3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2006 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
52 /** For construction of flyweights, etc. */
53 static library_init library_initializer;
55 /** Rotate bits of unsigned value by one bit to the left.
56 * This can be necesary if the user wants to define its own hashes. */
57 inline unsigned rotate_left(unsigned n)
59 return (n & 0x80000000U) ? (n << 1 | 0x00000001U) : (n << 1);
62 class scalar_products;
64 class const_preorder_iterator;
65 class const_postorder_iterator;
68 /** Lightweight wrapper for GiNaC's symbolic objects. Basically all it does is
69 * to hold a pointer to the other objects, manage the reference counting and
70 * provide methods for manipulation of these objects. (Some people call such
71 * a thing a proxy class.) */
73 friend class archive_node;
74 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
75 template<class T> friend inline const T &ex_to(const ex &);
76 template<class T> friend inline bool is_a(const ex &);
77 template<class T> friend inline bool is_exactly_a(const ex &);
79 // default constructor, copy constructor and assignment operator
85 ex(const basic & other);
92 /** Construct ex from string and a list of symbols. The input grammar is
93 * similar to the GiNaC output format. All symbols and indices to be used
94 * in the expression must be specified in a lst in the second argument.
95 * Undefined symbols and other parser errors will throw an exception. */
96 ex(const std::string &s, const ex &l);
99 // non-virtual functions in this class
101 /** Efficiently swap the contents of two expressions. */
102 void swap(ex & other) throw()
104 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
105 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
110 const_iterator begin() const throw();
111 const_iterator end() const throw();
112 const_preorder_iterator preorder_begin() const;
113 const_preorder_iterator preorder_end() const throw();
114 const_postorder_iterator postorder_begin() const;
115 const_postorder_iterator postorder_end() const throw();
118 ex eval(int level = 0) const { return bp->eval(level); }
119 ex evalf(int level = 0) const { return bp->evalf(level); }
120 ex evalm() const { return bp->evalm(); }
121 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
122 ex eval_integ() const { return bp->eval_integ(); }
125 void print(const print_context & c, unsigned level = 0) const;
126 void dbgprint() const;
127 void dbgprinttree() const;
130 bool info(unsigned inf) const { return bp->info(inf); }
133 size_t nops() const { return bp->nops(); }
134 ex op(size_t i) const { return bp->op(i); }
135 ex operator[](const ex & index) const { return (*bp)[index]; }
136 ex operator[](size_t i) const { return (*bp)[i]; }
137 ex & let_op(size_t i);
138 ex & operator[](const ex & index);
139 ex & operator[](size_t i);
143 // function for complex expressions
144 ex conjugate() const { return bp->conjugate(); }
145 ex real_part() const { return bp->real_part(); }
146 ex imag_part() const { return bp->imag_part(); }
149 bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
150 bool find(const ex & pattern, lst & found) const;
151 bool match(const ex & pattern) const;
152 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
155 ex subs(const exmap & m, unsigned options = 0) const;
156 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
157 ex subs(const ex & e, unsigned options = 0) const;
160 ex map(map_function & f) const { return bp->map(f); }
161 ex map(ex (*f)(const ex & e)) const;
163 // visitors and tree traversal
164 void accept(visitor & v) const { bp->accept(v); }
165 void traverse_preorder(visitor & v) const;
166 void traverse_postorder(visitor & v) const;
167 void traverse(visitor & v) const { traverse_preorder(v); }
170 bool is_polynomial(const ex & vars) const;
171 int degree(const ex & s) const { return bp->degree(s); }
172 int ldegree(const ex & s) const { return bp->ldegree(s); }
173 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
174 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
175 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
178 ex expand(unsigned options=0) const;
179 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
181 // differentiation and series expansion
182 ex diff(const symbol & s, unsigned nth = 1) const;
183 ex series(const ex & r, int order, unsigned options = 0) const;
185 // rational functions
186 ex normal(int level = 0) const;
187 ex to_rational(exmap & repl) const;
188 ex to_rational(lst & repl_lst) const;
189 ex to_polynomial(exmap & repl) const;
190 ex to_polynomial(lst & repl_lst) const;
193 ex numer_denom() const;
195 // polynomial algorithms
196 ex unit(const ex &x) const;
197 ex content(const ex &x) const;
198 numeric integer_content() const;
199 ex primpart(const ex &x) const;
200 ex primpart(const ex &x, const ex &cont) const;
201 void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
202 ex smod(const numeric &xi) const { return bp->smod(xi); }
203 numeric max_coefficient() const;
206 exvector get_free_indices() const { return bp->get_free_indices(); }
207 ex simplify_indexed(unsigned options = 0) const;
208 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
211 int compare(const ex & other) const;
212 bool is_equal(const ex & other) const;
213 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
214 bool is_zero_matrix() const;
217 ex symmetrize() const;
218 ex symmetrize(const lst & l) const;
219 ex antisymmetrize() const;
220 ex antisymmetrize(const lst & l) const;
221 ex symmetrize_cyclic() const;
222 ex symmetrize_cyclic(const lst & l) const;
225 unsigned return_type() const { return bp->return_type(); }
226 tinfo_t return_type_tinfo() const { return bp->return_type_tinfo(); }
228 unsigned gethash() const { return bp->gethash(); }
231 static ptr<basic> construct_from_basic(const basic & other);
232 static basic & construct_from_int(int i);
233 static basic & construct_from_uint(unsigned int i);
234 static basic & construct_from_long(long i);
235 static basic & construct_from_ulong(unsigned long i);
236 static basic & construct_from_double(double d);
237 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
238 void makewriteable();
239 void share(const ex & other) const;
244 mutable ptr<basic> bp; ///< pointer to basic object managed by this
248 // performance-critical inlined method implementations
250 // This needs to be a basic* because we don't know that numeric is derived
251 // from basic and we need a basic& for the ex default constructor
252 extern const basic *_num0_bp;
255 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
257 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
261 ex::ex(const basic & other) : bp(construct_from_basic(other))
263 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
267 ex::ex(int i) : bp(construct_from_int(i))
269 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
273 ex::ex(unsigned int i) : bp(construct_from_uint(i))
275 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
279 ex::ex(long i) : bp(construct_from_long(i))
281 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
285 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
287 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
291 ex::ex(double const d) : bp(construct_from_double(d))
293 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
297 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
299 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
303 int ex::compare(const ex & other) const
305 #ifdef GINAC_COMPARE_STATISTICS
306 compare_statistics.total_compares++;
308 if (bp == other.bp) // trivial case: both expressions point to same basic
310 #ifdef GINAC_COMPARE_STATISTICS
311 compare_statistics.nontrivial_compares++;
313 const int cmpval = bp->compare(*other.bp);
316 // Expressions point to different, but equal, trees: conserve
317 // memory and make subsequent compare() operations faster by
318 // making both expressions point to the same tree.
326 bool ex::is_equal(const ex & other) const
328 #ifdef GINAC_COMPARE_STATISTICS
329 compare_statistics.total_is_equals++;
331 if (bp == other.bp) // trivial case: both expressions point to same basic
333 #ifdef GINAC_COMPARE_STATISTICS
334 compare_statistics.nontrivial_is_equals++;
336 const bool equal = bp->is_equal(*other.bp);
339 // Expressions point to different, but equal, trees: conserve
340 // memory and make subsequent compare() operations faster by
341 // making both expressions point to the same tree.
351 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
353 friend class const_preorder_iterator;
354 friend class const_postorder_iterator;
357 const_iterator() throw() {}
360 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
363 // This should return an ex&, but that would be a reference to a
370 // This should return an ex*, but that would be a pointer to a
372 std::auto_ptr<ex> operator->() const
374 return std::auto_ptr<ex>(new ex(operator*()));
377 ex operator[](difference_type n) const
382 const_iterator &operator++() throw()
388 const_iterator operator++(int) throw()
390 const_iterator tmp = *this;
395 const_iterator &operator+=(difference_type n) throw()
401 const_iterator operator+(difference_type n) const throw()
403 return const_iterator(e, i + n);
406 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
408 return const_iterator(it.e, it.i + n);
411 const_iterator &operator--() throw()
417 const_iterator operator--(int) throw()
419 const_iterator tmp = *this;
424 const_iterator &operator-=(difference_type n) throw()
430 const_iterator operator-(difference_type n) const throw()
432 return const_iterator(e, i - n);
435 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
437 return lhs.i - rhs.i;
440 bool operator==(const const_iterator &other) const throw()
442 return are_ex_trivially_equal(e, other.e) && i == other.i;
445 bool operator!=(const const_iterator &other) const throw()
447 return !(*this == other);
450 bool operator<(const const_iterator &other) const throw()
455 bool operator>(const const_iterator &other) const throw()
457 return other < *this;
460 bool operator<=(const const_iterator &other) const throw()
462 return !(other < *this);
465 bool operator>=(const const_iterator &other) const throw()
467 return !(*this < other);
471 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
478 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
480 bool operator==(const _iter_rep &other) const throw()
482 return are_ex_trivially_equal(e, other.e) && i == other.i;
485 bool operator!=(const _iter_rep &other) const throw()
487 return !(*this == other);
495 } // namespace internal
497 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
499 const_preorder_iterator() throw() {}
501 const_preorder_iterator(const ex &e, size_t n)
