X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fadd.cpp;h=81a4f2fb1579d7147129d9c89f0763aafbd42b10;hp=c4e53360b1ed665dd9f7047bc7c63ba178697f1b;hb=cca88b51436e4b654d16a4d60cd0d1c66fcf5dd6;hpb=708e9e647029af699333fceffc0a76bef70a4709

diff --git a/ginac/add.cpp b/ginac/add.cpp
index c4e53360..81a4f2fb 100644
--- a/ginac/add.cpp
+++ b/ginac/add.cpp
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's sums of expressions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2014 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
@@ -17,36 +17,41 @@
  *
  *  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 <stdexcept>
-
 #include "add.h"
 #include "mul.h"
-#include "matrix.h"
 #include "archive.h"
-#include "debugmsg.h"
+#include "operators.h"
+#include "matrix.h"
 #include "utils.h"
+#include "clifford.h"
+#include "ncmul.h"
+#include "compiler.h"
+
+#include <iostream>
+#include <limits>
+#include <stdexcept>
+#include <string>
 
 namespace GiNaC {
 
-GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
+  print_func<print_context>(&add::do_print).
+  print_func<print_latex>(&add::do_print_latex).
+  print_func<print_csrc>(&add::do_print_csrc).
+  print_func<print_tree>(&add::do_print_tree).
+  print_func<print_python_repr>(&add::do_print_python_repr))
 
 //////////
-// default constructor, destructor, copy constructor assignment operator and helpers
+// default constructor
 //////////
 
 add::add()
 {
-	debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
 }
 
-DEFAULT_COPY(add)
-DEFAULT_DESTROY(add)
-
 //////////
 // other constructors
 //////////
@@ -55,48 +60,37 @@ DEFAULT_DESTROY(add)
 
 add::add(const ex & lh, const ex & rh)
 {
-	debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
-	overall_coeff = _ex0();
+	overall_coeff = _ex0;
 	construct_from_2_ex(lh,rh);
 	GINAC_ASSERT(is_canonical());
 }
 
 add::add(const exvector & v)
 {
-	debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
-	overall_coeff = _ex0();
+	overall_coeff = _ex0;
 	construct_from_exvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
 add::add(const epvector & v)
 {
-	debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
-	overall_coeff = _ex0();
+	overall_coeff = _ex0;
 	construct_from_epvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
 add::add(const epvector & v, const ex & oc)
 {
-	debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
 	overall_coeff = oc;
 	construct_from_epvector(v);
 	GINAC_ASSERT(is_canonical());
 }
 
-add::add(epvector * vp, const ex & oc)
+add::add(std::auto_ptr<epvector> vp, const ex & oc)
 {
-	debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
-	tinfo_key = TINFO_add;
-	GINAC_ASSERT(vp!=0);
+	GINAC_ASSERT(vp.get()!=0);
 	overall_coeff = oc;
 	construct_from_epvector(*vp);
-	delete vp;
 	GINAC_ASSERT(is_canonical());
 }
 
@@ -104,127 +98,124 @@ add::add(epvector * vp, const ex & oc)
 // archiving
 //////////
 
-DEFAULT_ARCHIVING(add)
+GINAC_BIND_UNARCHIVER(add);
 
 //////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
 //////////
 
 // public
 
-void add::print(const print_context & c, unsigned level) const
+void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 {
-	debugmsg("add print", LOGLEVEL_PRINT);
-
-	if (is_a<print_tree>(c)) {
+	if (precedence() <= level)
+		c.s << openbrace << '(';
 
-		inherited::print(c, level);
+	numeric coeff;
+	bool first = true;
 
-	} else if (is_a<print_csrc>(c)) {
+	// First print the overall numeric coefficient, if present
+	if (!overall_coeff.is_zero()) {
+		overall_coeff.print(c, 0);
+		first = false;
+	}
 
