3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2008 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
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
46 static void init_unarchivers();
53 /** For construction of flyweights, etc. */
54 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. It holds a pointer to
63 * the other object in order to do garbage collection by the method of
64 * reference counting. I.e., it is a smart pointer. Also, the constructor
65 * ex::ex(const basic & other) calls the methods that do automatic
66 * evaluation. E.g., x-x turns automatically into 0. */
68 friend class archive_node;
69 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
70 template<class T> friend inline const T &ex_to(const ex &);
71 template<class T> friend inline bool is_a(const ex &);
72 template<class T> friend inline bool is_exactly_a(const ex &);
74 // default constructor, copy constructor and assignment operator
80 ex(const basic & other);
87 /** Construct ex from string and a list of symbols. The input grammar is
88 * similar to the GiNaC output format. All symbols and indices to be used
89 * in the expression must be specified in a lst in the second argument.
90 * Undefined symbols and other parser errors will throw an exception. */
91 ex(const std::string &s, const ex &l);
94 // non-virtual functions in this class
96 /** Efficiently swap the contents of two expressions. */
97 void swap(ex & other) throw()
99 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
100 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
105 const_iterator begin() const throw();
106 const_iterator end() const throw();
107 const_preorder_iterator preorder_begin() const;
108 const_preorder_iterator preorder_end() const throw();
109 const_postorder_iterator postorder_begin() const;
110 const_postorder_iterator postorder_end() const throw();
113 ex eval(int level = 0) const { return bp->eval(level); }
114 ex evalf(int level = 0) const { return bp->evalf(level); }
115 ex evalm() const { return bp->evalm(); }
116 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
117 ex eval_integ() const { return bp->eval_integ(); }
120 void print(const print_context & c, unsigned level = 0) const;
121 void dbgprint() const;
122 void dbgprinttree() const;
125 bool info(unsigned inf) const { return bp->info(inf); }
128 size_t nops() const { return bp->nops(); }
129 ex op(size_t i) const { return bp->op(i); }
130 ex operator[](const ex & index) const { return (*bp)[index]; }
131 ex operator[](size_t i) const { return (*bp)[i]; }
132 ex & let_op(size_t i);
133 ex & operator[](const ex & index);
134 ex & operator[](size_t i);
138 // function for complex expressions
139 ex conjugate() const { return bp->conjugate(); }
140 ex real_part() const { return bp->real_part(); }
141 ex imag_part() const { return bp->imag_part(); }
144 bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
145 bool find(const ex & pattern, exset& found) const;
146 bool match(const ex & pattern) const;
147 bool match(const ex & pattern, exmap & repls) const { return bp->match(pattern, repls); }
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 bool is_polynomial(const ex & vars) const;
166 int degree(const ex & s) const { return bp->degree(s); }
167 int ldegree(const ex & s) const { return bp->ldegree(s); }
168 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
169 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
170 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
173 ex expand(unsigned options=0) const;
174 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
176 // differentiation and series expansion
177 ex diff(const symbol & s, unsigned nth = 1) const;
178 ex series(const ex & r, int order, unsigned options = 0) const;
180 // rational functions
181 ex normal(int level = 0) const;
182 ex to_rational(exmap & repl) const;
183 ex to_rational(lst & repl_lst) const;
184 ex to_polynomial(exmap & repl) const;
185 ex to_polynomial(lst & repl_lst) const;
188 ex numer_denom() const;
190 // polynomial algorithms
191 ex unit(const ex &x) const;
192 ex content(const ex &x) const;
193 numeric integer_content() const;
194 ex primpart(const ex &x) const;
195 ex primpart(const ex &x, const ex &cont) const;
196 void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
197 ex smod(const numeric &xi) const { return bp->smod(xi); }
198 numeric max_coefficient() const;
201 exvector get_free_indices() const { return bp->get_free_indices(); }
202 ex simplify_indexed(unsigned options = 0) const;
203 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
206 int compare(const ex & other) const;
207 bool is_equal(const ex & other) const;
208 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
209 bool is_zero_matrix() const;
212 ex symmetrize() const;
213 ex symmetrize(const lst & l) const;
214 ex antisymmetrize() const;
215 ex antisymmetrize(const lst & l) const;
216 ex symmetrize_cyclic() const;
217 ex symmetrize_cyclic(const lst & l) const;
220 unsigned return_type() const { return bp->return_type(); }
221 return_type_t return_type_tinfo() const { return bp->return_type_tinfo(); }
223 unsigned gethash() const { return bp->gethash(); }
226 static ptr<basic> construct_from_basic(const basic & other);
227 static basic & construct_from_int(int i);
228 static basic & construct_from_uint(unsigned int i);
229 static basic & construct_from_long(long i);
230 static basic & construct_from_ulong(unsigned long i);
231 static basic & construct_from_double(double d);
232 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
233 void makewriteable();
234 void share(const ex & other) const;
239 mutable ptr<basic> bp; ///< pointer to basic object managed by this
243 // performance-critical inlined method implementations
245 // This needs to be a basic* because we don't know that numeric is derived
246 // from basic and we need a basic& for the ex default constructor
247 extern const basic *_num0_bp;
250 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
252 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
256 ex::ex(const basic & other) : bp(construct_from_basic(other))
258 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
262 ex::ex(int i) : bp(construct_from_int(i))
264 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
268 ex::ex(unsigned int i) : bp(construct_from_uint(i))
270 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
274 ex::ex(long i) : bp(construct_from_long(i))
276 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
280 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
282 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
286 ex::ex(double const d) : bp(construct_from_double(d))
288 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
292 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
294 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
298 int ex::compare(const ex & other) const
300 #ifdef GINAC_COMPARE_STATISTICS
301 compare_statistics.total_compares++;
303 if (bp == other.bp) // trivial case: both expressions point to same basic
305 #ifdef GINAC_COMPARE_STATISTICS
306 compare_statistics.nontrivial_compares++;
308 const int cmpval = bp->compare(*other.bp);
311 // Expressions point to different, but equal, trees: conserve
312 // memory and make subsequent compare() operations faster by
313 // making both expressions point to the same tree.
321 bool ex::is_equal(const ex & other) const
323 #ifdef GINAC_COMPARE_STATISTICS
324 compare_statistics.total_is_equals++;
326 if (bp == other.bp) // trivial case: both expressions point to same basic
328 #ifdef GINAC_COMPARE_STATISTICS
329 compare_statistics.nontrivial_is_equals++;
331 const bool equal = bp->is_equal(*other.bp);
334 // Expressions point to different, but equal, trees: conserve
335 // memory and make subsequent compare() operations faster by
336 // making both expressions point to the same tree.
346 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
348 friend class const_preorder_iterator;
349 friend class const_postorder_iterator;
352 const_iterator() throw() {}
355 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
358 // This should return an ex&, but that would be a reference to a
365 // This should return an ex*, but that would be a pointer to a
367 std::auto_ptr<ex> operator->() const
369 return std::auto_ptr<ex>(new ex(operator*()));
372 ex operator[](difference_type n) const
377 const_iterator &operator++() throw()
383 const_iterator operator++(int) throw()
385 const_iterator tmp = *this;
390 const_iterator &operator+=(difference_type n) throw()
396 const_iterator operator+(difference_type n) const throw()
398 return const_iterator(e, i + n);
401 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
403 return const_iterator(it.e, it.i + n);
406 const_iterator &operator--() throw()
412 const_iterator operator--(int) throw()
414 const_iterator tmp = *this;
419 const_iterator &operator-=(difference_type n) throw()
425 const_iterator operator-(difference_type n) const throw()
427 return const_iterator(e, i - n);
430 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
432 return lhs.i - rhs.i;
435 bool operator==(const const_iterator &other) const throw()
437 return are_ex_trivially_equal(e, other.e) && i == other.i;
440 bool operator!=(const const_iterator &other) const throw()
442 return !(*this == other);
445 bool operator<(const const_iterator &other) const throw()
450 bool operator>(const const_iterator &other) const throw()
452 return other < *this;
455 bool operator<=(const const_iterator &other) const throw()
457 return !(other < *this);
460 bool operator>=(const const_iterator &other) const throw()
462 return !(*this < other);
466 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
473 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
475 bool operator==(const _iter_rep &other) const throw()
477 return are_ex_trivially_equal(e, other.e) && i == other.i;
480 bool operator!=(const _iter_rep &other) const throw()
482 return !(*this == other);
490 } // namespace internal
492 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
494 const_preorder_iterator() throw() {}
496 const_preorder_iterator(const ex &e, size_t n)
498 s.push(internal::_iter_rep(e, 0, n));
502 reference operator*() const
507 pointer operator->() const
512 const_preorder_iterator &operator++()
518 const_preorder_iterator operator++(int)
520 const_preorder_iterator tmp = *this;
525 bool operator==(const const_preorder_iterator &other) const throw()
