* 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
#ifndef __GINAC_EX_H__
#define __GINAC_EX_H__
+#include <iosfwd>
+#include <iterator>
+#include <functional>
+
#include "basic.h"
-#include "operators.h"
+#include "ptr.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))
-class symbol;
-class lst;
+/** 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;
+
+
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. */
+ * provide methods for manipulation of these objects. (Some people call such
+ * a thing a proxy class.) */
class ex
{
- friend class basic;
-
-// member functions
+ 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 &);
- // default ctor, dtor, copy ctor assignment operator and helpers
+ // default constructor, copy constructor and assignment operator
public:
- ex();
- ~ex();
+ ex() throw();
+#ifdef OBSCURE_CINT_HACK
ex(const ex & other);
- const ex & operator=(const ex & other);
- // other ctors
+ ex & operator=(const ex & other);
+#endif
+
+ // other constructors
public:
ex(const basic & other);
ex(int i);
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:
+ // Iterators
+ class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
+ {
+ friend class ex;
+
+ public:
+ const_iterator() throw() {}
+ const_iterator(const basic *bp_, size_t i_) throw() : bp(bp_), i(i_) {}
+
+ bool operator==(const const_iterator &other) const throw()
+ {
+ return bp == other.bp && i == other.i;
+ }
+
+ bool operator!=(const const_iterator &other) const throw()
+ {
+ return !(*this == other);
+ }
+
+ bool operator<(const const_iterator &other) const throw()
+ {
+ return i < other.i;
+ }
+
+ bool operator>(const const_iterator &other) const throw()
+ {
+ return other < *this;
+ }
+
+ bool operator<=(const const_iterator &other) const throw()
+ {
+ return !(other < *this);
+ }
+
+ bool operator>=(const const_iterator &other) const throw()
+ {
+ return !(*this < other);
+ }
+
+ // This should return an ex&, but that would be a reference to a
+ // temporary value
+ ex operator*() const
+ {
+ return bp->op(i);
+ }
+
+#if 0
+ // How do we make this work in the context of the "reference to
+ // temporary" problem? Return an auto_ptr?
+ pointer operator->() const
+ {
+ return &(operator*());
+ }
+#endif
+
+ const_iterator &operator++() throw()
+ {
+ ++i;
+ return *this;
+ }
+
+ const_iterator operator++(int) throw()
+ {
+ const_iterator tmp = *this;
+ ++i;
+ return tmp;
+ }
+
+ const_iterator &operator+=(difference_type n) throw()
+ {
+ i += n;
+ return *this;
+ }
+
+ const_iterator operator+(difference_type n) const throw()
+ {
+ return const_iterator(bp, i + n);
+ }
+
+ inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
+ {
+ return const_iterator(it.bp, it.i + n);
+ }
+
+ const_iterator &operator--() throw()
+ {
+ --i;
+ return *this;
+ }
+
+ const_iterator operator--(int) throw()
+ {
+ const_iterator tmp = *this;
+ --i;
+ return tmp;
+ }
+
+ const_iterator &operator-=(difference_type n) throw()
+ {
+ i -= n;
+ return *this;
+ }
+
+ const_iterator operator-(difference_type n) const throw()
+ {
+ return const_iterator(bp, i - n);
+ }
+
+ inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
+ {
+ return lhs.i - rhs.i;
+ }
+
+ ex operator[](difference_type n) const
+ {
+ return bp->op(i + n);
+ }
+
+ protected:
+ const basic *bp;
+ size_t i;
+ };
+
+ const_iterator begin() const throw() { return const_iterator(get_pointer(bp), 0); }
+ const_iterator end() const throw() { return const_iterator(get_pointer(bp), bp->nops()); }
+
+#if 0
+ // This doesn't work because of the "reference to temporary" problem
+ // in operator*()
+ typedef std::reverse_iterator<const_iterator> const_reverse_iterator;
+ const_reverse_iterator rbegin() const { return const_reverse_iterator(end()); }
+ const_reverse_iterator rend() const { return const_reverse_iterator(begin()); }
+#endif
// 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;
- void dbgprint(void) const;
- void dbgprinttree(void) const;
- bool info(unsigned inf) const;
- unsigned nops() const;
+ /** Efficiently swap the contents of two expressions. */
+ void swap(ex & other) throw()
+ {
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
+ GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
+ bp.swap(other.bp);
+ }
+
+ // evaluation
+ ex eval(int level = 0) const { return bp->eval(level); }
+ ex evalf(int level = 0) const { return bp->evalf(level); }
+ ex evalm() const { return bp->evalm(); }
+ ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
+
+ // printing
+ void print(const print_context & c, unsigned level = 0) const;
+ void dbgprint() const;
+ void dbgprinttree() const;
+
+ // info
+ bool info(unsigned inf) const { return bp->info(inf); }
+
+ // 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;
+
+ // pattern matching
+ bool has(const ex & pattern) const { return bp->has(pattern); }
+ bool find(const ex & pattern, lst & found) const;
+ bool match(const ex & pattern) const;
+ bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
+
+ // 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
+ 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)); }
+
+ // expand/collect
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)); }
- ex numer(void) const;
- ex 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;
- 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); }
+
+ // differentiation and series expansion
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;
- ex simplify_indexed(void) const;
+
+ // rational functions
+ ex normal(int level = 0) const;
+ ex to_rational(lst &repl_lst) const;
+ ex to_polynomial(lst &repl_lst) 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;
+ 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() const;
ex simplify_indexed(const scalar_products & sp) const;
- ex simplify_ncmul(const exvector & v) const;
- ex operator[](const ex & index) const;
- ex operator[](int i) const;
- ex op(int i) const;
- ex & let_op(int i);
- ex lhs(void) const;
- ex rhs(void) const;
+
+ // comparison
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() 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;
+ // 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(); }
+ unsigned 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();
+ void share(const ex & other) const;
#ifdef OBSCURE_CINT_HACK
public:
- static bool last_created_or_assigned_bp_can_be_converted_to_ex(void)
+ static bool last_created_or_assigned_bp_can_be_converted_to_ex()
{
if (last_created_or_assigned_bp==0) return false;
if ((last_created_or_assigned_bp->flags &
return true;
}
protected:
- void update_last_created_or_assigned_bp(void)
+ void update_last_created_or_assigned_bp()
{
- 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
// member variables
-public:
- basic *bp; ///< pointer to basic object managed by this
+private:
+ mutable ptr<basic> bp; ///< pointer to basic object managed by this
+
#ifdef OBSCURE_CINT_HACK
- static basic * last_created_or_assigned_bp;
+public:
+ static ptr<basic> last_created_or_assigned_bp;
static basic * dummy_bp;
static long last_created_or_assigned_exp;
#endif // def OBSCURE_CINT_HACK
// 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() throw() : 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;
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
-inline
-ex::~ex()
-{
- /*debugmsg("ex dtor",LOGLEVEL_DESTRUCT);*/
- GINAC_ASSERT(bp!=0);
- GINAC_ASSERT(bp->flags & status_flags::dynallocated);
- if (--bp->refcount == 0)
- delete bp;
-}
-
+#ifdef OBSCURE_CINT_HACK
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;
-#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
}
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);
- if (--bp->refcount==0)
- delete bp;
- ++other.bp->refcount;
bp = other.bp;
-#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
-#endif // def OBSCURE_CINT_HACK
return *this;
}
+#endif // def OBSCURE_CINT_HACK
inline
-ex::ex(const basic & other)
+ex::ex(const basic & other) : bp(construct_from_basic(other))
{
- /*debugmsg("ex ctor from basic",LOGLEVEL_CONSTRUCT);*/
- construct_from_basic(other);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(int i)
+ex::ex(int i) : bp(construct_from_int(i))
{
- /*debugmsg("ex ctor from int",LOGLEVEL_CONSTRUCT);*/
- construct_from_int(i);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(unsigned int i)
+ex::ex(unsigned int i) : bp(construct_from_uint(i))
{
- /*debugmsg("ex ctor from unsigned int",LOGLEVEL_CONSTRUCT);*/
- construct_from_uint(i);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(long i)
+ex::ex(long i) : bp(construct_from_long(i))
{
- /*debugmsg("ex ctor from long",LOGLEVEL_CONSTRUCT);*/
- construct_from_long(i);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(unsigned long i)
+ex::ex(unsigned long i) : bp(construct_from_ulong(i))
{
- /*debugmsg("ex ctor from unsigned long",LOGLEVEL_CONSTRUCT);*/
- construct_from_ulong(i);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(double const d)
+ex::ex(double const d) : bp(construct_from_double(d))
{
- /*debugmsg("ex ctor from double",LOGLEVEL_CONSTRUCT);*/
- construct_from_double(d);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
}
inline
-ex::ex(const std::string &s, const ex &l)
+ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
{
- /*debugmsg("ex ctor from string,lst",LOGLEVEL_CONSTRUCT);*/
- construct_from_string_and_lst(s, l);
+ GINAC_ASSERT(bp->flags & status_flags::dynallocated);
#ifdef OBSCURE_CINT_HACK
update_last_created_or_assigned_bp();
#endif // def OBSCURE_CINT_HACK
inline
int ex::compare(const ex & other) const
{
- GINAC_ASSERT(bp!=0);
- GINAC_ASSERT(other.bp!=0);
- if (bp==other.bp) // trivial case: both expressions point to same basic
+ if (bp == other.bp) // trivial case: both expressions point to same basic
return 0;
- return bp->compare(*other.bp);
+ const int cmpval = bp->compare(*other.bp);
+ if (cmpval == 0) {
+ // Expressions point to different, but equal, trees: conserve
+ // memory and make subsequent compare() operations faster by
+ // making both expression point to the same tree.
+ share(other);
+ }
+ return cmpval;
}
inline
bool ex::is_equal(const ex & other) const
{
- GINAC_ASSERT(bp!=0);
- GINAC_ASSERT(other.bp!=0);
- if (bp==other.bp) // trivial case: both expressions point to same basic
+ if (bp == other.bp) // trivial case: both expressions point to same basic
return true;
return bp->is_equal(*other.bp);
}
// 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;
}
// 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 bool has(const ex & thisex, const ex & pattern)
+{ return thisex.has(pattern); }
+
+inline bool find(const ex & thisex, const ex & pattern, lst & found)
+{ return thisex.find(pattern, found); }
-inline int degree(const ex & thisex, const symbol & s)
+inline int degree(const ex & thisex, const ex & 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); }
-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)
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 collect(const ex & thisex, const symbol & s)
-{ return thisex.collect(s); }
+inline ex to_polynomial(const ex & thisex, lst & repl_lst)
+{ return thisex.to_polynomial(repl_lst); }
+
+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 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 subs(const ex & thisex, const ex & e)
-{ return thisex.subs(e); }
+inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
+{ return thisex.match(pattern, repl_lst); }
+
+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 subs(const ex & thisex, const lst & ls, const lst & lr)
-{ return thisex.subs(ls, lr); }
+inline ex symmetrize(const ex & thisex)
+{ return thisex.symmetrize(); }
-inline ex op(const ex & thisex, int i)
+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, size_t i)
{ return thisex.op(i); }
inline ex lhs(const ex & thisex)
inline void swap(ex & e1, ex & e2)
{ e1.swap(e2); }
+/* 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 op0_is_equal : public std::binary_function<ex, ex, bool> {
+ bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
+};
+
+struct ex_swap : public std::binary_function<ex, ex, void> {
+ void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
+};
+
+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) { 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 &)) 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.
+ *
+ * @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
+
+// 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);
+}
+
+/** Specialization of std::iter_swap() for vector<ex> iterators. */
+template <>
+inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
+{
+ i1->swap(*i2);
+}
+
+/** Specialization of std::iter_swap() for list<ex> iterators. */
+template <>
+inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
+{
+ i1->swap(*i2);
+}
+
+} // namespace std
+
#endif // ndef __GINAC_EX_H__
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