-		if (precedence() <= level)
-			c.s << "(";
-	
-		// Print arguments, separated by "+"
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
-		while (it != itend) {
-		
-			// If the coefficient is -1, it is replaced by a single minus sign
-			if (it->coeff.compare(_num1()) == 0) {
-				it->rest.bp->print(c, precedence());
-			} else if (it->coeff.compare(_num_1()) == 0) {
-				c.s << "-";
-				it->rest.bp->print(c, precedence());
-			} else if (ex_to<numeric>(it->coeff).numer().compare(_num1()) == 0) {
-				it->rest.bp->print(c, precedence());
-				c.s << "/";
-				ex_to<numeric>(it->coeff).denom().print(c, precedence());
-			} else if (ex_to<numeric>(it->coeff).numer().compare(_num_1()) == 0) {
-				c.s << "-";
-				it->rest.bp->print(c, precedence());
-				c.s << "/";
-				ex_to<numeric>(it->coeff).denom().print(c, precedence());
+	// Then proceed with the remaining factors
+	epvector::const_iterator it = seq.begin(), itend = seq.end();
+	while (it != itend) {
+		coeff = ex_to<numeric>(it->coeff);
+		if (!first) {
+			if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
+		} else {
+			if (coeff.csgn() == -1) c.s << '-';
+			first = false;
+		}
+		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 {
-				it->coeff.bp->print(c, precedence());
-				c.s << "*";
-				it->rest.bp->print(c, precedence());
+				if (coeff.csgn() == -1)
+					(-coeff).print(c, precedence());
+				else
+					coeff.print(c, precedence());
 			}
-		
-			// Separator is "+", except if the following expression would have a leading minus sign
-			it++;
-			if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_exactly_a<numeric>(it->rest) && it->rest.compare(_num0()) < 0)))
-				c.s << "+";
-		}
-	
-		if (!overall_coeff.is_zero()) {
-			if (overall_coeff.info(info_flags::positive))
-				c.s << '+';
-			overall_coeff.bp->print(c, precedence());
+			c.s << mul_sym;
 		}
-	
-		if (precedence() <= level)
-			c.s << ")";
-
-	} else {
+		it->rest.print(c, precedence());
+		++it;
+	}
 
-		if (precedence() <= level) {
-			if (is_a<print_latex>(c))
-				c.s << "{(";
-			else
-				c.s << "(";
-		}
+	if (precedence() <= level)
+		c.s << ')' << closebrace;
+}
 
-		numeric coeff;
-		bool first = true;
+void add::do_print(const print_context & c, unsigned level) const
+{
+	print_add(c, "", "", "*", level);
+}
 
-		// First print the overall numeric coefficient, if present
-		if (!overall_coeff.is_zero()) {
-			if (!is_a<print_tree>(c))
-				overall_coeff.print(c, 0);
-			else
-				overall_coeff.print(c, precedence());
-			first = false;
-		}
+void add::do_print_latex(const print_latex & c, unsigned level) const
+{
+	print_add(c, "{", "}", " ", level);
+}
 
-		// Then proceed with the remaining factors
-		epvector::const_iterator it = seq.begin(), itend = seq.end();
-		while (it != itend) {
-			coeff = ex_to<numeric>(it->coeff);
-			if (!first) {
-				if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
-			} else {
-				if (coeff.csgn() == -1) c.s << '-';
-				first = false;
-			}
-			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 add::do_print_csrc(const print_csrc & c, unsigned level) const
+{
+	if (precedence() <= level)
+		c.s << "(";
+	
+	// Print arguments, separated by "+" or "-"
+	epvector::const_iterator it = seq.begin(), itend = seq.end();
+	char separator = ' ';
+	while (it != itend) {
+		
+		// If the coefficient is negative, separator is "-"
+		if (it->coeff.is_equal(_ex_1) || 
+			ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
+			separator = '-';
+		c.s << separator;
+		if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
+			it->rest.print(c, precedence());
+		} else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
+				 ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
+		{
+			it->rest.print(c, precedence());
+			c.s << '/';
+			ex_to<numeric>(it->coeff).denom().print(c, precedence());
+		} else {
+			it->coeff.print(c, precedence());
+			c.s << '*';
 			it->rest.print(c, precedence());
-			it++;
 		}
+		
+		++it;
+		separator = '+';
+	}
+	
+	if (!overall_coeff.is_zero()) {
+		if (overall_coeff.info(info_flags::positive)
+		 || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
+			c.s << '+';
+		overall_coeff.print(c, precedence());
+	}
+		
+	if (precedence() <= level)
+		c.s << ")";
+}
 
-		if (precedence() <= level) {
-			if (is_a<print_latex>(c))
-				c.s << ")}";
-			else
-				c.s << ")";
-		}
+void add::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 add::info(unsigned inf) const
@@ -234,6 +225,16 @@ bool add::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::positive:
+		case info_flags::nonnegative:
+		case info_flags::posint:
+		case info_flags::nonnegint:
+		case info_flags::even:
 		case info_flags::crational_polynomial:
 		case info_flags::rational_function: {
 			epvector::const_iterator i = seq.begin(), end = seq.end();
@@ -242,6 +243,8 @@ bool add::info(unsigned inf) const
 					return false;
 				++i;
 			}
+			if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
+				return true;
 			return overall_coeff.info(inf);
 		}
 		case info_flags::algebraic: {
@@ -257,9 +260,19 @@ bool add::info(unsigned inf) const
 	return inherited::info(inf);
 }
 
