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
399 // This should return an ex*, but that would be a pointer to a
401 std::auto_ptr<ex> operator->() const
403 return std::auto_ptr<ex>(new ex(operator*()));
406 ex operator[](difference_type n) const
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 const_iterator operator+(difference_type n, const const_iterator &it) throw()
437 return const_iterator(it.e, it.i + n);
440 const_iterator &operator--() throw()
446 const_iterator operator--(int) throw()
448 const_iterator tmp = *this;
453 const_iterator &operator-=(difference_type n) throw()
459 const_iterator operator-(difference_type n) const throw()
461 return const_iterator(e, i - n);
464 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
466 return lhs.i - rhs.i;
469 bool operator==(const const_iterator &other) const throw()
471 return are_ex_trivially_equal(e, other.e) && i == other.i;
474 bool operator!=(const const_iterator &other) const throw()
476 return !(*this == other);
479 bool operator<(const const_iterator &other) const throw()
484 bool operator>(const const_iterator &other) const throw()
486 return other < *this;
489 bool operator<=(const const_iterator &other) const throw()
491 return !(other < *this);
494 bool operator>=(const const_iterator &other) const throw()
496 return !(*this < other);
500 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
507 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
509 bool operator==(const _iter_rep &other) const throw()
511 return are_ex_trivially_equal(e, other.e) && i == other.i;
514 bool operator!=(const _iter_rep &other) const throw()
516 return !(*this == other);
524 } // namespace internal
526 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
529 const_preorder_iterator() throw() {}
531 // Provide implicit conversion from const_iterator, so begin() and
532 // end() can be used to create const_preorder_iterators
533 const_preorder_iterator(const const_iterator & cit)
535 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
541 const internal::_iter_rep & r = s.top();
545 std::auto_ptr<ex> operator->() const
547 return std::auto_ptr<ex>(new ex(operator*()));
550 const_preorder_iterator &operator++()
556 const_preorder_iterator operator++(int)
558 const_preorder_iterator tmp = *this;
563 bool operator==(const const_preorder_iterator &other) const throw()
568 bool operator!=(const const_preorder_iterator &other) const throw()
570 return !(*this == other);
574 std::stack<internal::_iter_rep> s;
578 internal::_iter_rep & current = s.top();
579 const ex & child = current.e.op(current.i);
580 size_t n = child.nops();
582 s.push(internal::_iter_rep(child, 0, n));
586 while (s.top().i == s.top().i_end && s.size() > 1) {
593 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
596 const_postorder_iterator() throw() {}
598 // Provide implicit conversion from const_iterator, so begin() and
599 // end() can be used to create const_postorder_iterators
600 const_postorder_iterator(const const_iterator & cit)
602 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
609 const internal::_iter_rep & r = s.top();
613 std::auto_ptr<ex> operator->() const
615 return std::auto_ptr<ex>(new ex(operator*()));
618 const_postorder_iterator &operator++()
624 const_postorder_iterator operator++(int)
626 const_postorder_iterator tmp = *this;
631 bool operator==(const const_postorder_iterator &other) const throw()
636 bool operator!=(const const_postorder_iterator &other) const throw()
638 return !(*this == other);
642 std::stack<internal::_iter_rep> s;
646 while (s.top().i != s.top().i_end && s.top().e.op(s.top().i).nops() > 0) {
647 const internal::_iter_rep & current = s.top();
648 const ex & child = current.e.op(current.i);
649 s.push(internal::_iter_rep(child, 0, child.nops()));
657 if (s.top().i == s.top().i_end && s.size() > 1)
662 inline const_iterator ex::begin() const throw()
664 return const_iterator(*this, 0);
667 inline const_iterator ex::end() const throw()
669 return const_iterator(*this, nops());
675 /** Compare two objects of class quickly without doing a deep tree traversal.
