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;
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
79 ex(const basic & other);
86 /** Construct ex from string and a list of symbols. The input grammar is
87 * similar to the GiNaC output format. All symbols and indices to be used
88 * in the expression must be specified in a lst in the second argument.
89 * Undefined symbols and other parser errors will throw an exception. */
90 ex(const std::string &s, const ex &l);
93 // non-virtual functions in this class
95 /** Efficiently swap the contents of two expressions. */
96 void swap(ex & other) throw()
98 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
99 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
104 const_iterator begin() const throw();
105 const_iterator end() const throw();
106 const_preorder_iterator preorder_begin() const;
107 const_preorder_iterator preorder_end() const throw();
108 const_postorder_iterator postorder_begin() const;
109 const_postorder_iterator postorder_end() const throw();
112 ex eval(int level = 0) const { return bp->eval(level); }
113 ex evalf(int level = 0) const { return bp->evalf(level); }
114 ex evalm() const { return bp->evalm(); }
115 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
116 ex eval_integ() const { return bp->eval_integ(); }
119 void print(const print_context & c, unsigned level = 0) const;
120 void dbgprint() const;
121 void dbgprinttree() const;
124 bool info(unsigned inf) const { return bp->info(inf); }
127 size_t nops() const { return bp->nops(); }
128 ex op(size_t i) const { return bp->op(i); }
129 ex operator[](const ex & index) const { return (*bp)[index]; }
130 ex operator[](size_t i) const { return (*bp)[i]; }
131 ex & let_op(size_t i);
132 ex & operator[](const ex & index);
133 ex & operator[](size_t i);
137 // complex conjugation
138 ex conjugate() const { return bp->conjugate(); }
141 bool has(const ex & pattern, unsigned options = 0) const { return bp->has(pattern, options); }
142 bool find(const ex & pattern, lst & found) const;
143 bool match(const ex & pattern) const;
144 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
147 ex subs(const exmap & m, unsigned options = 0) const;
148 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
149 ex subs(const ex & e, unsigned options = 0) const;
152 ex map(map_function & f) const { return bp->map(f); }
153 ex map(ex (*f)(const ex & e)) const;
155 // visitors and tree traversal
156 void accept(visitor & v) const { bp->accept(v); }
157 void traverse_preorder(visitor & v) const;
158 void traverse_postorder(visitor & v) const;
159 void traverse(visitor & v) const { traverse_preorder(v); }
162 int degree(const ex & s) const { return bp->degree(s); }
163 int ldegree(const ex & s) const { return bp->ldegree(s); }
164 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
165 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
166 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
169 ex expand(unsigned options=0) const;
170 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
172 // differentiation and series expansion
173 ex diff(const symbol & s, unsigned nth = 1) const;
174 ex series(const ex & r, int order, unsigned options = 0) const;
176 // rational functions
177 ex normal(int level = 0) const;
178 ex to_rational(exmap & repl) const;
179 ex to_rational(lst & repl_lst) const;
180 ex to_polynomial(exmap & repl) const;
181 ex to_polynomial(lst & repl_lst) const;
184 ex numer_denom() const;
186 // polynomial algorithms
187 ex unit(const ex &x) const;
188 ex content(const ex &x) const;
189 numeric integer_content() const;
190 ex primpart(const ex &x) const;
191 ex primpart(const ex &x, const ex &cont) const;
192 void unitcontprim(const ex &x, ex &u, ex &c, ex &p) const;
193 ex smod(const numeric &xi) const { return bp->smod(xi); }
194 numeric max_coefficient() const;
197 exvector get_free_indices() const { return bp->get_free_indices(); }
198 ex simplify_indexed(unsigned options = 0) const;
199 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
202 int compare(const ex & other) const;
203 bool is_equal(const ex & other) const;
204 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
207 ex symmetrize() const;
208 ex symmetrize(const lst & l) const;
209 ex antisymmetrize() const;
210 ex antisymmetrize(const lst & l) const;
211 ex symmetrize_cyclic() const;
212 ex symmetrize_cyclic(const lst & l) const;
215 unsigned return_type() const { return bp->return_type(); }
216 const basic* return_type_tinfo() const { return bp->return_type_tinfo(); }
218 unsigned gethash() const { return bp->gethash(); }
221 static ptr<basic> construct_from_basic(const basic & other);
222 static basic & construct_from_int(int i);
