X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fmul.cpp;h=4a66f310ccf0aaf6eb335898a2424ecd8a2b2834;hp=10f25ec7b4984ae6bd29e54d7ba6fd913363b406;hb=a053768864556ce627f958a38fb1169ab00b8229;hpb=0cf43f3096cbcfc7472ff9c8927c6eb74f2eeb8c

diff --git a/ginac/mul.cpp b/ginac/mul.cpp
index 10f25ec7..4a66f310 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) 1999-2003 Johannes Gutenberg University Mainz, Germany
  *
  *  This program is free software; you can redistribute it and/or modify
  *  it under the terms of the GNU General Public License as published by
@@ -20,6 +20,7 @@
  *  Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
  */
 
+#include <iostream>
 #include <vector>
 #include <stdexcept>
 
@@ -28,7 +29,6 @@
 #include "power.h"
 #include "matrix.h"
 #include "archive.h"
-#include "debugmsg.h"
 #include "utils.h"
 
 namespace GiNaC {
@@ -36,12 +36,11 @@ namespace GiNaC {
 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
 
 //////////
-// default ctor, dctor, copy ctor assignment operator and helpers
+// default ctor, dtor, copy ctor, assignment operator and helpers
 //////////
 
 mul::mul()
 {
-	debugmsg("mul default ctor",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
 }
 
@@ -56,34 +55,30 @@ DEFAULT_DESTROY(mul)
 
 mul::mul(const ex & lh, const ex & rh)
 {
-	debugmsg("mul ctor from ex,ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
-	overall_coeff = _ex1();
+	overall_coeff = _ex1;
 	construct_from_2_ex(lh,rh);
 	GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const exvector & v)
 {
-	debugmsg("mul ctor from exvector",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
-	overall_coeff = _ex1();
+	overall_coeff = _ex1;
 	construct_from_exvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const epvector & v)
 {
-	debugmsg("mul ctor from epvector",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
-	overall_coeff = _ex1();
+	overall_coeff = _ex1;
 	construct_from_epvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
 mul::mul(const epvector & v, const ex & oc)
 {
-	debugmsg("mul ctor from epvector,ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
 	overall_coeff = oc;
 	construct_from_epvector(v);
@@ -92,7 +87,6 @@ mul::mul(const epvector & v, const ex & oc)
 
 mul::mul(epvector * vp, const ex & oc)
 {
-	debugmsg("mul ctor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
 	GINAC_ASSERT(vp!=0);
 	overall_coeff = oc;
@@ -103,14 +97,13 @@ mul::mul(epvector * vp, const ex & oc)
 
 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 {
-	debugmsg("mul ctor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 	tinfo_key = TINFO_mul;
 	exvector factors;
 	factors.reserve(3);
 	factors.push_back(lh);
 	factors.push_back(mh);
 	factors.push_back(rh);
-	overall_coeff = _ex1();
+	overall_coeff = _ex1;
 	construct_from_exvector(factors);
 	GINAC_ASSERT(is_canonical());
 }
@@ -122,15 +115,13 @@ mul::mul(const ex & lh, const ex & mh, const ex & rh)
 DEFAULT_ARCHIVING(mul)
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
 void mul::print(const print_context & c, unsigned level) const
 {
-	debugmsg("mul print", LOGLEVEL_PRINT);
-
 	if (is_a<print_tree>(c)) {
 
 		inherited::print(c, level);
@@ -140,8 +131,8 @@ void mul::print(const print_context & c, unsigned level) const
 		if (precedence() <= level)
 			c.s << "(";
 
-		if (!overall_coeff.is_equal(_ex1())) {
-			overall_coeff.bp->print(c, precedence());
+		if (!overall_coeff.is_equal(_ex1)) {
+			overall_coeff.print(c, precedence());
 			c.s << "*";
 		}
 
@@ -150,25 +141,32 @@ void mul::print(const print_context & c, unsigned level) const
 		while (it != itend) {
 
 			// If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
-			if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
-				if (is_a<print_csrc_cl_N>(c))
+			bool needclosingparenthesis = false;
+			if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
+				if (is_a<print_csrc_cl_N>(c)) {
 					c.s << "recip(";
-				else
+					needclosingparenthesis = true;
+				} else
 					c.s << "1.0/";
 			}
 
 			// If the exponent is 1 or -1, it is left out
-			if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
+			if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 				it->rest.print(c, precedence());
-			else {
+			else if (it->coeff.info(info_flags::negint))
 				// Outer parens around ex needed for broken gcc-2.95 parser:
-				(ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).print(c, level);
-			}
+				(ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
+			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 (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
+				if (it->coeff.info(info_flags::negint))
 					c.s << "/";
 				else
 					c.s << "*";
@@ -178,6 +176,14 @@ void mul::print(const print_context & c, unsigned level) const
 		if (precedence() <= level)
 			c.s << ")";
 
+	} 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);
+		}
+		c.s << ')';
 	} else {
 
 		if (precedence() <= level) {
@@ -187,14 +193,12 @@ void mul::print(const print_context & c, unsigned level) const
 				c.s << "(";
 		}
 
-		bool first = true;
-
 		// First print the overall numeric coefficient
-		numeric coeff = ex_to_numeric(overall_coeff);
+		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_equal(_num1) &&
+			!coeff.is_equal(_num_1)) {
 			if (coeff.is_rational()) {
 				if (coeff.is_negative())
 					(-coeff).print(c);
@@ -214,17 +218,51 @@ void mul::print(const print_context & c, unsigned level) const
 
 		// 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 << ' ';
+		if (is_a<print_latex>(c)) {
+
+			// Separate factors into those with negative numeric exponent
+			// and all others
+			exvector neg_powers, others;
+			while (it != itend) {
+				GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
+				if (ex_to<numeric>(it->coeff).is_negative())
+					neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
 				else
-					c.s << '*';
+					others.push_back(recombine_pair_to_ex(*it));
+				++it;
+			}
+
+			if (!neg_powers.empty()) {
+
+				// Factors with negative exponent are printed as a fraction
+				c.s << "\\frac{";
+				mul(others).eval().print(c);
+				c.s << "}{";
+				mul(neg_powers).eval().print(c);
+				c.s << "}";
+
 			} else {
-				first = false;
+
+				// All other factors are printed in the ordinary way
+				exvector::const_iterator vit = others.begin(), vitend = others.end();
+				while (vit != vitend) {
+					c.s << ' ';
+					vit->print(c, precedence());
+					++vit;
+				}
+			}
+
+		} else {
+
+			bool first = true;
+			while (it != itend) {
+				if (!first)
+					c.s << '*';
+				else
+					first = false;
+				recombine_pair_to_ex(*it).print(c, precedence());
+				++it;
 			}
-			recombine_pair_to_ex(*it).print(c, precedence());
-			it++;
 		}
 
 		if (precedence() <= level) {
@@ -245,16 +283,20 @@ bool mul::info(unsigned inf) const
 		case info_flags::rational_polynomial:
 		case info_flags::crational_polynomial:
 		case info_flags::rational_function: {
-			for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
 				if (!(recombine_pair_to_ex(*i).info(inf)))
 					return false;
+				++i;
 			}
 			return overall_coeff.info(inf);
 		}
 		case info_flags::algebraic: {
-			for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+			epvector::const_iterator i = seq.begin(), end = seq.end();
+			while (i != end) {
 				if ((recombine_pair_to_ex(*i).info(inf)))
 					return true;
+				++i;
 			}
 			return false;
 		}
@@ -264,20 +306,26 @@ bool mul::info(unsigned inf) const
 
 int mul::degree(const ex & s) const
 {
+	// Sum up degrees of factors
 	int deg_sum = 0;
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if (ex_to_numeric(cit->coeff).is_integer())
-			deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		if (ex_to<numeric>(i->coeff).is_integer())
+			deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
+		++i;
 	}
 	return deg_sum;
 }
 
 int mul::ldegree(const ex & s) const
 {
+	// Sum up degrees of factors
 	int deg_sum = 0;
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if (ex_to_numeric(cit->coeff).is_integer())
-			deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		if (ex_to<numeric>(i->coeff).is_integer())
+			deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
+		++i;
 	}
 	return deg_sum;
 }
@@ -290,97 +338,103 @@ 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 it = seq.begin();
-		while (it!=seq.end()) {
-			coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
-			++it;
+		epvector::const_iterator i = seq.begin(), end = seq.end();
+		while (i != end) {
+			coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
+			++i;
 		}
 		coeffseq.push_back(overall_coeff);
 		return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 	}
 	