530 bool operator!=(const const_preorder_iterator &other) const throw()
532 return !(*this == other);
536 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
540 while (!s.empty() && s.top().i == s.top().i_end) {
547 internal::_iter_rep & current = s.top();
549 if (current.i != current.i_end) {
550 const ex & child = current.e.op(current.i);
551 s.push(internal::_iter_rep(child, 0, child.nops()));
556 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
558 const_postorder_iterator() throw() {}
560 const_postorder_iterator(const ex &e, size_t n)
562 s.push(internal::_iter_rep(e, 0, n));
567 reference operator*() const
572 pointer operator->() const
577 const_postorder_iterator &operator++()
583 const_postorder_iterator operator++(int)
585 const_postorder_iterator tmp = *this;
590 bool operator==(const const_postorder_iterator &other) const throw()
595 bool operator!=(const const_postorder_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) {
606 internal::_iter_rep & current = s.top();
607 const ex & child = current.e.op(current.i);
608 s.push(internal::_iter_rep(child, 0, child.nops()));
614 if (s.top().i == s.top().i_end)
623 inline const_iterator ex::begin() const throw()
625 return const_iterator(*this, 0);
628 inline const_iterator ex::end() const throw()
630 return const_iterator(*this, nops());
633 inline const_preorder_iterator ex::preorder_begin() const
635 return const_preorder_iterator(*this, nops());
638 inline const_preorder_iterator ex::preorder_end() const throw()
640 return const_preorder_iterator();
643 inline const_postorder_iterator ex::postorder_begin() const
645 return const_postorder_iterator(*this, nops());
648 inline const_postorder_iterator ex::postorder_end() const throw()
650 return const_postorder_iterator();
656 /** Compare two objects of class quickly without doing a deep tree traversal.
657 * @return "true" if they are equal
658 * "false" if equality cannot be established quickly (e1 and e2 may
659 * still be equal, in this case. */
660 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
662 return e1.bp == e2.bp;
665 /* Function objects for STL sort() etc. */
666 struct ex_is_less : public std::binary_function<ex, ex, bool> {
667 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
670 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
671 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
674 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
675 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
678 struct ex_swap : public std::binary_function<ex, ex, void> {
679 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
682 // Make it possible to print exvectors and exmaps
683 std::ostream & operator<<(std::ostream & os, const exvector & e);
684 std::ostream & operator<<(std::ostream & os, const exset & e);
685 std::ostream & operator<<(std::ostream & os, const exmap & e);
687 // wrapper functions around member functions
688 inline size_t nops(const ex & thisex)
689 { return thisex.nops(); }
691 inline ex expand(const ex & thisex, unsigned options = 0)
692 { return thisex.expand(options); }
694 inline ex conjugate(const ex & thisex)
695 { return thisex.conjugate(); }
697 inline ex real_part(const ex & thisex)
698 { return thisex.real_part(); }
700 inline ex imag_part(const ex & thisex)
701 { return thisex.imag_part(); }
703 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
704 { return thisex.has(pattern, options); }
706 inline bool find(const ex & thisex, const ex & pattern, exset& found)
707 { return thisex.find(pattern, found); }
709 inline bool is_polynomial(const ex & thisex, const ex & vars)
710 { return thisex.is_polynomial(vars); }
712 inline int degree(const ex & thisex, const ex & s)
713 { return thisex.degree(s); }
715 inline int ldegree(const ex & thisex, const ex & s)
716 { return thisex.ldegree(s); }
718 inline ex coeff(const ex & thisex, const ex & s, int n=1)
719 { return thisex.coeff(s, n); }
721 inline ex numer(const ex & thisex)
722 { return thisex.numer(); }
724 inline ex denom(const ex & thisex)
725 { return thisex.denom(); }
727 inline ex numer_denom(const ex & thisex)
728 { return thisex.numer_denom(); }
730 inline ex normal(const ex & thisex, int level=0)
731 { return thisex.normal(level); }
733 inline ex to_rational(const ex & thisex, lst & repl_lst)
734 { return thisex.to_rational(repl_lst); }
736 inline ex to_rational(const ex & thisex, exmap & repl)
737 { return thisex.to_rational(repl); }
739 inline ex to_polynomial(const ex & thisex, exmap & repl)
740 { return thisex.to_polynomial(repl); }
742 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
743 { return thisex.to_polynomial(repl_lst); }
745 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
746 { return thisex.collect(s, distributed); }
748 inline ex eval(const ex & thisex, int level = 0)
749 { return thisex.eval(level); }
751 inline ex evalf(const ex & thisex, int level = 0)
752 { return thisex.evalf(level); }
754 inline ex evalm(const ex & thisex)
755 { return thisex.evalm(); }
757 inline ex eval_integ(const ex & thisex)
758 { return thisex.eval_integ(); }
760 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
761 { return thisex.diff(s, nth); }
763 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
