X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=2b404877c9840aa53a071e712aa222e51680533a;hp=63f6381d27c4e960500b0d3b7ab2770576d36aec;hb=e100f94d92d574ea89a817eca8c58c5eb3418821;hpb=bf82f5b1d41738936afe763e1fa6aa347c81ba2c

diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index 63f6381d..2b404877 100644
--- a/ginac/mul.cpp
+++ b/ginac/mul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2015 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
@@ -17,45 +17,52 @@
  *
  *  You should have received a copy of the GNU General Public License
  *  along with this program; if not, write to the Free Software
- *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
+ *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <iostream>
-#include <vector>
-#include <stdexcept>
-
 #include "mul.h"
 #include "add.h"
 #include "power.h"
+#include "operators.h"
 #include "matrix.h"
+#include "indexed.h"
+#include "lst.h"
 #include "archive.h"
 #include "utils.h"
+#include "symbol.h"
+#include "compiler.h"
+
+#include <iostream>
+#include <limits>
+#include <stdexcept>
+#include <vector>
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(mul, expairseq,
+  print_func<print_context>(&mul::do_print).
+  print_func<print_latex>(&mul::do_print_latex).
+  print_func<print_csrc>(&mul::do_print_csrc).
+  print_func<print_tree>(&mul::do_print_tree).
+  print_func<print_python_repr>(&mul::do_print_python_repr))
+
 
 //////////
-// default ctor, dtor, copy ctor, assignment operator and helpers
+// default constructor
 //////////
 
 mul::mul()
 {
-	tinfo_key = TINFO_mul;
 }
 
-DEFAULT_COPY(mul)
-DEFAULT_DESTROY(mul)
-
 //////////
-// other ctors
+// other constructors
 //////////
 
 // public
 
 mul::mul(const ex & lh, const ex & rh)
 {
-	tinfo_key = TINFO_mul;
 	overall_coeff = _ex1;
 	construct_from_2_ex(lh,rh);
 	GINAC_ASSERT(is_canonical());
@@ -63,7 +70,6 @@ mul::mul(const ex & lh, const ex & rh)
 
 mul::mul(const exvector & v)
 {
-	tinfo_key = TINFO_mul;
 	overall_coeff = _ex1;
 	construct_from_exvector(v);
 	GINAC_ASSERT(is_canonical());
@@ -71,33 +77,28 @@ mul::mul(const exvector & v)
 
 mul::mul(const epvector & v)
 {
-	tinfo_key = TINFO_mul;
 	overall_coeff = _ex1;
 	construct_from_epvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(const epvector & v, const ex & oc)
+mul::mul(const epvector & v, const ex & oc, bool do_index_renaming)
 {
-	tinfo_key = TINFO_mul;
 	overall_coeff = oc;
-	construct_from_epvector(v);
+	construct_from_epvector(v, do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
-mul::mul(epvector * vp, const ex & oc)
+mul::mul(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming)
 {
-	tinfo_key = TINFO_mul;
-	GINAC_ASSERT(vp!=0);
+	GINAC_ASSERT(vp.get()!=0);
 	overall_coeff = oc;
-	construct_from_epvector(*vp);
-	delete vp;
+	construct_from_epvector(*vp, do_index_renaming);
 	GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 {
-	tinfo_key = TINFO_mul;
 	exvector factors;
 	factors.reserve(3);
 	factors.push_back(lh);
@@ -112,166 +113,162 @@ mul::mul(const ex & lh, const ex & mh, const ex & rh)
 // archiving
 //////////
 
-DEFAULT_ARCHIVING(mul)
-
 //////////
 // functions overriding virtual functions from base classes
 //////////
 
-// public
-
-void mul::print(const print_context & c, unsigned level) const
+void mul::print_overall_coeff(const print_context & c, const char *mul_sym) 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-2.95 parser:
-				(ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
+	const numeric &coeff = ex_to<numeric>(overall_coeff);
+	if (coeff.csgn() == -1)
+		c.s << '-';
+	if (!coeff.is_equal(*_num1_p) &&
+		!coeff.is_equal(*_num_1_p)) {
+		if (coeff.is_rational()) {
+			if (coeff.is_negative())
+				(-coeff).print(c);
 			else
-				// Outer parens around ex needed for broken gcc-2.95 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 << "*";
-			}
+				coeff.print(c);
+		} else {
+			if (coeff.csgn() == -1)
+				(-coeff).print(c, precedence());
+			else
+				coeff.print(c, precedence());
 		}
+		c.s << mul_sym;
+	}
+}
 
