3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
23 #ifndef __GINAC_EX_H__
24 #define __GINAC_EX_H__
37 /** Helper class to initialize the library. There must be one static object
38 * of this class in every object file that makes use of our flyweights in
39 * order to guarantee proper initialization. Hence we put it into this
40 * file which is included by every relevant file anyways. This is modeled
41 * after section 27.4.2.1.6 of the C++ standard, where cout and friends are
52 /** For construction of flyweights, etc. */
53 static library_init library_initializer;
56 class scalar_products;
60 /** Lightweight wrapper for GiNaC's symbolic objects. Basically all it does is
61 * to hold a pointer to the other objects, manage the reference counting and
62 * provide methods for manipulation of these objects. (Some people call such
63 * a thing a proxy class.) */
66 friend class archive_node;
67 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
68 template<class T> friend inline const T &ex_to(const ex &);
69 template<class T> friend inline bool is_a(const ex &);
70 template<class T> friend inline bool is_exactly_a(const ex &);
72 // default constructor, copy constructor and assignment operator
75 #ifdef OBSCURE_CINT_HACK
77 ex & operator=(const ex & other);
82 ex(const basic & other);
89 /** Construct ex from string and a list of symbols. The input grammar is
90 * similar to the GiNaC output format. All symbols and indices to be used
91 * in the expression must be specified in a lst in the second argument.
92 * Undefined symbols and other parser errors will throw an exception. */
93 ex(const std::string &s, const ex &l);
96 // non-virtual functions in this class
98 /** Efficiently swap the contents of two expressions. */
99 void swap(ex & other) throw()
101 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
102 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
107 const_iterator begin() const throw();
108 const_iterator end() const throw();
111 ex eval(int level = 0) const { return bp->eval(level); }
112 ex evalf(int level = 0) const { return bp->evalf(level); }
113 ex evalm() const { return bp->evalm(); }
114 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
117 void print(const print_context & c, unsigned level = 0) const;
118 void dbgprint() const;
119 void dbgprinttree() const;
122 bool info(unsigned inf) const { return bp->info(inf); }
125 size_t nops() const { return bp->nops(); }
126 ex op(size_t i) const { return bp->op(i); }
127 ex operator[](const ex & index) const { return (*bp)[index]; }
128 ex operator[](size_t i) const { return (*bp)[i]; }
129 ex & let_op(size_t i);
130 ex & operator[](const ex & index);
131 ex & operator[](size_t i);
135 // complex conjugation
136 ex conjugate() const { return bp->conjugate(); }
139 bool has(const ex & pattern) const { return bp->has(pattern); }
140 bool find(const ex & pattern, lst & found) const;
141 bool match(const ex & pattern) const;
142 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
145 ex subs(const exmap & m, unsigned options = 0) const;
146 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
147 ex subs(const ex & e, unsigned options = 0) const;
150 ex map(map_function & f) const { return bp->map(f); }
151 ex map(ex (*f)(const ex & e)) const;
153 // visitors and tree traversal
154 void accept(visitor & v) const { bp->accept(v); }
155 void traverse_preorder(visitor & v) const;
156 void traverse_postorder(visitor & v) const;
157 void traverse(visitor & v) const { traverse_preorder(v); }
160 int degree(const ex & s) const { return bp->degree(s); }
161 int ldegree(const ex & s) const { return bp->ldegree(s); }
162 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
163 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
164 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
167 ex expand(unsigned options=0) const;
168 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
170 // differentiation and series expansion
171 ex diff(const symbol & s, unsigned nth = 1) const;
172 ex series(const ex & r, int order, unsigned options = 0) const;
174 // rational functions
175 ex normal(int level = 0) const;
176 ex to_rational(exmap & repl) const;
177 ex to_rational(lst & repl_lst) const;
178 ex to_polynomial(exmap & repl) const;
179 ex to_polynomial(lst & repl_lst) const;
182 ex numer_denom() const;
184 // polynomial algorithms
185 ex unit(const ex &x) const;
186 ex content(const ex &x) const;
187 numeric integer_content() const;
188 ex primpart(const ex &x) const;
189 ex primpart(const ex &x, const ex &cont) const;
190 ex smod(const numeric &xi) const { return bp->smod(xi); }
191 numeric max_coefficient() const;
194 exvector get_free_indices() const { return bp->get_free_indices(); }
195 ex simplify_indexed(unsigned options = 0) const;
196 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
199 int compare(const ex & other) const;
200 bool is_equal(const ex & other) const;
201 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
204 ex symmetrize() const;
205 ex symmetrize(const lst & l) const;
206 ex antisymmetrize() const;
207 ex antisymmetrize(const lst & l) const;
208 ex symmetrize_cyclic() const;
209 ex symmetrize_cyclic(const lst & l) const;
212 unsigned return_type() const { return bp->return_type(); }
213 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
215 unsigned gethash() const { return bp->gethash(); }
218 static ptr<basic> construct_from_basic(const basic & other);
219 static basic & construct_from_int(int i);
220 static basic & construct_from_uint(unsigned int i);
221 static basic & construct_from_long(long i);
222 static basic & construct_from_ulong(unsigned long i);
223 static basic & construct_from_double(double d);
224 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
225 void makewriteable();
226 void share(const ex & other) const;
228 #ifdef OBSCURE_CINT_HACK
230 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
232 if (last_created_or_assigned_bp==0) return false;
233 if ((last_created_or_assigned_bp->flags &
234 status_flags::dynallocated)==0) return false;
235 if ((last_created_or_assigned_bp->flags &
236 status_flags::evaluated)==0) return false;
240 void update_last_created_or_assigned_bp()
242 last_created_or_assigned_bp = bp;
243 last_created_or_assigned_exp = (long)(void *)(this);
245 #endif // def OBSCURE_CINT_HACK
250 mutable ptr<basic> bp; ///< pointer to basic object managed by this
252 #ifdef OBSCURE_CINT_HACK
254 static ptr<basic> last_created_or_assigned_bp;
255 static basic * dummy_bp;
256 static long last_created_or_assigned_exp;
257 #endif // def OBSCURE_CINT_HACK
261 // performance-critical inlined method implementations
263 // This needs to be a basic* because we don't know that numeric is derived
264 // from basic and we need a basic& for the ex default constructor
265 extern const basic *_num0_bp;
268 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
270 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
271 #ifdef OBSCURE_CINT_HACK
272 update_last_created_or_assigned_bp();
273 #endif // def OBSCURE_CINT_HACK
276 #ifdef OBSCURE_CINT_HACK
278 ex::ex(const ex & other) : bp(other.bp)
280 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
281 update_last_created_or_assigned_bp();
285 ex & ex::operator=(const ex & other)
287 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
288 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
290 update_last_created_or_assigned_bp();
293 #endif // def OBSCURE_CINT_HACK
296 ex::ex(const basic & other) : bp(construct_from_basic(other))
298 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
299 #ifdef OBSCURE_CINT_HACK
300 update_last_created_or_assigned_bp();
301 #endif // def OBSCURE_CINT_HACK
305 ex::ex(int i) : bp(construct_from_int(i))
307 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
308 #ifdef OBSCURE_CINT_HACK
309 update_last_created_or_assigned_bp();
310 #endif // def OBSCURE_CINT_HACK
314 ex::ex(unsigned int i) : bp(construct_from_uint(i))
316 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
317 #ifdef OBSCURE_CINT_HACK
318 update_last_created_or_assigned_bp();
319 #endif // def OBSCURE_CINT_HACK
323 ex::ex(long i) : bp(construct_from_long(i))
325 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
326 #ifdef OBSCURE_CINT_HACK
327 update_last_created_or_assigned_bp();
328 #endif // def OBSCURE_CINT_HACK
332 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
334 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
335 #ifdef OBSCURE_CINT_HACK
336 update_last_created_or_assigned_bp();
337 #endif // def OBSCURE_CINT_HACK
341 ex::ex(double const d) : bp(construct_from_double(d))
343 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
344 #ifdef OBSCURE_CINT_HACK
345 update_last_created_or_assigned_bp();
346 #endif // def OBSCURE_CINT_HACK
350 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
352 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
353 #ifdef OBSCURE_CINT_HACK
354 update_last_created_or_assigned_bp();
355 #endif // def OBSCURE_CINT_HACK
359 int ex::compare(const ex & other) const
361 #ifdef GINAC_COMPARE_STATISTICS
362 compare_statistics.total_compares++;
364 if (bp == other.bp) // trivial case: both expressions point to same basic
366 #ifdef GINAC_COMPARE_STATISTICS
367 compare_statistics.nontrivial_compares++;
369 const int cmpval = bp->compare(*other.bp);
372 // Expressions point to different, but equal, trees: conserve
373 // memory and make subsequent compare() operations faster by
374 // making both expressions point to the same tree.
382 bool ex::is_equal(const ex & other) const
384 #ifdef GINAC_COMPARE_STATISTICS
385 compare_statistics.total_is_equals++;
387 if (bp == other.bp) // trivial case: both expressions point to same basic
389 #ifdef GINAC_COMPARE_STATISTICS
390 compare_statistics.nontrivial_is_equals++;
392 const bool equal = bp->is_equal(*other.bp);
395 // Expressions point to different, but equal, trees: conserve
396 // memory and make subsequent compare() operations faster by
397 // making both expressions point to the same tree.
407 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
410 friend class const_preorder_iterator;
411 friend class const_postorder_iterator;
414 const_iterator() throw() {}
417 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
420 // This should return an ex&, but that would be a reference to a
427 // This should return an ex*, but that would be a pointer to a
429 std::auto_ptr<ex> operator->() const
431 return std::auto_ptr<ex>(new ex(operator*()));
434 ex operator[](difference_type n) const
439 const_iterator &operator++() throw()
445 const_iterator operator++(int) throw()
447 const_iterator tmp = *this;
452 const_iterator &operator+=(difference_type n) throw()
458 const_iterator operator+(difference_type n) const throw()
460 return const_iterator(e, i + n);
463 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
465 return const_iterator(it.e, it.i + n);
468 const_iterator &operator--() throw()
474 const_iterator operator--(int) throw()
476 const_iterator tmp = *this;
481 const_iterator &operator-=(difference_type n) throw()
487 const_iterator operator-(difference_type n) const throw()
489 return const_iterator(e, i - n);
492 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
494 return lhs.i - rhs.i;
497 bool operator==(const const_iterator &other) const throw()
499 return are_ex_trivially_equal(e, other.e) && i == other.i;
502 bool operator!=(const const_iterator &other) const throw()
504 return !(*this == other);
507 bool operator<(const const_iterator &other) const throw()
512 bool operator>(const const_iterator &other) const throw()
514 return other < *this;
517 bool operator<=(const const_iterator &other) const throw()
519 return !(other < *this);
522 bool operator>=(const const_iterator &other) const throw()
524 return !(*this < other);
528 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
535 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
537 bool operator==(const _iter_rep &other) const throw()
539 return are_ex_trivially_equal(e, other.e) && i == other.i;
542 bool operator!=(const _iter_rep &other) const throw()
544 return !(*this == other);
552 } // namespace internal
554 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
557 const_preorder_iterator() throw() {}
559 // Provide implicit conversion from const_iterator, so ex::begin() and
560 // ex::end() can be used to create const_preorder_iterators
561 const_preorder_iterator(const const_iterator & cit)
563 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
572 std::auto_ptr<ex> operator->() const
574 return std::auto_ptr<ex>(new ex(operator*()));
577 const_preorder_iterator &operator++()
583 const_preorder_iterator operator++(int)
585 const_preorder_iterator tmp = *this;
590 bool operator==(const const_preorder_iterator &other) const throw()
592 return s.top() == other.s.top();
595 bool operator!=(const const_preorder_iterator &other) const throw()
597 return !(*this == other);
601 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
605 while (s.top().i == s.top().i_end && s.size() > 1) {
610 internal::_iter_rep & current = s.top();
612 if (current.i != current.i_end) {
613 const ex & child = current.e.op(current.i);
614 s.push(internal::_iter_rep(child, 0, child.nops()));
619 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
622 const_postorder_iterator() throw() {}
624 // Provide implicit conversion from const_iterator, so ex::begin() and
625 // ex::end() can be used to create const_postorder_iterators
