3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2016 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
37 // MSVC produces a different symbol for _ex0 when it is declared inside
38 // ex::is_zero() than when it is declared at top level as follows
42 /** Helper class to initialize the library. There must be one static object
43 * of this class in every object file that makes use of our flyweights in
44 * order to guarantee proper initialization. Hence we put it into this
45 * file which is included by every relevant file anyways. This is modeled
46 * after section 27.4.2.1.6 of the C++ standard, where cout and friends are
51 static void init_unarchivers();
58 /** For construction of flyweights, etc. */
59 static library_init library_initializer;
61 class scalar_products;
63 class const_preorder_iterator;
64 class const_postorder_iterator;
67 /** Lightweight wrapper for GiNaC's symbolic objects. It holds a pointer to
68 * the other object in order to do garbage collection by the method of
69 * reference counting. I.e., it is a smart pointer. Also, the constructor
70 * ex::ex(const basic & other) calls the methods that do automatic
71 * evaluation. E.g., x-x turns automatically into 0. */
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) noexcept
104 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
105 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
110 const_iterator begin() const noexcept;
111 const_iterator end() const noexcept;
112 const_preorder_iterator preorder_begin() const;
113 const_preorder_iterator preorder_end() const noexcept;
114 const_postorder_iterator postorder_begin() const;
115 const_postorder_iterator postorder_end() const noexcept;
118 ex eval() const { return bp->eval(); }
119 ex evalf() const { return bp->evalf(); }
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, exset& found) const;
151 bool match(const ex & pattern) const;
152 bool match(const ex & pattern, exmap & repls) const { return bp->match(pattern, repls); }
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
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 {
215 extern const ex _ex0;
217 return is_equal(_ex0);
219 bool is_zero_matrix() const;
222 ex symmetrize() const;
223 ex symmetrize(const lst & l) const;
224 ex antisymmetrize() const;
225 ex antisymmetrize(const lst & l) const;
226 ex symmetrize_cyclic() const;
227 ex symmetrize_cyclic(const lst & l) const;
230 unsigned return_type() const { return bp->return_type(); }
231 return_type_t return_type_tinfo() const { return bp->return_type_tinfo(); }
233 unsigned gethash() const { return bp->gethash(); }
236 static ptr<basic> construct_from_basic(const basic & other);
237 static basic & construct_from_int(int i);
238 static basic & construct_from_uint(unsigned int i);
239 static basic & construct_from_long(long i);
240 static basic & construct_from_ulong(unsigned long i);
241 static basic & construct_from_double(double d);
242 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
243 void makewriteable();
244 void share(const ex & other) const;
249 mutable ptr<basic> bp; ///< pointer to basic object managed by this
253 // performance-critical inlined method implementations
255 // This needs to be a basic* because we don't know that numeric is derived
256 // from basic and we need a basic& for the ex default constructor
257 extern const basic *_num0_bp;
260 ex::ex() noexcept : bp(*const_cast<basic *>(_num0_bp))
262 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
266 ex::ex(const basic & other) : bp(construct_from_basic(other))
268 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
272 ex::ex(int i) : bp(construct_from_int(i))
274 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
278 ex::ex(unsigned int i) : bp(construct_from_uint(i))
280 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
284 ex::ex(long i) : bp(construct_from_long(i))
286 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
290 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
292 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
296 ex::ex(double const d) : bp(construct_from_double(d))
298 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
302 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
304 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
308 int ex::compare(const ex & other) const
310 #ifdef GINAC_COMPARE_STATISTICS
311 compare_statistics.total_compares++;
313 if (bp == other.bp) // trivial case: both expressions point to same basic
315 #ifdef GINAC_COMPARE_STATISTICS
316 compare_statistics.nontrivial_compares++;
318 const int cmpval = bp->compare(*other.bp);
321 // Expressions point to different, but equal, trees: conserve
322 // memory and make subsequent compare() operations faster by
323 // making both expressions point to the same tree.
331 bool ex::is_equal(const ex & other) const
333 #ifdef GINAC_COMPARE_STATISTICS
334 compare_statistics.total_is_equals++;
336 if (bp == other.bp) // trivial case: both expressions point to same basic
338 #ifdef GINAC_COMPARE_STATISTICS
339 compare_statistics.nontrivial_is_equals++;
341 const bool equal = bp->is_equal(*other.bp);
344 // Expressions point to different, but equal, trees: conserve
345 // memory and make subsequent compare() operations faster by
346 // making both expressions point to the same tree.
