3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2005 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); }
120 ex eval_integ() const { return bp->eval_integ(); }
123 void print(const print_context & c, unsigned level = 0) const;
124 void dbgprint() const;
125 void dbgprinttree() const;
128 bool info(unsigned inf) const { return bp->info(inf); }
131 size_t nops() const { return bp->nops(); }
132 ex op(size_t i) const { return bp->op(i); }
133 ex operator[](const ex & index) const { return (*bp)[index]; }
134 ex operator[](size_t i) const { return (*bp)[i]; }
135 ex & let_op(size_t i);
136 ex & operator[](const ex & index);
137 ex & operator[](size_t i);
141 // complex conjugation
142 ex conjugate() const { return bp->conjugate(); }
145 bool has(const ex & pattern) const { return bp->has(pattern); }
146 bool find(const ex & pattern, lst & found) const;
147 bool match(const ex & pattern) const;
148 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
151 ex subs(const exmap & m, unsigned options = 0) const;
152 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
153 ex subs(const ex & e, unsigned options = 0) const;
156 ex map(map_function & f) const { return bp->map(f); }
157 ex map(ex (*f)(const ex & e)) const;
159 // visitors and tree traversal
160 void accept(visitor & v) const { bp->accept(v); }
161 void traverse_preorder(visitor & v) const;
162 void traverse_postorder(visitor & v) const;
163 void traverse(visitor & v) const { traverse_preorder(v); }
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); }
211 ex symmetrize() const;
212 ex symmetrize(const lst & l) const;
213 ex antisymmetrize() const;
214 ex antisymmetrize(const lst & l) const;
215 ex symmetrize_cyclic() const;
216 ex symmetrize_cyclic(const lst & l) const;
219 unsigned return_type() const { return bp->return_type(); }
220 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
222 unsigned gethash() const { return bp->gethash(); }
225 static ptr<basic> construct_from_basic(const basic & other);
226 static basic & construct_from_int(int i);
227 static basic & construct_from_uint(unsigned int i);
228 static basic & construct_from_long(long i);
229 static basic & construct_from_ulong(unsigned long i);
230 static basic & construct_from_double(double d);
231 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
232 void makewriteable();
233 void share(const ex & other) const;
235 #ifdef OBSCURE_CINT_HACK
237 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
239 if (last_created_or_assigned_bp==0) return false;
240 if ((last_created_or_assigned_bp->flags &
241 status_flags::dynallocated)==0) return false;
242 if ((last_created_or_assigned_bp->flags &
243 status_flags::evaluated)==0) return false;
247 void update_last_created_or_assigned_bp()
249 last_created_or_assigned_bp = bp;
250 last_created_or_assigned_exp = (long)(void *)(this);
252 #endif // def OBSCURE_CINT_HACK
257 mutable ptr<basic> bp; ///< pointer to basic object managed by this
259 #ifdef OBSCURE_CINT_HACK
261 static ptr<basic> last_created_or_assigned_bp;
262 static basic * dummy_bp;
263 static long last_created_or_assigned_exp;
264 #endif // def OBSCURE_CINT_HACK
268 // performance-critical inlined method implementations
270 // This needs to be a basic* because we don't know that numeric is derived
271 // from basic and we need a basic& for the ex default constructor
272 extern const basic *_num0_bp;
275 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
277 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
278 #ifdef OBSCURE_CINT_HACK
279 update_last_created_or_assigned_bp();
280 #endif // def OBSCURE_CINT_HACK
283 #ifdef OBSCURE_CINT_HACK
285 ex::ex(const ex & other) : bp(other.bp)
287 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
288 update_last_created_or_assigned_bp();
292 ex & ex::operator=(const ex & other)
294 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
295 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
297 update_last_created_or_assigned_bp();
300 #endif // def OBSCURE_CINT_HACK
303 ex::ex(const basic & other) : bp(construct_from_basic(other))
305 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
306 #ifdef OBSCURE_CINT_HACK
307 update_last_created_or_assigned_bp();
308 #endif // def OBSCURE_CINT_HACK
312 ex::ex(int i) : bp(construct_from_int(i))
314 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
315 #ifdef OBSCURE_CINT_HACK
316 update_last_created_or_assigned_bp();
317 #endif // def OBSCURE_CINT_HACK
321 ex::ex(unsigned int i) : bp(construct_from_uint(i))
