X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fex.h;h=606cd9d8e87ffc188441670fe1ff929ffadb02b1;hp=499229e09072e4c972a61bf691457cab0bf76b0b;hb=8cffcdf13d817a47f217f1a1043317d95969e070;hpb=9961dfdd7a383f09b1040e195a8817a85d945e58

diff --git a/ginac/ex.h b/ginac/ex.h
index 499229e0..606cd9d8 100644
--- a/ginac/ex.h
+++ b/ginac/ex.h
@@ -3,7 +3,7 @@
  *  Interface to GiNaC's light-weight expression handles. */
 
 /*
- *  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
@@ -17,43 +17,70 @@
  *
  *  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
  */
 
-#ifndef __GINAC_EX_H__
-#define __GINAC_EX_H__
+#ifndef GINAC_EX_H
+#define GINAC_EX_H
 
 #include "basic.h"
-#include "operators.h"
+#include "ptr.h"
 
-namespace GiNaC {
+#include <functional>
+#include <iosfwd>
+#include <iterator>
+#include <memory>
+#include <stack>
 
-// Sorry, this is the only constant to pollute the global scope, the other ones
-// are defined in utils.h and not visible from outside.
-class ex;
-extern const ex & _ex0(void);     ///<  single ex(numeric(0))
+namespace GiNaC {
+#ifdef _MSC_VER
+  // MSVC produces a different symbol for _ex0 when it is declared inside   
+  // ex::is_zero() than when it is declared at top level as follows
+  extern const ex _ex0;
+#endif
+
+/** Helper class to initialize the library.  There must be one static object
+ *  of this class in every object file that makes use of our flyweights in
+ *  order to guarantee proper initialization.  Hence we put it into this
+ *  file which is included by every relevant file anyways.  This is modeled
+ *  after section 27.4.2.1.6 of the C++ standard, where cout and friends are
+ *  set up.
+ *
+ *  @see utils.cpp */
+class library_init {
+	static void init_unarchivers();
+public:
+	library_init();
+	~library_init();
+private:
+	static int count;
+};
+/** For construction of flyweights, etc. */
+static library_init library_initializer;
 
-class symbol;
-class lst;
 class scalar_products;
-
-/** Lightweight wrapper for GiNaC's symbolic objects.  Basically all it does is
- *  to hold a pointer to the other objects, manage the reference counting and
- *  provide methods for manipulation of these objects.  (Some people call such
- *  a thing a proxy class.) */
-class ex
-{
-	friend class basic;
+class const_iterator;
+class const_preorder_iterator;
+class const_postorder_iterator;
+
+
+/** Lightweight wrapper for GiNaC's symbolic objects.  It holds a pointer to
+ *  the other object in order to do garbage collection by the method of
+ *  reference counting.  I.e., it is a smart pointer.  Also, the constructor
+ *  ex::ex(const basic & other) calls the methods that do automatic
+ *  evaluation.  E.g., x-x turns automatically into 0. */
+class ex {
+	friend class archive_node;
+	friend inline bool are_ex_trivially_equal(const ex &, const ex &);
+	template<class T> friend inline const T &ex_to(const ex &);
+	template<class T> friend inline bool is_a(const ex &);
+	template<class T> friend inline bool is_exactly_a(const ex &);
 	
-// member functions
-	
-	// default ctor, dtor, copy ctor assignment operator and helpers
+	// default constructor, copy constructor and assignment operator
 public:
-	ex();
-	~ex();
-	ex(const ex & other);
-	ex & operator=(const ex & other);
-	// other ctors
+	ex() noexcept;
+
+	// other constructors
 public:
 	ex(const basic & other);
 	ex(int i);
@@ -61,285 +88,634 @@ public:
 	ex(long i);
 	ex(unsigned long i);
 	ex(double const d);
+
 	/** Construct ex from string and a list of symbols. The input grammar is
-	 *  similar to the GiNaC output format. All symbols to be used in the
-	 *  expression must be specified in a lst in the second argument. Undefined
-	 *  symbols and other parser errors will throw an exception. */
+	 *  similar to the GiNaC output format. All symbols and indices to be used
+	 *  in the expression must be specified in a lst in the second argument.
+	 *  Undefined symbols and other parser errors will throw an exception. */
 	ex(const std::string &s, const ex &l);
 	