-	epvector::const_iterator it=seq.begin();
-	bool coeff_found = 0;
-	while (it!=seq.end()) {
-		ex t = recombine_pair_to_ex(*it);
-		ex c = t.coeff(s,n);
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	bool coeff_found = false;
+	while (i != end) {
+		ex t = recombine_pair_to_ex(*i);
+		ex c = t.coeff(s, n);
 		if (!c.is_zero()) {
 			coeffseq.push_back(c);
 			coeff_found = 1;
 		} else {
 			coeffseq.push_back(t);
 		}
-		++it;
+		++i;
 	}
 	if (coeff_found) {
 		coeffseq.push_back(overall_coeff);
 		return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 	}
 	
-	return _ex0();
+	return _ex0;
 }
 
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
+ *  stand for such expressions that contain a plain number.
+ *  - *(...,x;0) -> 0
+ *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
+ *  - *(x;1) -> x
+ *  - *(;c) -> c
+ *
+ *  @param level cut-off in recursive evaluation */
 ex mul::eval(int level) const
 {
-	// simplifications  *(...,x;0) -> 0
-	//                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
-	//                  *(x;1) -> x
-	//                  *(;c) -> c
-	
-	debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
-	
-	epvector * evaled_seqp = evalchildren(level);
-	if (evaled_seqp!=0) {
+	epvector *evaled_seqp = evalchildren(level);
+	if (evaled_seqp) {
 		// do more evaluation later
 		return (new mul(evaled_seqp,overall_coeff))->
 		           setflag(status_flags::dynallocated);
 	}
 	
 #ifdef DO_GINAC_ASSERT
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul)) ||
-		             (!(ex_to_numeric((*cit).coeff).is_integer())));
-		GINAC_ASSERT(!(cit->is_canonical_numeric()));
-		if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric))
+	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_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
+		GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 		/* for paranoia */
-		expair p = split_ex_to_pair(recombine_pair_to_ex(*cit));
-		GINAC_ASSERT(p.rest.is_equal((*cit).rest));
-		GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
+		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()));
+		GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 		return *this;
 	}
 	
 	int seq_size = seq.size();
-	if (overall_coeff.is_equal(_ex0())) {
+	if (overall_coeff.is_zero()) {
 		// *(...,x;0) -> 0
-		return _ex0();
+		return _ex0;
 	} else if (seq_size==0) {
 		// *(;c) -> c
 		return overall_coeff;
-	} else if (seq_size==1 && overall_coeff.is_equal(_ex1())) {
+	} else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 		// *(x;1) -> x
 		return recombine_pair_to_ex(*(seq.begin()));
 	} else if ((seq_size==1) &&
 	           is_ex_exactly_of_type((*seq.begin()).rest,add) &&
-	           ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
+	           ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 		// *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
-		const add & addref = ex_to_add((*seq.begin()).rest);
-		epvector distrseq;
-		distrseq.reserve(addref.seq.size());
-		for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
-			distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
+		const add & addref = ex_to<add>((*seq.begin()).rest);
+		epvector *distrseq = new epvector();
+		distrseq->reserve(addref.seq.size());
+		epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
+		while (i != end) {
+			distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
+			++i;
 		}
 		return (new add(distrseq,
-		                ex_to_numeric(addref.overall_coeff).
-		                mul_dyn(ex_to_numeric(overall_coeff))))
+		                ex_to<numeric>(addref.overall_coeff).
+		                mul_dyn(ex_to<numeric>(overall_coeff))))
 		      ->setflag(status_flags::dynallocated | status_flags::evaluated);
 	}
 	return this->hold();
@@ -394,23 +448,25 @@ ex mul::evalf(int level) const
 	if (level==-max_recursion_level)
 		throw(std::runtime_error("max recursion level reached"));
 	
