ex.h

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/*
 *  GiNaC Copyright (C) 1999-2020 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
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#ifndef GINAC_EX_H
#define GINAC_EX_H
 
#include "basic.h"
#include "ptr.h"
 
#include <functional>
#include <iosfwd>
#include <iterator>
#include <memory>
#include <stack>
 
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
 
class library_init {
    static void init_unarchivers();
public:
    library_init();
    ~library_init();
private:
    static int count;
};
static library_init library_initializer;
 
class scalar_products;
class const_iterator;
class const_preorder_iterator;
class const_postorder_iterator;
 
 
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 &);
    
    // default constructor, copy constructor and assignment operator
public:
    ex() noexcept;
 
    // other constructors
public:
    ex(const basic & other);
    ex(int i);
    ex(unsigned int i);
    ex(long i);
    ex(unsigned long i);
    ex(long long i);
    ex(unsigned long long i);
    ex(double const d);
 
    ex(const std::string &s, const ex &l);
    
public:
    // non-virtual functions in this class
public:
    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 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;
 
    // 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)); }
 
    // expand/collect
    ex expand(unsigned options=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;
 
    // 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() const { 
#ifndef _MSC_VER
      extern const ex _ex0;
#endif
      return is_equal(_ex0); 
    }
    bool is_zero_matrix() 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(); }
    return_type_t return_type_tinfo() const { return bp->return_type_tinfo(); }
 
    unsigned gethash() const { return bp->gethash(); }
 
private:
    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_longlong(long long i);
    static basic & construct_from_ulonglong(unsigned long 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;
 
// member variables
 
private:
    mutable ptr<basic> bp;  
};
 
 
// 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() noexcept : bp(*const_cast<basic *>(_num0_bp))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(const basic & other) : bp(construct_from_basic(other))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(int i) : bp(construct_from_int(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(unsigned int i) : bp(construct_from_uint(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(long i) : bp(construct_from_long(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(unsigned long i) : bp(construct_from_ulong(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(long long i) : bp(construct_from_longlong(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(unsigned long long i) : bp(construct_from_ulonglong(i))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(double const d) : bp(construct_from_double(d))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
{
    GINAC_ASSERT(bp->flags & status_flags::dynallocated);
}
 
inline
int ex::compare(const ex & other) const
{
#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
bool ex::is_equal(const ex & other) const
{
#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;
}
 
 
// 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
{
    return const_iterator(*this, 0);
}
 
inline const_iterator ex::end() const noexcept
{
    return const_iterator(*this, nops());
}
 
inline const_preorder_iterator ex::preorder_begin() const
{
    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
 
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 size_t nops(const ex & thisex)
{ return thisex.nops(); }
 
inline ex expand(const ex & thisex, unsigned options = 0)
{ return thisex.expand(options); }
 
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); }
 
inline int ldegree(const ex & thisex, const ex & s)
{ return thisex.ldegree(s); }
 
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.numer(); }
 
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)
{ return thisex.normal(); }
 
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)
{ return thisex.eval(); }
 
inline ex evalf(const ex & thisex)
{ return thisex.evalf(); }
 
inline ex evalm(const ex & thisex)
{ return thisex.evalm(); }
 
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); }
 
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, exmap& repl_lst)
{ return thisex.match(pattern, repl_lst); }
 
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, unsigned options = 0)
{ return thisex.simplify_indexed(sp, options); }
 
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, size_t i)
{ return thisex.op(i); }
 
inline ex lhs(const ex & thisex)
{ return thisex.lhs(); }
 
inline ex rhs(const ex & thisex)
{ return thisex.rhs(); }
 
inline bool is_zero(const ex & thisex)
{ return thisex.is_zero(); }
 
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
 
template <class T>
inline bool is_a(const ex &obj)
{
    return is_a<T>(*obj.bp);
}
 
template <class T>
inline bool is_exactly_a(const ex &obj)
{
    return is_exactly_a<T>(*obj.bp);
}
 
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 {
 
template <>
inline void swap(GiNaC::ex &a, GiNaC::ex &b)
{
    a.swap(b);
}
 
template<>
struct hash<GiNaC::ex>
{
    std::size_t operator()(const GiNaC::ex & e) const noexcept
    {
        return e.gethash();
    }
};
 
template<>
struct equal_to<GiNaC::ex>
{
    bool operator()(const GiNaC::ex &e1, const GiNaC::ex &e2) const noexcept
    {
        return e1.is_equal(e2);
    }
};
 
} // namespace std
 
#endif // ndef GINAC_EX_H