+bool add::is_polynomial(const ex & var) const
+{
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+		if (!(i->rest).is_polynomial(var)) {
+			return false;
+		}
+	}
+	return true;
+}
+
 int add::degree(const ex & s) const
 {
-	int deg = INT_MIN;
+	int deg = std::numeric_limits<int>::min();
 	if (!overall_coeff.is_zero())
 		deg = 0;
 	
@@ -276,7 +289,7 @@ int add::degree(const ex & s) const
 
 int add::ldegree(const ex & s) const
 {
-	int deg = INT_MAX;
+	int deg = std::numeric_limits<int>::max();
 	if (!overall_coeff.is_zero())
 		deg = 0;
 	
@@ -293,29 +306,45 @@ int add::ldegree(const ex & s) const
 
 ex add::coeff(const ex & s, int n) const
 {
-	epvector *coeffseq = new epvector();
+	std::auto_ptr<epvector> coeffseq(new epvector);
+	std::auto_ptr<epvector> coeffseq_cliff(new epvector);
+	int rl = clifford_max_label(s);
+	bool do_clifford = (rl != -1);
+	bool nonscalar = false;
 
 	// Calculate sum of coefficients in each term
 	epvector::const_iterator i = seq.begin(), end = seq.end();
 	while (i != end) {
 		ex restcoeff = i->rest.coeff(s, n);
-		if (!restcoeff.is_zero())
+ 		if (!restcoeff.is_zero()) {
+ 			if (do_clifford) {
+ 				if (clifford_max_label(restcoeff) == -1) {
+ 					coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
+				} else {
+ 					coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
+					nonscalar = true;
+ 				}
+			}
 			coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
+		}
 		++i;
 	}
 
-	return (new add(coeffseq, n==0 ? overall_coeff : _ex0()))->setflag(status_flags::dynallocated);
+	return (new add(nonscalar ? coeffseq_cliff : coeffseq,
+	                n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 }
 
+/** Perform automatic term rewriting rules in this class.  In the following
+ *  x stands for a symbolic variables of type ex and c stands for such
+ *  an expression that contain a plain number.
+ *  - +(;c) -> c
+ *  - +(x;0) -> x
+ *
+ *  @param level cut-off in recursive evaluation */
 ex add::eval(int level) const
 {
-	// simplifications: +(;c) -> c
-	//                  +(x;1) -> x
-	
-	debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
-	
-	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 add(evaled_seqp, overall_coeff))->
 		       setflag(status_flags::dynallocated);
@@ -324,10 +353,7 @@ ex add::eval(int level) const
 #ifdef DO_GINAC_ASSERT
 	epvector::const_iterator i = seq.begin(), end = seq.end();
 	while (i != end) {
-		GINAC_ASSERT(!is_ex_exactly_of_type(i->rest,add));
-		if (is_ex_exactly_of_type(i->rest,numeric))
-			dbgprint();
-		GINAC_ASSERT(!is_ex_exactly_of_type(i->rest,numeric));
+		GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 		++i;
 	}
 #endif // def DO_GINAC_ASSERT
@@ -339,21 +365,50 @@ ex add::eval(int level) const
 	}
 	
 	int seq_size = seq.size();
-	if (seq_size==0) {
+	if (seq_size == 0) {
 		// +(;c) -> c
 		return overall_coeff;
-	} else if ((seq_size==1) && overall_coeff.is_zero()) {
+	} else if (seq_size == 1 && overall_coeff.is_zero()) {
 		// +(x;0) -> x
 		return recombine_pair_to_ex(*(seq.begin()));
+	} else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
+		throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
+	}
+	
+	// if any terms in the sum still are purely numeric, then they are more
+	// appropriately collected into the overall coefficient
+	epvector::const_iterator last = seq.end();
+	epvector::const_iterator j = seq.begin();
+	int terms_to_collect = 0;
+	while (j != last) {
+		if (unlikely(is_a<numeric>(j->rest)))
+			++terms_to_collect;
+		++j;
+	}
+	if (terms_to_collect) {
+		std::auto_ptr<epvector> s(new epvector);
+		s->reserve(seq_size - terms_to_collect);
+		numeric oc = *_num1_p;
+		j = seq.begin();
+		while (j != last) {
+			if (unlikely(is_a<numeric>(j->rest)))
+				oc = oc.mul(ex_to<numeric>(j->rest)).mul(ex_to<numeric>(j->coeff));
+			else
+				s->push_back(*j);
+			++j;
+		}
+		return (new add(s, ex_to<numeric>(overall_coeff).add_dyn(oc)))
+		        ->setflag(status_flags::dynallocated);
 	}
+	
 	return this->hold();
 }
 
