X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginac%2Fex.h;h=336bb14f1c1c51640988515e3c7a647d90b9ffdf;hp=d16bdbc1998c5b31de414f232b42c8e675baa97a;hb=d7c5ca75b0fc9e58a8676681e3801869e47ad911;hpb=757406e244f4f257aafaa0f355d5376122cea10e diff --git a/ginac/ex.h b/ginac/ex.h index d16bdbc1..336bb14f 100644 --- a/ginac/ex.h +++ b/ginac/ex.h @@ -3,7 +3,7 @@ * Interface to GiNaC's light-weight expression handles. */ /* - * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany + * GiNaC Copyright (C) 1999-2007 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 @@ -17,14 +17,16 @@ * * 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__ #include +#include #include +#include #include "basic.h" #include "ptr.h" @@ -50,29 +52,27 @@ private: /** For construction of flyweights, etc. */ static library_init library_initializer; - class scalar_products; +class const_iterator; +class const_preorder_iterator; +class const_postorder_iterator; -/** 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 -{ +/** 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 bool are_ex_trivially_equal(const ex &, const ex &); - template friend const T &ex_to(const ex &); - template friend bool is_a(const ex &); - template friend bool is_exactly_a(const ex &); + friend inline bool are_ex_trivially_equal(const ex &, const ex &); + template friend inline const T &ex_to(const ex &); + template friend inline bool is_a(const ex &); + template friend inline bool is_exactly_a(const ex &); // default constructor, copy constructor and assignment operator public: - ex(); -#ifdef OBSCURE_CINT_HACK - ex(const ex & other); - ex & operator=(const ex & other); -#endif + ex() throw(); // other constructors public: @@ -89,21 +89,31 @@ public: * Undefined symbols and other parser errors will throw an exception. */ ex(const std::string &s, const ex &l); +public: // non-virtual functions in this class public: /** Efficiently swap the contents of two expressions. */ - void swap(ex & other) + void swap(ex & other) throw() { GINAC_ASSERT(bp->flags & status_flags::dynallocated); GINAC_ASSERT(other.bp->flags & status_flags::dynallocated); bp.swap(other.bp); } + // iterators + const_iterator begin() const throw(); + const_iterator end() const throw(); + const_preorder_iterator preorder_begin() const; + const_preorder_iterator preorder_end() const throw(); + const_postorder_iterator postorder_begin() const; + const_postorder_iterator postorder_end() const throw(); + // 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); } + ex eval_integ() const { return bp->eval_integ(); } // printing void print(const print_context & c, unsigned level = 0) const; @@ -124,8 +134,13 @@ public: 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) const { return bp->has(pattern); } + bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); } 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); } @@ -146,6 +161,7 @@ public: 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); } @@ -162,30 +178,34 @@ public: // rational functions ex normal(int level = 0) const; - ex to_rational(lst &repl_lst) const; - ex to_polynomial(lst &repl_lst) const; + ex to_rational(exmap & repl) const; + ex to_rational(lst & repl_lst) const; + ex to_polynomial(exmap & repl) const; + ex to_polynomial(lst & repl_lst) const; ex numer() const; ex denom() const; ex numer_denom() const; // polynomial algorithms - ex unit(const symbol &x) const; - ex content(const symbol &x) const; + ex unit(const ex &x) const; + ex content(const ex &x) const; numeric integer_content() const; - ex primpart(const symbol &x) const; - ex primpart(const symbol &x, const ex &cont) 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() const; - ex simplify_indexed(const scalar_products & sp) const; + 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 { extern const ex _ex0; return is_equal(_ex0); } + bool is_zero_matrix() const; // symmetry ex symmetrize() const; @@ -197,7 +217,7 @@ public: // noncommutativity unsigned return_type() const { return bp->return_type(); } - unsigned return_type_tinfo() const { return bp->return_type_tinfo(); } + tinfo_t return_type_tinfo() const { return bp->return_type_tinfo(); } unsigned gethash() const { return bp->gethash(); } @@ -210,37 +230,12 @@ private: static basic & construct_from_double(double d); static ptr 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() - { - 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() - { - last_created_or_assigned_bp = bp; - last_created_or_assigned_exp = (long)(void *)(this); - } -#endif // def OBSCURE_CINT_HACK + void share(const ex & other) const; // member variables private: - ptr bp; ///< pointer to basic object managed by this - -#ifdef OBSCURE_CINT_HACK -public: - static ptr last_created_or_assigned_bp; - static basic * dummy_bp; - static long last_created_or_assigned_exp; -#endif // def OBSCURE_CINT_HACK + mutable ptr bp; ///< pointer to basic object managed by this }; @@ -251,110 +246,407 @@ public: extern const basic *_num0_bp; inline -ex::ex() : bp(*const_cast(_num0_bp)) -{ - GINAC_ASSERT(bp->flags & status_flags::dynallocated); -#ifdef OBSCURE_CINT_HACK - update_last_created_or_assigned_bp(); -#endif // def OBSCURE_CINT_HACK -} - -#ifdef OBSCURE_CINT_HACK -inline -ex::ex(const ex & other) : bp(other.bp) -{ - GINAC_ASSERT((bp->flags) & status_flags::dynallocated); - update_last_created_or_assigned_bp(); -} - -inline -ex & ex::operator=(const ex & other) +ex::ex() throw() : bp(*const_cast(_num0_bp)) { GINAC_ASSERT(bp->flags & status_flags::dynallocated); - GINAC_ASSERT(other.bp->flags & status_flags::dynallocated); - bp = other.bp; - update_last_created_or_assigned_bp(); - return *this; } -#endif // def OBSCURE_CINT_HACK inline ex::ex(const basic & other) : bp(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) : bp(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) : bp(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) : bp(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) : bp(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) : bp(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) : bp(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 { +#ifdef GINAC_COMPARE_STATISTICS + compare_statistics.total_compares++; +#endif if (bp == other.bp) // trivial case: both expressions point to same basic return 0; - return bp->compare(*other.bp); +#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; - return bp->is_equal(*other.bp); +#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 { + friend class ex; + friend class const_preorder_iterator; + friend class const_postorder_iterator; + +public: + const_iterator() throw() {} + +private: + const_iterator(const ex &e_, size_t i_) throw() : 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::auto_ptr operator->() const + { + return std::auto_ptr(new ex(operator*())); + } + + ex operator[](difference_type n) const + { + return e.op(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(e, i + n); + } + + inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw() + { + return const_iterator(it.e, 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(e, i - n); + } + + inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw() + { + return lhs.i - rhs.i; + } + + bool operator==(const const_iterator &other) const throw() + { + return are_ex_trivially_equal(e, other.e) && 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); + } + +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 throw() + { + return are_ex_trivially_equal(e, other.e) && i == other.i; + } + + bool operator!=(const _iter_rep &other) const throw() + { + return !(*this == other); + } + + ex e; + size_t i; + size_t i_end; +}; + +} // namespace internal + +class const_preorder_iterator : public std::iterator { +public: + const_preorder_iterator() throw() {} + + 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 throw() + { + return s == other.s; + } + + bool operator!=(const const_preorder_iterator &other) const throw() + { + return !(*this == other); + } + +private: + std::stack > 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 { +public: + const_postorder_iterator() throw() {} + + 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 throw() + { + return s == other.s; + } + + bool operator!=(const const_postorder_iterator &other) const throw() + { + return !(*this == other); + } + +private: + std::stack > 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 throw() +{ + return const_iterator(*this, 0); +} + +inline const_iterator ex::end() const throw() +{ + 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 throw() +{ + 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 throw() +{ + return const_postorder_iterator(); } @@ -369,6 +661,28 @@ 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 : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; } +}; + +struct ex_is_equal : public std::binary_function { + bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); } +}; + +struct op0_is_equal : public std::binary_function { + 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 { + 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(); } @@ -376,12 +690,24 @@ inline size_t nops(const ex & thisex) inline ex expand(const ex & thisex, unsigned options = 0) { return thisex.expand(options); } -inline bool has(const ex & thisex, const ex & pattern) -{ return thisex.has(pattern); } +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, lst & 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); } @@ -406,6 +732,12 @@ inline ex normal(const ex & thisex, int level=0) 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 to_polynomial(const ex & thisex, lst & repl_lst) { return thisex.to_polynomial(repl_lst); } @@ -421,6 +753,9 @@ inline ex evalf(const ex & thisex, int level = 0) 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); } @@ -430,11 +765,11 @@ inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 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, 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(); } @@ -469,29 +804,6 @@ inline bool is_zero(const ex & thisex) 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::iterator i1, std::vector::iterator i2) -{ i1->swap(*i2); } - - -/* Function objects for STL sort() etc. */ -struct ex_is_less : public std::binary_function { - bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; } -}; - -struct ex_is_equal : public std::binary_function { - bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); } -}; - -struct op0_is_equal : public std::binary_function { - 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 { - 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); @@ -549,6 +861,52 @@ public: ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); } }; +template +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) { return (c.*ptr)(e); } +}; + +template +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) { return (c.*ptr)(e, arg1); } +}; + +template +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) { return (c.*ptr)(e, arg1, arg2); } +}; + +template +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) { return (c.*ptr)(e, arg1, arg2, arg3); } +}; + inline ex ex::map(ex f(const ex &)) const { pointer_to_map_function fcn(f); @@ -574,7 +932,9 @@ inline bool is_exactly_a(const ex &obj) /** 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. + * 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 @@ -588,4 +948,31 @@ inline const T &ex_to(const ex &e) } // 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 iterators. */ +template <> +inline void iter_swap(vector::iterator i1, vector::iterator i2) +{ + i1->swap(*i2); +} + +/** Specialization of std::iter_swap() for list iterators. */ +template <> +inline void iter_swap(list::iterator i1, list::iterator i2) +{ + i1->swap(*i2); +} + +} // namespace std + #endif // ndef __GINAC_EX_H__