626 const_postorder_iterator(const const_iterator & cit)
628 size_t n = cit.e.nops();
630 s.push(internal::_iter_rep(cit.e, cit.i, n));
641 std::auto_ptr<ex> operator->() const
643 return std::auto_ptr<ex>(new ex(operator*()));
646 const_postorder_iterator &operator++()
652 const_postorder_iterator operator++(int)
654 const_postorder_iterator tmp = *this;
659 bool operator==(const const_postorder_iterator &other) const throw()
664 bool operator!=(const const_postorder_iterator &other) const throw()
666 return !(*this == other);
670 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
674 while (s.top().i != s.top().i_end) {
675 internal::_iter_rep & current = s.top();
676 const ex & child = current.e.op(current.i);
677 s.push(internal::_iter_rep(child, 0, child.nops()));
683 if (s.top().i == s.top().i_end)
692 inline const_iterator ex::begin() const throw()
694 return const_iterator(*this, 0);
697 inline const_iterator ex::end() const throw()
699 return const_iterator(*this, nops());
705 /** Compare two objects of class quickly without doing a deep tree traversal.
706 * @return "true" if they are equal
707 * "false" if equality cannot be established quickly (e1 and e2 may
708 * still be equal, in this case. */
709 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
711 return e1.bp == e2.bp;
714 /* Function objects for STL sort() etc. */
715 struct ex_is_less : public std::binary_function<ex, ex, bool> {
716 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
719 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
720 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
723 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
724 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
727 struct ex_swap : public std::binary_function<ex, ex, void> {
728 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
731 // wrapper functions around member functions
732 inline size_t nops(const ex & thisex)
733 { return thisex.nops(); }
735 inline ex expand(const ex & thisex, unsigned options = 0)
736 { return thisex.expand(options); }
738 inline bool has(const ex & thisex, const ex & pattern)
739 { return thisex.has(pattern); }
741 inline bool find(const ex & thisex, const ex & pattern, lst & found)
742 { return thisex.find(pattern, found); }
744 inline int degree(const ex & thisex, const ex & s)
745 { return thisex.degree(s); }
747 inline int ldegree(const ex & thisex, const ex & s)
748 { return thisex.ldegree(s); }
750 inline ex coeff(const ex & thisex, const ex & s, int n=1)
751 { return thisex.coeff(s, n); }
753 inline ex numer(const ex & thisex)
754 { return thisex.numer(); }
756 inline ex denom(const ex & thisex)
757 { return thisex.denom(); }
759 inline ex numer_denom(const ex & thisex)
760 { return thisex.numer_denom(); }
762 inline ex normal(const ex & thisex, int level=0)
763 { return thisex.normal(level); }
765 inline ex to_rational(const ex & thisex, lst & repl_lst)
766 { return thisex.to_rational(repl_lst); }
768 inline ex to_rational(const ex & thisex, exmap & repl)
769 { return thisex.to_rational(repl); }
771 inline ex to_polynomial(const ex & thisex, exmap & repl)
772 { return thisex.to_polynomial(repl); }
774 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
775 { return thisex.to_polynomial(repl_lst); }
777 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
778 { return thisex.collect(s, distributed); }
780 inline ex eval(const ex & thisex, int level = 0)
781 { return thisex.eval(level); }
783 inline ex evalf(const ex & thisex, int level = 0)
784 { return thisex.evalf(level); }
786 inline ex evalm(const ex & thisex)
787 { return thisex.evalm(); }
789 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
790 { return thisex.diff(s, nth); }
792 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
793 { return thisex.series(r, order, options); }
795 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
796 { return thisex.match(pattern, repl_lst); }
798 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