-ex add::evalm(void) const
+ex add::evalm() const
 {
 	// Evaluate children first and add up all matrices. Stop if there's one
 	// term that is not a matrix.
-	epvector *s = new epvector;
+	std::auto_ptr<epvector> s(new epvector);
 	s->reserve(seq.size());
 
 	bool all_matrices = true;
@@ -364,7 +419,7 @@ ex add::evalm(void) const
 	while (it != itend) {
 		const ex &m = recombine_pair_to_ex(*it).evalm();
 		s->push_back(split_ex_to_pair(m));
-		if (is_ex_of_type(m, matrix)) {
+		if (is_a<matrix>(m)) {
 			if (first_term) {
 				sum = ex_to<matrix>(m);
 				first_term = false;
@@ -372,22 +427,83 @@ ex add::evalm(void) const
 				sum = sum.add(ex_to<matrix>(m));
 		} else
 			all_matrices = false;
-		it++;
+		++it;
 	}
 
-	if (all_matrices) {
-		delete s;
+	if (all_matrices)
 		return sum + overall_coeff;
-	} else
+	else
 		return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 }
 
-ex add::simplify_ncmul(const exvector & v) const
+ex add::conjugate() const
+{
+	exvector *v = 0;
+	for (size_t i=0; i<nops(); ++i) {
+		if (v) {
+			v->push_back(op(i).conjugate());
+			continue;
+		}
+		ex term = op(i);
+		ex ccterm = term.conjugate();
+		if (are_ex_trivially_equal(term, ccterm))
+			continue;
+		v = new exvector;
+		v->reserve(nops());
+		for (size_t j=0; j<i; ++j)
+			v->push_back(op(j));
+		v->push_back(ccterm);
+	}
+	if (v) {
+		ex result = add(*v);
+		delete v;
+		return result;
+	}
+	return *this;
+}
+
+ex add::real_part() const
+{
+	epvector v;
+	v.reserve(seq.size());
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+		if ((i->coeff).info(info_flags::real)) {
+			ex rp = (i->rest).real_part();
+			if (!rp.is_zero())
+				v.push_back(expair(rp, i->coeff));
+		} else {
+			ex rp=recombine_pair_to_ex(*i).real_part();
+			if (!rp.is_zero())
+				v.push_back(split_ex_to_pair(rp));
+		}
+	return (new add(v, overall_coeff.real_part()))
+		-> setflag(status_flags::dynallocated);
+}
+
+ex add::imag_part() const
+{
+	epvector v;
+	v.reserve(seq.size());
+	for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+		if ((i->coeff).info(info_flags::real)) {
+			ex ip = (i->rest).imag_part();
+			if (!ip.is_zero())
+				v.push_back(expair(ip, i->coeff));
+		} else {
+			ex ip=recombine_pair_to_ex(*i).imag_part();
+			if (!ip.is_zero())
+				v.push_back(split_ex_to_pair(ip));
+		}
+	return (new add(v, overall_coeff.imag_part()))
+		-> setflag(status_flags::dynallocated);
+}
+
+ex add::eval_ncmul(const exvector & v) const
 {
 	if (seq.empty())
-		return inherited::simplify_ncmul(v);
+		return inherited::eval_ncmul(v);
 	else
-		return seq.begin()->rest.simplify_ncmul(v);
+		return seq.begin()->rest.eval_ncmul(v);
 }    
 
 // protected
@@ -396,7 +512,7 @@ ex add::simplify_ncmul(const exvector & v) const
  *  @see ex::diff */
 ex add::derivative(const symbol & y) const
 {
-	epvector *s = new epvector();
+	std::auto_ptr<epvector> s(new epvector);
 	s->reserve(seq.size());
 	
 	// Only differentiate the "rest" parts of the expairs. This is faster
@@ -407,7 +523,7 @@ ex add::derivative(const symbol & y) const
 		s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 		++i;
 	}
-	return (new add(s, _ex0()))->setflag(status_flags::dynallocated);
+	return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 }
 
 int add::compare_same_type(const basic & other) const
@@ -415,74 +531,71 @@ int add::compare_same_type(const basic & other) const
 	return inherited::compare_same_type(other);
 }
 
