X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=16bbc5b229ac9f21c26bcadbfacb1a26c5b6790f;hp=64b090af6ecdd1f721e69617b022625c1ef5df26;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=9bf900398c9e10c1cd486377038c24f9410fcb08

diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index 64b090af..16bbc5b2 100644
--- a/ginac/mul.cpp
+++ b/ginac/mul.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's products of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2019 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 +77,34 @@ 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(epvector && vp)
+{
+	overall_coeff = _ex1;
+	construct_from_epvector(std::move(vp));
+	GINAC_ASSERT(is_canonical());
+}
+
+mul::mul(epvector && vp, const ex & oc, bool do_index_renaming)
 {
-	tinfo_key = TINFO_mul;
-	GINAC_ASSERT(vp!=0);
 	overall_coeff = oc;
-	construct_from_epvector(*vp);
-	delete vp;
+	construct_from_epvector(std::move(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);
@@ -112,119 +119,154 @@ 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 << "*";
+	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
+				coeff.print(c);
+		} else {
+			if (coeff.csgn() == -1)
+				(-coeff).print(c, precedence());
+			else
+				coeff.print(c, precedence());
 		}
+		c.s << mul_sym;
+	}
+}
 
-		// Print arguments, separated by "*" or "/"
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
-		while (it != itend) {
+void mul::do_print(const print_context & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << '(';
+
+	print_overall_coeff(c, "*");
+
+	bool first = true;
+	for (auto & it : seq) {
+		if (!first)
+			c.s << '*';
+		else
+			first = false;
+		recombine_pair_to_ex(it).print(c, precedence());
+	}
 
-			// 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 (is_a<print_csrc_cl_N>(c))
-					c.s << "recip(";
-				else
-					c.s << "1.0/";
-			}
+	if (precedence() <= level)
+		c.s << ')';
+}
 
-			// 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.print(c, precedence());
-			else {
-				// Outer parens around ex needed for broken gcc-2.95 parser:
-				(ex(power(it->rest, abs(ex_to<numeric>(it->coeff))))).print(c, level);
-			}
+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
+	exvector neg_powers, others;
+	for (auto & it : seq) {
+		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));
+	}
 
-			// Separator is "/" for negative integer powers, "*" otherwise
-			++it;
-			if (it != itend) {
-				if (ex_to<numeric>(it->coeff).is_integer() && it->coeff.compare(_num0) < 0)
-					c.s << "/";
-				else
-					c.s << "*";
-			}
-		}
+	if (!neg_powers.empty()) {
 
-		if (precedence() <= level)
-			c.s << ")";
+		// 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 {
 
-		if (precedence() <= level) {
-			if (is_a<print_latex>(c))
-				c.s << "{(";
-			else
-				c.s << "(";
+		// All other factors are printed in the ordinary way
+		for (auto & vit : others) {
+			c.s << ' ';
+			vit.print(c, precedence());
 		}
+	}
 
-		bool first = true;
+	if (precedence() <= level)
+		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_csrc(const print_csrc & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << "(";
+
+	if (!overall_coeff.is_equal(_ex1)) {
+		if (overall_coeff.is_equal(_ex_1))
+			c.s << "-";
+		else {
+			overall_coeff.print(c, precedence());
+			c.s << "*";
 		}
+	}
 
-		// Then proceed with the remaining factors
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
-		while (it != itend) {
-			if (!first) {
-				if (is_a<print_latex>(c))
-					c.s << ' ';
-				else
-					c.s << '*';
-			} else {
-				first = false;
-			}
-			recombine_pair_to_ex(*it).print(c, precedence());
-			++it;
+	// Print arguments, separated by "*" or "/"
+	auto 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))
+			ex(power(it->rest, -ex_to<numeric>(it->coeff))).print(c, level);
+		else
+			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
@@ -234,38 +276,135 @@ 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();
-			while (i != end) {
-				if (!(recombine_pair_to_ex(*i).info(inf)))
+			for (auto & it : seq) {
+				if (!recombine_pair_to_ex(it).info(inf))
 					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: {
-			epvector::const_iterator i = seq.begin(), end = seq.end();
-			while (i != end) {
-				if ((recombine_pair_to_ex(*i).info(inf)))
-					return true;
-				++i;
+		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;
+			for (auto & it : seq) {
+				const ex& factor = recombine_pair_to_ex(it);
+				if (factor.info(info_flags::positive))
+					continue;
+				else if (factor.info(info_flags::negative))
+					pos = !pos;
+				else
+					return false;
 			}
-			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;
+			for (auto & it : seq) {
+				const ex& factor = recombine_pair_to_ex(it);
+				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;
+			for (auto & it : seq) {
+				const ex& factor = recombine_pair_to_ex(it);
+				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;
+			for (auto & it : seq) {
+				const ex& factor = recombine_pair_to_ex(it);
+				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;
+			for (auto & it : seq) {
+				const ex& term = recombine_pair_to_ex(it);
+				if (term.info(info_flags::positive) || term.info(info_flags::negative))
+					return false;
+			}
+			setflag(status_flags::purely_indefinite);
+			return true;
 		}
 	}
 	return inherited::info(inf);
 }
 