356 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
358 friend class const_preorder_iterator;
359 friend class const_postorder_iterator;
362 const_iterator() noexcept {}
365 const_iterator(const ex &e_, size_t i_) noexcept : e(e_), i(i_) {}
368 // This should return an ex&, but that would be a reference to a
375 // This should return an ex*, but that would be a pointer to a
377 std::unique_ptr<ex> operator->() const
379 return std::unique_ptr<ex>(new ex(operator*()));
382 ex operator[](difference_type n) const
387 const_iterator &operator++() noexcept
393 const_iterator operator++(int) noexcept
395 const_iterator tmp = *this;
400 const_iterator &operator+=(difference_type n) noexcept
406 const_iterator operator+(difference_type n) const noexcept
408 return const_iterator(e, i + n);
411 inline friend const_iterator operator+(difference_type n, const const_iterator &it) noexcept
413 return const_iterator(it.e, it.i + n);
416 const_iterator &operator--() noexcept
422 const_iterator operator--(int) noexcept
424 const_iterator tmp = *this;
429 const_iterator &operator-=(difference_type n) noexcept
435 const_iterator operator-(difference_type n) const noexcept
437 return const_iterator(e, i - n);
440 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) noexcept
442 return lhs.i - rhs.i;
445 bool operator==(const const_iterator &other) const noexcept
447 return are_ex_trivially_equal(e, other.e) && i == other.i;
450 bool operator!=(const const_iterator &other) const noexcept
452 return !(*this == other);
455 bool operator<(const const_iterator &other) const noexcept
460 bool operator>(const const_iterator &other) const noexcept
462 return other < *this;
465 bool operator<=(const const_iterator &other) const noexcept
467 return !(other < *this);
470 bool operator>=(const const_iterator &other) const noexcept
472 return !(*this < other);
476 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
483 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
485 bool operator==(const _iter_rep &other) const noexcept
487 return are_ex_trivially_equal(e, other.e) && i == other.i;
490 bool operator!=(const _iter_rep &other) const noexcept
492 return !(*this == other);
500 } // namespace internal
502 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
504 const_preorder_iterator() noexcept {}
506 const_preorder_iterator(const ex &e, size_t n)
508 s.push(internal::_iter_rep(e, 0, n));
512 reference operator*() const
517 pointer operator->() const
522 const_preorder_iterator &operator++()
528 const_preorder_iterator operator++(int)
530 const_preorder_iterator tmp = *this;
535 bool operator==(const const_preorder_iterator &other) const noexcept
540 bool operator!=(const const_preorder_iterator &other) const noexcept
542 return !(*this == other);
546 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep>> s;
550 while (!s.empty() && s.top().i == s.top().i_end) {
557 internal::_iter_rep & current = s.top();
559 if (current.i != current.i_end) {
560 const ex & child = current.e.op(current.i);
561 s.push(internal::_iter_rep(child, 0, child.nops()));
566 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
568 const_postorder_iterator() noexcept {}
570 const_postorder_iterator(const ex &e, size_t n)
572 s.push(internal::_iter_rep(e, 0, n));
577 reference operator*() const
582 pointer operator->() const
587 const_postorder_iterator &operator++()
593 const_postorder_iterator operator++(int)
595 const_postorder_iterator tmp = *this;
600 bool operator==(const const_postorder_iterator &other) const noexcept
605 bool operator!=(const const_postorder_iterator &other) const noexcept
607 return !(*this == other);
611 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep>> s;
615 while (s.top().i != s.top().i_end) {
616 internal::_iter_rep & current = s.top();
617 const ex & child = current.e.op(current.i);
618 s.push(internal::_iter_rep(child, 0, child.nops()));
624 if (s.top().i == s.top().i_end)
633 inline const_iterator ex::begin() const noexcept
635 return const_iterator(*this, 0);
638 inline const_iterator ex::end() const noexcept
640 return const_iterator(*this, nops());
643 inline const_preorder_iterator ex::preorder_begin() const
645 return const_preorder_iterator(*this, nops());
648 inline const_preorder_iterator ex::preorder_end() const noexcept
650 return const_preorder_iterator();
653 inline const_postorder_iterator ex::postorder_begin() const
655 return const_postorder_iterator(*this, nops());
658 inline const_postorder_iterator ex::postorder_end() const noexcept
660 return const_postorder_iterator();
666 /** Compare two objects of class quickly without doing a deep tree traversal.