-	epvector s;
-	s.reserve(seq.size());
-	
+	epvector *s = new epvector();
+	s->reserve(seq.size());
+
 	--level;
-	for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
-		s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
-		                                          (*it).coeff));
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
+		                                           i->coeff));
+		++i;
 	}
-	return mul(s,overall_coeff.evalf(level));
+	return mul(s, overall_coeff.evalf(level));
 }
 
 ex mul::evalm(void) const
 {
 	// numeric*matrix
-	if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1())
+	if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 	 && is_ex_of_type(seq[0].rest, matrix))
-		return ex_to_matrix(seq[0].rest).mul(ex_to_numeric(overall_coeff));
+		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
@@ -421,22 +477,22 @@ ex mul::evalm(void) const
 	bool have_matrix = false;
 	epvector::iterator the_matrix;
 
-	epvector::const_iterator it = seq.begin(), itend = seq.end();
-	while (it != itend) {
-		const ex &m = recombine_pair_to_ex(*it).evalm();
+	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)) {
 			have_matrix = true;
 			the_matrix = s->end() - 1;
 		}
-		it++;
+		++i;
 	}
 
 	if (have_matrix) {
 
 		// The product contained a matrix. We will multiply all other factors
 		// into that matrix.
-		matrix m = ex_to_matrix(the_matrix->rest);
+		matrix m = ex_to<matrix>(the_matrix->rest);
 		s->erase(the_matrix);
 		ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 		return m.mul_scalar(scalar);
@@ -447,14 +503,15 @@ ex mul::evalm(void) const
 
 ex mul::simplify_ncmul(const exvector & v) const
 {
-	if (seq.size()==0) {
+	if (seq.empty())
 		return inherited::simplify_ncmul(v);
-	}
 
 	// Find first noncommutative element and call its simplify_ncmul()
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if (cit->rest.return_type() == return_types::noncommutative)
-			return cit->rest.simplify_ncmul(v);
+	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;
 	}
 	return inherited::simplify_ncmul(v);
 }
@@ -465,15 +522,21 @@ ex mul::simplify_ncmul(const exvector & v) const
  *  @see ex::diff */
 ex mul::derivative(const symbol & s) const
 {
+	unsigned num = seq.size();
 	exvector addseq;
-	addseq.reserve(seq.size());
+	addseq.reserve(num);
 	
 	// D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
-	for (unsigned i=0; i!=seq.size(); ++i) {
-		epvector mulseq = seq;
-		mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
-		                             seq[i].rest.diff(s));
-		addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
+	epvector mulseq = seq;
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	epvector::iterator i2 = mulseq.begin();
+	while (i != end) {
+		expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
+		                             i->rest.diff(s));
+		ep.swap(*i2);
+		addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
+		ep.swap(*i2);
+		++i; ++i2;
 	}
 	return (new add(addseq))->setflag(status_flags::dynallocated);
 }
@@ -490,30 +553,32 @@ bool mul::is_equal_same_type(const basic & other) const
 
 unsigned mul::return_type(void) const
 {
-	if (seq.size()==0) {
+	if (seq.empty()) {
 		// mul without factors: should not happen, but commutes
 		return return_types::commutative;
 	}
 	
-	bool all_commutative = 1;
-	unsigned rt;
-	epvector::const_iterator cit_noncommutative_element; // point to first found nc element
+	bool all_commutative = true;
+	epvector::const_iterator noncommutative_element; // point to first found nc element
 	
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		rt=(*cit).rest.return_type();
-		if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
-		if ((rt==return_types::noncommutative)&&(all_commutative)) {
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		unsigned rt = i->rest.return_type();
+		if (rt == return_types::noncommutative_composite)
+			return rt; // one ncc -> mul also ncc
+		if ((rt == return_types::noncommutative) && (all_commutative)) {
 			// first nc element found, remember position
-			cit_noncommutative_element = cit;
-			all_commutative = 0;
+			noncommutative_element = i;
+			all_commutative = false;
 		}
-		if ((rt==return_types::noncommutative)&&(!all_commutative)) {
+		if ((rt == return_types::noncommutative) && (!all_commutative)) {
 			// another nc element found, compare type_infos
-			if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
+			if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 				// diffent types -> mul is ncc
 				return return_types::noncommutative_composite;
 			}
 		}
+		++i;
 	}
 	// all factors checked
 	return all_commutative ? return_types::commutative : return_types::noncommutative;
@@ -521,13 +586,15 @@ unsigned mul::return_type(void) const
    
 unsigned mul::return_type_tinfo(void) const
 {
-	if (seq.size()==0)
+	if (seq.empty())
 		return tinfo_key;  // mul without factors: should not happen
 	
