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;
58 class const_preorder_iterator;
59 class const_postorder_iterator;
62 /** Lightweight wrapper for GiNaC's symbolic objects. Basically all it does is
63 * to hold a pointer to the other objects, manage the reference counting and
64 * provide methods for manipulation of these objects. (Some people call such
65 * a thing a proxy class.) */
67 friend class archive_node;
68 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
69 template<class T> friend inline const T &ex_to(const ex &);
70 template<class T> friend inline bool is_a(const ex &);
71 template<class T> friend inline bool is_exactly_a(const ex &);
73 // default constructor, copy constructor and assignment operator
76 #ifdef OBSCURE_CINT_HACK
78 ex & operator=(const ex & other);
83 ex(const basic & other);
90 /** Construct ex from string and a list of symbols. The input grammar is
91 * similar to the GiNaC output format. All symbols and indices to be used
92 * in the expression must be specified in a lst in the second argument.
93 * Undefined symbols and other parser errors will throw an exception. */
94 ex(const std::string &s, const ex &l);
97 // non-virtual functions in this class
99 /** Efficiently swap the contents of two expressions. */
100 void swap(ex & other) throw()
102 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
103 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
108 const_iterator begin() const throw();
109 const_iterator end() const throw();
110 const_preorder_iterator preorder_begin() const;
111 const_preorder_iterator preorder_end() const throw();
112 const_postorder_iterator postorder_begin() const;
113 const_postorder_iterator postorder_end() const throw();
116 ex eval(int level = 0) const { return bp->eval(level); }
117 ex evalf(int level = 0) const { return bp->evalf(level); }
118 ex evalm() const { return bp->evalm(); }
119 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
122 void print(const print_context & c, unsigned level = 0) const;
123 void dbgprint() const;
124 void dbgprinttree() const;
127 bool info(unsigned inf) const { return bp->info(inf); }
130 size_t nops() const { return bp->nops(); }
131 ex op(size_t i) const { return bp->op(i); }
132 ex operator[](const ex & index) const { return (*bp)[index]; }
133 ex operator[](size_t i) const { return (*bp)[i]; }
134 ex & let_op(size_t i);
135 ex & operator[](const ex & index);
136 ex & operator[](size_t i);
140 // complex conjugation
141 ex conjugate() const { return bp->conjugate(); }
144 bool has(const ex & pattern) const { return bp->has(pattern); }
145 bool find(const ex & pattern, lst & found) const;
146 bool match(const ex & pattern) const;
147 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
150 ex subs(const exmap & m, unsigned options = 0) const;
151 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
152 ex subs(const ex & e, unsigned options = 0) const;
155 ex map(map_function & f) const { return bp->map(f); }
156 ex map(ex (*f)(const ex & e)) const;
158 // visitors and tree traversal
159 void accept(visitor & v) const { bp->accept(v); }
160 void traverse_preorder(visitor & v) const;
161 void traverse_postorder(visitor & v) const;
162 void traverse(visitor & v) const { traverse_preorder(v); }
165 int degree(const ex & s) const { return bp->degree(s); }
166 int ldegree(const ex & s) const { return bp->ldegree(s); }
167 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
168 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
169 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
172 ex expand(unsigned options=0) const;
173 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
175 // differentiation and series expansion
176 ex diff(const symbol & s, unsigned nth = 1) const;
177 ex series(const ex & r, int order, unsigned options = 0) const;
179 // rational functions
180 ex normal(int level = 0) const;
181 ex to_rational(exmap & repl) const;
182 ex to_rational(lst & repl_lst) const;
183 ex to_polynomial(exmap & repl) const;
184 ex to_polynomial(lst & repl_lst) const;
187 ex numer_denom() const;
189 // polynomial algorithms
190 ex unit(const ex &x) const;
191 ex content(const ex &x) const;
192 numeric integer_content() const;
193 ex primpart(const ex &x) const;
194 ex primpart(const ex &x, const ex &cont) const;
195 ex smod(const numeric &xi) const { return bp->smod(xi); }
196 numeric max_coefficient() const;
199 exvector get_free_indices() const { return bp->get_free_indices(); }
200 ex simplify_indexed(unsigned options = 0) const;
201 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
204 int compare(const ex & other) const;