-bool add::is_equal_same_type(const basic & other) const
-{
-	return inherited::is_equal_same_type(other);
-}
-
-unsigned add::return_type(void) const
+unsigned add::return_type() const
 {
 	if (seq.empty())
 		return return_types::commutative;
 	else
 		return seq.begin()->rest.return_type();
 }
-   
-unsigned add::return_type_tinfo(void) const
+
+return_type_t add::return_type_tinfo() const
 {
 	if (seq.empty())
-		return tinfo_key;
+		return make_return_type_t<add>();
 	else
 		return seq.begin()->rest.return_type_tinfo();
 }
 
-ex add::thisexpairseq(const epvector & v, const ex & oc) const
+// Note: do_index_renaming is ignored because it makes no sense for an add.
+ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 {
 	return (new add(v,oc))->setflag(status_flags::dynallocated);
 }
 
-ex add::thisexpairseq(epvector * vp, const ex & oc) const
+// Note: do_index_renaming is ignored because it makes no sense for an add.
+ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 {
 	return (new add(vp,oc))->setflag(status_flags::dynallocated);
 }
 
 expair add::split_ex_to_pair(const ex & e) const
 {
-	if (is_ex_exactly_of_type(e,mul)) {
+	if (is_exactly_a<mul>(e)) {
 		const mul &mulref(ex_to<mul>(e));
-		ex numfactor = mulref.overall_coeff;
+		const ex &numfactor = mulref.overall_coeff;
 		mul *mulcopyp = new mul(mulref);
-		mulcopyp->overall_coeff = _ex1();
+		mulcopyp->overall_coeff = _ex1;
 		mulcopyp->clearflag(status_flags::evaluated);
 		mulcopyp->clearflag(status_flags::hash_calculated);
 		mulcopyp->setflag(status_flags::dynallocated);
 		return expair(*mulcopyp,numfactor);
 	}
-	return expair(e,_ex1());
+	return expair(e,_ex1);
 }
 
 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 										  const ex & c) const
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
-	if (is_ex_exactly_of_type(e, mul)) {
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
+	if (is_exactly_a<mul>(e)) {
 		const mul &mulref(ex_to<mul>(e));
-		ex numfactor = mulref.overall_coeff;
+		const ex &numfactor = mulref.overall_coeff;
 		mul *mulcopyp = new mul(mulref);
-		mulcopyp->overall_coeff = _ex1();
+		mulcopyp->overall_coeff = _ex1;
 		mulcopyp->clearflag(status_flags::evaluated);
 		mulcopyp->clearflag(status_flags::hash_calculated);
 		mulcopyp->setflag(status_flags::dynallocated);
-		if (are_ex_trivially_equal(c, _ex1()))
+		if (c.is_equal(_ex1))
 			return expair(*mulcopyp, numfactor);
-		else if (are_ex_trivially_equal(numfactor, _ex1()))
+		else if (numfactor.is_equal(_ex1))
 			return expair(*mulcopyp, c);
 		else
 			return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
-	} else if (is_ex_exactly_of_type(e, numeric)) {
-		if (are_ex_trivially_equal(c, _ex1()))
-			return expair(e, _ex1());
-		return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1());
+	} else if (is_exactly_a<numeric>(e)) {
+		if (c.is_equal(_ex1))
+			return expair(e, _ex1);
+		return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 	}
 	return expair(e, c);
 }
@@ -490,36 +603,33 @@ expair add::combine_ex_with_coeff_to_pair(const ex & e,
 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 											const ex & c) const
 {
-	GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
-	GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
+	GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
+	GINAC_ASSERT(is_exactly_a<numeric>(c));
 
-	if (is_ex_exactly_of_type(p.rest,numeric)) {
-		GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1())); // should be normalized
-		return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1());
+	if (is_exactly_a<numeric>(p.rest)) {
+		GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
+		return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 	}
 
 	return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 }
-	
+
 ex add::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 p.rest*p.coeff;
+		return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 }
 
 ex add::expand(unsigned options) const
 {
-	if (options == 0 && (flags & status_flags::expanded))
-		return *this;
-	
-	epvector *vp = expandchildren(options);
-	if (vp == NULL) {
+	std::auto_ptr<epvector> vp = expandchildren(options);
+	if (vp.get() == 0) {
 		// the terms have not changed, so it is safe to declare this expanded
 		return (options == 0) ? setflag(status_flags::expanded) : *this;
 	}
-	
+
 	return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 }