////////
@@ -791,7 +786,7 @@ unsigned mul::precedence = 50;
 //////////
 
 const mul some_mul;
-const type_info & typeid_mul = typeid(some_mul);
+const std::type_info & typeid_mul = typeid(some_mul);
 
 #ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC