3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2011 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
36 // MSVC produces a different symbol for _ex0 when it is declared inside
37 // ex::is_zero() than when it is declared at top level as follows
41 /** Helper class to initialize the library. There must be one static object
42 * of this class in every object file that makes use of our flyweights in
43 * order to guarantee proper initialization. Hence we put it into this
44 * file which is included by every relevant file anyways. This is modeled
45 * after section 27.4.2.1.6 of the C++ standard, where cout and friends are
50 static void init_unarchivers();
57 /** For construction of flyweights, etc. */
58 static library_init library_initializer;
60 class scalar_products;
62 class const_preorder_iterator;
63 class const_postorder_iterator;
66 /** Lightweight wrapper for GiNaC's symbolic objects. It holds a pointer to
67 * the other object in order to do garbage collection by the method of
68 * reference counting. I.e., it is a smart pointer. Also, the constructor
69 * ex::ex(const basic & other) calls the methods that do automatic
70 * evaluation. E.g., x-x turns automatically into 0. */
72 friend class archive_node;
73 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
74 template<class T> friend inline const T &ex_to(const ex &);
75 template<class T> friend inline bool is_a(const ex &);
76 template<class T> friend inline bool is_exactly_a(const ex &);
78 // default constructor, copy constructor and assignment operator
84 ex(const basic & other);
91 /** Construct ex from string and a list of symbols. The input grammar is
92 * similar to the GiNaC output format. All symbols and indices to be used
93 * in the expression must be specified in a lst in the second argument.
94 * Undefined symbols and other parser errors will throw an exception. */
95 ex(const std::string &s, const ex &l);
98 // non-virtual functions in this class
100 /** Efficiently swap the contents of two expressions. */
101 void swap(ex & other) throw()
103 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
104 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
109 const_iterator begin() const throw();
110 const_iterator end() const throw();
111 const_preorder_iterator preorder_begin() const;
112 const_preorder_iterator preorder_end() const throw();
113 const_postorder_iterator postorder_begin() const;
114 const_postorder_iterator postorder_end() const throw();
117 ex eval(int level = 0) const { return bp->eval(level); }
118 ex evalf(int level = 0) const { return bp->evalf(level); }
119 ex evalm() const { return bp->evalm(); }
120 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
121 ex eval_integ() const { return bp->eval_integ(); }
124 void print(const print_context & c, unsigned level = 0) const;
125 void dbgprint() const;
126 void dbgprinttree() const;
129 bool info(unsigned inf) const { return bp->info(inf); }
132 size_t nops() const { return bp->nops(); }
133 ex op(size_t i) const { return bp->op(i); }
134 ex operator[](const ex & index) const { return (*bp)[index]; }
135 ex operator[](size_t i) const { return (*bp)[i]; }
136 ex & let_op(size_t i);
137 ex & operator[](const ex & index);
138 ex & operator[](size_t i);
142 // function for complex expressions
143 ex conjugate() const { return bp->conjugate(); }
144 ex real_part() const { return bp->real_part(); }
145 ex imag_part() const { return bp->imag_part(); }
148 bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
149 bool find(const ex & pattern, exset& found) const;
150 bool match(const ex & pattern) const;
151 bool match(const ex & pattern, exmap & repls) const { return bp->match(pattern, repls); }
154 ex subs(const exmap & m, unsigned options = 0) const;
155 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
156 ex subs(const ex & e, unsigned options = 0) const;
159 ex map(map_function & f) const { return bp->map(f); }
160 ex map(ex (*f)(const ex & e)) const;
162 // visitors and tree traversal
163 void accept(visitor & v) const { bp->accept(v); }
164 void traverse_preorder(visitor & v) const;
165 void traverse_postorder(visitor & v) const;
166 void traverse(visitor & v) const { traverse_preorder(v); }
169 bool is_polynomial(const ex & vars) const;
170 int degree(const ex & s) const { return bp->degree(s); }
171 int ldegree(const ex & s) const { return bp->ldegree(s); }
172 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
173 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
174 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
177 ex expand(unsigned options=0) const;
178 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
180 // differentiation and series expansion
181 ex diff(const symbol & s, unsigned nth = 1) const;
182 ex series(const ex & r, int order, unsigned options = 0) const;
184 // rational functions
185 ex normal(int level = 0) const;
186 ex to_rational(exmap & repl) const;
187 ex to_rational(lst & repl_lst) const;
188 ex to_polynomial(exmap & repl) const;
189 ex to_polynomial(lst & repl_lst) const;
192 ex numer_denom() const;
194 // polynomial algorithms
195 ex unit(const ex &x) const;
196 ex content(const ex &x) const;
197 numeric integer_content() const;
198 ex primpart(const ex &x) const;
199 ex primpart(const ex &x, const ex &cont) const;
200 void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
201 ex smod(const numeric &xi) const { return bp->smod(xi); }
202 numeric max_coefficient() const;
205 exvector get_free_indices() const { return bp->get_free_indices(); }
206 ex simplify_indexed(unsigned options = 0) const;
207 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
210 int compare(const ex & other) const;
211 bool is_equal(const ex & other) const;
212 bool is_zero() const {
214 extern const ex _ex0;
216 return is_equal(_ex0);
218 bool is_zero_matrix() const;
221 ex symmetrize() const;
222 ex symmetrize(const lst & l) const;
223 ex antisymmetrize() const;
224 ex antisymmetrize(const lst & l) const;
225 ex symmetrize_cyclic() const;
226 ex symmetrize_cyclic(const lst & l) const;
229 unsigned return_type() const { return bp->return_type(); }
230 return_type_t return_type_tinfo() const { return bp->return_type_tinfo(); }
232 unsigned gethash() const { return bp->gethash(); }
235 static ptr<basic> construct_from_basic(const basic & other);
236 static basic & construct_from_int(int i);
237 static basic & construct_from_uint(unsigned int i);
238 static basic & construct_from_long(long i);
239 static basic & construct_from_ulong(unsigned long i);
240 static basic & construct_from_double(double d);
241 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
242 void makewriteable();
243 void share(const ex & other) const;
248 mutable ptr<basic> bp; ///< pointer to basic object managed by this
252 // performance-critical inlined method implementations
254 // This needs to be a basic* because we don't know that numeric is derived
255 // from basic and we need a basic& for the ex default constructor
256 extern const basic *_num0_bp;
259 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
261 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
265 ex::ex(const basic & other) : bp(construct_from_basic(other))
267 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
271 ex::ex(int i) : bp(construct_from_int(i))
273 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
277 ex::ex(unsigned int i) : bp(construct_from_uint(i))
279 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
283 ex::ex(long i) : bp(construct_from_long(i))
285 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
289 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
291 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
295 ex::ex(double const d) : bp(construct_from_double(d))
297 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
301 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
303 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
307 int ex::compare(const ex & other) const
309 #ifdef GINAC_COMPARE_STATISTICS
310 compare_statistics.total_compares++;
312 if (bp == other.bp) // trivial case: both expressions point to same basic
314 #ifdef GINAC_COMPARE_STATISTICS
315 compare_statistics.nontrivial_compares++;
317 const int cmpval = bp->compare(*other.bp);
320 // Expressions point to different, but equal, trees: conserve
321 // memory and make subsequent compare() operations faster by
322 // making both expressions point to the same tree.
330 bool ex::is_equal(const ex & other) const
332 #ifdef GINAC_COMPARE_STATISTICS
333 compare_statistics.total_is_equals++;
335 if (bp == other.bp) // trivial case: both expressions point to same basic
337 #ifdef GINAC_COMPARE_STATISTICS
338 compare_statistics.nontrivial_is_equals++;
340 const bool equal = bp->is_equal(*other.bp);
343 // Expressions point to different, but equal, trees: conserve
344 // memory and make subsequent compare() operations faster by
345 // making both expressions point to the same tree.
355 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
357 friend class const_preorder_iterator;
358 friend class const_postorder_iterator;
361 const_iterator() throw() {}
364 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
367 // This should return an ex&, but that would be a reference to a
374 // This should return an ex*, but that would be a pointer to a
376 std::auto_ptr<ex> operator->() const
378 return std::auto_ptr<ex>(new ex(operator*()));
381 ex operator[](difference_type n) const
386 const_iterator &operator++() throw()
392 const_iterator operator++(int) throw()
394 const_iterator tmp = *this;
399 const_iterator &operator+=(difference_type n) throw()
405 const_iterator operator+(difference_type n) const throw()
407 return const_iterator(e, i + n);
410 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
412 return const_iterator(it.e, it.i + n);
415 const_iterator &operator--() throw()
421 const_iterator operator--(int) throw()
423 const_iterator tmp = *this;
428 const_iterator &operator-=(difference_type n) throw()
434 const_iterator operator-(difference_type n) const throw()
436 return const_iterator(e, i - n);
439 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
441 return lhs.i - rhs.i;
444 bool operator==(const const_iterator &other) const throw()
446 return are_ex_trivially_equal(e, other.e) && i == other.i;
449 bool operator!=(const const_iterator &other) const throw()
451 return !(*this == other);
454 bool operator<(const const_iterator &other) const throw()
459 bool operator>(const const_iterator &other) const throw()
461 return other < *this;
464 bool operator<=(const const_iterator &other) const throw()
466 return !(other < *this);
469 bool operator>=(const const_iterator &other) const throw()
471 return !(*this < other);
475 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
482 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
484 bool operator==(const _iter_rep &other) const throw()
486 return are_ex_trivially_equal(e, other.e) && i == other.i;
489 bool operator!=(const _iter_rep &other) const throw()
491 return !(*this == other);
499 } // namespace internal
501 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
503 const_preorder_iterator() throw() {}
505 const_preorder_iterator(const ex &e, size_t n)
507 s.push(internal::_iter_rep(e, 0, n));
511 reference operator*() const
516 pointer operator->() const
521 const_preorder_iterator &operator++()
527 const_preorder_iterator operator++(int)
529 const_preorder_iterator tmp = *this;
534 bool operator==(const const_preorder_iterator &other) const throw()
539 bool operator!=(const const_preorder_iterator &other) const throw()
541 return !(*this == other);
545 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
549 while (!s.empty() && s.top().i == s.top().i_end) {
556 internal::_iter_rep & current = s.top();
558 if (current.i != current.i_end) {
559 const ex & child = current.e.op(current.i);
560 s.push(internal::_iter_rep(child, 0, child.nops()));
565 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
567 const_postorder_iterator() throw() {}
569 const_postorder_iterator(const ex &e, size_t n)
571 s.push(internal::_iter_rep(e, 0, n));
576 reference operator*() const
581 pointer operator->() const
586 const_postorder_iterator &operator++()
592 const_postorder_iterator operator++(int)
594 const_postorder_iterator tmp = *this;
599 bool operator==(const const_postorder_iterator &other) const throw()
604 bool operator!=(const const_postorder_iterator &other) const throw()
606 return !(*this == other);
610 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
614 while (s.top().i != s.top().i_end) {
615 internal::_iter_rep & current = s.top();
616 const ex & child = current.e.op(current.i);
617 s.push(internal::_iter_rep(child, 0, child.nops()));
623 if (s.top().i == s.top().i_end)
632 inline const_iterator ex::begin() const throw()
634 return const_iterator(*this, 0);
637 inline const_iterator ex::end() const throw()
639 return const_iterator(*this, nops());
642 inline const_preorder_iterator ex::preorder_begin() const
644 return const_preorder_iterator(*this, nops());
647 inline const_preorder_iterator ex::preorder_end() const throw()
649 return const_preorder_iterator();
652 inline const_postorder_iterator ex::postorder_begin() const
654 return const_postorder_iterator(*this, nops());
657 inline const_postorder_iterator ex::postorder_end() const throw()
659 return const_postorder_iterator();
665 /** Compare two objects of class quickly without doing a deep tree traversal.
666 * @return "true" if they are equal
667 * "false" if equality cannot be established quickly (e1 and e2 may
668 * still be equal, in this case. */
669 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
671 return e1.bp == e2.bp;
674 /* Function objects for STL sort() etc. */
675 struct ex_is_less : public std::binary_function<ex, ex, bool> {
676 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
679 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
680 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
683 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
684 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
687 struct ex_swap : public std::binary_function<ex, ex, void> {
688 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
691 // Make it possible to print exvectors and exmaps
692 std::ostream & operator<<(std::ostream & os, const exvector & e);
693 std::ostream & operator<<(std::ostream & os, const exset & e);
694 std::ostream & operator<<(std::ostream & os, const exmap & e);
696 // wrapper functions around member functions
697 inline size_t nops(const ex & thisex)
698 { return thisex.nops(); }
700 inline ex expand(const ex & thisex, unsigned options = 0)
701 { return thisex.expand(options); }
703 inline ex conjugate(const ex & thisex)
704 { return thisex.conjugate(); }
706 inline ex real_part(const ex & thisex)
707 { return thisex.real_part(); }
709 inline ex imag_part(const ex & thisex)
710 { return thisex.imag_part(); }
712 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
713 { return thisex.has(pattern, options); }
715 inline bool find(const ex & thisex, const ex & pattern, exset& found)
716 { return thisex.find(pattern, found); }
718 inline bool is_polynomial(const ex & thisex, const ex & vars)
719 { return thisex.is_polynomial(vars); }
721 inline int degree(const ex & thisex, const ex & s)
722 { return thisex.degree(s); }
724 inline int ldegree(const ex & thisex, const ex & s)
725 { return thisex.ldegree(s); }
727 inline ex coeff(const ex & thisex, const ex & s, int n=1)
728 { return thisex.coeff(s, n); }
730 inline ex numer(const ex & thisex)
731 { return thisex.numer(); }
733 inline ex denom(const ex & thisex)
734 { return thisex.denom(); }
736 inline ex numer_denom(const ex & thisex)
737 { return thisex.numer_denom(); }
739 inline ex normal(const ex & thisex, int level=0)
740 { return thisex.normal(level); }
742 inline ex to_rational(const ex & thisex, lst & repl_lst)
743 { return thisex.to_rational(repl_lst); }
745 inline ex to_rational(const ex & thisex, exmap & repl)
746 { return thisex.to_rational(repl); }
748 inline ex to_polynomial(const ex & thisex, exmap & repl)
749 { return thisex.to_polynomial(repl); }
751 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
752 { return thisex.to_polynomial(repl_lst); }
754 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
755 { return thisex.collect(s, distributed); }
757 inline ex eval(const ex & thisex, int level = 0)
758 { return thisex.eval(level); }
760 inline ex evalf(const ex & thisex, int level = 0)
761 { return thisex.evalf(level); }
763 inline ex evalm(const ex & thisex)
764 { return thisex.evalm(); }
766 inline ex eval_integ(const ex & thisex)
767 { return thisex.eval_integ(); }
769 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
770 { return thisex.diff(s, nth); }
772 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
773 { return thisex.series(r, order, options); }
775 inline bool match(const ex & thisex, const ex & pattern, exmap& repl_lst)
776 { return thisex.match(pattern, repl_lst); }
778 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
779 { return thisex.simplify_indexed(options); }
781 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
782 { return thisex.simplify_indexed(sp, options); }
784 inline ex symmetrize(const ex & thisex)
785 { return thisex.symmetrize(); }
787 inline ex symmetrize(const ex & thisex, const lst & l)
788 { return thisex.symmetrize(l); }
790 inline ex antisymmetrize(const ex & thisex)
791 { return thisex.antisymmetrize(); }
793 inline ex antisymmetrize(const ex & thisex, const lst & l)
794 { return thisex.antisymmetrize(l); }
796 inline ex symmetrize_cyclic(const ex & thisex)
797 { return thisex.symmetrize_cyclic(); }
799 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
800 { return thisex.symmetrize_cyclic(l); }
802 inline ex op(const ex & thisex, size_t i)
803 { return thisex.op(i); }
805 inline ex lhs(const ex & thisex)
806 { return thisex.lhs(); }
808 inline ex rhs(const ex & thisex)
809 { return thisex.rhs(); }
811 inline bool is_zero(const ex & thisex)
812 { return thisex.is_zero(); }
814 inline void swap(ex & e1, ex & e2)
817 inline ex ex::subs(const exmap & m, unsigned options) const
819 return bp->subs(m, options);
822 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
823 { return thisex.subs(m, options); }
825 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
826 { return thisex.subs(ls, lr, options); }
828 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
829 { return thisex.subs(e, options); }
832 /* Convert function pointer to function object suitable for map(). */
833 class pointer_to_map_function : public map_function {
835 ex (*ptr)(const ex &);
837 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
838 ex operator()(const ex & e) { return ptr(e); }
842 class pointer_to_map_function_1arg : public map_function {
844 ex (*ptr)(const ex &, T1);
847 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
848 ex operator()(const ex & e) { return ptr(e, arg1); }
851 template<class T1, class T2>
852 class pointer_to_map_function_2args : public map_function {
854 ex (*ptr)(const ex &, T1, T2);
858 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
859 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
862 template<class T1, class T2, class T3>
863 class pointer_to_map_function_3args : public map_function {
865 ex (*ptr)(const ex &, T1, T2, T3);
870 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) {}
871 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
875 class pointer_to_member_to_map_function : public map_function {
877 ex (C::*ptr)(const ex &);
880 explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
881 ex operator()(const ex & e) { return (c.*ptr)(e); }
884 template<class C, class T1>
885 class pointer_to_member_to_map_function_1arg : public map_function {
887 ex (C::*ptr)(const ex &, T1);
891 explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
892 ex operator()(const ex & e) { return (c.*ptr)(e, arg1); }
895 template<class C, class T1, class T2>
896 class pointer_to_member_to_map_function_2args : public map_function {
898 ex (C::*ptr)(const ex &, T1, T2);
903 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) {}
904 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2); }
907 template<class C, class T1, class T2, class T3>
908 class pointer_to_member_to_map_function_3args : public map_function {
910 ex (C::*ptr)(const ex &, T1, T2, T3);
916 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) {}
917 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2, arg3); }
920 inline ex ex::map(ex f(const ex &)) const
922 pointer_to_map_function fcn(f);
926 // convenience type checker template functions
928 /** Check if ex is a handle to a T, including base classes. */
930 inline bool is_a(const ex &obj)
932 return is_a<T>(*obj.bp);
935 /** Check if ex is a handle to a T, not including base classes. */
937 inline bool is_exactly_a(const ex &obj)
939 return is_exactly_a<T>(*obj.bp);
942 /** Return a reference to the basic-derived class T object embedded in an
943 * expression. This is fast but unsafe: the result is undefined if the
944 * expression does not contain a T object at its top level. Hence, you
945 * should generally check the type of e first. Also, you shouldn't cache
946 * the returned reference because GiNaC's garbage collector may destroy
947 * the referenced object any time it's used in another expression.
949 * @param e expression
950 * @return reference to object of class T
951 * @see is_exactly_a<class T>() */
953 inline const T &ex_to(const ex &e)
955 GINAC_ASSERT(is_a<T>(e));
956 return static_cast<const T &>(*e.bp);
962 // Specializations of Standard Library algorithms
965 /** Specialization of std::swap() for ex objects. */
967 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
972 /** Specialization of std::iter_swap() for vector<ex> iterators. */
974 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
979 /** Specialization of std::iter_swap() for list<ex> iterators. */
981 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
988 #endif // ndef GINAC_EX_H