subs() and normal() use maps instead of lists, resulting in a huge performance
[ginac.git] / ginac / mul.cpp
index efabd3b..2c84565 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2003 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
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <vector>
 #include <stdexcept>
+#include <limits>
 
 #include "mul.h"
 #include "add.h"
 #include "power.h"
+#include "operators.h"
+#include "matrix.h"
+#include "lst.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
+// default constructor
 //////////
 
-// public
-
 mul::mul()
 {
-    debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
-    tinfo_key = TINFO_mul;
-}
-
-mul::~mul()
-{
-    debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
-    destroy(0);
-}
-
-mul::mul(const mul & 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;
-}
-
-// protected
-
-void mul::copy(const mul & other)
-{
-    inherited::copy(other);
-}
-
-void mul::destroy(bool call_parent)
-{
-    if (call_parent) inherited::destroy(call_parent);
+       tinfo_key = TINFO_mul;
 }
 
 //////////
@@ -90,663 +55,881 @@ 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());
+       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());
+       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());
+       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());
+       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());
+       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());
+       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());
 }
 
 //////////
 // 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);
-}
+DEFAULT_ARCHIVING(mul)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
-
-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 << ")";
+void mul::print(const print_context & c, unsigned level) const
+{
+       if (is_a<print_tree>(c)) {
+
+               inherited::print(c, level);
+
+       } else if (is_a<print_csrc>(c)) {
+
+               if (precedence() <= level)
+                       c.s << "(";
+
+               if (!overall_coeff.is_equal(_ex1)) {
+                       overall_coeff.print(c, precedence());
+                       c.s << "*";
+               }
+
+               // Print arguments, separated by "*" or "/"
+               epvector::const_iterator it = seq.begin(), itend = seq.end();
+               while (it != itend) {
+
+                       // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
+                       bool needclosingparenthesis = false;
+                       if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
+                               if (is_a<print_csrc_cl_N>(c)) {
+                                       c.s << "recip(";
+                                       needclosingparenthesis = true;
+                               } else
+                                       c.s << "1.0/";
+                       }
+
+                       // If the exponent is 1 or -1, it is left out
+                       if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
+                               it->rest.print(c, precedence());
+                       else if (it->coeff.info(info_flags::negint))
+                               // Outer parens around ex needed for broken GCC parser:
+                               (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
+                       else
+                               // Outer parens around ex needed for broken GCC parser:
+                               (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
+
+                       if (needclosingparenthesis)
+                               c.s << ")";
+
+                       // Separator is "/" for negative integer powers, "*" otherwise
+                       ++it;
+                       if (it != itend) {
+                               if (it->coeff.info(info_flags::negint))
+                                       c.s << "/";
+                               else
+                                       c.s << "*";
+                       }
+               }
+
+               if (precedence() <= level)
+                       c.s << ")";
+
+       } else if (is_a<print_python_repr>(c)) {
+               c.s << class_name() << '(';
+               op(0).print(c);
+               for (size_t i=1; i<nops(); ++i) {
+                       c.s << ',';
+                       op(i).print(c);
+               }
+               c.s << ')';
+       } else {
+
+               if (precedence() <= level) {
+                       if (is_a<print_latex>(c))
+                               c.s << "{(";
+                       else
+                               c.s << "(";
+               }
+
+               // First print the overall numeric coefficient
+               const numeric &coeff = ex_to<numeric>(overall_coeff);
+               if (coeff.csgn() == -1)
+                       c.s << '-';
+               if (!coeff.is_equal(_num1) &&
+                       !coeff.is_equal(_num_1)) {
+                       if (coeff.is_rational()) {
+                               if (coeff.is_negative())
+                                       (-coeff).print(c);
+                               else
+                                       coeff.print(c);
+                       } else {
+                               if (coeff.csgn() == -1)
+                                       (-coeff).print(c, precedence());
+                               else
+                                       coeff.print(c, precedence());
+                       }
+                       if (is_a<print_latex>(c))
+                               c.s << ' ';
+                       else
+                               c.s << '*';
+               }
+
+               // Then proceed with the remaining factors
+               epvector::const_iterator it = seq.begin(), itend = seq.end();
+               if (is_a<print_latex>(c)) {
+
+                       // Separate factors into those with negative numeric exponent
+                       // and all others
+                       exvector neg_powers, others;
+                       while (it != itend) {
+                               GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
+                               if (ex_to<numeric>(it->coeff).is_negative())
+                                       neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
+                               else
+                                       others.push_back(recombine_pair_to_ex(*it));
+                               ++it;
+                       }
+
+                       if (!neg_powers.empty()) {
+
+                               // Factors with negative exponent are printed as a fraction
+                               c.s << "\\frac{";
+                               mul(others).eval().print(c);
+                               c.s << "}{";
+                               mul(neg_powers).eval().print(c);
+                               c.s << "}";
+
+                       } else {
+
+                               // All other factors are printed in the ordinary way
+                               exvector::const_iterator vit = others.begin(), vitend = others.end();
+                               while (vit != vitend) {
+                                       c.s << ' ';
+                                       vit->print(c, precedence());
+                                       ++vit;
+                               }
+                       }
+
+               } else {
+
+                       bool first = true;
+                       while (it != itend) {
+                               if (!first)
+                                       c.s << '*';
+                               else
+                                       first = false;
+                               recombine_pair_to_ex(*it).print(c, precedence());
+                               ++it;
+                       }
+               }
+
+               if (precedence() <= level) {
+                       if (is_a<print_latex>(c))
+                               c.s << ")}";
+                       else
+                               c.s << ")";
+               }
+       }
 }
 
 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;
-
-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 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;
-}
-
-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();
-}
-
+       switch (inf) {
+               case info_flags::polynomial:
+               case info_flags::integer_polynomial:
+               case info_flags::cinteger_polynomial:
+               case info_flags::rational_polynomial:
+               case info_flags::crational_polynomial:
+               case info_flags::rational_function: {
+                       epvector::const_iterator i = seq.begin(), end = seq.end();
+                       while (i != end) {
+                               if (!(recombine_pair_to_ex(*i).info(inf)))
+                                       return false;
+                               ++i;
+                       }
+                       return overall_coeff.info(inf);
+               }
+               case info_flags::algebraic: {
+                       epvector::const_iterator i = seq.begin(), end = seq.end();
+                       while (i != end) {
+                               if ((recombine_pair_to_ex(*i).info(inf)))
+                                       return true;
+                               ++i;
+                       }
+                       return false;
+               }
+       }
+       return inherited::info(inf);
+}
+
+int mul::degree(const ex & s) const
+{
+       // Sum up degrees of factors
+       int deg_sum = 0;
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               if (ex_to<numeric>(i->coeff).is_integer())
+                       deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
+               ++i;
+       }
+       return deg_sum;
+}
+
+int mul::ldegree(const ex & s) const
+{
+       // Sum up degrees of factors
+       int deg_sum = 0;
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               if (ex_to<numeric>(i->coeff).is_integer())
+                       deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
+               ++i;
+       }
+       return deg_sum;
+}
+
+ex mul::coeff(const ex & 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 i = seq.begin(), end = seq.end();
+               while (i != end) {
+                       coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
+                       ++i;
+               }
+               coeffseq.push_back(overall_coeff);
+               return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+       }
+       
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       bool coeff_found = false;
+       while (i != end) {
+               ex t = recombine_pair_to_ex(*i);
+               ex c = t.coeff(s, n);
+               if (!c.is_zero()) {
+                       coeffseq.push_back(c);
+                       coeff_found = 1;
+               } else {
+                       coeffseq.push_back(t);
+               }
+               ++i;
+       }
+       if (coeff_found) {
+               coeffseq.push_back(overall_coeff);
+               return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+       }
+       
+       return _ex0;
+}
+
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ *  stand for such expressions that contain a plain number.
+ *  - *(...,x;0) -> 0
+ *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
+ *  - *(x;1) -> x
+ *  - *(;c) -> c
+ *
+ *  @param level cut-off in recursive evaluation */
 ex mul::eval(int level) const
 {
-    // simplifications  *(...,x;0) -> 0
-    //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
-    //                  *(x;1) -> x
-    //                  *(;c) -> c
-
-    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) {
+               // 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 */
-    }
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
+                            (!(ex_to<numeric>(i->coeff).is_integer())));
+               GINAC_ASSERT(!(i->is_canonical_numeric()));
+               if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
+                   print(print_tree(std::cerr));
+               GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
+               /* for paranoia */
+               expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
+               GINAC_ASSERT(p.rest.is_equal(i->rest));
+               GINAC_ASSERT(p.coeff.is_equal(i->coeff));
+               /* end paranoia */
+               ++i;
+       }
 #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_zero()) {
+               // *(...,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_exactly_a<add>((*seq.begin()).rest) &&
+                  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 = new epvector();
+               distrseq->reserve(addref.seq.size());
+               epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
+               while (i != end) {
+                       distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
+                       ++i;
+               }
+               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));
-}
-
-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;
-}
-
-ex mul::simplify_ncmul(const exvector & v) const
-{
-    throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
+       if (level==1)
+               return mul(seq,overall_coeff);
+       
+       if (level==-max_recursion_level)
+               throw(std::runtime_error("max recursion level reached"));
+       
+       epvector *s = new epvector();
+       s->reserve(seq.size());
+
+       --level;
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
+                                                          i->coeff));
+               ++i;
+       }
+       return mul(s, overall_coeff.evalf(level));
+}
+
+ex mul::evalm() const
+{
+       // numeric*matrix
+       if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
+        && is_a<matrix>(seq[0].rest))
+               return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
+
+       // Evaluate children first, look whether there are any matrices at all
+       // (there can be either no matrices or one matrix; if there were more
+       // than one matrix, it would be a non-commutative product)