-	// functions overriding virtual functions from bases classes
-	// none
-	
-	// new virtual functions which can be overridden by derived classes
-	// none
-
+public:
 	// non-virtual functions in this class
 public:
-	void swap(ex & other);
+	/** Efficiently swap the contents of two expressions. */
+	void swap(ex & other) noexcept
+	{
+		GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+		GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
+		bp.swap(other.bp);
+	}
+
+	// iterators
+	const_iterator begin() const noexcept;
+	const_iterator end() const noexcept;
+	const_preorder_iterator preorder_begin() const;
+	const_preorder_iterator preorder_end() const noexcept;
+	const_postorder_iterator postorder_begin() const;
+	const_postorder_iterator postorder_end() const noexcept;
+
+	// evaluation
+	ex eval() const { return bp->eval(); }
+	ex evalf() const { return bp->evalf(); }
+	ex evalm() const { return bp->evalm(); }
+	ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
+	ex eval_integ() const { return bp->eval_integ(); }
+
+	// printing
 	void print(const print_context & c, unsigned level = 0) const;
-	void printtree(std::ostream & os) const;
-	void dbgprint(void) const;
-	void dbgprinttree(void) const;
+	void dbgprint() const;
+	void dbgprinttree() const;
+
+	// info
 	bool info(unsigned inf) const { return bp->info(inf); }
-	unsigned nops() const { return bp->nops(); }
-	ex expand(unsigned options=0) const;
-	bool has(const ex & other) const { return bp->has(other); }
+
+	// operand access
+	size_t nops() const { return bp->nops(); }
+	ex op(size_t i) const { return bp->op(i); }
+	ex operator[](const ex & index) const { return (*bp)[index]; }
+	ex operator[](size_t i) const { return (*bp)[i]; }
+	ex & let_op(size_t i);
+	ex & operator[](const ex & index);
+	ex & operator[](size_t i);
+	ex lhs() const;
+	ex rhs() const;
+
+	// function for complex expressions
+	ex conjugate() const { return bp->conjugate(); }
+	ex real_part() const { return bp->real_part(); }
+	ex imag_part() const { return bp->imag_part(); }
+
+	// pattern matching
+	bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
+	bool find(const ex & pattern, exset& found) const;
+	bool match(const ex & pattern) const;
+	bool match(const ex & pattern, exmap & repls) const { return bp->match(pattern, repls); }
+
+	// substitutions
+	ex subs(const exmap & m, unsigned options = 0) const;
+	ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
+	ex subs(const ex & e, unsigned options = 0) const;
+
+	// function mapping
+	ex map(map_function & f) const { return bp->map(f); }
+	ex map(ex (*f)(const ex & e)) const;
+
+	// visitors and tree traversal
+	void accept(visitor & v) const { bp->accept(v); }
+	void traverse_preorder(visitor & v) const;
+	void traverse_postorder(visitor & v) const;
+	void traverse(visitor & v) const { traverse_preorder(v); }
+
+	// degree/coeff
+	bool is_polynomial(const ex & vars) const;
 	int degree(const ex & s) const { return bp->degree(s); }
 	int ldegree(const ex & s) const { return bp->ldegree(s); }
 	ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
 	ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
 	ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
-	ex numer(void) const;
-	ex denom(void) const;
-	ex numer_denom(void) const;
-	ex unit(const symbol &x) const;
-	ex content(const symbol &x) const;
-	numeric integer_content(void) const;
-	ex primpart(const symbol &x) const;
-	ex primpart(const symbol &x, const ex &cont) const;
-	ex normal(int level = 0) const;
-	ex to_rational(lst &repl_lst) const;
-	ex smod(const numeric &xi) const;
-	numeric max_coefficient(void) const;
+
+	// expand/collect
+	ex expand(unsigned options=0) const;
 	ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
-	ex eval(int level = 0) const { return bp->eval(level); }
-	ex evalf(int level = 0) const { return bp->evalf(level); }
+
+	// differentiation and series expansion
 	ex diff(const symbol & s, unsigned nth = 1) const;
 	ex series(const ex & r, int order, unsigned options = 0) const;
-	bool match(const ex & pattern) const;
-	bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
-	ex subs(const lst & ls, const lst & lr, bool no_pattern = false) const { return bp->subs(ls, lr, no_pattern); }
-	ex subs(const ex & e, bool no_pattern = false) const { return bp->subs(e, no_pattern); }
-	exvector get_free_indices(void) const { return bp->get_free_indices(); }
-	ex simplify_indexed(void) const;
-	ex simplify_indexed(const scalar_products & sp) const;
-	ex symmetrize(void) const;
-	ex symmetrize(const lst & l) const;
-	ex antisymmetrize(void) const;
-	ex antisymmetrize(const lst & l) const;
-	ex simplify_ncmul(const exvector & v) const { return bp->simplify_ncmul(v); }
-	ex operator[](const ex & index) const;
-	ex operator[](int i) const;
-	ex op(int i) const { return bp->op(i); }
-	ex & let_op(int i);
-	ex lhs(void) const;
-	ex rhs(void) const;
+
+	// rational functions
+	ex normal() const;
+	ex to_rational(exmap & repl) const;
+	ex to_polynomial(exmap & repl) const;
+	ex numer() const;
+	ex denom() const;
+	ex numer_denom() const;
+
+	// polynomial algorithms
+	ex unit(const ex &x) const;
+	ex content(const ex &x) const;
+	numeric integer_content() const;
+	ex primpart(const ex &x) const;
+	ex primpart(const ex &x, const ex &cont) const;
+	void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
+	ex smod(const numeric &xi) const { return bp->smod(xi); }
+	numeric max_coefficient() const;
+
+	// indexed objects
+	exvector get_free_indices() const { return bp->get_free_indices(); }
+	ex simplify_indexed(unsigned options = 0) const;
+	ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
+
+	// comparison
 	int compare(const ex & other) const;
 	bool is_equal(const ex & other) const;
-	bool is_zero(void) const { return is_equal(_ex0()); }
+	bool is_zero() const { 
+#ifndef _MSC_VER
+	  extern const ex _ex0;
+#endif
+	  return is_equal(_ex0); 
+	}
+	bool is_zero_matrix() const;
 	