-		if (precedence() <= level)
-			c.s << ")";
+void mul::do_print(const print_context & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << '(';
+
+	print_overall_coeff(c, "*");
+
+	epvector::const_iterator it = seq.begin(), itend = seq.end();
+	bool first = true;
+	while (it != itend) {
+		if (!first)
+			c.s << '*';
+		else
+			first = false;
+		recombine_pair_to_ex(*it).print(c, precedence());
+		++it;
+	}
 
-	} else if (is_a<print_python_repr>(c)) {
-		c.s << class_name() << '(';
-		op(0).print(c);
-		for (unsigned i=1; i<nops(); ++i) {
-			c.s << ',';
-			op(i).print(c);
-		}
+	if (precedence() <= level)
 		c.s << ')';
-	} else {
+}
 
-		if (precedence() <= level) {
-			if (is_a<print_latex>(c))
-				c.s << "{(";
-			else
-				c.s << "(";
-		}
-
-		// First print the overall numeric coefficient
-		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 << '*';
-		}
+void mul::do_print_latex(const print_latex & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << "{(";
+
+	print_overall_coeff(c, " ");
+
+	// Separate factors into those with negative numeric exponent
+	// and all others
+	epvector::const_iterator it = seq.begin(), itend = seq.end();
+	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;
+	}
 
-		// Then proceed with the remaining factors
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
-		if (is_a<print_latex>(c)) {
+	if (!neg_powers.empty()) {
 
-			// 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;
-			}
+		// 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 << "}";
 
-			if (!neg_powers.empty()) {
+	} else {
 
-				// 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 << "}";
+		// 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 {
+	if (precedence() <= level)
+		c.s << ")}";
+}
 
-				// 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;
-				}
-			}
+void mul::do_print_csrc(const print_csrc & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << "(";
 
-		} else {
+	if (!overall_coeff.is_equal(_ex1)) {
+		if (overall_coeff.is_equal(_ex_1))
+			c.s << "-";
+		else {
+			overall_coeff.print(c, precedence());
+			c.s << "*";
+		}
+	}
 
-			bool first = true;
-			while (it != itend) {
-				if (!first)
-					c.s << '*';
-				else
-					first = false;
-				recombine_pair_to_ex(*it).print(c, precedence());
-				++it;
-			}
+	// 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 (precedence() <= level) {
-			if (is_a<print_latex>(c))
-				c.s << ")}";
+		// 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 << ")";
+				c.s << "*";
 		}
 	}
+
+	if (precedence() <= level)
+		c.s << ")";
+}
+
+void mul::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+	c.s << class_name() << '(';
+	op(0).print(c);
+	for (size_t i=1; i<nops(); ++i) {
+		c.s << ',';
+		op(i).print(c);
+	}
+	c.s << ')';
 }
 
 bool mul::info(unsigned inf) const
@@ -281,6 +278,12 @@ bool mul::info(unsigned inf) const
 		case info_flags::integer_polynomial:
 		case info_flags::cinteger_polynomial:
 		case info_flags::rational_polynomial:
+		case info_flags::real:
+		case info_flags::rational:
+		case info_flags::integer:
+		case info_flags::crational:
+		case info_flags::cinteger:
+		case info_flags::even:
 		case info_flags::crational_polynomial:
 		case info_flags::rational_function: {
 			epvector::const_iterator i = seq.begin(), end = seq.end();
@@ -289,6 +292,8 @@ bool mul::info(unsigned inf) const
 					return false;
 				++i;
 			}
+			if (overall_coeff.is_equal(*_num1_p) && inf == info_flags::even)
+				return true;
 			return overall_coeff.info(inf);
 		}
 		case info_flags::algebraic: {
@@ -300,10 +305,114 @@ bool mul::info(unsigned inf) const
 			}
 			return false;
 		}
+		case info_flags::positive:
+		case info_flags::negative: {
+			if ((inf==info_flags::positive) && (flags & status_flags::is_positive))
+				return true;
+			else if ((inf==info_flags::negative) && (flags & status_flags::is_negative))
+				return true;
+			if (flags & status_flags::purely_indefinite)
+				return false;
+
+			bool pos = true;
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
+				const ex& factor = recombine_pair_to_ex(*i++);
+				if (factor.info(info_flags::positive))
+					continue;
+				else if (factor.info(info_flags::negative))
+					pos = !pos;
+				else
+					return false;
+			}
+			if (overall_coeff.info(info_flags::negative))
+				pos = !pos;
+			setflag(pos ? status_flags::is_positive : status_flags::is_negative);
+			return (inf == info_flags::positive? pos : !pos);
+		}
+		case info_flags::nonnegative: {
+			if  (flags & status_flags::is_positive)
+				return true;
+			bool pos = true;
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
+				const ex& factor = recombine_pair_to_ex(*i++);
+				if (factor.info(info_flags::nonnegative) || factor.info(info_flags::positive))
+					continue;
+				else if (factor.info(info_flags::negative))
+					pos = !pos;
+				else
+					return false;
+			}
+			return (overall_coeff.info(info_flags::negative)? !pos : pos);
+		}
+		case info_flags::posint:
+		case info_flags::negint: {
+			bool pos = true;
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
+				const ex& factor = recombine_pair_to_ex(*i++);
+				if (factor.info(info_flags::posint))
+					continue;
+				else if (factor.info(info_flags::negint))
+					pos = !pos;
+				else
+					return false;
+			}
+			if (overall_coeff.info(info_flags::negint))
+				pos = !pos;
+			else if (!overall_coeff.info(info_flags::posint))
+				return false;
+			return (inf ==info_flags::posint? pos : !pos); 
+		}
+		case info_flags::nonnegint: {
+			bool pos = true;
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
+				const ex& factor = recombine_pair_to_ex(*i++);
+				if (factor.info(info_flags::nonnegint) || factor.info(info_flags::posint))
+					continue;
+				else if (factor.info(info_flags::negint))
+					pos = !pos;
+				else
+					return false;
+			}
+			if (overall_coeff.info(info_flags::negint))
+				pos = !pos;
+			else if (!overall_coeff.info(info_flags::posint))
+				return false;
+			return pos; 
+		}
+		case info_flags::indefinite: {
+			if (flags & status_flags::purely_indefinite)
+				return true;
+			if (flags & (status_flags::is_positive | status_flags::is_negative))
+				return false;
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
+				const ex& term = recombine_pair_to_ex(*i);
+				if (term.info(info_flags::positive) || term.info(info_flags::negative))
+					return false;
+				++i;
+			}
+			setflag(status_flags::purely_indefinite);
+			return true;
+		}
 	}
 	return inherited::info(inf);
 }
 
+bool mul::is_polynomial(const ex & var) const
+{
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+		if (!i->rest.is_polynomial(var) ||
+		    (i->rest.has(var) && !i->coeff.info(info_flags::nonnegint))) {
+			return false;
+		}
+	}
+	return true;
+}
+
 int mul::degree(const ex & s) const
 {
 	// Sum up degrees of factors
@@ -311,7 +420,11 @@ int mul::degree(const ex & s) const
 	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();
+			deg_sum += recombine_pair_to_ex(*i).degree(s);
+		else {
+			if (i->rest.has(s))
+				throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
+		}
 		++i;
 	}
 	return deg_sum;
@@ -324,7 +437,11 @@ int mul::ldegree(const ex & s) const
 	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();
+			deg_sum += recombine_pair_to_ex(*i).ldegree(s);
+		else {
+			if (i->rest.has(s))
+				throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
+		}
 		++i;
 	}
 	return deg_sum;
@@ -379,38 +496,20 @@ ex mul::coeff(const ex & s, int n) const
  *  @param level cut-off in recursive evaluation */
 ex mul::eval(int level) const
 {
-	epvector *evaled_seqp = evalchildren(level);
-	if (evaled_seqp) {
+	std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
+	if (evaled_seqp.get()) {
 		// do more evaluation later
-		return (new mul(evaled_seqp,overall_coeff))->
+		return (new mul(evaled_seqp, overall_coeff))->
 		           setflag(status_flags::dynallocated);
 	}
 	