503 s.push(internal::_iter_rep(e, 0, n));
507 reference operator*() const
512 pointer operator->() const
517 const_preorder_iterator &operator++()
523 const_preorder_iterator operator++(int)
525 const_preorder_iterator tmp = *this;
530 bool operator==(const const_preorder_iterator &other) const throw()
535 bool operator!=(const const_preorder_iterator &other) const throw()
537 return !(*this == other);
541 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
545 while (!s.empty() && s.top().i == s.top().i_end) {
552 internal::_iter_rep & current = s.top();
554 if (current.i != current.i_end) {
555 const ex & child = current.e.op(current.i);
556 s.push(internal::_iter_rep(child, 0, child.nops()));
561 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
563 const_postorder_iterator() throw() {}
565 const_postorder_iterator(const ex &e, size_t n)
567 s.push(internal::_iter_rep(e, 0, n));
572 reference operator*() const
577 pointer operator->() const
582 const_postorder_iterator &operator++()
588 const_postorder_iterator operator++(int)
590 const_postorder_iterator tmp = *this;
595 bool operator==(const const_postorder_iterator &other) const throw()
600 bool operator!=(const const_postorder_iterator &other) const throw()
602 return !(*this == other);
606 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
610 while (s.top().i != s.top().i_end) {
611 internal::_iter_rep & current = s.top();
612 const ex & child = current.e.op(current.i);
613 s.push(internal::_iter_rep(child, 0, child.nops()));
619 if (s.top().i == s.top().i_end)
628 inline const_iterator ex::begin() const throw()
630 return const_iterator(*this, 0);
633 inline const_iterator ex::end() const throw()
635 return const_iterator(*this, nops());
638 inline const_preorder_iterator ex::preorder_begin() const
640 return const_preorder_iterator(*this, nops());
643 inline const_preorder_iterator ex::preorder_end() const throw()
645 return const_preorder_iterator();
648 inline const_postorder_iterator ex::postorder_begin() const
650 return const_postorder_iterator(*this, nops());
653 inline const_postorder_iterator ex::postorder_end() const throw()
655 return const_postorder_iterator();
661 /** Compare two objects of class quickly without doing a deep tree traversal.
662 * @return "true" if they are equal
663 * "false" if equality cannot be established quickly (e1 and e2 may
664 * still be equal, in this case. */
665 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
667 return e1.bp == e2.bp;
670 /* Function objects for STL sort() etc. */
671 struct ex_is_less : public std::binary_function<ex, ex, bool> {
672 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
675 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
676 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
679 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
680 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
683 struct ex_swap : public std::binary_function<ex, ex, void> {
684 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
687 // Make it possible to print exvectors and exmaps
688 std::ostream & operator<<(std::ostream & os, const exvector & e);
689 std::ostream & operator<<(std::ostream & os, const exmap & e);
691 // wrapper functions around member functions
692 inline size_t nops(const ex & thisex)
693 { return thisex.nops(); }
695 inline ex expand(const ex & thisex, unsigned options = 0)
696 { return thisex.expand(options); }
698 inline ex conjugate(const ex & thisex)
699 { return thisex.conjugate(); }
701 inline ex real_part(const ex & thisex)
702 { return thisex.real_part(); }
704 inline ex imag_part(const ex & thisex)
705 { return thisex.imag_part(); }
707 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
708 { return thisex.has(pattern, options); }
710 inline bool find(const ex & thisex, const ex & pattern, lst & found)
711 { return thisex.find(pattern, found); }
713 inline bool is_polynomial(const ex & thisex, const ex & vars)
714 { return thisex.is_polynomial(vars); }
716 inline int degree(const ex & thisex, const ex & s)
717 { return thisex.degree(s); }
719 inline int ldegree(const ex & thisex, const ex & s)
720 { return thisex.ldegree(s); }
722 inline ex coeff(const ex & thisex, const ex & s, int n=1)
723 { return thisex.coeff(s, n); }
725 inline ex numer(const ex & thisex)
726 { return thisex.numer(); }
728 inline ex denom(const ex & thisex)
729 { return thisex.denom(); }
731 inline ex numer_denom(const ex & thisex)
732 { return thisex.numer_denom(); }
734 inline ex normal(const ex & thisex, int level=0)
735 { return thisex.normal(level); }
737 inline ex to_rational(const ex & thisex, lst & repl_lst)
738 { return thisex.to_rational(repl_lst); }
740 inline ex to_rational(const ex & thisex, exmap & repl)
741 { return thisex.to_rational(repl); }
743 inline ex to_polynomial(const ex & thisex, exmap & repl)
744 { return thisex.to_polynomial(repl); }
746 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
747 { return thisex.to_polynomial(repl_lst); }
749 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
750 { return thisex.collect(s, distributed); }
752 inline ex eval(const ex & thisex, int level = 0)
753 { return thisex.eval(level); }
755 inline ex evalf(const ex & thisex, int level = 0)
756 { return thisex.evalf(level); }
758 inline ex evalm(const ex & thisex)
759 { return thisex.evalm(); }
761 inline ex eval_integ(const ex & thisex)
762 { return thisex.eval_integ(); }
