3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2003 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;
60 /** Lightweight wrapper for GiNaC's symbolic objects. Basically all it does is
61 * to hold a pointer to the other objects, manage the reference counting and
62 * provide methods for manipulation of these objects. (Some people call such
63 * a thing a proxy class.) */
66 friend class archive_node;
67 friend inline bool are_ex_trivially_equal(const ex &, const ex &);
68 template<class T> friend inline const T &ex_to(const ex &);
69 template<class T> friend inline bool is_a(const ex &);
70 template<class T> friend inline bool is_exactly_a(const ex &);
72 // default constructor, copy constructor and assignment operator
75 #ifdef OBSCURE_CINT_HACK
77 ex & operator=(const ex & other);
82 ex(const basic & other);
89 /** Construct ex from string and a list of symbols. The input grammar is
90 * similar to the GiNaC output format. All symbols and indices to be used
91 * in the expression must be specified in a lst in the second argument.
92 * Undefined symbols and other parser errors will throw an exception. */
93 ex(const std::string &s, const ex &l);
96 // non-virtual functions in this class
98 /** Efficiently swap the contents of two expressions. */
99 void swap(ex & other) throw()
101 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
102 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
107 const_iterator begin() const throw();
108 const_iterator end() const throw();
111 ex eval(int level = 0) const { return bp->eval(level); }
112 ex evalf(int level = 0) const { return bp->evalf(level); }
113 ex evalm() const { return bp->evalm(); }
114 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
117 void print(const print_context & c, unsigned level = 0) const;
118 void dbgprint() const;
119 void dbgprinttree() const;
122 bool info(unsigned inf) const { return bp->info(inf); }
125 size_t nops() const { return bp->nops(); }
126 ex op(size_t i) const { return bp->op(i); }
127 ex operator[](const ex & index) const { return (*bp)[index]; }
128 ex operator[](size_t i) const { return (*bp)[i]; }
129 ex & let_op(size_t i);
130 ex & operator[](const ex & index);
131 ex & operator[](size_t i);
136 bool has(const ex & pattern) const { return bp->has(pattern); }
137 bool find(const ex & pattern, lst & found) const;
138 bool match(const ex & pattern) const;
139 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
142 ex subs(const exmap & m, unsigned options = 0) const;
143 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
144 ex subs(const ex & e, unsigned options = 0) const;
147 ex map(map_function & f) const { return bp->map(f); }
148 ex map(ex (*f)(const ex & e)) const;
150 // visitors and tree traversal
151 void accept(visitor & v) const { bp->accept(v); }
152 void traverse_preorder(visitor & v) const;
153 void traverse_postorder(visitor & v) const;
154 void traverse(visitor & v) const { traverse_preorder(v); }
157 int degree(const ex & s) const { return bp->degree(s); }
158 int ldegree(const ex & s) const { return bp->ldegree(s); }
159 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
160 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
161 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
164 ex expand(unsigned options=0) const;
165 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
167 // differentiation and series expansion
168 ex diff(const symbol & s, unsigned nth = 1) const;
169 ex series(const ex & r, int order, unsigned options = 0) const;
171 // rational functions
172 ex normal(int level = 0) const;
173 ex to_rational(lst &repl_lst) const;
174 ex to_polynomial(lst &repl_lst) const;
177 ex numer_denom() const;
179 // polynomial algorithms
180 ex unit(const ex &x) const;
181 ex content(const ex &x) const;
182 numeric integer_content() const;
183 ex primpart(const ex &x) const;
184 ex primpart(const ex &x, const ex &cont) const;
185 ex smod(const numeric &xi) const { return bp->smod(xi); }
186 numeric max_coefficient() const;
189 exvector get_free_indices() const { return bp->get_free_indices(); }
190 ex simplify_indexed() const;
191 ex simplify_indexed(const scalar_products & sp) const;
194 int compare(const ex & other) const;
195 bool is_equal(const ex & other) const;
196 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
199 ex symmetrize() const;
200 ex symmetrize(const lst & l) const;
201 ex antisymmetrize() const;
202 ex antisymmetrize(const lst & l) const;
203 ex symmetrize_cyclic() const;
204 ex symmetrize_cyclic(const lst & l) const;
207 unsigned return_type() const { return bp->return_type(); }