799 { return thisex.simplify_indexed(options); }
801 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
802 { return thisex.simplify_indexed(sp, options); }
804 inline ex symmetrize(const ex & thisex)
805 { return thisex.symmetrize(); }
807 inline ex symmetrize(const ex & thisex, const lst & l)
808 { return thisex.symmetrize(l); }
810 inline ex antisymmetrize(const ex & thisex)
811 { return thisex.antisymmetrize(); }
813 inline ex antisymmetrize(const ex & thisex, const lst & l)
814 { return thisex.antisymmetrize(l); }
816 inline ex symmetrize_cyclic(const ex & thisex)
817 { return thisex.symmetrize_cyclic(); }
819 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
820 { return thisex.symmetrize_cyclic(l); }
822 inline ex op(const ex & thisex, size_t i)
823 { return thisex.op(i); }
825 inline ex lhs(const ex & thisex)
826 { return thisex.lhs(); }
828 inline ex rhs(const ex & thisex)
829 { return thisex.rhs(); }
831 inline bool is_zero(const ex & thisex)
832 { return thisex.is_zero(); }
834 inline void swap(ex & e1, ex & e2)
837 inline ex ex::subs(const exmap & m, unsigned options) const
839 return bp->subs(m, options);
842 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
843 { return thisex.subs(m, options); }
845 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
846 { return thisex.subs(ls, lr, options); }
848 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
849 { return thisex.subs(e, options); }
852 /* Convert function pointer to function object suitable for map(). */
853 class pointer_to_map_function : public map_function {
855 ex (*ptr)(const ex &);
857 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
858 ex operator()(const ex & e) { return ptr(e); }
862 class pointer_to_map_function_1arg : public map_function {
864 ex (*ptr)(const ex &, T1);
867 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
868 ex operator()(const ex & e) { return ptr(e, arg1); }
871 template<class T1, class T2>
872 class pointer_to_map_function_2args : public map_function {
874 ex (*ptr)(const ex &, T1, T2);
878 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
879 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
882 template<class T1, class T2, class T3>
883 class pointer_to_map_function_3args : public map_function {
885 ex (*ptr)(const ex &, T1, T2, T3);
890 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) {}
891 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
894 inline ex ex::map(ex f(const ex &)) const
896 pointer_to_map_function fcn(f);
900 // convenience type checker template functions
902 /** Check if ex is a handle to a T, including base classes. */
904 inline bool is_a(const ex &obj)
906 return is_a<T>(*obj.bp);
909 /** Check if ex is a handle to a T, not including base classes. */
911 inline bool is_exactly_a(const ex &obj)
913 return is_exactly_a<T>(*obj.bp);
916 /** Return a reference to the basic-derived class T object embedded in an
917 * expression. This is fast but unsafe: the result is undefined if the
918 * expression does not contain a T object at its top level. Hence, you
919 * should generally check the type of e first. Also, you shouldn't cache
920 * the returned reference because GiNaC's garbage collector may destroy
921 * the referenced object any time it's used in another expression.
923 * @param e expression
924 * @return reference to object of class T
925 * @see is_exactly_a<class T>() */
927 inline const T &ex_to(const ex &e)
929 GINAC_ASSERT(is_a<T>(e));
930 return static_cast<const T &>(*e.bp);
936 // Specializations of Standard Library algorithms
939 /** Specialization of std::swap() for ex objects. */
941 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
946 /** Specialization of std::iter_swap() for vector<ex> iterators. */
948 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
953 /** Specialization of std::iter_swap() for list<ex> iterators. */
955 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
962 #endif // ndef __GINAC_EX_H__