- prepared for 1.0.13 release

[ginac.git] / ginac / ex.h

diff --git a/ginac/ex.h b/ginac/ex.h
index f2feba7338446cd0ab9257ac4955b5fab957d65d..208151df99fbc97616bbc1d74b3b89f5b1de187f 100644 (file)
--- a/ginac/ex.h
+++ b/ginac/ex.h
@@ -3,7 +3,7 @@
  *  Interface to GiNaC's light-weight expression handles. */
 
 /*
  *  Interface to GiNaC's light-weight expression handles. */
 
 /*

- *  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
  *
  *  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


@@ -23,35 +23,64 @@
 #ifndef __GINAC_EX_H__
 #define __GINAC_EX_H__
 
 #ifndef __GINAC_EX_H__
 #define __GINAC_EX_H__
 

+#include <iosfwd>
+#include <functional>
+

 #include "basic.h"
 #include "operators.h"
 
 namespace GiNaC {
 
 #include "basic.h"
 #include "operators.h"
 
 namespace GiNaC {
 

-// 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))
+/** 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 {
+public:
+       library_init();
+       ~library_init();
+private:
+       static int count;
+};
+/** For construction of flyweights, etc. */
+static library_init library_initializer;
+
+// Current versions of Cint don't link data declared extern within functions.
+// FIXME: Fix Cint and later remove this from here.
+#if defined(G__CINTVERSION)
+extern const class numeric *_num0_p;
+#endif
+

 
 class symbol;
 class lst;
 class scalar_products;
 
 
 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
 /** 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. */
+ *  provide methods for manipulation of these objects.  (Some people call such
+ *  a thing a proxy class.) */

 class ex
 {
 class ex
 {

-       friend class basic;
+       friend class archive_node;
+       friend bool are_ex_trivially_equal(const ex &, const ex &);
+       template<class T> friend const T &ex_to(const ex &);
+       template<class T> friend bool is_a(const ex &);
+       template<class T> friend bool is_exactly_a(const ex &);

        
 // member functions
        
        
 // member functions
        

-       // default ctor, dtor, copy ctor assignment operator and helpers
+       // default ctor, dtor, copy ctor, assignment operator and helpers

 public:
        ex();
        ~ex();
        ex(const ex & other);
 public:
        ex();
        ~ex();
        ex(const ex & other);

-       const ex & operator=(const ex & other);
+       ex & operator=(const ex & other);

        // other ctors
 public:
        ex(const basic & other);
        // other ctors
 public:
        ex(const basic & other);


@@ -60,75 +89,89 @@ public:
        ex(long i);
        ex(unsigned long i);
        ex(double const d);
        ex(long i);
        ex(unsigned long i);
        ex(double const d);

+

        /** Construct ex from string and a list of symbols. The input grammar is
        /** 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);
        
        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
-

        // non-virtual functions in this class
 public:
        // non-virtual functions in this class
 public:

-       void swap(ex & other);
-       void printraw(std::ostream & os) const;
-       void printtree(std::ostream & os, unsigned indent=0) const;
-       void print(std::ostream & os, unsigned upper_precedence=0) const;
-       void printcsrc(std::ostream & os, unsigned type, const char *var_name) const;
+       /** Efficiently swap the contents of two expressions. */
+       void swap(ex & other)
+       {
+               GINAC_ASSERT(bp!=0);
+               GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+               GINAC_ASSERT(other.bp!=0);
+               GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
+       
+               basic * tmpbp = bp;
+               bp = other.bp;
+               other.bp = tmpbp;
+       }
+
+       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(void) const;
        void dbgprinttree(void) const;

-       bool info(unsigned inf) const;
-       unsigned nops() const;
+       bool info(unsigned inf) const { return bp->info(inf); }
+       unsigned nops() const { return bp->nops(); }

        ex expand(unsigned options=0) const;
        ex expand(unsigned options=0) const;

-       bool has(const ex & other) const;
-       int degree(const symbol & s) const;
-       int ldegree(const symbol & s) const;
-       ex coeff(const symbol & s, int n=1) const;
-       ex lcoeff(const symbol & s) const { return coeff(s, degree(s)); }
-       ex tcoeff(const symbol & s) const { return coeff(s, ldegree(s)); }
+       bool has(const ex & pattern) const { return bp->has(pattern); }
+       ex map(map_function & f) const { return bp->map(f); }
+       ex map(ex (*f)(const ex & e)) const;
+       bool find(const ex & pattern, lst & found) 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(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 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;
+       ex to_rational(lst &repl_lst) const { return bp->to_rational(repl_lst); }
+       ex smod(const numeric &xi) const { return bp->smod(xi); }

        numeric max_coefficient(void) const;
        numeric max_coefficient(void) const;

-       ex collect(const symbol & s) const;
-       ex eval(int level = 0) const;
-       ex evalf(int level = 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); }
+       ex evalm(void) const { return bp->evalm(); }

        ex diff(const symbol & s, unsigned nth = 1) const;
        ex series(const ex & r, int order, unsigned options = 0) const;
        ex diff(const symbol & s, unsigned nth = 1) const;
        ex series(const ex & r, int order, unsigned options = 0) const;

-       ex subs(const lst & ls, const lst & lr) const;
-       ex subs(const ex & e) const;
-       exvector get_free_indices(void) 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 simplify_indexed(void) const;
        ex simplify_indexed(const scalar_products & sp) const;

-       ex simplify_ncmul(const exvector & v) const;
+       ex symmetrize(void) const;
+       ex symmetrize(const lst & l) const;
+       ex antisymmetrize(void) const;
+       ex antisymmetrize(const lst & l) const;
+       ex symmetrize_cyclic(void) const;
+       ex symmetrize_cyclic(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 operator[](const ex & index) const;
        ex operator[](int i) const;

-       ex op(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;
        int compare(const ex & other) const;
        bool is_equal(const ex & other) const;
        ex & let_op(int i);
        ex lhs(void) const;
        ex rhs(void) const;
        int compare(const ex & other) const;
        bool is_equal(const ex & other) const;

-       bool is_zero(void) const { return is_equal(_ex0()); }
-       
-       unsigned return_type(void) const;
-       unsigned return_type_tinfo(void) const;
-       unsigned gethash(void) const;
+       bool is_zero(void) const { extern const ex _ex0; return is_equal(_ex0); }

        
        

-       ex exadd(const ex & rh) const;
-       ex exmul(const ex & rh) const;
-       ex exncmul(const ex & rh) 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(); }

 private:
        void construct_from_basic(const basic & other);
        void construct_from_int(int i);
 private:
        void construct_from_basic(const basic & other);
        void construct_from_int(int i);


@@ -167,7 +210,7 @@ protected:
 // member variables
 
 public:
 // member variables
 
 public:

-       basic *bp;      ///< pointer to basic object managed by this
+       basic *bp;      ///< pointer to basic object managed by this, direct manipulation deprecated

 #ifdef OBSCURE_CINT_HACK
        static basic * last_created_or_assigned_bp;
        static basic * dummy_bp;
 #ifdef OBSCURE_CINT_HACK
        static basic * last_created_or_assigned_bp;
        static basic * dummy_bp;


@@ -179,12 +222,12 @@ public:
 // performance-critical inlined method implementations
 
 inline
 // performance-critical inlined method implementations
 
 inline

-ex::ex() : bp(_ex0().bp)
+ex::ex()

 {
 {

-       /*debugmsg("ex default ctor",LOGLEVEL_CONSTRUCT);*/
-       GINAC_ASSERT(_ex0().bp!=0);
-       GINAC_ASSERT(_ex0().bp->flags & status_flags::dynallocated);
+       extern const class numeric *_num0_p;
+       bp = (basic*)_num0_p;

        GINAC_ASSERT(bp!=0);
        GINAC_ASSERT(bp!=0);

+       GINAC_ASSERT(bp->flags & status_flags::dynallocated);

        ++bp->refcount;
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        ++bp->refcount;
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -194,7 +237,6 @@ ex::ex() : bp(_ex0().bp)
 inline
 ex::~ex()
 {
 inline
 ex::~ex()
 {

-       /*debugmsg("ex dtor",LOGLEVEL_DESTRUCT);*/

        GINAC_ASSERT(bp!=0);
        GINAC_ASSERT(bp->flags & status_flags::dynallocated);
        if (--bp->refcount == 0)
        GINAC_ASSERT(bp!=0);
        GINAC_ASSERT(bp->flags & status_flags::dynallocated);
        if (--bp->refcount == 0)


@@ -204,7 +246,6 @@ ex::~ex()
 inline
 ex::ex(const ex & other) : bp(other.bp)
 {
 inline
 ex::ex(const ex & other) : bp(other.bp)
 {

-       /*debugmsg("ex copy ctor",LOGLEVEL_CONSTRUCT);*/

        GINAC_ASSERT(bp!=0);
        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
        ++bp->refcount;
        GINAC_ASSERT(bp!=0);
        GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
        ++bp->refcount;


@@ -214,16 +255,16 @@ ex::ex(const ex & other) : bp(other.bp)
 }
 
 inline
 }
 
 inline

-const ex & ex::operator=(const ex & other)
+ex & ex::operator=(const ex & other)

 {
 {

-       /*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);
        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;
        if (--bp->refcount==0)
                delete bp;

-       ++other.bp->refcount;

        bp = other.bp;
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        bp = other.bp;
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -234,7 +275,6 @@ const ex & ex::operator=(const ex & other)
 inline
 ex::ex(const basic & other)
 {
 inline
 ex::ex(const basic & other)
 {

-       /*debugmsg("ex ctor from basic",LOGLEVEL_CONSTRUCT);*/

        construct_from_basic(other);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_basic(other);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -244,7 +284,6 @@ ex::ex(const basic & other)
 inline
 ex::ex(int i)
 {
 inline
 ex::ex(int i)
 {

-       /*debugmsg("ex ctor from int",LOGLEVEL_CONSTRUCT);*/

        construct_from_int(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_int(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -254,7 +293,6 @@ ex::ex(int i)
 inline
 ex::ex(unsigned int i)
 {
 inline
 ex::ex(unsigned int i)
 {

-       /*debugmsg("ex ctor from unsigned int",LOGLEVEL_CONSTRUCT);*/

        construct_from_uint(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_uint(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -264,7 +302,6 @@ ex::ex(unsigned int i)
 inline
 ex::ex(long i)
 {
 inline
 ex::ex(long i)
 {

-       /*debugmsg("ex ctor from long",LOGLEVEL_CONSTRUCT);*/

        construct_from_long(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_long(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -274,7 +311,6 @@ ex::ex(long i)
 inline
 ex::ex(unsigned long i)
 {
 inline
 ex::ex(unsigned long i)
 {

-       /*debugmsg("ex ctor from unsigned long",LOGLEVEL_CONSTRUCT);*/

        construct_from_ulong(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_ulong(i);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -284,7 +320,6 @@ ex::ex(unsigned long i)
 inline
 ex::ex(double const d)
 {
 inline
 ex::ex(double const d)
 {

-       /*debugmsg("ex ctor from double",LOGLEVEL_CONSTRUCT);*/

        construct_from_double(d);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();
        construct_from_double(d);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -294,7 +329,6 @@ ex::ex(double const d)
 inline
 ex::ex(const std::string &s, const ex &l)
 {
 inline
 ex::ex(const std::string &s, const ex &l)
 {

-       /*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();
        construct_from_string_and_lst(s, l);
 #ifdef OBSCURE_CINT_HACK
        update_last_created_or_assigned_bp();


@@ -323,6 +357,11 @@ bool ex::is_equal(const ex & other) const
 
 
 // utility functions
 
 
 // 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;
 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
 {
        return e1.bp == e2.bp;


@@ -335,16 +374,19 @@ inline unsigned nops(const ex & thisex)
 inline ex expand(const ex & thisex, unsigned options = 0)
 { return thisex.expand(options); }
 
 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 bool has(const ex & thisex, const ex & pattern)
+{ return thisex.has(pattern); }

 
 

-inline int degree(const ex & thisex, const symbol & s)
+inline bool find(const ex & thisex, const ex & pattern, lst & found)
+{ return thisex.find(pattern, found); }
+
+inline int degree(const ex & thisex, const ex & s)

 { return thisex.degree(s); }
 
 { return thisex.degree(s); }
 

-inline int ldegree(const ex & thisex, const symbol & s)
+inline int ldegree(const ex & thisex, const ex & s)

 { return thisex.ldegree(s); }
 
 { return thisex.ldegree(s); }
 

-inline ex coeff(const ex & thisex, const symbol & s, int n=1)
+inline ex coeff(const ex & thisex, const ex & s, int n=1)

 { return thisex.coeff(s, n); }
 
 inline ex numer(const ex & thisex)
 { return thisex.coeff(s, n); }
 
 inline ex numer(const ex & thisex)


@@ -353,14 +395,17 @@ inline ex numer(const ex & thisex)
 inline ex denom(const ex & thisex)
 { return thisex.denom(); }
 
 inline ex denom(const ex & thisex)
 { return thisex.denom(); }
 

+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 to_rational(const ex & thisex, lst & repl_lst)
 { return thisex.to_rational(repl_lst); }
 
 inline ex normal(const ex & thisex, int level=0)
 { return thisex.normal(level); }
 
 inline ex to_rational(const ex & thisex, lst & repl_lst)
 { return thisex.to_rational(repl_lst); }
 

-inline ex collect(const ex & thisex, const symbol & s)
-{ return thisex.collect(s); }
+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, int level = 0)
 { return thisex.eval(level); }


@@ -368,18 +413,48 @@ inline ex eval(const ex & thisex, int level = 0)
 inline ex evalf(const ex & thisex, int level = 0)
 { return thisex.evalf(level); }
 
 inline ex evalf(const ex & thisex, int level = 0)
 { return thisex.evalf(level); }
 

+inline ex evalm(const ex & thisex)
+{ return thisex.evalm(); }
+

 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
 { return thisex.diff(s, nth); }
 
 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
 { return thisex.series(r, order, options); }
 
 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
 { return thisex.diff(s, nth); }
 
 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)
+{ 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 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, const scalar_products & sp)
+{ return thisex.simplify_indexed(sp); }
+
+inline ex symmetrize(const ex & thisex)
+{ return thisex.symmetrize(); }
+
+inline ex symmetrize(const ex & thisex, const lst & l)
+{ return thisex.symmetrize(l); }
+
+inline ex antisymmetrize(const ex & thisex)
+{ return thisex.antisymmetrize(); }
+
+inline ex antisymmetrize(const ex & thisex, const lst & l)
+{ return thisex.antisymmetrize(l); }
+
+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, int i)
 { return thisex.op(i); }
 
 inline ex op(const ex & thisex, int i)
 { return thisex.op(i); }
 


@@ -395,6 +470,74 @@ inline bool is_zero(const ex & thisex)
 inline void swap(ex & e1, ex & e2)
 { e1.swap(e2); }
 
 inline void swap(ex & e1, ex & e2)
 { e1.swap(e2); }
 

+// This makes STL algorithms use the more efficient swap operation for ex objects
+inline void iter_swap(std::vector<ex>::iterator i1, std::vector<ex>::iterator i2)
+{ i1->swap(*i2); }
+
+
+/* Function objects for STL sort() etc. */
+struct ex_is_less : public std::binary_function<ex, ex, bool> {
+       bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
+};
+
+struct ex_is_equal : public std::binary_function<ex, ex, bool> {
+       bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
+};
+
+struct ex_swap : public std::binary_function<ex, ex, void> {
+       void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
+};
+
+
+/* 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) { 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) { 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) { 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) { return ptr(e, arg1, arg2, arg3); }
+};
+
+inline ex ex::map(ex (*f)(const ex & e)) const
+{
+       pointer_to_map_function fcn(f);
+       return bp->map(fcn);
+}
+
+

 } // namespace GiNaC
 
 #endif // ndef __GINAC_EX_H__
 } // namespace GiNaC
 
 #endif // ndef __GINAC_EX_H__