 	// return type_info of first noncommutative element
-	for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
-		if ((*cit).rest.return_type()==return_types::noncommutative)
-			return (*cit).rest.return_type_tinfo();
+	epvector::const_iterator i = seq.begin(), end = seq.end();
+	while (i != end) {
+		if (i->rest.return_type() == return_types::noncommutative)
+			return i->rest.return_type_tinfo();
+		++i;
 	}
 	// no noncommutative element found, should not happen
 	return tinfo_key;
@@ -535,22 +602,22 @@ unsigned mul::return_type_tinfo(void) const
 
 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 {
-	return (new mul(v,oc))->setflag(status_flags::dynallocated);
+	return (new mul(v, oc))->setflag(status_flags::dynallocated);
 }
 
 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 {
-	return (new mul(vp,oc))->setflag(status_flags::dynallocated);
+	return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 }
 
 expair mul::split_ex_to_pair(const ex & e) const
 {
 	if (is_ex_exactly_of_type(e,power)) {
-		const power & powerref = ex_to_power(e);
+		const power & powerref = ex_to<power>(e);
 		if (is_ex_exactly_of_type(powerref.exponent,numeric))
 			return expair(powerref.basis,powerref.exponent);
 	}
-	return expair(e,_ex1());
+	return expair(e,_ex1);
 }
 	
 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
@@ -560,7 +627,7 @@ expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 	// we create a temporary power object
 	// otherwise it would be hard to correctly simplify
 	// expression like (4^(1/3))^(3/2)
-	if (are_ex_trivially_equal(c,_ex1()))
+	if (are_ex_trivially_equal(c,_ex1))
 		return split_ex_to_pair(e);
 	
 	return split_ex_to_pair(power(e,c));
@@ -573,7 +640,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 	// we create a temporary power object
 	// otherwise it would be hard to correctly simplify
 	// expression like (4^(1/3))^(3/2)
-	if (are_ex_trivially_equal(c,_ex1()))
+	if (are_ex_trivially_equal(c,_ex1))
 		return p;
 	
 	return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
@@ -581,7 +648,7 @@ expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 	
 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)) 
 		return p.rest;
 	else
 		return power(p.rest,p.coeff);
@@ -590,7 +657,7 @@ ex mul::recombine_pair_to_ex(const expair & p) const
 bool mul::expair_needs_further_processing(epp it)
 {
 	if (is_ex_exactly_of_type((*it).rest,mul) &&
-		ex_to_numeric((*it).coeff).is_integer()) {
+		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;
@@ -602,7 +669,7 @@ bool mul::expair_needs_further_processing(epp it)
 			*it = ep;
 			return true;
 		}
-		if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
+		if (ex_to<numeric>((*it).coeff).is_equal(_num1)) {
 			// combined pair has coeff 1 and must be moved to the end
 			return true;
 		}
@@ -612,71 +679,127 @@ bool mul::expair_needs_further_processing(epp it)
 
 ex mul::default_overall_coeff(void) const
 {
-	return _ex1();
+	return _ex1;
 }
 
 void mul::combine_overall_coeff(const ex & c)
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
-	overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
+	GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
+	overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 }
 
 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
-	overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
+	GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c1));
+	GINAC_ASSERT(is_exactly_a<numeric>(c2));
+	overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 }
 
 bool mul::can_make_flat(const expair & p) const
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
+	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());
+	return ex_to<numeric>(p.coeff).is_equal(_num1);
 }
 