764 { return thisex.series(r, order, options); }
766 inline bool match(const ex & thisex, const ex & pattern, exmap& repl_lst)
767 { return thisex.match(pattern, repl_lst); }
769 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
770 { return thisex.simplify_indexed(options); }
772 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
773 { return thisex.simplify_indexed(sp, options); }
775 inline ex symmetrize(const ex & thisex)
776 { return thisex.symmetrize(); }
778 inline ex symmetrize(const ex & thisex, const lst & l)
779 { return thisex.symmetrize(l); }
781 inline ex antisymmetrize(const ex & thisex)
782 { return thisex.antisymmetrize(); }
784 inline ex antisymmetrize(const ex & thisex, const lst & l)
785 { return thisex.antisymmetrize(l); }
787 inline ex symmetrize_cyclic(const ex & thisex)
788 { return thisex.symmetrize_cyclic(); }
790 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
791 { return thisex.symmetrize_cyclic(l); }
793 inline ex op(const ex & thisex, size_t i)
794 { return thisex.op(i); }
796 inline ex lhs(const ex & thisex)
797 { return thisex.lhs(); }
799 inline ex rhs(const ex & thisex)
800 { return thisex.rhs(); }
802 inline bool is_zero(const ex & thisex)
803 { return thisex.is_zero(); }
805 inline void swap(ex & e1, ex & e2)
808 inline ex ex::subs(const exmap & m, unsigned options) const
810 return bp->subs(m, options);
813 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
814 { return thisex.subs(m, options); }
816 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
817 { return thisex.subs(ls, lr, options); }
819 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
820 { return thisex.subs(e, options); }
823 /* Convert function pointer to function object suitable for map(). */
824 class pointer_to_map_function : public map_function {
826 ex (*ptr)(const ex &);
828 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
829 ex operator()(const ex & e) { return ptr(e); }
833 class pointer_to_map_function_1arg : public map_function {
835 ex (*ptr)(const ex &, T1);
838 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
839 ex operator()(const ex & e) { return ptr(e, arg1); }
842 template<class T1, class T2>
843 class pointer_to_map_function_2args : public map_function {
845 ex (*ptr)(const ex &, T1, T2);
849 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
850 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
853 template<class T1, class T2, class T3>
854 class pointer_to_map_function_3args : public map_function {
856 ex (*ptr)(const ex &, T1, T2, T3);
861 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) {}
862 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
866 class pointer_to_member_to_map_function : public map_function {
868 ex (C::*ptr)(const ex &);
871 explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
872 ex operator()(const ex & e) { return (c.*ptr)(e); }
875 template<class C, class T1>
876 class pointer_to_member_to_map_function_1arg : public map_function {
878 ex (C::*ptr)(const ex &, T1);
882 explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
883 ex operator()(const ex & e) { return (c.*ptr)(e, arg1); }
886 template<class C, class T1, class T2>
887 class pointer_to_member_to_map_function_2args : public map_function {
889 ex (C::*ptr)(const ex &, T1, T2);
894 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) {}
895 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2); }
898 template<class C, class T1, class T2, class T3>
899 class pointer_to_member_to_map_function_3args : public map_function {
901 ex (C::*ptr)(const ex &, T1, T2, T3);
907 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) {}
908 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2, arg3); }
911 inline ex ex::map(ex f(const ex &)) const
913 pointer_to_map_function fcn(f);
917 // convenience type checker template functions
919 /** Check if ex is a handle to a T, including base classes. */
921 inline bool is_a(const ex &obj)
923 return is_a<T>(*obj.bp);
926 /** Check if ex is a handle to a T, not including base classes. */
928 inline bool is_exactly_a(const ex &obj)
930 return is_exactly_a<T>(*obj.bp);
933 /** Return a reference to the basic-derived class T object embedded in an
934 * expression. This is fast but unsafe: the result is undefined if the
935 * expression does not contain a T object at its top level. Hence, you
936 * should generally check the type of e first. Also, you shouldn't cache
937 * the returned reference because GiNaC's garbage collector may destroy
938 * the referenced object any time it's used in another expression.
940 * @param e expression
941 * @return reference to object of class T
942 * @see is_exactly_a<class T>() */
944 inline const T &ex_to(const ex &e)
946 GINAC_ASSERT(is_a<T>(e));
947 return static_cast<const T &>(*e.bp);
953 // Specializations of Standard Library algorithms
956 /** Specialization of std::swap() for ex objects. */
958 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
963 /** Specialization of std::iter_swap() for vector<ex> iterators. */
965 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
970 /** Specialization of std::iter_swap() for list<ex> iterators. */
972 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
979 #endif // ndef __GINAC_EX_H__