667 * @return "true" if they are equal
668 * "false" if equality cannot be established quickly (e1 and e2 may
669 * still be equal, in this case. */
670 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
672 return e1.bp == e2.bp;
675 /* Function objects for STL sort() etc. */
676 struct ex_is_less : public std::binary_function<ex, ex, bool> {
677 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
680 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
681 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
684 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
685 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
688 struct ex_swap : public std::binary_function<ex, ex, void> {
689 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
692 // Make it possible to print exvectors and exmaps
693 std::ostream & operator<<(std::ostream & os, const exvector & e);
694 std::ostream & operator<<(std::ostream & os, const exset & e);
695 std::ostream & operator<<(std::ostream & os, const exmap & e);
697 // wrapper functions around member functions
698 inline size_t nops(const ex & thisex)
699 { return thisex.nops(); }
701 inline ex expand(const ex & thisex, unsigned options = 0)
702 { return thisex.expand(options); }
704 inline ex conjugate(const ex & thisex)
705 { return thisex.conjugate(); }
707 inline ex real_part(const ex & thisex)
708 { return thisex.real_part(); }
710 inline ex imag_part(const ex & thisex)
711 { return thisex.imag_part(); }
713 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
714 { return thisex.has(pattern, options); }
716 inline bool find(const ex & thisex, const ex & pattern, exset& found)
717 { return thisex.find(pattern, found); }
719 inline bool is_polynomial(const ex & thisex, const ex & vars)
720 { return thisex.is_polynomial(vars); }
722 inline int degree(const ex & thisex, const ex & s)
723 { return thisex.degree(s); }
725 inline int ldegree(const ex & thisex, const ex & s)
726 { return thisex.ldegree(s); }
728 inline ex coeff(const ex & thisex, const ex & s, int n=1)
729 { return thisex.coeff(s, n); }
731 inline ex numer(const ex & thisex)
732 { return thisex.numer(); }
734 inline ex denom(const ex & thisex)
735 { return thisex.denom(); }
737 inline ex numer_denom(const ex & thisex)
738 { return thisex.numer_denom(); }
740 inline ex normal(const ex & thisex)
741 { return thisex.normal(); }
743 inline ex to_rational(const ex & thisex, lst & repl_lst)
744 { return thisex.to_rational(repl_lst); }
746 inline ex to_rational(const ex & thisex, exmap & repl)
747 { return thisex.to_rational(repl); }
749 inline ex to_polynomial(const ex & thisex, exmap & repl)
750 { return thisex.to_polynomial(repl); }
752 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
753 { return thisex.to_polynomial(repl_lst); }
755 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
756 { return thisex.collect(s, distributed); }
758 inline ex eval(const ex & thisex)
759 { return thisex.eval(); }
761 inline ex evalf(const ex & thisex)
762 { return thisex.evalf(); }
764 inline ex evalm(const ex & thisex)
765 { return thisex.evalm(); }
767 inline ex eval_integ(const ex & thisex)
768 { return thisex.eval_integ(); }
770 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
771 { return thisex.diff(s, nth); }
773 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
774 { return thisex.series(r, order, options); }
776 inline bool match(const ex & thisex, const ex & pattern, exmap& repl_lst)
777 { return thisex.match(pattern, repl_lst); }
779 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
780 { return thisex.simplify_indexed(options); }
782 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
783 { return thisex.simplify_indexed(sp, options); }
785 inline ex symmetrize(const ex & thisex)
786 { return thisex.symmetrize(); }
788 inline ex symmetrize(const ex & thisex, const lst & l)
789 { return thisex.symmetrize(l); }
791 inline ex antisymmetrize(const ex & thisex)
792 { return thisex.antisymmetrize(); }
794 inline ex antisymmetrize(const ex & thisex, const lst & l)
795 { return thisex.antisymmetrize(l); }
797 inline ex symmetrize_cyclic(const ex & thisex)
798 { return thisex.symmetrize_cyclic(); }
800 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
801 { return thisex.symmetrize_cyclic(l); }