323 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
324 #ifdef OBSCURE_CINT_HACK
325 update_last_created_or_assigned_bp();
326 #endif // def OBSCURE_CINT_HACK
330 ex::ex(long i) : bp(construct_from_long(i))
332 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
333 #ifdef OBSCURE_CINT_HACK
334 update_last_created_or_assigned_bp();
335 #endif // def OBSCURE_CINT_HACK
339 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
341 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
342 #ifdef OBSCURE_CINT_HACK
343 update_last_created_or_assigned_bp();
344 #endif // def OBSCURE_CINT_HACK
348 ex::ex(double const d) : bp(construct_from_double(d))
350 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
351 #ifdef OBSCURE_CINT_HACK
352 update_last_created_or_assigned_bp();
353 #endif // def OBSCURE_CINT_HACK
357 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
359 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
360 #ifdef OBSCURE_CINT_HACK
361 update_last_created_or_assigned_bp();
362 #endif // def OBSCURE_CINT_HACK
366 int ex::compare(const ex & other) const
368 #ifdef GINAC_COMPARE_STATISTICS
369 compare_statistics.total_compares++;
371 if (bp == other.bp) // trivial case: both expressions point to same basic
373 #ifdef GINAC_COMPARE_STATISTICS
374 compare_statistics.nontrivial_compares++;
376 const int cmpval = bp->compare(*other.bp);
379 // Expressions point to different, but equal, trees: conserve
380 // memory and make subsequent compare() operations faster by
381 // making both expressions point to the same tree.
389 bool ex::is_equal(const ex & other) const
391 #ifdef GINAC_COMPARE_STATISTICS
392 compare_statistics.total_is_equals++;
394 if (bp == other.bp) // trivial case: both expressions point to same basic
396 #ifdef GINAC_COMPARE_STATISTICS
397 compare_statistics.nontrivial_is_equals++;
399 const bool equal = bp->is_equal(*other.bp);
402 // Expressions point to different, but equal, trees: conserve
403 // memory and make subsequent compare() operations faster by
404 // making both expressions point to the same tree.
414 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
416 friend class const_preorder_iterator;
417 friend class const_postorder_iterator;
420 const_iterator() throw() {}
423 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
426 // This should return an ex&, but that would be a reference to a
433 // This should return an ex*, but that would be a pointer to a
435 std::auto_ptr<ex> operator->() const
437 return std::auto_ptr<ex>(new ex(operator*()));
440 ex operator[](difference_type n) const
445 const_iterator &operator++() throw()
451 const_iterator operator++(int) throw()
453 const_iterator tmp = *this;
458 const_iterator &operator+=(difference_type n) throw()
464 const_iterator operator+(difference_type n) const throw()
466 return const_iterator(e, i + n);
469 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
471 return const_iterator(it.e, it.i + n);
474 const_iterator &operator--() throw()
480 const_iterator operator--(int) throw()
482 const_iterator tmp = *this;
487 const_iterator &operator-=(difference_type n) throw()
493 const_iterator operator-(difference_type n) const throw()
495 return const_iterator(e, i - n);
498 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
500 return lhs.i - rhs.i;
503 bool operator==(const const_iterator &other) const throw()
505 return are_ex_trivially_equal(e, other.e) && i == other.i;
508 bool operator!=(const const_iterator &other) const throw()
510 return !(*this == other);
513 bool operator<(const const_iterator &other) const throw()
518 bool operator>(const const_iterator &other) const throw()
520 return other < *this;
523 bool operator<=(const const_iterator &other) const throw()
525 return !(other < *this);
528 bool operator>=(const const_iterator &other) const throw()
530 return !(*this < other);
534 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
541 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
543 bool operator==(const _iter_rep &other) const throw()
545 return are_ex_trivially_equal(e, other.e) && i == other.i;
548 bool operator!=(const _iter_rep &other) const throw()
550 return !(*this == other);
558 } // namespace internal
560 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
562 const_preorder_iterator() throw() {}
564 const_preorder_iterator(const ex &e, size_t n)
566 s.push(internal::_iter_rep(e, 0, n));
570 reference operator*() const
575 pointer operator->() const
580 const_preorder_iterator &operator++()
586 const_preorder_iterator operator++(int)
588 const_preorder_iterator tmp = *this;
593 bool operator==(const const_preorder_iterator &other) const throw()
598 bool operator!=(const const_preorder_iterator &other) const throw()
600 return !(*this == other);
604 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
608 while (!s.empty() && s.top().i == s.top().i_end) {
615 internal::_iter_rep & current = s.top();
617 if (current.i != current.i_end) {
618 const ex & child = current.e.op(current.i);
619 s.push(internal::_iter_rep(child, 0, child.nops()));
624 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
626 const_postorder_iterator() throw() {}
628 const_postorder_iterator(const ex &e, size_t n)
630 s.push(internal::_iter_rep(e, 0, n));
635 reference operator*() const
640 pointer operator->() const
645 const_postorder_iterator &operator++()
651 const_postorder_iterator operator++(int)
653 const_postorder_iterator tmp = *this;
658 bool operator==(const const_postorder_iterator &other) const throw()
663 bool operator!=(const const_postorder_iterator &other) const throw()
665 return !(*this == other);
669 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
673 while (s.top().i != s.top().i_end) {
674 internal::_iter_rep & current = s.top();
675 const ex & child = current.e.op(current.i);
676 s.push(internal::_iter_rep(child, 0, child.nops()));
682 if (s.top().i == s.top().i_end)
691 inline const_iterator ex::begin() const throw()
693 return const_iterator(*this, 0);
696 inline const_iterator ex::end() const throw()
698 return const_iterator(*this, nops());
701 inline const_preorder_iterator ex::preorder_begin() const
703 return const_preorder_iterator(*this, nops());
706 inline const_preorder_iterator ex::preorder_end() const throw()
708 return const_preorder_iterator();
711 inline const_postorder_iterator ex::postorder_begin() const
713 return const_postorder_iterator(*this, nops());
716 inline const_postorder_iterator ex::postorder_end() const throw()
718 return const_postorder_iterator();
724 /** Compare two objects of class quickly without doing a deep tree traversal.
725 * @return "true" if they are equal
726 * "false" if equality cannot be established quickly (e1 and e2 may
727 * still be equal, in this case. */
728 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
730 return e1.bp == e2.bp;
733 /* Function objects for STL sort() etc. */
734 struct ex_is_less : public std::binary_function<ex, ex, bool> {
735 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
738 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
739 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
742 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
743 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
746 struct ex_swap : public std::binary_function<ex, ex, void> {
747 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
750 // wrapper functions around member functions
751 inline size_t nops(const ex & thisex)
752 { return thisex.nops(); }
754 inline ex expand(const ex & thisex, unsigned options = 0)
755 { return thisex.expand(options); }
757 inline ex conjugate(const ex & thisex)
758 { return thisex.conjugate(); }
760 inline bool has(const ex & thisex, const ex & pattern)
761 { return thisex.has(pattern); }
763 inline bool find(const ex & thisex, const ex & pattern, lst & found)
764 { return thisex.find(pattern, found); }
766 inline int degree(const ex & thisex, const ex & s)
767 { return thisex.degree(s); }
769 inline int ldegree(const ex & thisex, const ex & s)
770 { return thisex.ldegree(s); }
772 inline ex coeff(const ex & thisex, const ex & s, int n=1)
773 { return thisex.coeff(s, n); }
775 inline ex numer(const ex & thisex)
776 { return thisex.numer(); }
778 inline ex denom(const ex & thisex)
779 { return thisex.denom(); }
781 inline ex numer_denom(const ex & thisex)
782 { return thisex.numer_denom(); }
784 inline ex normal(const ex & thisex, int level=0)
785 { return thisex.normal(level); }
787 inline ex to_rational(const ex & thisex, lst & repl_lst)
788 { return thisex.to_rational(repl_lst); }
790 inline ex to_rational(const ex & thisex, exmap & repl)
791 { return thisex.to_rational(repl); }
793 inline ex to_polynomial(const ex & thisex, exmap & repl)
794 { return thisex.to_polynomial(repl); }
796 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
797 { return thisex.to_polynomial(repl_lst); }
799 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
800 { return thisex.collect(s, distributed); }
802 inline ex eval(const ex & thisex, int level = 0)
803 { return thisex.eval(level); }
805 inline ex evalf(const ex & thisex, int level = 0)
806 { return thisex.evalf(level); }
808 inline ex evalm(const ex & thisex)
809 { return thisex.evalm(); }
811 inline ex eval_integ(const ex & thisex)
812 { return thisex.eval_integ(); }
814 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
815 { return thisex.diff(s, nth); }
817 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
818 { return thisex.series(r, order, options); }
820 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
821 { return thisex.match(pattern, repl_lst); }
823 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
824 { return thisex.simplify_indexed(options); }
826 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
827 { return thisex.simplify_indexed(sp, options); }
829 inline ex symmetrize(const ex & thisex)
830 { return thisex.symmetrize(); }
832 inline ex symmetrize(const ex & thisex, const lst & l)
833 { return thisex.symmetrize(l); }
835 inline ex antisymmetrize(const ex & thisex)
836 { return thisex.antisymmetrize(); }
838 inline ex antisymmetrize(const ex & thisex, const lst & l)
839 { return thisex.antisymmetrize(l); }
841 inline ex symmetrize_cyclic(const ex & thisex)
842 { return thisex.symmetrize_cyclic(); }
844 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
845 { return thisex.symmetrize_cyclic(l); }
847 inline ex op(const ex & thisex, size_t i)
848 { return thisex.op(i); }
850 inline ex lhs(const ex & thisex)
851 { return thisex.lhs(); }
853 inline ex rhs(const ex & thisex)
854 { return thisex.rhs(); }
856 inline bool is_zero(const ex & thisex)
857 { return thisex.is_zero(); }
859 inline void swap(ex & e1, ex & e2)
862 inline ex ex::subs(const exmap & m, unsigned options) const
864 return bp->subs(m, options);
867 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
868 { return thisex.subs(m, options); }
870 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
871 { return thisex.subs(ls, lr, options); }
873 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
874 { return thisex.subs(e, options); }
877 /* Convert function pointer to function object suitable for map(). */
878 class pointer_to_map_function : public map_function {
880 ex (*ptr)(const ex &);
882 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
883 ex operator()(const ex & e) { return ptr(e); }
887 class pointer_to_map_function_1arg : public map_function {
889 ex (*ptr)(const ex &, T1);
892 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
893 ex operator()(const ex & e) { return ptr(e, arg1); }
896 template<class T1, class T2>
897 class pointer_to_map_function_2args : public map_function {
899 ex (*ptr)(const ex &, T1, T2);
903 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
904 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
907 template<class T1, class T2, class T3>
908 class pointer_to_map_function_3args : public map_function {
910 ex (*ptr)(const ex &, T1, T2, T3);
915 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) {}
916 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
919 inline ex ex::map(ex f(const ex &)) const
921 pointer_to_map_function fcn(f);
925 // convenience type checker template functions
927 /** Check if ex is a handle to a T, including base classes. */
929 inline bool is_a(const ex &obj)
931 return is_a<T>(*obj.bp);
934 /** Check if ex is a handle to a T, not including base classes. */
936 inline bool is_exactly_a(const ex &obj)
938 return is_exactly_a<T>(*obj.bp);
941 /** Return a reference to the basic-derived class T object embedded in an
942 * expression. This is fast but unsafe: the result is undefined if the
943 * expression does not contain a T object at its top level. Hence, you
944 * should generally check the type of e first. Also, you shouldn't cache
945 * the returned reference because GiNaC's garbage collector may destroy
946 * the referenced object any time it's used in another expression.
948 * @param e expression
949 * @return reference to object of class T
950 * @see is_exactly_a<class T>() */
952 inline const T &ex_to(const ex &e)
954 GINAC_ASSERT(is_a<T>(e));
955 return static_cast<const T &>(*e.bp);
961 // Specializations of Standard Library algorithms
964 /** Specialization of std::swap() for ex objects. */
966 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
971 /** Specialization of std::iter_swap() for vector<ex> iterators. */
973 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
978 /** Specialization of std::iter_swap() for list<ex> iterators. */
980 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
987 #endif // ndef __GINAC_EX_H__