+bool mul::is_polynomial(const ex & var) const
+{
+	for (auto & it : seq) {
+		if (!it.rest.is_polynomial(var) ||
+		    (it.rest.has(var) && !it.coeff.info(info_flags::nonnegint))) {
+			return false;
+		}
+	}
+	return true;
+}
+
 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;
+	for (auto & it : seq) {
+		if (ex_to<numeric>(it.coeff).is_integer())
+			deg_sum += recombine_pair_to_ex(it).degree(s);
+		else {
+			if (it.rest.has(s))
+				throw std::runtime_error("mul::degree() undefined degree because of non-integer exponent");
+		}
 	}
 	return deg_sum;
 }
@@ -274,11 +413,13 @@ 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;
+	for (auto & it : seq) {
+		if (ex_to<numeric>(it.coeff).is_integer())
+			deg_sum += recombine_pair_to_ex(it).ldegree(s);
+		else {
+			if (it.rest.has(s))
+				throw std::runtime_error("mul::ldegree() undefined degree because of non-integer exponent");
+		}
 	}
 	return deg_sum;
 }
@@ -291,19 +432,15 @@ ex mul::coeff(const ex & s, int n) const
 	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;
-		}
+		for (auto & it : seq)
+			coeffseq.push_back(recombine_pair_to_ex(it).coeff(s,n));
 		coeffseq.push_back(overall_coeff);
-		return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+		return dynallocate<mul>(coeffseq);
 	}
 	
-	epvector::const_iterator i = seq.begin(), end = seq.end();
 	bool coeff_found = false;
-	while (i != end) {
-		ex t = recombine_pair_to_ex(*i);
+	for (auto & it : seq) {
+		ex t = recombine_pair_to_ex(it);
 		ex c = t.coeff(s, n);
 		if (!c.is_zero()) {
 			coeffseq.push_back(c);
@@ -311,11 +448,10 @@ ex mul::coeff(const ex & s, int n) const
 		} else {
 			coeffseq.push_back(t);
 		}
-		++i;
 	}
 	if (coeff_found) {
 		coeffseq.push_back(overall_coeff);
-		return (new mul(coeffseq))->setflag(status_flags::dynallocated);
+		return dynallocate<mul>(coeffseq);
 	}
 	
 	return _ex0;
@@ -328,42 +464,22 @@ ex mul::coeff(const ex & s, int n) const
  *  - *(+(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
+ */
+ex mul::eval() const
 {
-	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
-	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();
+
+	const epvector evaled = evalchildren();
+	if (unlikely(!evaled.empty())) {
+		// start over evaluating a new object
+		return dynallocate<mul>(std::move(evaled), overall_coeff);
+	}
+
+	size_t seq_size = seq.size();
 	if (overall_coeff.is_zero()) {
 		// *(...,x;0) -> 0
 		return _ex0;
@@ -374,71 +490,158 @@ 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();
-		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));
+		epvector distrseq;
+		distrseq.reserve(addref.seq.size());
+		for (auto & it : addref.seq) {
+			distrseq.push_back(addref.combine_pair_with_coeff_to_pair(it, overall_coeff));
+		}
+		return dynallocate<add>(std::move(distrseq),
+		                        ex_to<numeric>(addref.overall_coeff).mul_dyn(ex_to<numeric>(overall_coeff)))
+			.setflag(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
+
+		auto i = seq.begin(), last = seq.end();
+		auto j = seq.begin();
+		epvector s;
+		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 = dynallocate<add>(addref);
+			primitive.clearflag(status_flags::hash_calculated);
+			primitive.overall_coeff = ex_to<numeric>(primitive.overall_coeff).div_dyn(c);
+			for (auto & ai : primitive.seq)
+				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 dynallocate<mul>(std::move(s), ex_to<numeric>(overall_coeff).mul_dyn(oc));
 		}
-		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
+ex mul::evalf() const
 {
-	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());
+	epvector s;
+	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;
+	for (auto & it : seq)
+		s.push_back(expair(it.rest.evalf(), it.coeff));
+	return dynallocate<mul>(std::move(s), overall_coeff.evalf());
+}
+
+void mul::find_real_imag(ex & rp, ex & ip) const
+{
+	rp = overall_coeff.real_part();
+	ip = overall_coeff.imag_part();
+	for (auto & it : seq) {
+		ex factor = recombine_pair_to_ex(it);
+		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;
+		}
 	}
-	return mul(s, overall_coeff.evalf(level));
+	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(void) const
+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;
-	s->reserve(seq.size());
+	epvector s;
+	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_ex_of_type(m, matrix)) {
+	for (auto & it : seq) {
+		const ex &m = recombine_pair_to_ex(it).evalm();
+		s.push_back(split_ex_to_pair(m));
+		if (is_a<matrix>(m)) {
 			have_matrix = true;
-			the_matrix = s->end() - 1;
+			the_matrix = s.end() - 1;
 		}
-		++i;
 	}
 