-#ifdef DO_GINAC_ASSERT
-	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_ex_exactly_of_type(recombine_pair_to_ex(*i), numeric))
-		    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();
+	size_t seq_size = seq.size();
 	if (overall_coeff.is_zero()) {
 		// *(...,x;0) -> 0
 		return _ex0;
@@ -421,11 +520,11 @@ ex mul::eval(int level) const
 		// *(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)) {
+	           is_exactly_a<add>((*seq.begin()).rest) &&
+	           ex_to<numeric>((*seq.begin()).coeff).is_equal(*_num1_p)) {
 		// *(+(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();
+		std::auto_ptr<epvector> distrseq(new epvector);
 		distrseq->reserve(addref.seq.size());
 		epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 		while (i != end) {
@@ -434,9 +533,80 @@ ex mul::eval(int level) const
 		}
 		return (new add(distrseq,
 		                ex_to<numeric>(addref.overall_coeff).
-		                mul_dyn(ex_to<numeric>(overall_coeff))))
-		      ->setflag(status_flags::dynallocated | status_flags::evaluated);
+		                mul_dyn(ex_to<numeric>(overall_coeff)))
+		       )->setflag(status_flags::dynallocated | status_flags::evaluated);
+	} else if ((seq_size >= 2) && (! (flags & status_flags::expanded))) {
+		// Strip the content and the unit part from each term. Thus
+		// things like (-x+a)*(3*x-3*a) automagically turn into - 3*(x-a)^2
+
+		epvector::const_iterator last = seq.end();
+		epvector::const_iterator i = seq.begin();
+		epvector::const_iterator j = seq.begin();
+		std::auto_ptr<epvector> s(new epvector);
+		numeric oc = *_num1_p;
+		bool something_changed = false;
+		while (i!=last) {
+			if (likely(! (is_a<add>(i->rest) && i->coeff.is_equal(_ex1)))) {
+				// power::eval has such a rule, no need to handle powers here
+				++i;
+				continue;
+			}
+
+			// XXX: What is the best way to check if the polynomial is a primitive? 
+			numeric c = i->rest.integer_content();
+			const numeric lead_coeff =
+				ex_to<numeric>(ex_to<add>(i->rest).seq.begin()->coeff).div(c);
+			const bool canonicalizable = lead_coeff.is_integer();
+
+			// XXX: The main variable is chosen in a random way, so this code 
+			// does NOT transform the term into the canonical form (thus, in some
+			// very unlucky event it can even loop forever). Hopefully the main
+			// variable will be the same for all terms in *this
+			const bool unit_normal = lead_coeff.is_pos_integer();
+			if (likely((c == *_num1_p) && ((! canonicalizable) || unit_normal))) {
+				++i;
+				continue;
+			}
+
+			if (! something_changed) {
+				s->reserve(seq_size);
+				something_changed = true;
+			}
+
+			while ((j!=i) && (j!=last)) {
+				s->push_back(*j);
+				++j;
+			}
+
+			if (! unit_normal)
+				c = c.mul(*_num_1_p);
+
+			oc = oc.mul(c);
+
+			// divide add by the number in place to save at least 2 .eval() calls
+			const add& addref = ex_to<add>(i->rest);
+			add* primitive = new add(addref);
+			primitive->setflag(status_flags::dynallocated);
+			primitive->clearflag(status_flags::hash_calculated);
+			primitive->overall_coeff = ex_to<numeric>(primitive->overall_coeff).div_dyn(c);
+			for (epvector::iterator ai = primitive->seq.begin(); ai != primitive->seq.end(); ++ai)
+				ai->coeff = ex_to<numeric>(ai->coeff).div_dyn(c);
+			
+			s->push_back(expair(*primitive, _ex1));
+
+			++i;
+			++j;
+		}
+		if (something_changed) {
+			while (j!=last) {
+				s->push_back(*j);
+				++j;
+			}
+			return (new mul(s, ex_to<numeric>(overall_coeff).mul_dyn(oc))
+			       )->setflag(status_flags::dynallocated);
+		}
 	}
+
 	return this->hold();
 }
 
@@ -448,7 +618,7 @@ ex mul::evalf(int level) const
 	if (level==-max_recursion_level)
 		throw(std::runtime_error("max recursion level reached"));
 	
-	epvector *s = new epvector();
+	std::auto_ptr<epvector> s(new epvector);
 	s->reserve(seq.size());
 
 	--level;
@@ -461,17 +631,52 @@ ex mul::evalf(int level) const
 	return mul(s, overall_coeff.evalf(level));
 }
 
-ex mul::evalm(void) const
+void mul::find_real_imag(ex & rp, ex & ip) const
+{
+	rp = overall_coeff.real_part();
+	ip = overall_coeff.imag_part();
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+		ex factor = recombine_pair_to_ex(*i);
+		ex new_rp = factor.real_part();
+		ex new_ip = factor.imag_part();
+		if(new_ip.is_zero()) {
+			rp *= new_rp;
+			ip *= new_rp;
+		} else {
+			ex temp = rp*new_rp - ip*new_ip;
+			ip = ip*new_rp + rp*new_ip;
+			rp = temp;
+		}
+	}
+	rp = rp.expand();
+	ip = ip.expand();
+}
+
+ex mul::real_part() const
+{
+	ex rp, ip;
+	find_real_imag(rp, ip);
+	return rp;
+}
+
+ex mul::imag_part() const
+{
+	ex rp, ip;
+	find_real_imag(rp, ip);
+	return ip;
+}
+
+ex mul::evalm() const
 {
 	// numeric*matrix
 	if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
-	 && is_ex_of_type(seq[0].rest, matrix))
+	 && 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;
+	std::auto_ptr<epvector> s(new epvector);
 	s->reserve(seq.size());
 
 	bool have_matrix = false;
@@ -481,7 +686,7 @@ ex mul::evalm(void) const
 	while (i != end) {
 		const ex &m = recombine_pair_to_ex(*i).evalm();
 		s->push_back(split_ex_to_pair(m));
-		if (is_ex_of_type(m, matrix)) {
+		if (is_a<matrix>(m)) {
 			have_matrix = true;
 			the_matrix = s->end() - 1;
 		}
@@ -501,28 +706,217 @@ ex mul::evalm(void) const
 		return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 }
 
-ex mul::simplify_ncmul(const exvector & v) const
+ex mul::eval_ncmul(const exvector & v) const
 {
 	if (seq.empty())
-		return inherited::simplify_ncmul(v);
+		return inherited::eval_ncmul(v);
 
-	// Find first noncommutative element and call its simplify_ncmul()
+	// 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.simplify_ncmul(v);
+			return i->rest.eval_ncmul(v);
 		++i;
 	}
-	return inherited::simplify_ncmul(v);
+	return inherited::eval_ncmul(v);
+}
+
+bool tryfactsubs(const ex & origfactor, const ex & patternfactor, int & nummatches, exmap& 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;
+	}
+
+	exmap 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;
+}
+
+/** Checks whether e matches to the pattern pat and the (possibly to be updated)
+  * list of replacements repls. This matching is in the sense of algebraic
+  * substitutions. Matching starts with pat.op(factor) of the pattern because
+  * the factors before this one have already been matched. The (possibly
+  * updated) number of matches is in nummatches. subsed[i] is true for factors
+  * that already have been replaced by previous substitutions and matched[i]
+  * is true for factors that have been matched by the current match.
+  */
+bool algebraic_match_mul_with_mul(const mul &e, const ex &pat, exmap& repls,
+                                  int factor, int &nummatches, const std::vector<bool> &subsed,
+                                  std::vector<bool> &matched)
+{
+	GINAC_ASSERT(subsed.size() == e.nops());
+	GINAC_ASSERT(matched.size() == e.nops());
+
+	if (factor == (int)pat.nops())
+		return true;
+
+	for (size_t i=0; i<e.nops(); ++i) {
+		if(subsed[i] || matched[i])
+			continue;
+		exmap newrepls = repls;
+		int newnummatches = nummatches;
+		if (tryfactsubs(e.op(i), pat.op(factor), newnummatches, newrepls)) {
+			matched[i] = true;
+			if (algebraic_match_mul_with_mul(e, pat, newrepls, factor+1,
+					newnummatches, subsed, matched)) {
+				repls = newrepls;
+				nummatches = newnummatches;
+				return true;
+			}
+			else
+				matched[i] = false;
+		}
+	}
+
+	return false;
+}
+
+bool mul::has(const ex & pattern, unsigned options) const
+{
+	if(!(options & has_options::algebraic))
+		return basic::has(pattern,options);
+	if(is_a<mul>(pattern)) {
+		exmap repls;
+		int nummatches = std::numeric_limits<int>::max();
+		std::vector<bool> subsed(nops(), false);
+		std::vector<bool> matched(nops(), false);
+		if(algebraic_match_mul_with_mul(*this, pattern, repls, 0, nummatches,
+				subsed, matched))
+			return true;
+	}
+	return basic::has(pattern, options);
 }
 
+ex mul::algebraic_subs_mul(const exmap & m, unsigned options) const
+{	
+	std::vector<bool> subsed(nops(), false);
+	ex divide_by = 1;
+	ex multiply_by = 1;
+
+	for (exmap::const_iterator it = m.begin(); it != m.end(); ++it) {
+
+		if (is_exactly_a<mul>(it->first)) {
+retry1:
+			int nummatches = std::numeric_limits<int>::max();
+			std::vector<bool> currsubsed(nops(), false);
+			exmap repls;
+			
+			if(!algebraic_match_mul_with_mul(*this, it->first, repls, 0, nummatches, subsed, currsubsed))
+				continue;
+
+			for (size_t j=0; j<subsed.size(); j++)
+				if (currsubsed[j])
+					subsed[j] = true;
+			ex subsed_pattern
+				= it->first.subs(repls, subs_options::no_pattern);
+			divide_by *= power(subsed_pattern, nummatches);
+			ex subsed_result
+				= it->second.subs(repls, subs_options::no_pattern);
+			multiply_by *= power(subsed_result, nummatches);
+			goto retry1;
+
+		} else {
+
+			for (size_t j=0; j<this->nops(); j++) {
+				int nummatches = std::numeric_limits<int>::max();
+				exmap repls;
+				if (!subsed[j] && tryfactsubs(op(j), it->first, nummatches, repls)){
+					subsed[j] = true;
+					ex subsed_pattern
+						= it->first.subs(repls, subs_options::no_pattern);
+					divide_by *= power(subsed_pattern, nummatches);
+					ex subsed_result
+						= it->second.subs(repls, subs_options::no_pattern);
+					multiply_by *= power(subsed_result, 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::algebraic);
+
+	return ((*this)/divide_by)*multiply_by;
+}
+
+ex mul::conjugate() const
+{
+	// The base class' method is wrong here because we have to be careful at
+	// branch cuts. power::conjugate takes care of that already, so use it.
+	epvector *newepv = 0;
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+		if (newepv) {
+			newepv->push_back(split_ex_to_pair(recombine_pair_to_ex(*i).conjugate()));
+			continue;
+		}
+		ex x = recombine_pair_to_ex(*i);
+		ex c = x.conjugate();
+		if (c.is_equal(x)) {
+			continue;
+		}
+		newepv = new epvector;
+		newepv->reserve(seq.size());
+		for (epvector::const_iterator j=seq.begin(); j!=i; ++j) {
+			newepv->push_back(*j);
+		}
+		newepv->push_back(split_ex_to_pair(c));
+	}
+	ex x = overall_coeff.conjugate();
+	if (!newepv && are_ex_trivially_equal(x, overall_coeff)) {
+		return *this;
+	}
+	ex result = thisexpairseq(newepv ? *newepv : seq, x);
+	delete newepv;
+	return result;
+}
+
+
 // protected
 
 /** Implementation of ex::diff() for a product.  It applies the product rule.
  *  @see ex::diff */
 ex mul::derivative(const symbol & s) const
 {
-	unsigned num = seq.size();
+	size_t num = seq.size();
 	exvector addseq;
 	addseq.reserve(num);
 	
@@ -546,15 +940,10 @@ 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
+unsigned mul::return_type() const
 {
 	if (seq.empty()) {
-		// mul without factors: should not happen, but commutes
+		// mul without factors: should not happen, but commutates
 		return return_types::commutative;
 	}
 	
@@ -574,8 +963,8 @@ unsigned mul::return_type(void) const
 		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;
+					// different types -> mul is ncc
+					return return_types::noncommutative_composite;
 			}
 		}
 		++i;
@@ -583,11 +972,11 @@ unsigned mul::return_type(void) const
 	// all factors checked
 	return all_commutative ? return_types::commutative : return_types::noncommutative;
 }
-   
-unsigned mul::return_type_tinfo(void) const
+
+return_type_t mul::return_type_tinfo() const
 {
 	if (seq.empty())
-		return tinfo_key;  // mul without factors: should not happen
+		return make_return_type_t<mul>(); // mul without factors: should not happen
 	
 	// return type_info of first noncommutative element
 	epvector::const_iterator i = seq.begin(), end = seq.end();
@@ -597,87 +986,87 @@ unsigned mul::return_type_tinfo(void) const
 		++i;
 	}
 	// no noncommutative element found, should not happen
-	return tinfo_key;
+	return make_return_type_t<mul>();
 }
 
-ex mul::thisexpairseq(const epvector & v, const ex & oc) const
+ex mul::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 {
-	return (new mul(v, oc))->setflag(status_flags::dynallocated);
+	return (new mul(v, oc, do_index_renaming))->setflag(status_flags::dynallocated);
 }
 
-ex mul::thisexpairseq(epvector * vp, const ex & oc) const
+ex mul::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 {
-	return (new mul(vp, oc))->setflag(status_flags::dynallocated);
+	return (new mul(vp, oc, do_index_renaming))->setflag(status_flags::dynallocated);
 }
 
 expair mul::split_ex_to_pair(const ex & e) const
 {
-	if (is_ex_exactly_of_type(e,power)) {
+	if (is_exactly_a<power>(e)) {
 		const power & powerref = ex_to<power>(e);
-		if (is_ex_exactly_of_type(powerref.exponent,numeric))
+		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
+	// otherwise it would be hard to correctly evaluate
 	// expression like (4^(1/3))^(3/2)
-	if (are_ex_trivially_equal(c,_ex1))
+	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
+	// otherwise it would be hard to correctly evaluate
 	// expression like (4^(1/3))^(3/2)
-	if (are_ex_trivially_equal(c,_ex1))
+	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 (ex_to<numeric>(p.coeff).is_equal(_num1)) 
+	if (ex_to<numeric>(p.coeff).is_equal(*_num1_p)) 
 		return p.rest;
 	else
-		return power(p.rest,p.coeff);
+		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()) {
+	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_ex_exactly_of_type((*it).rest,numeric)) {
-		expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
+	if (is_exactly_a<numeric>(it->rest)) {
+		if (it->coeff.is_equal(_ex1)) {
+			// pair has coeff 1 and must be moved to the end
+			return true;
+		}
+		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
+ex mul::default_overall_coeff() const
 {
 	return _ex1;
 }
@@ -703,48 +1092,60 @@ bool mul::can_make_flat(const expair & p) const
 	// 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);
+	return ex_to<numeric>(p.coeff).is_equal(*_num1_p);
+}
+
+bool mul::can_be_further_expanded(const ex & e)
+{
+	if (is_exactly_a<mul>(e)) {
+		for (epvector::const_iterator cit = ex_to<mul>(e).seq.begin(); cit != ex_to<mul>(e).seq.end(); ++cit) {
+			if (is_exactly_a<add>(cit->rest) && cit->coeff.info(info_flags::posint))
+				return true;
+		}
+	} else if (is_exactly_a<power>(e)) {
+		if (is_exactly_a<add>(e.op(0)) && e.op(1).info(info_flags::posint))
+			return true;
+	}
+	return false;
 }
 
 ex mul::expand(unsigned options) const
 {
+	{
+	// trivial case: expanding the monomial (~ 30% of all calls)
+		epvector::const_iterator i = seq.begin(), seq_end = seq.end();
+		while ((i != seq.end()) &&  is_a<symbol>(i->rest) && i->coeff.info(info_flags::integer))
+			++i;
+		if (i == seq_end) {
+			setflag(status_flags::expanded);
+			return *this;
+		}
+	}
+
+	// do not rename indices if the object has no indices at all
+	if ((!(options & expand_options::expand_rename_idx)) && 
+			this->info(info_flags::has_indices))
+		options |= expand_options::expand_rename_idx;
+
+	const bool skip_idx_rename = !(options & expand_options::expand_rename_idx);
+
 	// First, expand the children
-	epvector * expanded_seqp = expandchildren(options);
-	const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
+	std::auto_ptr<epvector> expanded_seqp = expandchildren(options);
+	const epvector & expanded_seq = (expanded_seqp.get() ? *expanded_seqp : seq);
 