205 bool is_equal(const ex & other) const;
206 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
209 ex symmetrize() const;
210 ex symmetrize(const lst & l) const;
211 ex antisymmetrize() const;
212 ex antisymmetrize(const lst & l) const;
213 ex symmetrize_cyclic() const;
214 ex symmetrize_cyclic(const lst & l) const;
217 unsigned return_type() const { return bp->return_type(); }
218 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
220 unsigned gethash() const { return bp->gethash(); }
223 static ptr<basic> construct_from_basic(const basic & other);
224 static basic & construct_from_int(int i);
225 static basic & construct_from_uint(unsigned int i);
226 static basic & construct_from_long(long i);
227 static basic & construct_from_ulong(unsigned long i);
228 static basic & construct_from_double(double d);
229 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
230 void makewriteable();
231 void share(const ex & other) const;
233 #ifdef OBSCURE_CINT_HACK
235 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
237 if (last_created_or_assigned_bp==0) return false;
238 if ((last_created_or_assigned_bp->flags &
239 status_flags::dynallocated)==0) return false;
240 if ((last_created_or_assigned_bp->flags &
241 status_flags::evaluated)==0) return false;
245 void update_last_created_or_assigned_bp()
247 last_created_or_assigned_bp = bp;
248 last_created_or_assigned_exp = (long)(void *)(this);
250 #endif // def OBSCURE_CINT_HACK
255 mutable ptr<basic> bp; ///< pointer to basic object managed by this
257 #ifdef OBSCURE_CINT_HACK
259 static ptr<basic> last_created_or_assigned_bp;
260 static basic * dummy_bp;
261 static long last_created_or_assigned_exp;
262 #endif // def OBSCURE_CINT_HACK
266 // performance-critical inlined method implementations
268 // This needs to be a basic* because we don't know that numeric is derived
269 // from basic and we need a basic& for the ex default constructor
270 extern const basic *_num0_bp;
273 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
275 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
276 #ifdef OBSCURE_CINT_HACK
277 update_last_created_or_assigned_bp();
278 #endif // def OBSCURE_CINT_HACK
281 #ifdef OBSCURE_CINT_HACK
283 ex::ex(const ex & other) : bp(other.bp)
285 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
286 update_last_created_or_assigned_bp();
290 ex & ex::operator=(const ex & other)
292 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
293 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
295 update_last_created_or_assigned_bp();
298 #endif // def OBSCURE_CINT_HACK
301 ex::ex(const basic & other) : bp(construct_from_basic(other))
303 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
304 #ifdef OBSCURE_CINT_HACK
305 update_last_created_or_assigned_bp();
306 #endif // def OBSCURE_CINT_HACK
310 ex::ex(int i) : bp(construct_from_int(i))
312 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
313 #ifdef OBSCURE_CINT_HACK
314 update_last_created_or_assigned_bp();
315 #endif // def OBSCURE_CINT_HACK
319 ex::ex(unsigned int i) : bp(construct_from_uint(i))
321 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
322 #ifdef OBSCURE_CINT_HACK
323 update_last_created_or_assigned_bp();
324 #endif // def OBSCURE_CINT_HACK
328 ex::ex(long i) : bp(construct_from_long(i))
330 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
331 #ifdef OBSCURE_CINT_HACK
332 update_last_created_or_assigned_bp();
333 #endif // def OBSCURE_CINT_HACK
337 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
339 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
340 #ifdef OBSCURE_CINT_HACK
341 update_last_created_or_assigned_bp();
342 #endif // def OBSCURE_CINT_HACK
346 ex::ex(double const d) : bp(construct_from_double(d))
348 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
349 #ifdef OBSCURE_CINT_HACK
350 update_last_created_or_assigned_bp();
351 #endif // def OBSCURE_CINT_HACK
355 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
357 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
358 #ifdef OBSCURE_CINT_HACK
359 update_last_created_or_assigned_bp();
360 #endif // def OBSCURE_CINT_HACK
364 int ex::compare(const ex & other) const
366 #ifdef GINAC_COMPARE_STATISTICS
367 compare_statistics.total_compares++;
369 if (bp == other.bp) // trivial case: both expressions point to same basic
371 #ifdef GINAC_COMPARE_STATISTICS
372 compare_statistics.nontrivial_compares++;
374 const int cmpval = bp->compare(*other.bp);
377 // Expressions point to different, but equal, trees: conserve
378 // memory and make subsequent compare() operations faster by
379 // making both expressions point to the same tree.
387 bool ex::is_equal(const ex & other) const
389 #ifdef GINAC_COMPARE_STATISTICS
390 compare_statistics.total_is_equals++;
392 if (bp == other.bp) // trivial case: both expressions point to same basic
394 #ifdef GINAC_COMPARE_STATISTICS
395 compare_statistics.nontrivial_is_equals++;
397 const bool equal = bp->is_equal(*other.bp);
400 // Expressions point to different, but equal, trees: conserve
401 // memory and make subsequent compare() operations faster by
402 // making both expressions point to the same tree.
412 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
414 friend class const_preorder_iterator;
415 friend class const_postorder_iterator;
418 const_iterator() throw() {}
421 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
424 // This should return an ex&, but that would be a reference to a
431 // This should return an ex*, but that would be a pointer to a
433 std::auto_ptr<ex> operator->() const
435 return std::auto_ptr<ex>(new ex(operator*()));
438 ex operator[](difference_type n) const
443 const_iterator &operator++() throw()
449 const_iterator operator++(int) throw()
451 const_iterator tmp = *this;
456 const_iterator &operator+=(difference_type n) throw()
462 const_iterator operator+(difference_type n) const throw()
464 return const_iterator(e, i + n);
467 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
469 return const_iterator(it.e, it.i + n);
472 const_iterator &operator--() throw()
478 const_iterator operator--(int) throw()
480 const_iterator tmp = *this;
485 const_iterator &operator-=(difference_type n) throw()
491 const_iterator operator-(difference_type n) const throw()
493 return const_iterator(e, i - n);
496 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
498 return lhs.i - rhs.i;
501 bool operator==(const const_iterator &other) const throw()
503 return are_ex_trivially_equal(e, other.e) && i == other.i;
506 bool operator!=(const const_iterator &other) const throw()
508 return !(*this == other);
511 bool operator<(const const_iterator &other) const throw()
516 bool operator>(const const_iterator &other) const throw()
518 return other < *this;
521 bool operator<=(const const_iterator &other) const throw()
523 return !(other < *this);
526 bool operator>=(const const_iterator &other) const throw()
528 return !(*this < other);
532 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
539 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
541 bool operator==(const _iter_rep &other) const throw()
543 return are_ex_trivially_equal(e, other.e) && i == other.i;
546 bool operator!=(const _iter_rep &other) const throw()
548 return !(*this == other);
556 } // namespace internal
558 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
560 const_preorder_iterator() throw() {}
562 const_preorder_iterator(const ex &e, size_t n)
564 s.push(internal::_iter_rep(e, 0, n));
568 reference operator*() const
573 pointer operator->() const
578 const_preorder_iterator &operator++()
584 const_preorder_iterator operator++(int)
586 const_preorder_iterator tmp = *this;
591 bool operator==(const const_preorder_iterator &other) const throw()
596 bool operator!=(const const_preorder_iterator &other) const throw()
598 return !(*this == other);
602 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
606 while (!s.empty() && s.top().i == s.top().i_end) {
613 internal::_iter_rep & current = s.top();
615 if (current.i != current.i_end) {
616 const ex & child = current.e.op(current.i);
617 s.push(internal::_iter_rep(child, 0, child.nops()));
622 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
624 const_postorder_iterator() throw() {}
626 const_postorder_iterator(const ex &e, size_t n)
628 s.push(internal::_iter_rep(e, 0, n));
633 reference operator*() const
638 pointer operator->() const
643 const_postorder_iterator &operator++()
649 const_postorder_iterator operator++(int)
651 const_postorder_iterator tmp = *this;
656 bool operator==(const const_postorder_iterator &other) const throw()
661 bool operator!=(const const_postorder_iterator &other) const throw()
663 return !(*this == other);
667 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
671 while (s.top().i != s.top().i_end) {
672 internal::_iter_rep & current = s.top();
673 const ex & child = current.e.op(current.i);
674 s.push(internal::_iter_rep(child, 0, child.nops()));
680 if (s.top().i == s.top().i_end)
689 inline const_iterator ex::begin() const throw()
691 return const_iterator(*this, 0);
694 inline const_iterator ex::end() const throw()
696 return const_iterator(*this, nops());
699 inline const_preorder_iterator ex::preorder_begin() const
701 return const_preorder_iterator(*this, nops());
704 inline const_preorder_iterator ex::preorder_end() const throw()
706 return const_preorder_iterator();
709 inline const_postorder_iterator ex::postorder_begin() const
711 return const_postorder_iterator(*this, nops());
714 inline const_postorder_iterator ex::postorder_end() const throw()
716 return const_postorder_iterator();
722 /** Compare two objects of class quickly without doing a deep tree traversal.
723 * @return "true" if they are equal
724 * "false" if equality cannot be established quickly (e1 and e2 may
725 * still be equal, in this case. */
726 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
728 return e1.bp == e2.bp;
731 /* Function objects for STL sort() etc. */
732 struct ex_is_less : public std::binary_function<ex, ex, bool> {
733 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
736 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
737 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
740 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
741 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
744 struct ex_swap : public std::binary_function<ex, ex, void> {
745 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
748 // wrapper functions around member functions
749 inline size_t nops(const ex & thisex)
750 { return thisex.nops(); }
752 inline ex expand(const ex & thisex, unsigned options = 0)
753 { return thisex.expand(options); }
755 inline ex conjugate(const ex & thisex)
756 { return thisex.conjugate(); }
758 inline bool has(const ex & thisex, const ex & pattern)
759 { return thisex.has(pattern); }
761 inline bool find(const ex & thisex, const ex & pattern, lst & found)
762 { return thisex.find(pattern, found); }
764 inline int degree(const ex & thisex, const ex & s)
765 { return thisex.degree(s); }
767 inline int ldegree(const ex & thisex, const ex & s)
768 { return thisex.ldegree(s); }
770 inline ex coeff(const ex & thisex, const ex & s, int n=1)
771 { return thisex.coeff(s, n); }
773 inline ex numer(const ex & thisex)
774 { return thisex.numer(); }
776 inline ex denom(const ex & thisex)
777 { return thisex.denom(); }
779 inline ex numer_denom(const ex & thisex)
780 { return thisex.numer_denom(); }
782 inline ex normal(const ex & thisex, int level=0)
783 { return thisex.normal(level); }
785 inline ex to_rational(const ex & thisex, lst & repl_lst)
786 { return thisex.to_rational(repl_lst); }
788 inline ex to_rational(const ex & thisex, exmap & repl)
789 { return thisex.to_rational(repl); }
791 inline ex to_polynomial(const ex & thisex, exmap & repl)
792 { return thisex.to_polynomial(repl); }
794 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
795 { return thisex.to_polynomial(repl_lst); }
797 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
798 { return thisex.collect(s, distributed); }
800 inline ex eval(const ex & thisex, int level = 0)
801 { return thisex.eval(level); }
803 inline ex evalf(const ex & thisex, int level = 0)
804 { return thisex.evalf(level); }
806 inline ex evalm(const ex & thisex)
807 { return thisex.evalm(); }
809 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
810 { return thisex.diff(s, nth); }
812 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
813 { return thisex.series(r, order, options); }
815 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
816 { return thisex.match(pattern, repl_lst); }
818 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
819 { return thisex.simplify_indexed(options); }
821 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
822 { return thisex.simplify_indexed(sp, options); }
824 inline ex symmetrize(const ex & thisex)
825 { return thisex.symmetrize(); }
827 inline ex symmetrize(const ex & thisex, const lst & l)
828 { return thisex.symmetrize(l); }
830 inline ex antisymmetrize(const ex & thisex)
831 { return thisex.antisymmetrize(); }
833 inline ex antisymmetrize(const ex & thisex, const lst & l)
834 { return thisex.antisymmetrize(l); }
836 inline ex symmetrize_cyclic(const ex & thisex)
837 { return thisex.symmetrize_cyclic(); }
839 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
840 { return thisex.symmetrize_cyclic(l); }
842 inline ex op(const ex & thisex, size_t i)
843 { return thisex.op(i); }
845 inline ex lhs(const ex & thisex)
846 { return thisex.lhs(); }
848 inline ex rhs(const ex & thisex)
849 { return thisex.rhs(); }
851 inline bool is_zero(const ex & thisex)
852 { return thisex.is_zero(); }
854 inline void swap(ex & e1, ex & e2)
857 inline ex ex::subs(const exmap & m, unsigned options) const
859 return bp->subs(m, options);
862 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
863 { return thisex.subs(m, options); }
865 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
866 { return thisex.subs(ls, lr, options); }
868 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
869 { return thisex.subs(e, options); }
872 /* Convert function pointer to function object suitable for map(). */
873 class pointer_to_map_function : public map_function {
875 ex (*ptr)(const ex &);
877 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
878 ex operator()(const ex & e) { return ptr(e); }
882 class pointer_to_map_function_1arg : public map_function {
884 ex (*ptr)(const ex &, T1);
887 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
888 ex operator()(const ex & e) { return ptr(e, arg1); }
891 template<class T1, class T2>
892 class pointer_to_map_function_2args : public map_function {
894 ex (*ptr)(const ex &, T1, T2);
898 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
899 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
902 template<class T1, class T2, class T3>
903 class pointer_to_map_function_3args : public map_function {
905 ex (*ptr)(const ex &, T1, T2, T3);
910 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) {}
911 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
914 inline ex ex::map(ex f(const ex &)) const
916 pointer_to_map_function fcn(f);
920 // convenience type checker template functions
922 /** Check if ex is a handle to a T, including base classes. */
924 inline bool is_a(const ex &obj)
926 return is_a<T>(*obj.bp);
929 /** Check if ex is a handle to a T, not including base classes. */
931 inline bool is_exactly_a(const ex &obj)
933 return is_exactly_a<T>(*obj.bp);
936 /** Return a reference to the basic-derived class T object embedded in an
937 * expression. This is fast but unsafe: the result is undefined if the
938 * expression does not contain a T object at its top level. Hence, you
939 * should generally check the type of e first. Also, you shouldn't cache
940 * the returned reference because GiNaC's garbage collector may destroy
941 * the referenced object any time it's used in another expression.
943 * @param e expression
944 * @return reference to object of class T
945 * @see is_exactly_a<class T>() */
947 inline const T &ex_to(const ex &e)
949 GINAC_ASSERT(is_a<T>(e));
950 return static_cast<const T &>(*e.bp);
956 // Specializations of Standard Library algorithms
959 /** Specialization of std::swap() for ex objects. */
961 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
966 /** Specialization of std::iter_swap() for vector<ex> iterators. */
968 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
973 /** Specialization of std::iter_swap() for list<ex> iterators. */
975 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
982 #endif // ndef __GINAC_EX_H__