 	if (have_matrix) {
@@ -446,52 +649,236 @@ ex mul::evalm(void) const
 		// 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);
+		s.erase(the_matrix);
+		ex scalar = dynallocate<mul>(std::move(s), overall_coeff);
 		return m.mul_scalar(scalar);
 
 	} else
-		return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
+		return dynallocate<mul>(std::move(s), overall_coeff);
 }
 
-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()
-	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);
-		++i;
+	// Find first noncommutative element and call its eval_ncmul()
+	for (auto & it : seq)
+		if (it.rest.return_type() == return_types::noncommutative)
+			return it.rest.eval_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;
 	}
-	return inherited::simplify_ncmul(v);
+
+	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 (auto & it : m) {
+
+		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 *= pow(subsed_pattern, nummatches);
+			ex subsed_result
+				= it.second.subs(repls, subs_options::no_pattern);
+			multiply_by *= pow(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 *= pow(subsed_pattern, nummatches);
+					ex subsed_result
+						= it.second.subs(repls, subs_options::no_pattern);
+					multiply_by *= pow(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.
+	std::unique_ptr<epvector> newepv(nullptr);
+	for (auto 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.reset(new epvector);
+		newepv->reserve(seq.size());
+		for (auto 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;
+	}
+	return thisexpairseq(newepv ? std::move(*newepv) : seq, x);
+}
+
+
 // 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);
 	
 	// 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();
+	auto i = seq.begin(), end = seq.end();
+	auto i2 = mulseq.begin();
 	while (i != end) {
-		expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
+		expair ep = split_ex_to_pair(pow(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));
+		addseq.push_back(dynallocate<mul>(mulseq, overall_coeff * i->coeff));
 		ep.swap(*i2);
 		++i; ++i2;
 	}
-	return (new add(addseq))->setflag(status_flags::dynallocated);
+	return dynallocate<add>(addseq);
 }
 
 int mul::compare_same_type(const basic & other) const
@@ -499,15 +886,10 @@ 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;
 	}
 	
@@ -527,8 +909,8 @@ 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;
@@ -536,101 +918,116 @@ 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();
-	while (i != end) {
-		if (i->rest.return_type() == return_types::noncommutative)
-			return i->rest.return_type_tinfo();
-		++i;
-	}
+	for (auto & it : seq)
+		if (it.rest.return_type() == return_types::noncommutative)
+			return it.rest.return_type_tinfo();
+
 	// 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 dynallocate<mul>(v, oc, do_index_renaming);
 }
 
-ex mul::thisexpairseq(epvector * vp, const ex & oc) const
+ex mul::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const
 {
-	return (new mul(vp, oc))->setflag(status_flags::dynallocated);
+	return dynallocate<mul>(std::move(vp), oc, do_index_renaming);
 }
 
 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
 {
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
+
+	// First, try a common shortcut:
+	if (is_exactly_a<symbol>(e))
+		return expair(e, c);
+
+	// trivial case: exponent 1
+	if (c.is_equal(_ex1))
+		return split_ex_to_pair(e);
+
 	// 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))
-		return split_ex_to_pair(e);
-	
-	return split_ex_to_pair(power(e,c));
+	return split_ex_to_pair(pow(e,c));
 }
-	
+
 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
                                             const ex & c) const
 {
+	GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
+
+	// First, try a common shortcut:
+	if (is_exactly_a<symbol>(p.rest))
+		return expair(p.rest, p.coeff * c);
+
+	// trivial case: exponent 1
+	if (c.is_equal(_ex1))
+		return p;
+	if (p.coeff.is_equal(_ex1))
+		return expair(p.rest, c);
+
 	// 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))
-		return p;
-	
-	return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
+	return split_ex_to_pair(pow(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 (p.coeff.is_equal(_ex1))
 		return p.rest;
 	else
-		return power(p.rest,p.coeff);
+		return dynallocate<power>(p.rest, p.coeff);
 }
 