208 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
210 unsigned gethash() const { return bp->gethash(); }
213 static ptr<basic> construct_from_basic(const basic & other);
214 static basic & construct_from_int(int i);
215 static basic & construct_from_uint(unsigned int i);
216 static basic & construct_from_long(long i);
217 static basic & construct_from_ulong(unsigned long i);
218 static basic & construct_from_double(double d);
219 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
220 void makewriteable();
221 void share(const ex & other) const;
223 #ifdef OBSCURE_CINT_HACK
225 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
227 if (last_created_or_assigned_bp==0) return false;
228 if ((last_created_or_assigned_bp->flags &
229 status_flags::dynallocated)==0) return false;
230 if ((last_created_or_assigned_bp->flags &
231 status_flags::evaluated)==0) return false;
235 void update_last_created_or_assigned_bp()
237 last_created_or_assigned_bp = bp;
238 last_created_or_assigned_exp = (long)(void *)(this);
240 #endif // def OBSCURE_CINT_HACK
245 mutable ptr<basic> bp; ///< pointer to basic object managed by this
247 #ifdef OBSCURE_CINT_HACK
249 static ptr<basic> last_created_or_assigned_bp;
250 static basic * dummy_bp;
251 static long last_created_or_assigned_exp;
252 #endif // def OBSCURE_CINT_HACK
256 // performance-critical inlined method implementations
258 // This needs to be a basic* because we don't know that numeric is derived
259 // from basic and we need a basic& for the ex default constructor
260 extern const basic *_num0_bp;
263 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
265 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
266 #ifdef OBSCURE_CINT_HACK
267 update_last_created_or_assigned_bp();
268 #endif // def OBSCURE_CINT_HACK
271 #ifdef OBSCURE_CINT_HACK
273 ex::ex(const ex & other) : bp(other.bp)
275 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
276 update_last_created_or_assigned_bp();
280 ex & ex::operator=(const ex & other)
282 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
283 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
285 update_last_created_or_assigned_bp();
288 #endif // def OBSCURE_CINT_HACK
291 ex::ex(const basic & other) : bp(construct_from_basic(other))
293 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
294 #ifdef OBSCURE_CINT_HACK
295 update_last_created_or_assigned_bp();
296 #endif // def OBSCURE_CINT_HACK
300 ex::ex(int i) : bp(construct_from_int(i))
302 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
303 #ifdef OBSCURE_CINT_HACK
304 update_last_created_or_assigned_bp();
305 #endif // def OBSCURE_CINT_HACK
309 ex::ex(unsigned int i) : bp(construct_from_uint(i))
311 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
312 #ifdef OBSCURE_CINT_HACK
313 update_last_created_or_assigned_bp();
314 #endif // def OBSCURE_CINT_HACK
318 ex::ex(long i) : bp(construct_from_long(i))
320 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
321 #ifdef OBSCURE_CINT_HACK
322 update_last_created_or_assigned_bp();
323 #endif // def OBSCURE_CINT_HACK
327 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
329 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
330 #ifdef OBSCURE_CINT_HACK
331 update_last_created_or_assigned_bp();
332 #endif // def OBSCURE_CINT_HACK
336 ex::ex(double const d) : bp(construct_from_double(d))
338 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
339 #ifdef OBSCURE_CINT_HACK
340 update_last_created_or_assigned_bp();
341 #endif // def OBSCURE_CINT_HACK
345 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
347 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
348 #ifdef OBSCURE_CINT_HACK
349 update_last_created_or_assigned_bp();
350 #endif // def OBSCURE_CINT_HACK
354 int ex::compare(const ex & other) const
356 if (bp == other.bp) // trivial case: both expressions point to same basic
358 const int cmpval = bp->compare(*other.bp);
360 // Expressions point to different, but equal, trees: conserve
361 // memory and make subsequent compare() operations faster by
362 // making both expression point to the same tree.
369 bool ex::is_equal(const ex & other) const
371 if (bp == other.bp) // trivial case: both expressions point to same basic
373 return bp->is_equal(*other.bp);
379 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
382 friend class const_preorder_iterator;
383 friend class const_postorder_iterator;
386 const_iterator() throw() {}
389 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
392 // This should return an ex&, but that would be a reference to a
400 // How do we make this work in the context of the "reference to
401 // temporary" problem? Return an auto_ptr?