+       epvector *s = new epvector;
+       s->reserve(seq.size());
+
+       bool have_matrix = false;
+       epvector::iterator the_matrix;
+
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               const ex &m = recombine_pair_to_ex(*i).evalm();
+               s->push_back(split_ex_to_pair(m));
+               if (is_a<matrix>(m)) {
+                       have_matrix = true;
+                       the_matrix = s->end() - 1;
+               }
+               ++i;
+       }
+
+       if (have_matrix) {
+
+               // The product contained a matrix. We will multiply all other factors
+               // into that matrix.
+               matrix m = ex_to<matrix>(the_matrix->rest);
+               s->erase(the_matrix);
+               ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+               return m.mul_scalar(scalar);
+
+       } else
+               return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+}
+
+ex mul::eval_ncmul(const exvector & v) const
+{
+       if (seq.empty())
+               return inherited::eval_ncmul(v);
+
+       // Find first noncommutative element and call its eval_ncmul()
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               if (i->rest.return_type() == return_types::noncommutative)
+                       return i->rest.eval_ncmul(v);
+               ++i;
+       }
+       return inherited::eval_ncmul(v);
+}
+
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, lst & repls)
+{      
+       ex origbase;
+       int origexponent;
+       int origexpsign;
+
+       if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
+               origbase = origfactor.op(0);
+               int expon = ex_to<numeric>(origfactor.op(1)).to_int();
+               origexponent = expon > 0 ? expon : -expon;
+               origexpsign = expon > 0 ? 1 : -1;
+       } else {
+               origbase = origfactor;
+               origexponent = 1;
+               origexpsign = 1;
+       }
+
+       ex patternbase;
+       int patternexponent;
+       int patternexpsign;
+
+       if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
+               patternbase = patternfactor.op(0);
+               int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
+               patternexponent = expon > 0 ? expon : -expon;
+               patternexpsign = expon > 0 ? 1 : -1;
+       } else {
+               patternbase = patternfactor;
+               patternexponent = 1;
+               patternexpsign = 1;
+       }
+
+       lst saverepls = repls;
+       if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
+               return false;
+       repls = saverepls;
+
+       int newnummatches = origexponent / patternexponent;
+       if (newnummatches < nummatches)
+               nummatches = newnummatches;
+       return true;
+}
+
+ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
+{      
+       std::vector<bool> subsed(seq.size(), false);
+       exvector subsresult(seq.size());
+
+       for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+
+               if (is_exactly_a<mul>(it->first)) {
+
+                       int nummatches = std::numeric_limits<int>::max();
+                       std::vector<bool> currsubsed(seq.size(), false);
+                       bool succeed = true;
+                       lst repls;
+
+                       for (size_t j=0; j<it->first.nops(); j++) {
+                               bool found=false;
+                               for (size_t k=0; k<nops(); k++) {
+                                       if (currsubsed[k] || subsed[k])
+                                               continue;
+                                       if (tryfactsubs(op(k), it->first.op(j), nummatches, repls)) {
+                                               currsubsed[k] = true;
+                                               found = true;
+                                               break;
+                                       }
+                               }
+                               if (!found) {
+                                       succeed = false;
+                                       break;
+                               }
+                       }
+                       if (!succeed)
+                               continue;
+
+                       bool foundfirstsubsedfactor = false;
+                       for (size_t j=0; j<subsed.size(); j++) {
+                               if (currsubsed[j]) {
+                                       if (foundfirstsubsedfactor)
+                                               subsresult[j] = op(j);
+                                       else {
+                                               foundfirstsubsedfactor = true;
+                                               subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches);
+                                       }
+                                       subsed[j] = true;
+                               }
+                       }
+
+               } else {
+
+                       int nummatches = std::numeric_limits<int>::max();
+                       lst repls;
+
+                       for (size_t j=0; j<this->nops(); j++) {
+                               if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)) {
+                                       subsed[j] = true;
+                                       subsresult[j] = op(j) * power(it->second.subs(ex(repls), subs_options::subs_no_pattern) / it->first.subs(ex(repls), subs_options::subs_no_pattern), nummatches);
+                               }
+                       }
+               }
+       }
+
+       bool subsfound = false;
+       for (size_t i=0; i<subsed.size(); i++) {
+               if (subsed[i]) {
+                       subsfound = true;
+                       break;
+               }
+       }
+       if (!subsfound)
+               return subs_one_level(m, options | subs_options::subs_algebraic);
+
+       exvector ev; ev.reserve(nops());
+       for (size_t i=0; i<nops(); i++) {
+               if (subsed[i])
+                       ev.push_back(subsresult[i]);
+               else
+                       ev.push_back(op(i));
+       }
+
+       return (new mul(ev))->setflag(status_flags::dynallocated);
 }
 