 ex mul::expand(unsigned options) const
 {
-	if (flags & status_flags::expanded)
-		return *this;
-	
-	exvector sub_expanded_seq;
-	
+	// First, expand the children
 	epvector * expanded_seqp = expandchildren(options);
-	
-	const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
-	
+	const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
+
+	// Now, look for all the factors that are sums and multiply each one out
+	// with the next one that is found while collecting the factors which are
+	// not sums
 	int number_of_adds = 0;
+	ex last_expanded = _ex1;
 	epvector non_adds;
 	non_adds.reserve(expanded_seq.size());
-	epvector::const_iterator cit = expanded_seq.begin();
-	epvector::const_iterator last = expanded_seq.end();
-	ex last_expanded(_ex1());
-	while (cit!=last) {
-		if (is_ex_exactly_of_type((*cit).rest,add) &&
-			((*cit).coeff.is_equal(_ex1()))) {
+	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)) {
-				// expand adds
-				const add & add1 = ex_to_add(last_expanded);
-				const add & add2 = ex_to_add((*cit).rest);
-				int n1 = add1.nops();
-				int n2 = add2.nops();
+			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(n1*n2);
+				distrseq.reserve(n2);
 				for (int i1=0; i1<n1; ++i1) {
-					for (int i2=0; i2<n2; ++i2) {
-						distrseq.push_back(add1.op(i1)*add2.op(i2));
+					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
+				// Expand a product of two sums, aggressive version.
+				// Caring for the overall coefficients in separate loops can
+				// sometimes give a performance gain of up to 15%!
+
+				const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
+				// add2 is for the inner loop and should be the bigger of the two sums
+				// in the presence of asymptotically good sorting:
+				const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
+				const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
+				const epvector::const_iterator add1begin = add1.seq.begin();
+				const epvector::const_iterator add1end   = add1.seq.end();
+				const epvector::const_iterator add2begin = add2.seq.begin();
+				const epvector::const_iterator add2end   = add2.seq.end();
+				epvector distrseq;
+				distrseq.reserve(add1.seq.size()+add2.seq.size());
+				// Multiply add2 with the overall coefficient of add1 and append it to distrseq:
+				if (!add1.overall_coeff.is_zero()) {
+					if (add1.overall_coeff.is_equal(_ex1))
+						distrseq.insert(distrseq.end(),add2begin,add2end);
+					else
+						for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
+							distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
+				}
+				// Multiply add1 with the overall coefficient of add2 and append it to distrseq:
+				if (!add2.overall_coeff.is_zero()) {
+					if (add2.overall_coeff.is_equal(_ex1))
+						distrseq.insert(distrseq.end(),add1begin,add1end);
+					else
+						for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
+							distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
+				}
+				// Compute the new overall coefficient and put it together:
+				ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
+				// Multiply explicitly all non-numeric terms of add1 and add2:
+				for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
+					// We really have to combine terms here in order to compactify
+					// the result.  Otherwise it would become waayy tooo bigg.
+					numeric oc;
+					distrseq.clear();
+					for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
+						// Don't push_back expairs which might have a rest that evaluates to a numeric,
+						// since that would violate an invariant of expairseq:
+						const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
+						if (is_ex_exactly_of_type(rest, numeric))
+							oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
+						else
+							distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
 					}
+					tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
 				}
-				last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+				last_expanded = tmp_accu;
+#endif
 			} else {
 				non_adds.push_back(split_ex_to_pair(last_expanded));
-				last_expanded = (*cit).rest;
+				last_expanded = cit->rest;
 			}
 		} else {
 			non_adds.push_back(*cit);
@@ -685,23 +808,26 @@ ex mul::expand(unsigned options) const
 	}
 	if (expanded_seqp)
 		delete expanded_seqp;
-
-	if (is_ex_exactly_of_type(last_expanded,add)) {
-		add const & finaladd = ex_to_add(last_expanded);
+	
+	// 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);
 		exvector distrseq;
 		int n = finaladd.nops();
 		distrseq.reserve(n);
 		for (int 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 | status_flags::expanded));
+			distrseq.push_back((new mul(factors, overall_coeff))->
+			                    setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 		}
 		return ((new add(distrseq))->
-		        setflag(status_flags::dynallocated | status_flags::expanded));
+		        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 | status_flags::expanded);
+	return (new mul(non_adds, overall_coeff))->
+	        setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 }
 
   
@@ -725,7 +851,7 @@ ex mul::expand(unsigned options) const
  *  pointer, if sequence is unchanged. */
 epvector * mul::expandchildren(unsigned options) const
 {
-	epvector::const_iterator last = seq.end();
+	const epvector::const_iterator last = seq.end();
 	epvector::const_iterator cit = seq.begin();
 	while (cit!=last) {
 		const ex & factor = recombine_pair_to_ex(*cit);