676 * @return "true" if they are equal
677 * "false" if equality cannot be established quickly (e1 and e2 may
678 * still be equal, in this case. */
679 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
681 return e1.bp == e2.bp;
684 // wrapper functions around member functions
685 inline size_t nops(const ex & thisex)
686 { return thisex.nops(); }
688 inline ex expand(const ex & thisex, unsigned options = 0)
689 { return thisex.expand(options); }
691 inline bool has(const ex & thisex, const ex & pattern)
692 { return thisex.has(pattern); }
694 inline bool find(const ex & thisex, const ex & pattern, lst & found)
695 { return thisex.find(pattern, found); }
697 inline int degree(const ex & thisex, const ex & s)
698 { return thisex.degree(s); }
700 inline int ldegree(const ex & thisex, const ex & s)
701 { return thisex.ldegree(s); }
703 inline ex coeff(const ex & thisex, const ex & s, int n=1)
704 { return thisex.coeff(s, n); }
706 inline ex numer(const ex & thisex)
707 { return thisex.numer(); }
709 inline ex denom(const ex & thisex)
710 { return thisex.denom(); }
712 inline ex numer_denom(const ex & thisex)
713 { return thisex.numer_denom(); }
715 inline ex normal(const ex & thisex, int level=0)
716 { return thisex.normal(level); }
718 inline ex to_rational(const ex & thisex, lst & repl_lst)
719 { return thisex.to_rational(repl_lst); }
721 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
722 { return thisex.to_polynomial(repl_lst); }
724 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
725 { return thisex.collect(s, distributed); }
727 inline ex eval(const ex & thisex, int level = 0)
728 { return thisex.eval(level); }
730 inline ex evalf(const ex & thisex, int level = 0)
731 { return thisex.evalf(level); }
733 inline ex evalm(const ex & thisex)
734 { return thisex.evalm(); }
736 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
737 { return thisex.diff(s, nth); }
739 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
740 { return thisex.series(r, order, options); }
742 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
743 { return thisex.match(pattern, repl_lst); }
745 inline ex simplify_indexed(const ex & thisex)
746 { return thisex.simplify_indexed(); }
748 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp)
749 { return thisex.simplify_indexed(sp); }
751 inline ex symmetrize(const ex & thisex)
752 { return thisex.symmetrize(); }
754 inline ex symmetrize(const ex & thisex, const lst & l)
755 { return thisex.symmetrize(l); }
757 inline ex antisymmetrize(const ex & thisex)
758 { return thisex.antisymmetrize(); }
760 inline ex antisymmetrize(const ex & thisex, const lst & l)
761 { return thisex.antisymmetrize(l); }
763 inline ex symmetrize_cyclic(const ex & thisex)
764 { return thisex.symmetrize_cyclic(); }
766 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
767 { return thisex.symmetrize_cyclic(l); }
769 inline ex op(const ex & thisex, size_t i)
770 { return thisex.op(i); }
772 inline ex lhs(const ex & thisex)
773 { return thisex.lhs(); }
775 inline ex rhs(const ex & thisex)
776 { return thisex.rhs(); }
778 inline bool is_zero(const ex & thisex)
779 { return thisex.is_zero(); }
781 inline void swap(ex & e1, ex & e2)
784 /* Function objects for STL sort() etc. */
785 struct ex_is_less : public std::binary_function<ex, ex, bool> {
786 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
789 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
790 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
793 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
794 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
797 struct ex_swap : public std::binary_function<ex, ex, void> {
798 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
801 inline ex ex::subs(const exmap & m, unsigned options) const
803 return bp->subs(m, options);
806 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
807 { return thisex.subs(m, options); }
809 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
810 { return thisex.subs(ls, lr, options); }
812 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
813 { return thisex.subs(e, options); }
816 /* Convert function pointer to function object suitable for map(). */
817 class pointer_to_map_function : public map_function {
819 ex (*ptr)(const ex &);
821 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
822 ex operator()(const ex & e) { return ptr(e); }
826 class pointer_to_map_function_1arg : public map_function {
828 ex (*ptr)(const ex &, T1);
831 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
832 ex operator()(const ex & e) { return ptr(e, arg1); }
835 template<class T1, class T2>
836 class pointer_to_map_function_2args : public map_function {
838 ex (*ptr)(const ex &, T1, T2);
842 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
843 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
846 template<class T1, class T2, class T3>
847 class pointer_to_map_function_3args : public map_function {
849 ex (*ptr)(const ex &, T1, T2, T3);
854 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) {}
855 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
858 inline ex ex::map(ex f(const ex &)) const
860 pointer_to_map_function fcn(f);
864 // convenience type checker template functions
866 /** Check if ex is a handle to a T, including base classes. */
868 inline bool is_a(const ex &obj)
870 return is_a<T>(*obj.bp);
873 /** Check if ex is a handle to a T, not including base classes. */
875 inline bool is_exactly_a(const ex &obj)
877 return is_exactly_a<T>(*obj.bp);
880 /** Return a reference to the basic-derived class T object embedded in an
881 * expression. This is fast but unsafe: the result is undefined if the
882 * expression does not contain a T object at its top level. Hence, you
883 * should generally check the type of e first. Also, you shouldn't cache
884 * the returned reference because GiNaC's garbage collector may destroy
885 * the referenced object any time it's used in another expression.
887 * @param e expression
888 * @return reference to object of class T
889 * @see is_exactly_a<class T>() */
891 inline const T &ex_to(const ex &e)
893 GINAC_ASSERT(is_a<T>(e));
894 return static_cast<const T &>(*e.bp);
900 // Specializations of Standard Library algorithms
903 /** Specialization of std::swap() for ex objects. */
905 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
910 /** Specialization of std::iter_swap() for vector<ex> iterators. */
912 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
917 /** Specialization of std::iter_swap() for list<ex> iterators. */
919 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
926 #endif // ndef __GINAC_EX_H__