223 static basic & construct_from_uint(unsigned int i);
224 static basic & construct_from_long(long i);
225 static basic & construct_from_ulong(unsigned long i);
226 static basic & construct_from_double(double d);
227 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
228 void makewriteable();
229 void share(const ex & other) const;
234 mutable ptr<basic> bp; ///< pointer to basic object managed by this
238 // performance-critical inlined method implementations
240 // This needs to be a basic* because we don't know that numeric is derived
241 // from basic and we need a basic& for the ex default constructor
242 extern const basic *_num0_bp;
245 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
247 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
251 ex::ex(const basic & other) : bp(construct_from_basic(other))
253 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
257 ex::ex(int i) : bp(construct_from_int(i))
259 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
263 ex::ex(unsigned int i) : bp(construct_from_uint(i))
265 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
269 ex::ex(long i) : bp(construct_from_long(i))
271 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
275 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
277 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
281 ex::ex(double const d) : bp(construct_from_double(d))
283 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
287 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
289 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
293 int ex::compare(const ex & other) const
295 #ifdef GINAC_COMPARE_STATISTICS
296 compare_statistics.total_compares++;
298 if (bp == other.bp) // trivial case: both expressions point to same basic
300 #ifdef GINAC_COMPARE_STATISTICS
301 compare_statistics.nontrivial_compares++;
303 const int cmpval = bp->compare(*other.bp);
306 // Expressions point to different, but equal, trees: conserve
307 // memory and make subsequent compare() operations faster by
308 // making both expressions point to the same tree.
316 bool ex::is_equal(const ex & other) const
318 #ifdef GINAC_COMPARE_STATISTICS
319 compare_statistics.total_is_equals++;
321 if (bp == other.bp) // trivial case: both expressions point to same basic
323 #ifdef GINAC_COMPARE_STATISTICS
324 compare_statistics.nontrivial_is_equals++;
326 const bool equal = bp->is_equal(*other.bp);
329 // Expressions point to different, but equal, trees: conserve
330 // memory and make subsequent compare() operations faster by
331 // making both expressions point to the same tree.
341 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
343 friend class const_preorder_iterator;
344 friend class const_postorder_iterator;
347 const_iterator() throw() {}
350 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
353 // This should return an ex&, but that would be a reference to a
360 // This should return an ex*, but that would be a pointer to a
362 std::auto_ptr<ex> operator->() const
364 return std::auto_ptr<ex>(new ex(operator*()));
367 ex operator[](difference_type n) const
372 const_iterator &operator++() throw()
378 const_iterator operator++(int) throw()
380 const_iterator tmp = *this;
385 const_iterator &operator+=(difference_type n) throw()
391 const_iterator operator+(difference_type n) const throw()
393 return const_iterator(e, i + n);
396 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
398 return const_iterator(it.e, it.i + n);
401 const_iterator &operator--() throw()
407 const_iterator operator--(int) throw()
409 const_iterator tmp = *this;
414 const_iterator &operator-=(difference_type n) throw()
420 const_iterator operator-(difference_type n) const throw()
422 return const_iterator(e, i - n);
425 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
427 return lhs.i - rhs.i;
430 bool operator==(const const_iterator &other) const throw()
432 return are_ex_trivially_equal(e, other.e) && i == other.i;
435 bool operator!=(const const_iterator &other) const throw()
437 return !(*this == other);
440 bool operator<(const const_iterator &other) const throw()
445 bool operator>(const const_iterator &other) const throw()
447 return other < *this;
450 bool operator<=(const const_iterator &other) const throw()
452 return !(other < *this);
455 bool operator>=(const const_iterator &other) const throw()
457 return !(*this < other);
461 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
468 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
470 bool operator==(const _iter_rep &other) const throw()
472 return are_ex_trivially_equal(e, other.e) && i == other.i;
475 bool operator!=(const _iter_rep &other) const throw()
477 return !(*this == other);
485 } // namespace internal
487 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
489 const_preorder_iterator() throw() {}
491 const_preorder_iterator(const ex &e, size_t n)
493 s.push(internal::_iter_rep(e, 0, n));
497 reference operator*() const
502 pointer operator->() const
507 const_preorder_iterator &operator++()
513 const_preorder_iterator operator++(int)
515 const_preorder_iterator tmp = *this;
520 bool operator==(const const_preorder_iterator &other) const throw()
525 bool operator!=(const const_preorder_iterator &other) const throw()
527 return !(*this == other);
531 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
535 while (!s.empty() && s.top().i == s.top().i_end) {
542 internal::_iter_rep & current = s.top();
544 if (current.i != current.i_end) {
545 const ex & child = current.e.op(current.i);
546 s.push(internal::_iter_rep(child, 0, child.nops()));
551 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &> {
553 const_postorder_iterator() throw() {}
555 const_postorder_iterator(const ex &e, size_t n)
557 s.push(internal::_iter_rep(e, 0, n));
562 reference operator*() const
567 pointer operator->() const
572 const_postorder_iterator &operator++()
578 const_postorder_iterator operator++(int)
580 const_postorder_iterator tmp = *this;
585 bool operator==(const const_postorder_iterator &other) const throw()
590 bool operator!=(const const_postorder_iterator &other) const throw()
592 return !(*this == other);
596 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
600 while (s.top().i != s.top().i_end) {
601 internal::_iter_rep & current = s.top();
602 const ex & child = current.e.op(current.i);
603 s.push(internal::_iter_rep(child, 0, child.nops()));
609 if (s.top().i == s.top().i_end)
618 inline const_iterator ex::begin() const throw()
620 return const_iterator(*this, 0);
623 inline const_iterator ex::end() const throw()
625 return const_iterator(*this, nops());
628 inline const_preorder_iterator ex::preorder_begin() const
630 return const_preorder_iterator(*this, nops());
633 inline const_preorder_iterator ex::preorder_end() const throw()
635 return const_preorder_iterator();
638 inline const_postorder_iterator ex::postorder_begin() const
640 return const_postorder_iterator(*this, nops());
643 inline const_postorder_iterator ex::postorder_end() const throw()
645 return const_postorder_iterator();
651 /** Compare two objects of class quickly without doing a deep tree traversal.
652 * @return "true" if they are equal
653 * "false" if equality cannot be established quickly (e1 and e2 may
654 * still be equal, in this case. */
655 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
657 return e1.bp == e2.bp;
660 /* Function objects for STL sort() etc. */
661 struct ex_is_less : public std::binary_function<ex, ex, bool> {
662 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
665 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
666 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
669 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
670 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
673 struct ex_swap : public std::binary_function<ex, ex, void> {
674 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
677 // wrapper functions around member functions
678 inline size_t nops(const ex & thisex)
679 { return thisex.nops(); }
681 inline ex expand(const ex & thisex, unsigned options = 0)
682 { return thisex.expand(options); }
684 inline ex conjugate(const ex & thisex)
685 { return thisex.conjugate(); }
687 inline bool has(const ex & thisex, const ex & pattern, unsigned options = 0)
688 { return thisex.has(pattern, options); }
690 inline bool find(const ex & thisex, const ex & pattern, lst & found)
691 { return thisex.find(pattern, found); }
693 inline int degree(const ex & thisex, const ex & s)
694 { return thisex.degree(s); }
696 inline int ldegree(const ex & thisex, const ex & s)
697 { return thisex.ldegree(s); }
699 inline ex coeff(const ex & thisex, const ex & s, int n=1)
700 { return thisex.coeff(s, n); }
702 inline ex numer(const ex & thisex)
703 { return thisex.numer(); }
705 inline ex denom(const ex & thisex)
706 { return thisex.denom(); }
708 inline ex numer_denom(const ex & thisex)
709 { return thisex.numer_denom(); }
711 inline ex normal(const ex & thisex, int level=0)
712 { return thisex.normal(level); }
714 inline ex to_rational(const ex & thisex, lst & repl_lst)
715 { return thisex.to_rational(repl_lst); }
717 inline ex to_rational(const ex & thisex, exmap & repl)
718 { return thisex.to_rational(repl); }
720 inline ex to_polynomial(const ex & thisex, exmap & repl)
721 { return thisex.to_polynomial(repl); }
723 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
724 { return thisex.to_polynomial(repl_lst); }
726 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
727 { return thisex.collect(s, distributed); }
729 inline ex eval(const ex & thisex, int level = 0)
730 { return thisex.eval(level); }
732 inline ex evalf(const ex & thisex, int level = 0)
733 { return thisex.evalf(level); }
735 inline ex evalm(const ex & thisex)
736 { return thisex.evalm(); }
738 inline ex eval_integ(const ex & thisex)
739 { return thisex.eval_integ(); }
741 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
742 { return thisex.diff(s, nth); }
744 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
745 { return thisex.series(r, order, options); }
747 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
748 { return thisex.match(pattern, repl_lst); }
750 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
751 { return thisex.simplify_indexed(options); }
753 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
754 { return thisex.simplify_indexed(sp, options); }
756 inline ex symmetrize(const ex & thisex)
757 { return thisex.symmetrize(); }
759 inline ex symmetrize(const ex & thisex, const lst & l)
760 { return thisex.symmetrize(l); }
762 inline ex antisymmetrize(const ex & thisex)
763 { return thisex.antisymmetrize(); }
765 inline ex antisymmetrize(const ex & thisex, const lst & l)
766 { return thisex.antisymmetrize(l); }
768 inline ex symmetrize_cyclic(const ex & thisex)
769 { return thisex.symmetrize_cyclic(); }
771 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
772 { return thisex.symmetrize_cyclic(l); }
774 inline ex op(const ex & thisex, size_t i)
775 { return thisex.op(i); }
777 inline ex lhs(const ex & thisex)
778 { return thisex.lhs(); }
780 inline ex rhs(const ex & thisex)
781 { return thisex.rhs(); }
783 inline bool is_zero(const ex & thisex)
784 { return thisex.is_zero(); }
786 inline void swap(ex & e1, ex & e2)
789 inline ex ex::subs(const exmap & m, unsigned options) const
791 return bp->subs(m, options);
794 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
795 { return thisex.subs(m, options); }
797 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
798 { return thisex.subs(ls, lr, options); }
800 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
801 { return thisex.subs(e, options); }
804 /* Convert function pointer to function object suitable for map(). */
805 class pointer_to_map_function : public map_function {
807 ex (*ptr)(const ex &);
809 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
810 ex operator()(const ex & e) { return ptr(e); }
814 class pointer_to_map_function_1arg : public map_function {
816 ex (*ptr)(const ex &, T1);
819 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
820 ex operator()(const ex & e) { return ptr(e, arg1); }
823 template<class T1, class T2>
824 class pointer_to_map_function_2args : public map_function {
826 ex (*ptr)(const ex &, T1, T2);
830 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
831 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
834 template<class T1, class T2, class T3>
835 class pointer_to_map_function_3args : public map_function {
837 ex (*ptr)(const ex &, T1, T2, T3);
842 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) {}
843 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
846 inline ex ex::map(ex f(const ex &)) const
848 pointer_to_map_function fcn(f);
852 // convenience type checker template functions
854 /** Check if ex is a handle to a T, including base classes. */
856 inline bool is_a(const ex &obj)
858 return is_a<T>(*obj.bp);
861 /** Check if ex is a handle to a T, not including base classes. */
863 inline bool is_exactly_a(const ex &obj)
865 return is_exactly_a<T>(*obj.bp);
868 /** Return a reference to the basic-derived class T object embedded in an
869 * expression. This is fast but unsafe: the result is undefined if the
870 * expression does not contain a T object at its top level. Hence, you
871 * should generally check the type of e first. Also, you shouldn't cache
872 * the returned reference because GiNaC's garbage collector may destroy
873 * the referenced object any time it's used in another expression.
875 * @param e expression
876 * @return reference to object of class T
877 * @see is_exactly_a<class T>() */
879 inline const T &ex_to(const ex &e)
881 GINAC_ASSERT(is_a<T>(e));
882 return static_cast<const T &>(*e.bp);
888 // Specializations of Standard Library algorithms
891 /** Specialization of std::swap() for ex objects. */
893 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
898 /** Specialization of std::iter_swap() for vector<ex> iterators. */
900 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
905 /** Specialization of std::iter_swap() for list<ex> iterators. */
907 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
914 #endif // ndef __GINAC_EX_H__