764 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
765 { return thisex.diff(s, nth); }
767 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
768 { return thisex.series(r, order, options); }
770 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
771 { return thisex.match(pattern, repl_lst); }
773 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
774 { return thisex.simplify_indexed(options); }
776 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
777 { return thisex.simplify_indexed(sp, options); }
779 inline ex symmetrize(const ex & thisex)
780 { return thisex.symmetrize(); }
782 inline ex symmetrize(const ex & thisex, const lst & l)
783 { return thisex.symmetrize(l); }
785 inline ex antisymmetrize(const ex & thisex)
786 { return thisex.antisymmetrize(); }
788 inline ex antisymmetrize(const ex & thisex, const lst & l)
789 { return thisex.antisymmetrize(l); }
791 inline ex symmetrize_cyclic(const ex & thisex)
792 { return thisex.symmetrize_cyclic(); }
794 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
795 { return thisex.symmetrize_cyclic(l); }
797 inline ex op(const ex & thisex, size_t i)
798 { return thisex.op(i); }
800 inline ex lhs(const ex & thisex)
801 { return thisex.lhs(); }
803 inline ex rhs(const ex & thisex)
804 { return thisex.rhs(); }
806 inline bool is_zero(const ex & thisex)
807 { return thisex.is_zero(); }
809 inline void swap(ex & e1, ex & e2)
812 inline ex ex::subs(const exmap & m, unsigned options) const
814 return bp->subs(m, options);
817 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
818 { return thisex.subs(m, options); }
820 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
821 { return thisex.subs(ls, lr, options); }
823 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
824 { return thisex.subs(e, options); }
827 /* Convert function pointer to function object suitable for map(). */
828 class pointer_to_map_function : public map_function {
830 ex (*ptr)(const ex &);
832 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
833 ex operator()(const ex & e) { return ptr(e); }
837 class pointer_to_map_function_1arg : public map_function {
839 ex (*ptr)(const ex &, T1);
842 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
843 ex operator()(const ex & e) { return ptr(e, arg1); }
846 template<class T1, class T2>
847 class pointer_to_map_function_2args : public map_function {
849 ex (*ptr)(const ex &, T1, T2);
853 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
854 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
857 template<class T1, class T2, class T3>
858 class pointer_to_map_function_3args : public map_function {
860 ex (*ptr)(const ex &, T1, T2, T3);
865 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) {}
866 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
870 class pointer_to_member_to_map_function : public map_function {
872 ex (C::*ptr)(const ex &);
875 explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
876 ex operator()(const ex & e) { return (c.*ptr)(e); }
879 template<class C, class T1>
880 class pointer_to_member_to_map_function_1arg : public map_function {
882 ex (C::*ptr)(const ex &, T1);
886 explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
887 ex operator()(const ex & e) { return (c.*ptr)(e, arg1); }
890 template<class C, class T1, class T2>
891 class pointer_to_member_to_map_function_2args : public map_function {
893 ex (C::*ptr)(const ex &, T1, T2);
898 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) {}
899 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2); }
902 template<class C, class T1, class T2, class T3>
903 class pointer_to_member_to_map_function_3args : public map_function {
905 ex (C::*ptr)(const ex &, T1, T2, T3);
911 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) {}
912 ex operator()(const ex & e) { return (c.*ptr)(e, arg1, arg2, arg3); }
915 inline ex ex::map(ex f(const ex &)) const
917 pointer_to_map_function fcn(f);
921 // convenience type checker template functions
923 /** Check if ex is a handle to a T, including base classes. */
925 inline bool is_a(const ex &obj)
927 return is_a<T>(*obj.bp);
930 /** Check if ex is a handle to a T, not including base classes. */
932 inline bool is_exactly_a(const ex &obj)
934 return is_exactly_a<T>(*obj.bp);
937 /** Return a reference to the basic-derived class T object embedded in an
938 * expression. This is fast but unsafe: the result is undefined if the
939 * expression does not contain a T object at its top level. Hence, you
940 * should generally check the type of e first. Also, you shouldn't cache
941 * the returned reference because GiNaC's garbage collector may destroy
942 * the referenced object any time it's used in another expression.
944 * @param e expression
945 * @return reference to object of class T
946 * @see is_exactly_a<class T>() */
948 inline const T &ex_to(const ex &e)
950 GINAC_ASSERT(is_a<T>(e));
951 return static_cast<const T &>(*e.bp);
957 // Specializations of Standard Library algorithms
960 /** Specialization of std::swap() for ex objects. */
962 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
967 /** Specialization of std::iter_swap() for vector<ex> iterators. */
969 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
974 /** Specialization of std::iter_swap() for list<ex> iterators. */
976 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
983 #endif // ndef __GINAC_EX_H__