-	unsigned return_type(void) const { return bp->return_type(); }
-	unsigned return_type_tinfo(void) const { return bp->return_type_tinfo(); }
-	unsigned gethash(void) const { return bp->gethash(); }
+	// symmetry
+	ex symmetrize() const;
+	ex symmetrize(const lst & l) const;
+	ex antisymmetrize() const;
+	ex antisymmetrize(const lst & l) const;
+	ex symmetrize_cyclic() const;
+	ex symmetrize_cyclic(const lst & l) const;
+
+	// noncommutativity
+	unsigned return_type() const { return bp->return_type(); }
+	return_type_t return_type_tinfo() const { return bp->return_type_tinfo(); }
+
+	unsigned gethash() const { return bp->gethash(); }
+
 private:
-	void construct_from_basic(const basic & other);
-	void construct_from_int(int i);
-	void construct_from_uint(unsigned int i);
-	void construct_from_long(long i);
-	void construct_from_ulong(unsigned long i);
-	void construct_from_double(double d);
-	void construct_from_string_and_lst(const std::string &s, const ex &l);
+	static ptr<basic> construct_from_basic(const basic & other);
+	static basic & construct_from_int(int i);
+	static basic & construct_from_uint(unsigned int i);
+	static basic & construct_from_long(long i);
+	static basic & construct_from_ulong(unsigned long i);
+	static basic & construct_from_double(double d);
+	static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
 	void makewriteable();
-
-#ifdef OBSCURE_CINT_HACK
-public:
-	static bool last_created_or_assigned_bp_can_be_converted_to_ex(void)
-	{
-		if (last_created_or_assigned_bp==0) return false;
-		if ((last_created_or_assigned_bp->flags &
-			 status_flags::dynallocated)==0) return false;
-		if ((last_created_or_assigned_bp->flags &
-			 status_flags::evaluated)==0) return false;
-		return true;
-	}
-protected:
-	void update_last_created_or_assigned_bp(void)
-	{
-		if (last_created_or_assigned_bp!=0) {
-			if (--last_created_or_assigned_bp->refcount == 0) {
-				delete last_created_or_assigned_bp;
-			}
-		}
-		last_created_or_assigned_bp = bp;
-		++last_created_or_assigned_bp->refcount;
-		last_created_or_assigned_exp = (long)(void *)(this);
-	}
-#endif // def OBSCURE_CINT_HACK
+	void share(const ex & other) const;
 
 // member variables
 
-public:
-	basic *bp;      ///< pointer to basic object managed by this
-#ifdef OBSCURE_CINT_HACK
-	static basic * last_created_or_assigned_bp;
-	static basic * dummy_bp;
-	static long last_created_or_assigned_exp;
-#endif // def OBSCURE_CINT_HACK
+private:
+	mutable ptr<basic> bp;  ///< pointer to basic object managed by this
 };
 
 
 // performance-critical inlined method implementations
 
+// This needs to be a basic* because we don't know that numeric is derived
+// from basic and we need a basic& for the ex default constructor
+extern const basic *_num0_bp;
+
 inline
-ex::ex() : bp(_ex0().bp)
+ex::ex() noexcept : bp(*const_cast<basic *>(_num0_bp))
 {
-	/*debugmsg("ex default ctor",LOGLEVEL_CONSTRUCT);*/
-	GINAC_ASSERT(_ex0().bp!=0);
-	GINAC_ASSERT(_ex0().bp->flags & status_flags::dynallocated);
-	GINAC_ASSERT(bp!=0);
-	++bp->refcount;
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex::~ex()
+ex::ex(const basic & other) : bp(construct_from_basic(other))
 {
-	/*debugmsg("ex dtor",LOGLEVEL_DESTRUCT);*/
-	GINAC_ASSERT(bp!=0);
 	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-	if (--bp->refcount == 0)
-		delete bp;
 }
 
 inline
-ex::ex(const ex & other) : bp(other.bp)
+ex::ex(int i) : bp(construct_from_int(i))
 {
-	/*debugmsg("ex copy ctor",LOGLEVEL_CONSTRUCT);*/
-	GINAC_ASSERT(bp!=0);
-	GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
-	++bp->refcount;
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex & ex::operator=(const ex & other)
+ex::ex(unsigned int i) : bp(construct_from_uint(i))
 {
-	/*debugmsg("ex operator=",LOGLEVEL_ASSIGNMENT);*/
-	GINAC_ASSERT(bp!=0);
 	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
-	GINAC_ASSERT(other.bp!=0);
-	GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
-	// NB: must first increment other.bp->refcount, since other might be *this.
-	++other.bp->refcount;
-	if (--bp->refcount==0)
-		delete bp;
-	bp = other.bp;
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
-	return *this;
 }
 
 inline
-ex::ex(const basic & other)
+ex::ex(long i) : bp(construct_from_long(i))
 {
-	/*debugmsg("ex ctor from basic",LOGLEVEL_CONSTRUCT);*/
-	construct_from_basic(other);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex::ex(int i)
+ex::ex(unsigned long i) : bp(construct_from_ulong(i))
 {
-	/*debugmsg("ex ctor from int",LOGLEVEL_CONSTRUCT);*/
-	construct_from_int(i);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex::ex(unsigned int i)
+ex::ex(double const d) : bp(construct_from_double(d))
 {
-	/*debugmsg("ex ctor from unsigned int",LOGLEVEL_CONSTRUCT);*/
-	construct_from_uint(i);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex::ex(long i)
+ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
 {
-	/*debugmsg("ex ctor from long",LOGLEVEL_CONSTRUCT);*/
-	construct_from_long(i);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	GINAC_ASSERT(bp->flags & status_flags::dynallocated);
 }
 
 inline
-ex::ex(unsigned long i)
+int ex::compare(const ex & other) const
 {
-	/*debugmsg("ex ctor from unsigned long",LOGLEVEL_CONSTRUCT);*/
-	construct_from_ulong(i);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+#ifdef GINAC_COMPARE_STATISTICS
+	compare_statistics.total_compares++;
+#endif
+	if (bp == other.bp)  // trivial case: both expressions point to same basic
+		return 0;
+#ifdef GINAC_COMPARE_STATISTICS
+	compare_statistics.nontrivial_compares++;
+#endif
+	const int cmpval = bp->compare(*other.bp);
+#if 1
+	if (cmpval == 0) {
+		// Expressions point to different, but equal, trees: conserve
+		// memory and make subsequent compare() operations faster by
+		// making both expressions point to the same tree.
+		share(other);
+	}
+#endif
+	return cmpval;
 }
 
 inline
-ex::ex(double const d)
+bool ex::is_equal(const ex & other) const
 {
-	/*debugmsg("ex ctor from double",LOGLEVEL_CONSTRUCT);*/
-	construct_from_double(d);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+#ifdef GINAC_COMPARE_STATISTICS
+	compare_statistics.total_is_equals++;
+#endif
+	if (bp == other.bp)  // trivial case: both expressions point to same basic
+		return true;
+#ifdef GINAC_COMPARE_STATISTICS
+	compare_statistics.nontrivial_is_equals++;
+#endif
+	const bool equal = bp->is_equal(*other.bp);
+#if 0
+	if (equal) {
+		// Expressions point to different, but equal, trees: conserve
+		// memory and make subsequent compare() operations faster by
+		// making both expressions point to the same tree.
+		share(other);
+	}
+#endif
+	return equal;
 }
 
-inline
-ex::ex(const std::string &s, const ex &l)
+
+// Iterators
+
+class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
+	friend class ex;
+	friend class const_preorder_iterator;
+	friend class const_postorder_iterator;
+
+public:
+	const_iterator() noexcept {}
+
+private:
+	const_iterator(const ex &e_, size_t i_) noexcept : e(e_), i(i_) {}
+
+public:
+	// This should return an ex&, but that would be a reference to a
+	// temporary value
+	ex operator*() const
+	{
+		return e.op(i);
+	}
+
+	// This should return an ex*, but that would be a pointer to a
+	// temporary value
+	std::unique_ptr<ex> operator->() const
+	{
+		return std::unique_ptr<ex>(new ex(operator*()));
+	}
+
+	ex operator[](difference_type n) const
+	{
+		return e.op(i + n);
+	}
+
+	const_iterator &operator++() noexcept
+	{
+		++i;
+		return *this;
+	}
+
+	const_iterator operator++(int) noexcept
+	{
+		const_iterator tmp = *this;
+		++i;
+		return tmp;
+	}
+
+	const_iterator &operator+=(difference_type n) noexcept
+	{
+		i += n;
+		return *this;
+	}
+
+	const_iterator operator+(difference_type n) const noexcept
+	{
+		return const_iterator(e, i + n);
+	}
+
+	inline friend const_iterator operator+(difference_type n, const const_iterator &it) noexcept
+	{
+		return const_iterator(it.e, it.i + n);
+	}
+
+	const_iterator &operator--() noexcept
+	{
+		--i;
+		return *this;
+	}
+
+	const_iterator operator--(int) noexcept
+	{
+		const_iterator tmp = *this;
+		--i;
+		return tmp;
+	}
+
+	const_iterator &operator-=(difference_type n) noexcept
+	{
+		i -= n;
+		return *this;
+	}
+
+	const_iterator operator-(difference_type n) const noexcept
+	{
+		return const_iterator(e, i - n);
+	}
+
+	inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) noexcept
+	{
+		return lhs.i - rhs.i;
+	}
+
+	bool operator==(const const_iterator &other) const noexcept
+	{
+		return are_ex_trivially_equal(e, other.e) && i == other.i;
+	}
+
+	bool operator!=(const const_iterator &other) const noexcept
+	{
+		return !(*this == other);
+	}
+
+	bool operator<(const const_iterator &other) const noexcept
+	{
+		return i < other.i;
+	}
+
+	bool operator>(const const_iterator &other) const noexcept
+	{
+		return other < *this;
+	}
+
+	bool operator<=(const const_iterator &other) const noexcept
+	{
+		return !(other < *this);
+	}
+
+	bool operator>=(const const_iterator &other) const noexcept
+	{
+		return !(*this < other);
+	}
+
+protected:
+	ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
+	size_t i;
+};
+
+namespace internal {
+
+struct _iter_rep {
+	_iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
+
+	bool operator==(const _iter_rep &other) const noexcept
+	{
+		return are_ex_trivially_equal(e, other.e) && i == other.i;
+	}
+
+	bool operator!=(const _iter_rep &other) const noexcept
+	{
+		return !(*this == other);
+	}
+
+	ex e;
+	size_t i;
+	size_t i_end;
+};
+
+} // namespace internal
+
+class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
+public:
+	const_preorder_iterator() noexcept {}
+
+	const_preorder_iterator(const ex &e, size_t n)
+	{
+		s.push(internal::_iter_rep(e, 0, n));
+	}
+
+public:
+	reference operator*() const
+	{
+		return s.top().e;
+	}
+
+	pointer operator->() const
+	{
+		return &(s.top().e);
+	}
+
+	const_preorder_iterator &operator++()
+	{
+		increment();
+		return *this;
+	}
+
+	const_preorder_iterator operator++(int)
+	{
+		const_preorder_iterator tmp = *this;
+		increment();
+		return tmp;
+	}
+
+	bool operator==(const const_preorder_iterator &other) const noexcept
+	{
+		return s == other.s;
+	}
+
+	bool operator!=(const const_preorder_iterator &other) const noexcept
+	{
+		return !(*this == other);
+	}
+
+private:
+	std::stack<internal::_iter_rep, std::vector<internal::_iter_rep>> s;
+
+	void increment()
+	{
+		while (!s.empty() && s.top().i == s.top().i_end) {
+			s.pop();
+			if (s.empty())
+				return;
+			++s.top().i;
+		}
+
+		internal::_iter_rep & current = s.top();
+
+		if (current.i != current.i_end) {
+			const ex & child = current.e.op(current.i);
+			s.push(internal::_iter_rep(child, 0, child.nops()));
+		}
+	}
+};
+
+class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
+public:
+	const_postorder_iterator() noexcept {}
+
+	const_postorder_iterator(const ex &e, size_t n)
+	{
+		s.push(internal::_iter_rep(e, 0, n));
+		descend();
+	}
+
+public:
+	reference operator*() const
+	{
+		return s.top().e;
+	}
+
+	pointer operator->() const
+	{
+		return &(s.top().e);
+	}
+
+	const_postorder_iterator &operator++()
+	{
+		increment();
+		return *this;
+	}
+
+	const_postorder_iterator operator++(int)
+	{
+		const_postorder_iterator tmp = *this;
+		increment();
+		return tmp;
+	}
+
+	bool operator==(const const_postorder_iterator &other) const noexcept
+	{
+		return s == other.s;
+	}
+
+	bool operator!=(const const_postorder_iterator &other) const noexcept
+	{
+		return !(*this == other);
+	}
+
+private:
+	std::stack<internal::_iter_rep, std::vector<internal::_iter_rep>> s;
+
+	void descend()
+	{
+		while (s.top().i != s.top().i_end) {
+			internal::_iter_rep & current = s.top();
+			const ex & child = current.e.op(current.i);
+			s.push(internal::_iter_rep(child, 0, child.nops()));
+		}
+	}
+
+	void increment()
+	{
+		if (s.top().i == s.top().i_end)
+			s.pop();
+		if (!s.empty()) {
+			++s.top().i;
+			descend();
+		}
+	}
+};
+
+inline const_iterator ex::begin() const noexcept
 {
-	/*debugmsg("ex ctor from string,lst",LOGLEVEL_CONSTRUCT);*/
-	construct_from_string_and_lst(s, l);
-#ifdef OBSCURE_CINT_HACK
-	update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
+	return const_iterator(*this, 0);
 }
 
-inline
-int ex::compare(const ex & other) const
+inline const_iterator ex::end() const noexcept
 {
-	GINAC_ASSERT(bp!=0);
-	GINAC_ASSERT(other.bp!=0);
-	if (bp==other.bp)  // trivial case: both expressions point to same basic
-		return 0;
-	return bp->compare(*other.bp);
+	return const_iterator(*this, nops());
 }
 
-inline
-bool ex::is_equal(const ex & other) const
+inline const_preorder_iterator ex::preorder_begin() const
 {
-	GINAC_ASSERT(bp!=0);
-	GINAC_ASSERT(other.bp!=0);
-	if (bp==other.bp)  // trivial case: both expressions point to same basic
-		return true;
-	return bp->is_equal(*other.bp);
+	return const_preorder_iterator(*this, nops());
+}
+
+inline const_preorder_iterator ex::preorder_end() const noexcept
+{
+	return const_preorder_iterator();
+}
+
+inline const_postorder_iterator ex::postorder_begin() const
+{
+	return const_postorder_iterator(*this, nops());
+}
+
+inline const_postorder_iterator ex::postorder_end() const noexcept
+{
+	return const_postorder_iterator();
 }
 
 
 // utility functions
+
+/** Compare two objects of class quickly without doing a deep tree traversal.
+ *  @return "true" if they are equal
+ *          "false" if equality cannot be established quickly (e1 and e2 may
+ *          still be equal, in this case. */
 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
 {
 	return e1.bp == e2.bp;
 }
 
+/* Function objects for STL sort() etc. */
+struct ex_is_less {
+	bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
+};
+
+struct ex_is_equal {
+	bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
+};
+
+struct op0_is_equal {
+	bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
+};
+
+struct ex_swap {
+	void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
+};
+
+// Make it possible to print exvectors and exmaps
+std::ostream & operator<<(std::ostream & os, const exvector & e);
+std::ostream & operator<<(std::ostream & os, const exset & e);
+std::ostream & operator<<(std::ostream & os, const exmap & e);
+
 // wrapper functions around member functions
-inline unsigned nops(const ex & thisex)
+inline size_t nops(const ex & thisex)
 { return thisex.nops(); }
 
 inline ex expand(const ex & thisex, unsigned options = 0)
 { return thisex.expand(options); }
 
-inline bool has(const ex & thisex, const ex & other)
-{ return thisex.has(other); }
+inline ex conjugate(const ex & thisex)
+{ return thisex.conjugate(); }
+
+inline ex real_part(const ex & thisex)
+{ return thisex.real_part(); }
+
+inline ex imag_part(const ex & thisex)
+{ return thisex.imag_part(); }
+
+inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
+{ return thisex.has(pattern, options); }
+
+inline bool find(const ex & thisex, const ex & pattern, exset& found)
+{ return thisex.find(pattern, found); }
+
+inline bool is_polynomial(const ex & thisex, const ex & vars)
+{ return thisex.is_polynomial(vars); }
 
 inline int degree(const ex & thisex, const ex & s)
 { return thisex.degree(s); }
@@ -359,20 +735,29 @@ inline ex denom(const ex & thisex)
 inline ex numer_denom(const ex & thisex)
 { return thisex.numer_denom(); }
 
-inline ex normal(const ex & thisex, int level=0)
-{ return thisex.normal(level); }
+inline ex normal(const ex & thisex)
+{ return thisex.normal(); }
 
-inline ex to_rational(const ex & thisex, lst & repl_lst)
-{ return thisex.to_rational(repl_lst); }
+inline ex to_rational(const ex & thisex, exmap & repl)
+{ return thisex.to_rational(repl); }
+
+inline ex to_polynomial(const ex & thisex, exmap & repl)
+{ return thisex.to_polynomial(repl); }
 
 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
 { return thisex.collect(s, distributed); }
 
-inline ex eval(const ex & thisex, int level = 0)
-{ return thisex.eval(level); }
+inline ex eval(const ex & thisex)
+{ return thisex.eval(); }
+
+inline ex evalf(const ex & thisex)
+{ return thisex.evalf(); }
+
+inline ex evalm(const ex & thisex)
+{ return thisex.evalm(); }
 
-inline ex evalf(const ex & thisex, int level = 0)
-{ return thisex.evalf(level); }
+inline ex eval_integ(const ex & thisex)
+{ return thisex.eval_integ(); }
 
 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
 { return thisex.diff(s, nth); }
@@ -380,20 +765,14 @@ inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
 { return thisex.series(r, order, options); }
 
-inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
+inline bool match(const ex & thisex, const ex & pattern, exmap& repl_lst)
 { return thisex.match(pattern, repl_lst); }
 
-inline ex subs(const ex & thisex, const ex & e)
-{ return thisex.subs(e); }
-
-inline ex subs(const ex & thisex, const lst & ls, const lst & lr)
-{ return thisex.subs(ls, lr); }
-
-inline ex simplify_indexed(const ex & thisex)
-{ return thisex.simplify_indexed(); }
+inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
+{ return thisex.simplify_indexed(options); }
 
-inline ex simplify_indexed(const ex & thisex, const scalar_products & sp)
-{ return thisex.simplify_indexed(sp); }
+inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
+{ return thisex.simplify_indexed(sp, options); }
 
 inline ex symmetrize(const ex & thisex)
 { return thisex.symmetrize(); }
@@ -407,7 +786,13 @@ inline ex antisymmetrize(const ex & thisex)
 inline ex antisymmetrize(const ex & thisex, const lst & l)
 { return thisex.antisymmetrize(l); }
 
-inline ex op(const ex & thisex, int i)
+inline ex symmetrize_cyclic(const ex & thisex)
+{ return thisex.symmetrize_cyclic(); }
+
+inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
+{ return thisex.symmetrize_cyclic(l); }
+
+inline ex op(const ex & thisex, size_t i)
 { return thisex.op(i); }
 
 inline ex lhs(const ex & thisex)
@@ -422,6 +807,161 @@ inline bool is_zero(const ex & thisex)
 inline void swap(ex & e1, ex & e2)
 { e1.swap(e2); }
 
+inline ex ex::subs(const exmap & m, unsigned options) const
+{
+	return bp->subs(m, options);
+}
+
+inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
+{ return thisex.subs(m, options); }
+
+inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
+{ return thisex.subs(ls, lr, options); }
+
+inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
+{ return thisex.subs(e, options); }
+
+
+/* Convert function pointer to function object suitable for map(). */
+class pointer_to_map_function : public map_function {
+protected:
+	ex (*ptr)(const ex &);
+public:
+	explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
+	ex operator()(const ex & e) override { return ptr(e); }
+};
+
+template<class T1>
+class pointer_to_map_function_1arg : public map_function {
+protected:
+	ex (*ptr)(const ex &, T1);
+	T1 arg1;
+public:
+	explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
+	ex operator()(const ex & e) override { return ptr(e, arg1); }
+};
+
+template<class T1, class T2>
+class pointer_to_map_function_2args : public map_function {
+protected:
+	ex (*ptr)(const ex &, T1, T2);
+	T1 arg1;
+	T2 arg2;
+public:
+	explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
+	ex operator()(const ex & e) override { return ptr(e, arg1, arg2); }
+};
+
+template<class T1, class T2, class T3>
+class pointer_to_map_function_3args : public map_function {
+protected:
+	ex (*ptr)(const ex &, T1, T2, T3);
+	T1 arg1;
+	T2 arg2;
+	T3 arg3;
+public:
+	explicit pointer_to_map_function_3args(ex x(const ex &, T1, T2, T3), T1 a1, T2 a2, T3 a3) : ptr(x), arg1(a1), arg2(a2), arg3(a3) {}
+	ex operator()(const ex & e) override { return ptr(e, arg1, arg2, arg3); }
+};
+
+template<class C>
+class pointer_to_member_to_map_function : public map_function {
+protected:
+	ex (C::*ptr)(const ex &);
+	C &c;
+public:
+	explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
+	ex operator()(const ex & e) override { return (c.*ptr)(e); }
+};
+
+template<class C, class T1>
+class pointer_to_member_to_map_function_1arg : public map_function {
+protected:
+	ex (C::*ptr)(const ex &, T1);
+	C &c;
+	T1 arg1;
+public:
+	explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
+	ex operator()(const ex & e) override { return (c.*ptr)(e, arg1); }
+};
+
+template<class C, class T1, class T2>
+class pointer_to_member_to_map_function_2args : public map_function {
+protected:
+	ex (C::*ptr)(const ex &, T1, T2);
+	C &c;
+	T1 arg1;
+	T2 arg2;
+public:
+	explicit pointer_to_member_to_map_function_2args(ex (C::*member)(const ex&, T1, T2), C &obj, T1 a1, T2 a2) : ptr(member), c(obj), arg1(a1), arg2(a2) {}
+	ex operator()(const ex & e) override { return (c.*ptr)(e, arg1, arg2); }
+};
+
+template<class C, class T1, class T2, class T3>
+class pointer_to_member_to_map_function_3args : public map_function {
+protected:
+	ex (C::*ptr)(const ex &, T1, T2, T3);
+	C &c;
+	T1 arg1;
+	T2 arg2;
+	T3 arg3;
+public:
+	explicit pointer_to_member_to_map_function_3args(ex (C::*member)(const ex &, T1, T2, T3), C &obj, T1 a1, T2 a2, T3 a3) : ptr(member), c(obj), arg1(a1), arg2(a2), arg3(a3) {}
+	ex operator()(const ex & e) override { return (c.*ptr)(e, arg1, arg2, arg3); }
+};
+
+inline ex ex::map(ex f(const ex &)) const
+{
+	pointer_to_map_function fcn(f);
+	return bp->map(fcn);
+}
+
+// convenience type checker template functions
+
+/** Check if ex is a handle to a T, including base classes. */
+template <class T>
+inline bool is_a(const ex &obj)
+{
+	return is_a<T>(*obj.bp);
+}
+
+/** Check if ex is a handle to a T, not including base classes. */
+template <class T>
+inline bool is_exactly_a(const ex &obj)
+{
+	return is_exactly_a<T>(*obj.bp);
+}
+
+/** Return a reference to the basic-derived class T object embedded in an
+ *  expression.  This is fast but unsafe: the result is undefined if the
+ *  expression does not contain a T object at its top level.  Hence, you
+ *  should generally check the type of e first.  Also, you shouldn't cache
+ *  the returned reference because GiNaC's garbage collector may destroy
+ *  the referenced object any time it's used in another expression.
+ *
+ *  @param e expression
+ *  @return reference to object of class T
+ *  @see is_exactly_a<class T>() */
+template <class T>
+inline const T &ex_to(const ex &e)
+{
+	GINAC_ASSERT(is_a<T>(e));
+	return static_cast<const T &>(*e.bp);
+}
+
 } // namespace GiNaC
 
-#endif // ndef __GINAC_EX_H__
+
+// Specializations of Standard Library algorithms
+namespace std {
+
+/** Specialization of std::swap() for ex objects. */
+template <>
+inline void swap(GiNaC::ex &a, GiNaC::ex &b)
+{
+	a.swap(b);
+}
+
+} // namespace std
+
+#endif // ndef GINAC_EX_H