 bool mul::expair_needs_further_processing(epp it)
 {
-	if (is_ex_exactly_of_type((*it).rest,mul) &&
-		ex_to<numeric>((*it).coeff).is_integer()) {
+	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;
 }
@@ -653,75 +1050,190 @@ void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 bool mul::can_make_flat(const expair & p) const
 {
 	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);
+
+	// (x*y)^c == x^c*y^c  if c ∈ ℤ
+	return p.coeff.info(info_flags::integer);
+}
+
+bool mul::can_be_further_expanded(const ex & e)
+{
+	if (is_exactly_a<mul>(e)) {
+		for (auto & it : ex_to<mul>(e).seq) {
+			if (is_exactly_a<add>(it.rest) && it.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
 {
+	// Check for trivial case: expanding the monomial (~ 30% of all calls)
+	bool monomial_case = true;
+	for (const auto & i : seq) {
+		if (!is_a<symbol>(i.rest) || !i.coeff.info(info_flags::integer)) {
+			monomial_case = false;
+			break;
+		}
+	}
+	if (monomial_case) {
+		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;
+	epvector expanded = expandchildren(options);
+	const epvector & expanded_seq = (expanded.empty() ? seq : expanded);
 
 	// 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) &&
-			(cit->coeff.is_equal(_ex1))) {
-			++number_of_adds;
-			if (is_ex_exactly_of_type(last_expanded, add)) {
-				const add & add1 = ex_to<add>(last_expanded);
-				const add & add2 = ex_to<add>(cit->rest);
-				int n1 = add1.nops();
-				int n2 = add2.nops();
-				exvector distrseq;
-				distrseq.reserve(n1*n2);
-				for (int i1=0; i1<n1; ++i1) {
-					for (int i2=0; i2<n2; ++i2) {
-						distrseq.push_back(add1.op(i1) * add2.op(i2));
+
+	for (const auto & cit : expanded_seq) {
+		if (is_exactly_a<add>(cit.rest) &&
+			(cit.coeff.is_equal(_ex1))) {
+			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));
+				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(), add2.seq.begin(), add2.seq.end());
+					else
+						for (const auto & i : add2.seq)
+							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(), add1.seq.begin(), add1.seq.end());
+					else
+						for (const auto & i : add1.seq)
+							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 = dynallocate<add>(distrseq, add1.overall_coeff*add2.overall_coeff);
+
+				exvector add1_dummy_indices, add2_dummy_indices, add_indices;
+				lst dummy_subs;
+
+				if (!skip_idx_rename) {
+					for (const auto & i : add1.seq) {
+						add_indices = get_all_dummy_indices_safely(i.rest);
+						add1_dummy_indices.insert(add1_dummy_indices.end(), add_indices.begin(), add_indices.end());
+					}
+					for (const auto & i : add2.seq) {
+						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 (const auto & i2 : add2.seq) {
+					// We really have to combine terms here in order to compactify
+					// the result.  Otherwise it would become waayy tooo bigg.
+					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 (const auto & i1 : add1.seq) {
+						// 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 = dynallocate<mul>(i1.rest, i2_new);
+						if (is_exactly_a<numeric>(rest)) {
+							oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1.coeff).mul(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 += dynallocate<add>(std::move(distrseq2), oc);
 				}
-				last_expanded = (new add(distrseq))->
-				                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
+				last_expanded = tmp_accu;
 			} else {
-				non_adds.push_back(split_ex_to_pair(last_expanded));
-				last_expanded = cit->rest;
+				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);
+			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 = dynallocate<mul>(factors, overall_coeff);
+			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)));
+
+		return dynallocate<add>(distrseq).setflag(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 = dynallocate<mul>(non_adds, overall_coeff);
+	if (can_be_further_expanded(result)) {
+		return result.expand();
+	} else {
+		if (options == 0)
+			ex_to<basic>(result).setflag(status_flags::expanded);
+		return result;
+	}
 }
 
   
@@ -738,44 +1250,47 @@ 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
+ *  @return epvector containing expanded pairs, empty if no members
+ *    had to be changed. */
+epvector mul::expandchildren(unsigned options) const
 {
-	const epvector::const_iterator last = seq.end();
-	epvector::const_iterator cit = seq.begin();
+	auto cit = seq.begin(), last = seq.end();
 	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());
+			epvector s;
+			s.reserve(seq.size());
 			
 			// copy parts of seq which are known not to have changed
-			epvector::const_iterator cit2 = seq.begin();
+			auto cit2 = seq.begin();
 			while (cit2!=cit) {
-				s->push_back(*cit2);
+				s.push_back(*cit2);
 				++cit2;
 			}
+
 			// copy first changed element
-			s->push_back(split_ex_to_pair(expanded_factor));
+			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)));
+				s.push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 				++cit2;
 			}
 			return s;
 		}
 		++cit;
 	}
-	
-	return 0; // nothing has changed
+
+	return epvector(); // nothing has changed
 }
 
+GINAC_BIND_UNARCHIVER(mul);
+
 } // namespace GiNaC