803 inline ex op(const ex & thisex, size_t i)
804 { return thisex.op(i); }
806 inline ex lhs(const ex & thisex)
807 { return thisex.lhs(); }
809 inline ex rhs(const ex & thisex)
810 { return thisex.rhs(); }
812 inline bool is_zero(const ex & thisex)
813 { return thisex.is_zero(); }
815 inline void swap(ex & e1, ex & e2)
818 inline ex ex::subs(const exmap & m, unsigned options) const
820 return bp->subs(m, options);
823 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
824 { return thisex.subs(m, options); }
826 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
827 { return thisex.subs(ls, lr, options); }
829 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
830 { return thisex.subs(e, options); }
833 /* Convert function pointer to function object suitable for map(). */
834 class pointer_to_map_function : public map_function {
836 ex (*ptr)(const ex &);
838 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
839 ex operator()(const ex & e) override { return ptr(e); }
843 class pointer_to_map_function_1arg : public map_function {
845 ex (*ptr)(const ex &, T1);
848 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
849 ex operator()(const ex & e) override { return ptr(e, arg1); }
852 template<class T1, class T2>
853 class pointer_to_map_function_2args : public map_function {
855 ex (*ptr)(const ex &, T1, T2);
859 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
860 ex operator()(const ex & e) override { return ptr(e, arg1, arg2); }
863 template<class T1, class T2, class T3>
864 class pointer_to_map_function_3args : public map_function {
866 ex (*ptr)(const ex &, T1, T2, T3);
871 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) {}
872 ex operator()(const ex & e) override { return ptr(e, arg1, arg2, arg3); }
876 class pointer_to_member_to_map_function : public map_function {
878 ex (C::*ptr)(const ex &);
881 explicit pointer_to_member_to_map_function(ex (C::*member)(const ex &), C &obj) : ptr(member), c(obj) {}
882 ex operator()(const ex & e) override { return (c.*ptr)(e); }
885 template<class C, class T1>
886 class pointer_to_member_to_map_function_1arg : public map_function {
888 ex (C::*ptr)(const ex &, T1);
892 explicit pointer_to_member_to_map_function_1arg(ex (C::*member)(const ex &, T1), C &obj, T1 a1) : ptr(member), c(obj), arg1(a1) {}
893 ex operator()(const ex & e) override { return (c.*ptr)(e, arg1); }
896 template<class C, class T1, class T2>
897 class pointer_to_member_to_map_function_2args : public map_function {
899 ex (C::*ptr)(const ex &, T1, T2);
904 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) {}
905 ex operator()(const ex & e) override { return (c.*ptr)(e, arg1, arg2); }
908 template<class C, class T1, class T2, class T3>
909 class pointer_to_member_to_map_function_3args : public map_function {
911 ex (C::*ptr)(const ex &, T1, T2, T3);
917 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) {}
918 ex operator()(const ex & e) override { return (c.*ptr)(e, arg1, arg2, arg3); }
921 inline ex ex::map(ex f(const ex &)) const
923 pointer_to_map_function fcn(f);
927 // convenience type checker template functions
929 /** Check if ex is a handle to a T, including base classes. */
931 inline bool is_a(const ex &obj)
933 return is_a<T>(*obj.bp);
936 /** Check if ex is a handle to a T, not including base classes. */
938 inline bool is_exactly_a(const ex &obj)
940 return is_exactly_a<T>(*obj.bp);
943 /** Return a reference to the basic-derived class T object embedded in an
944 * expression. This is fast but unsafe: the result is undefined if the
945 * expression does not contain a T object at its top level. Hence, you
946 * should generally check the type of e first. Also, you shouldn't cache
947 * the returned reference because GiNaC's garbage collector may destroy
948 * the referenced object any time it's used in another expression.
950 * @param e expression
951 * @return reference to object of class T
952 * @see is_exactly_a<class T>() */
954 inline const T &ex_to(const ex &e)
956 GINAC_ASSERT(is_a<T>(e));
957 return static_cast<const T &>(*e.bp);
963 // Specializations of Standard Library algorithms
966 /** Specialization of std::swap() for ex objects. */
968 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
975 #endif // ndef GINAC_EX_H