402 pointer operator->() const
404 return &(operator*());
408 ex operator[](difference_type n) const
413 const_iterator &operator++() throw()
419 const_iterator operator++(int) throw()
421 const_iterator tmp = *this;
426 const_iterator &operator+=(difference_type n) throw()
432 const_iterator operator+(difference_type n) const throw()
434 return const_iterator(e, i + n);
437 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
439 return const_iterator(it.e, it.i + n);
442 const_iterator &operator--() throw()
448 const_iterator operator--(int) throw()
450 const_iterator tmp = *this;
455 const_iterator &operator-=(difference_type n) throw()
461 const_iterator operator-(difference_type n) const throw()
463 return const_iterator(e, i - n);
466 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
468 return lhs.i - rhs.i;
471 bool operator==(const const_iterator &other) const throw()
473 return are_ex_trivially_equal(e, other.e) && i == other.i;
476 bool operator!=(const const_iterator &other) const throw()
478 return !(*this == other);
481 bool operator<(const const_iterator &other) const throw()
486 bool operator>(const const_iterator &other) const throw()
488 return other < *this;
491 bool operator<=(const const_iterator &other) const throw()
493 return !(other < *this);
496 bool operator>=(const const_iterator &other) const throw()
498 return !(*this < other);
502 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
509 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
511 bool operator==(const _iter_rep &other) const throw()
513 return are_ex_trivially_equal(e, other.e) && i == other.i;
516 bool operator!=(const _iter_rep &other) const throw()
518 return !(*this == other);
526 } // namespace internal
528 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
531 const_preorder_iterator() throw() {}
533 // Provide implicit conversion from const_iterator, so begin() and
534 // end() can be used to create const_preorder_iterators
535 const_preorder_iterator(const const_iterator & cit)
537 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
543 const internal::_iter_rep & r = s.top();
547 // operator->() not implemented (see above)
549 const_preorder_iterator &operator++()
555 const_preorder_iterator operator++(int)
557 const_preorder_iterator tmp = *this;
562 bool operator==(const const_preorder_iterator &other) const throw()
567 bool operator!=(const const_preorder_iterator &other) const throw()
569 return !(*this == other);
573 std::stack<internal::_iter_rep> s;
577 internal::_iter_rep & current = s.top();
578 const ex & child = current.e.op(current.i);
579 size_t n = child.nops();
581 s.push(internal::_iter_rep(child, 0, n));
585 while (s.top().i == s.top().i_end && s.size() > 1) {
592 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
595 const_postorder_iterator() throw() {}
597 // Provide implicit conversion from const_iterator, so begin() and
598 // end() can be used to create const_postorder_iterators
599 const_postorder_iterator(const const_iterator & cit)
601 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
608 const internal::_iter_rep & r = s.top();
612 // operator->() not implemented
614 const_postorder_iterator &operator++()
620 const_postorder_iterator operator++(int)
622 const_postorder_iterator tmp = *this;
627 bool operator==(const const_postorder_iterator &other) const throw()
632 bool operator!=(const const_postorder_iterator &other) const throw()
634 return !(*this == other);
638 std::stack<internal::_iter_rep> s;
642 while (s.top().i != s.top().i_end && s.top().e.op(s.top().i).nops() > 0) {
643 const internal::_iter_rep & current = s.top();
644 const ex & child = current.e.op(current.i);
645 s.push(internal::_iter_rep(child, 0, child.nops()));
653 if (s.top().i == s.top().i_end && s.size() > 1)
658 inline const_iterator ex::begin() const throw()
660 return const_iterator(*this, 0);
663 inline const_iterator ex::end() const throw()
665 return const_iterator(*this, nops());
671 /** Compare two objects of class quickly without doing a deep tree traversal.
672 * @return "true" if they are equal
673 * "false" if equality cannot be established quickly (e1 and e2 may
674 * still be equal, in this case. */
675 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
677 return e1.bp == e2.bp;
680 // wrapper functions around member functions
681 inline size_t nops(const ex & thisex)
682 { return thisex.nops(); }
684 inline ex expand(const ex & thisex, unsigned options = 0)
685 { return thisex.expand(options); }
687 inline bool has(const ex & thisex, const ex & pattern)
688 { return thisex.has(pattern); }
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_polynomial(const ex & thisex, lst & repl_lst)
718 { return thisex.to_polynomial(repl_lst); }
720 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
721 { return thisex.collect(s, distributed); }
723 inline ex eval(const ex & thisex, int level = 0)
724 { return thisex.eval(level); }
726 inline ex evalf(const ex & thisex, int level = 0)
727 { return thisex.evalf(level); }
729 inline ex evalm(const ex & thisex)
730 { return thisex.evalm(); }
732 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
733 { return thisex.diff(s, nth); }
735 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
736 { return thisex.series(r, order, options); }
738 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
739 { return thisex.match(pattern, repl_lst); }
741 inline ex simplify_indexed(const ex & thisex)
742 { return thisex.simplify_indexed(); }
744 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp)
745 { return thisex.simplify_indexed(sp); }
747 inline ex symmetrize(const ex & thisex)
748 { return thisex.symmetrize(); }
750 inline ex symmetrize(const ex & thisex, const lst & l)
751 { return thisex.symmetrize(l); }
753 inline ex antisymmetrize(const ex & thisex)
754 { return thisex.antisymmetrize(); }
756 inline ex antisymmetrize(const ex & thisex, const lst & l)
757 { return thisex.antisymmetrize(l); }
759 inline ex symmetrize_cyclic(const ex & thisex)
760 { return thisex.symmetrize_cyclic(); }
762 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
763 { return thisex.symmetrize_cyclic(l); }
765 inline ex op(const ex & thisex, size_t i)
766 { return thisex.op(i); }
768 inline ex lhs(const ex & thisex)
769 { return thisex.lhs(); }
771 inline ex rhs(const ex & thisex)
772 { return thisex.rhs(); }
774 inline bool is_zero(const ex & thisex)
775 { return thisex.is_zero(); }
777 inline void swap(ex & e1, ex & e2)
780 /* Function objects for STL sort() etc. */
781 struct ex_is_less : public std::binary_function<ex, ex, bool> {
782 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
785 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
786 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
789 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
790 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
793 struct ex_swap : public std::binary_function<ex, ex, void> {
794 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
797 inline ex ex::subs(const exmap & m, unsigned options) const
799 return bp->subs(m, options);
802 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
803 { return thisex.subs(m, options); }
805 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
806 { return thisex.subs(ls, lr, options); }
808 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
809 { return thisex.subs(e, options); }
812 /* Convert function pointer to function object suitable for map(). */
813 class pointer_to_map_function : public map_function {
815 ex (*ptr)(const ex &);
817 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
818 ex operator()(const ex & e) { return ptr(e); }
822 class pointer_to_map_function_1arg : public map_function {
824 ex (*ptr)(const ex &, T1);
827 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
828 ex operator()(const ex & e) { return ptr(e, arg1); }
831 template<class T1, class T2>
832 class pointer_to_map_function_2args : public map_function {
834 ex (*ptr)(const ex &, T1, T2);
838 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
839 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
842 template<class T1, class T2, class T3>
843 class pointer_to_map_function_3args : public map_function {
845 ex (*ptr)(const ex &, T1, T2, T3);
850 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) {}
851 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
854 inline ex ex::map(ex f(const ex &)) const
856 pointer_to_map_function fcn(f);
860 // convenience type checker template functions
862 /** Check if ex is a handle to a T, including base classes. */
864 inline bool is_a(const ex &obj)
866 return is_a<T>(*obj.bp);
869 /** Check if ex is a handle to a T, not including base classes. */
871 inline bool is_exactly_a(const ex &obj)
873 return is_exactly_a<T>(*obj.bp);
876 /** Return a reference to the basic-derived class T object embedded in an
877 * expression. This is fast but unsafe: the result is undefined if the
878 * expression does not contain a T object at its top level. Hence, you
879 * should generally check the type of e first.
881 * @param e expression
882 * @return reference to object of class T
883 * @see is_exactly_a<class T>() */
885 inline const T &ex_to(const ex &e)
887 GINAC_ASSERT(is_a<T>(e));
888 return static_cast<const T &>(*e.bp);
894 // Specializations of Standard Library algorithms
897 /** Specialization of std::swap() for ex objects. */
899 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
904 /** Specialization of std::iter_swap() for vector<ex> iterators. */
906 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
911 /** Specialization of std::iter_swap() for list<ex> iterators. */
913 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
920 #endif // ndef __GINAC_EX_H__