 // 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);
+       size_t num = seq.size();
+       exvector addseq;
+       addseq.reserve(num);
+       
+       // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
+       epvector mulseq = seq;
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       epvector::iterator i2 = mulseq.begin();
+       while (i != end) {
+               expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
+                                            i->rest.diff(s));
+               ep.swap(*i2);
+               addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
+               ep.swap(*i2);
+               ++i; ++i2;
+       }
+       return (new add(addseq))->setflag(status_flags::dynallocated);
 }
 
 int mul::compare_same_type(const basic & other) const
 {
-    return inherited::compare_same_type(other);
-}
-
-bool mul::is_equal_same_type(const basic & other) const
-{
-    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;
+       return inherited::compare_same_type(other);
+}
+
+unsigned mul::return_type() const
+{
+       if (seq.empty()) {
+               // mul without factors: should not happen, but commutes
+               return return_types::commutative;
+       }
+       
+       bool all_commutative = true;
+       epvector::const_iterator noncommutative_element; // point to first found nc element
+       
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               unsigned rt = i->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
+                       noncommutative_element = i;
+                       all_commutative = false;
+               }
+               if ((rt == return_types::noncommutative) && (!all_commutative)) {
+                       // another nc element found, compare type_infos
+                       if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
+                               // diffent types -> mul is ncc
+                               return return_types::noncommutative_composite;
+                       }
+               }
+               ++i;
+       }
+       // 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;
+unsigned mul::return_type_tinfo() const
+{
+       if (seq.empty())
+               return tinfo_key;  // mul without factors: should not happen
+       
+       // return type_info of first noncommutative element
+       epvector::const_iterator i = seq.begin(), end = seq.end();
+       while (i != end) {
+               if (i->rest.return_type() == return_types::noncommutative)
+                       return i->rest.return_type_tinfo();
+               ++i;
+       }
+       // 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_exactly_a<power>(e)) {
+               const power & powerref = ex_to<power>(e);
+               if (is_exactly_a<numeric>(powerref.exponent))
+                       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 evaluate
+       // expression like (4^(1/3))^(3/2)
+       if (c.is_equal(_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 evaluate
+       // expression like (4^(1/3))^(3/2)
+       if (c.is_equal(_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 (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 }
 
 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_exactly_a<mul>(it->rest) &&
+               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_exactly_a<numeric>(it->rest)) {
+               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 (it->coeff.is_equal(_ex1)) {
+                       // combined pair has coeff 1 and must be moved to the end
+                       return true;
+               }
+       }
+       return false;
 }       
 