 	// 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_ex_exactly_of_type(cit->rest, add) &&
+
+	for (epvector::const_iterator cit = expanded_seq.begin(); cit != expanded_seq.end(); ++cit) {
+		if (is_exactly_a<add>(cit->rest) &&
 			(cit->coeff.is_equal(_ex1))) {
-			++number_of_adds;
-			if (is_ex_exactly_of_type(last_expanded, add)) {
-#if 0
-				// Expand a product of two sums, simple and robust version.
-				const add & add1 = ex_to<add>(last_expanded);
-				const add & add2 = ex_to<add>(cit->rest);
-				const int n1 = add1.nops();
-				const int n2 = add2.nops();
-				ex tmp_accu;
-				exvector distrseq;
-				distrseq.reserve(n2);
-				for (int i1=0; i1<n1; ++i1) {
-					distrseq.clear();
-					// cache the first operand (for efficiency):
-					const ex op1 = add1.op(i1);
-					for (int i2=0; i2<n2; ++i2)
-						distrseq.push_back(op1 * add2.op(i2));
-					tmp_accu += (new add(distrseq))->
-					             setflag(status_flags::dynallocated);
-				}
-				last_expanded = tmp_accu;
-#else
+			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%!
@@ -760,6 +1161,7 @@ ex mul::expand(unsigned options) const
 				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))
@@ -768,6 +1170,7 @@ ex mul::expand(unsigned options) const
 						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))
@@ -776,58 +1179,104 @@ ex mul::expand(unsigned options) const
 						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);
+
+				exvector add1_dummy_indices, add2_dummy_indices, add_indices;
+				lst dummy_subs;
+
+				if (!skip_idx_rename) {
+					for (epvector::const_iterator i=add1begin; i!=add1end; ++i) {
+						add_indices = get_all_dummy_indices_safely(i->rest);
+						add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
+					}
+					for (epvector::const_iterator i=add2begin; i!=add2end; ++i) {
+						add_indices = get_all_dummy_indices_safely(i->rest);
+						add2_dummy_indices.insert(add2_dummy_indices.end(), add_indices.begin(), add_indices.end());
+					}
+
+					sort(add1_dummy_indices.begin(), add1_dummy_indices.end(), ex_is_less());
+					sort(add2_dummy_indices.begin(), add2_dummy_indices.end(), ex_is_less());
+					dummy_subs = rename_dummy_indices_uniquely(add1_dummy_indices, add2_dummy_indices);
+				}
+
 				// Multiply explicitly all non-numeric terms of add1 and add2:
-				for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+				for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
 					// 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) {
+					numeric oc(*_num0_p);
+					epvector distrseq2;
+					distrseq2.reserve(add1.seq.size());
+					const ex i2_new = (skip_idx_rename || (dummy_subs.op(0).nops() == 0) ?
+							i2->rest :
+							i2->rest.subs(ex_to<lst>(dummy_subs.op(0)), 
+								ex_to<lst>(dummy_subs.op(1)), subs_options::no_pattern));
+					for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
 						// 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_ex_exactly_of_type(rest, numeric))
+						const ex rest = (new mul(i1->rest, i2_new))->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))));
+						} else {
+							distrseq2.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);
-				}
+					tmp_accu += (new add(distrseq2, oc))->setflag(status_flags::dynallocated);
+				} 
 				last_expanded = tmp_accu;
-#endif
 			} else {
-				non_adds.push_back(split_ex_to_pair(last_expanded));
+				if (!last_expanded.is_equal(_ex1))
+					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_ex_exactly_of_type(last_expanded, add)) {
-		const add & finaladd = ex_to<add>(last_expanded);
+	if (is_exactly_a<add>(last_expanded)) {
+		size_t n = last_expanded.nops();
 		exvector distrseq;
-		int n = finaladd.nops();
 		distrseq.reserve(n);
-		for (int i=0; i<n; ++i) {
+		exvector va;
+		if (! skip_idx_rename) {
+			va = get_all_dummy_indices_safely(mul(non_adds));
+			sort(va.begin(), va.end(), ex_is_less());
+		}
+
+		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)));
+			if (skip_idx_rename)
+				factors.push_back(split_ex_to_pair(last_expanded.op(i)));
+			else
+				factors.push_back(split_ex_to_pair(rename_dummy_indices_uniquely(va, last_expanded.op(i))));
+			ex term = (new mul(factors, overall_coeff))->setflag(status_flags::dynallocated);
+			if (can_be_further_expanded(term)) {
+				distrseq.push_back(term.expand());
+			} else {
+				if (options == 0)
+					ex_to<basic>(term).setflag(status_flags::expanded);
+				distrseq.push_back(term);
+			}
 		}
+
 		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));
+	ex result = (new mul(non_adds, overall_coeff))->setflag(status_flags::dynallocated);
+	if (can_be_further_expanded(result)) {
+		return result.expand();
+	} else {
+		if (options == 0)
+			ex_to<basic>(result).setflag(status_flags::expanded);
+		return result;
+	}
 }
 
   
@@ -844,12 +1293,12 @@ ex mul::expand(unsigned options) const
 
 /** 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.
+ *  to allow for early cancellations 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
+std::auto_ptr<epvector> mul::expandchildren(unsigned options) const
 {
 	const epvector::const_iterator last = seq.end();
 	epvector::const_iterator cit = seq.begin();
@@ -859,7 +1308,7 @@ epvector * mul::expandchildren(unsigned options) const
 		if (!are_ex_trivially_equal(factor,expanded_factor)) {
 			
 			// something changed, copy seq, eval and return it
-			epvector *s = new epvector;
+			std::auto_ptr<epvector> s(new epvector);
 			s->reserve(seq.size());
 			
 			// copy parts of seq which are known not to have changed
@@ -868,9 +1317,11 @@ epvector * mul::expandchildren(unsigned options) const
 				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)));
@@ -881,7 +1332,9 @@ epvector * mul::expandchildren(unsigned options) const
 		++cit;
 	}
 	
-	return 0; // nothing has changed
+	return std::auto_ptr<epvector>(0); // nothing has changed
 }
 
+GINAC_BIND_UNARCHIVER(mul);
+
 } // namespace GiNaC