-ex mul::default_overall_coeff(void) const
+ex mul::default_overall_coeff() 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_exactly_a<numeric>(overall_coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c));
+       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_exactly_a<numeric>(overall_coeff));
+       GINAC_ASSERT(is_exactly_a<numeric>(c1));
+       GINAC_ASSERT(is_exactly_a<numeric>(c2));
+       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_exactly_a<numeric>(p.coeff));
+       // 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
 {
-    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]));
-        }
-        /*
-        cout << "mul::expand() term begin" << endl;
-        for (epvector::const_iterator cit=term.begin(); cit!=term.end(); ++cit) {
-            cout << "rest" << endl;
-            (*cit).rest.printtree(cout);
-            cout << "coeff" << endl;
-            (*cit).coeff.printtree(cout);
-        }
-        cout << "mul::expand() term end" << endl;
-        */
-        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;
-    }
-    /*
-    cout << "mul::expand() distrseq begin" << endl;
-    for (exvector::const_iterator cit=distrseq.begin(); cit!=distrseq.end(); ++cit) {
-        (*cit).printtree(cout);
-    }
-    cout << "mul::expand() distrseq end" << endl;
-    */
-
-    return (new add(distrseq))->setflag(status_flags::dynallocated |
-                                        status_flags::expanded);
-}
-
+       // First, expand the children
+       epvector * expanded_seqp = expandchildren(options);
+       const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
+
+       // Now, look for all the factors that are sums and multiply each one out
+       // with the next one that is found while collecting the factors which are
+       // not sums
+       int number_of_adds = 0;
+       ex last_expanded = _ex1;
+       epvector non_adds;
+       non_adds.reserve(expanded_seq.size());
+       epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
+       while (cit != last) {
+               if (is_exactly_a<add>(cit->rest) &&
+                       (cit->coeff.is_equal(_ex1))) {
+                       ++number_of_adds;
+                       if (is_exactly_a<add>(last_expanded)) {
+
+                               // Expand a product of two sums, aggressive version.
+                               // Caring for the overall coefficients in separate loops can
+                               // sometimes give a performance gain of up to 15%!
+
+                               const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
+                               // add2 is for the inner loop and should be the bigger of the two sums
+                               // in the presence of asymptotically good sorting:
+                               const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
+                               const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
+                               const epvector::const_iterator add1begin = add1.seq.begin();
+                               const epvector::const_iterator add1end   = add1.seq.end();
+                               const epvector::const_iterator add2begin = add2.seq.begin();
+                               const epvector::const_iterator add2end   = add2.seq.end();
+                               epvector distrseq;
+                               distrseq.reserve(add1.seq.size()+add2.seq.size());
+                               // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
+                               if (!add1.overall_coeff.is_zero()) {
+                                       if (add1.overall_coeff.is_equal(_ex1))
+                                               distrseq.insert(distrseq.end(),add2begin,add2end);
+                                       else
+                                               for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
+                                                       distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
+                               }
+                               // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
+                               if (!add2.overall_coeff.is_zero()) {
+                                       if (add2.overall_coeff.is_equal(_ex1))
+                                               distrseq.insert(distrseq.end(),add1begin,add1end);
+                                       else
+                                               for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
+                                                       distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
+                               }
+                               // Compute the new overall coefficient and put it together:
+                               ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
+                               // Multiply explicitly all non-numeric terms of add1 and add2:
+                               for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+                                       // We really have to combine terms here in order to compactify
+                                       // the result.  Otherwise it would become waayy tooo bigg.
+                                       numeric oc;
+                                       distrseq.clear();
+                                       for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+                                               // Don't push_back expairs which might have a rest that evaluates to a numeric,
+                                               // since that would violate an invariant of expairseq:
+                                               const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
+                                               if (is_exactly_a<numeric>(rest))
+                                                       oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
+                                               else
+                                                       distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
+                                       }
+                                       tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
+                               }
+                               last_expanded = tmp_accu;
+
+                       } else {
+                               non_adds.push_back(split_ex_to_pair(last_expanded));
+                               last_expanded = cit->rest;
+                       }
+               } else {
+                       non_adds.push_back(*cit);
+               }
+               ++cit;
+       }
+       if (expanded_seqp)
+               delete expanded_seqp;
+       
+       // Now the only remaining thing to do is to multiply the factors which
+       // were not sums into the "last_expanded" sum
+       if (is_exactly_a<add>(last_expanded)) {
+               const add & finaladd = ex_to<add>(last_expanded);
+               exvector distrseq;
+               size_t n = finaladd.nops();
+               distrseq.reserve(n);
+               for (size_t i=0; i<n; ++i) {
+                       epvector factors = non_adds;
+                       factors.push_back(split_ex_to_pair(finaladd.op(i)));
+                       distrseq.push_back((new mul(factors, overall_coeff))->
+                                           setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
+               }
+               return ((new add(distrseq))->
+                       setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
+       }
+       non_adds.push_back(split_ex_to_pair(last_expanded));
+       return (new mul(non_adds, overall_coeff))->
+               setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+}
+
+  
 //////////
 // new virtual functions which can be overridden by derived classes
 //////////
@@ -757,57 +940,47 @@ ex mul::expand(unsigned options) const
 // non-virtual functions in this class
 //////////
 
+
+/** Member-wise expand the expairs representing this sequence.  This must be
+ *  overridden from expairseq::expandchildren() and done iteratively in order
+ *  to allow for early cancallations and thus safe memory.
+ *
+ *  @see mul::expand()
+ *  @return pointer to epvector containing expanded representation or zero
+ *  pointer, if sequence is unchanged. */
 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
+       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
 }
-   
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned mul::precedence=50;
-
-
-//////////
-// global constants
-//////////
-
-const mul some_mul;
-const type_info & typeid_mul=typeid(some_mul);
 
-#ifndef NO_NAMESPACE_GINAC
 } // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC