3 * Interface to GiNaC's light-weight expression handles. */
6 * GiNaC Copyright (C) 1999-2004 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);
135 // complex conjugation
136 ex conjugate() const { return bp->conjugate(); }
139 bool has(const ex & pattern) const { return bp->has(pattern); }
140 bool find(const ex & pattern, lst & found) const;
141 bool match(const ex & pattern) const;
142 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
145 ex subs(const exmap & m, unsigned options = 0) const;
146 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const;
147 ex subs(const ex & e, unsigned options = 0) const;
150 ex map(map_function & f) const { return bp->map(f); }
151 ex map(ex (*f)(const ex & e)) const;
153 // visitors and tree traversal
154 void accept(visitor & v) const { bp->accept(v); }
155 void traverse_preorder(visitor & v) const;
156 void traverse_postorder(visitor & v) const;
157 void traverse(visitor & v) const { traverse_preorder(v); }
160 int degree(const ex & s) const { return bp->degree(s); }
161 int ldegree(const ex & s) const { return bp->ldegree(s); }
162 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
163 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
164 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
167 ex expand(unsigned options=0) const;
168 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
170 // differentiation and series expansion
171 ex diff(const symbol & s, unsigned nth = 1) const;
172 ex series(const ex & r, int order, unsigned options = 0) const;
174 // rational functions
175 ex normal(int level = 0) const;
176 ex to_rational(exmap & repl) const;
177 ex to_rational(lst & repl_lst) const;
178 ex to_polynomial(exmap & repl) const;
179 ex to_polynomial(lst & repl_lst) const;
182 ex numer_denom() const;
184 // polynomial algorithms
185 ex unit(const ex &x) const;
186 ex content(const ex &x) const;
187 numeric integer_content() const;
188 ex primpart(const ex &x) const;
189 ex primpart(const ex &x, const ex &cont) const;
190 ex smod(const numeric &xi) const { return bp->smod(xi); }
191 numeric max_coefficient() const;
194 exvector get_free_indices() const { return bp->get_free_indices(); }
195 ex simplify_indexed(unsigned options = 0) const;
196 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
199 int compare(const ex & other) const;
200 bool is_equal(const ex & other) const;
201 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
204 ex symmetrize() const;
205 ex symmetrize(const lst & l) const;
206 ex antisymmetrize() const;
207 ex antisymmetrize(const lst & l) const;
208 ex symmetrize_cyclic() const;
209 ex symmetrize_cyclic(const lst & l) const;
212 unsigned return_type() const { return bp->return_type(); }
213 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
215 unsigned gethash() const { return bp->gethash(); }
218 static ptr<basic> construct_from_basic(const basic & other);
219 static basic & construct_from_int(int i);
220 static basic & construct_from_uint(unsigned int i);
221 static basic & construct_from_long(long i);
222 static basic & construct_from_ulong(unsigned long i);
223 static basic & construct_from_double(double d);
224 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
225 void makewriteable();
226 void share(const ex & other) const;
228 #ifdef OBSCURE_CINT_HACK
230 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
232 if (last_created_or_assigned_bp==0) return false;
233 if ((last_created_or_assigned_bp->flags &
234 status_flags::dynallocated)==0) return false;
235 if ((last_created_or_assigned_bp->flags &
236 status_flags::evaluated)==0) return false;
240 void update_last_created_or_assigned_bp()
242 last_created_or_assigned_bp = bp;
243 last_created_or_assigned_exp = (long)(void *)(this);
245 #endif // def OBSCURE_CINT_HACK
250 mutable ptr<basic> bp; ///< pointer to basic object managed by this
252 #ifdef OBSCURE_CINT_HACK
254 static ptr<basic> last_created_or_assigned_bp;
255 static basic * dummy_bp;
256 static long last_created_or_assigned_exp;
257 #endif // def OBSCURE_CINT_HACK
261 // performance-critical inlined method implementations
263 // This needs to be a basic* because we don't know that numeric is derived
264 // from basic and we need a basic& for the ex default constructor
265 extern const basic *_num0_bp;
268 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
270 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
271 #ifdef OBSCURE_CINT_HACK
272 update_last_created_or_assigned_bp();
273 #endif // def OBSCURE_CINT_HACK
276 #ifdef OBSCURE_CINT_HACK
278 ex::ex(const ex & other) : bp(other.bp)
280 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
281 update_last_created_or_assigned_bp();
285 ex & ex::operator=(const ex & other)
287 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
288 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
290 update_last_created_or_assigned_bp();
293 #endif // def OBSCURE_CINT_HACK
296 ex::ex(const basic & other) : bp(construct_from_basic(other))
298 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
299 #ifdef OBSCURE_CINT_HACK
300 update_last_created_or_assigned_bp();
301 #endif // def OBSCURE_CINT_HACK
305 ex::ex(int i) : bp(construct_from_int(i))
307 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
308 #ifdef OBSCURE_CINT_HACK
309 update_last_created_or_assigned_bp();
310 #endif // def OBSCURE_CINT_HACK
314 ex::ex(unsigned int i) : bp(construct_from_uint(i))
316 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
317 #ifdef OBSCURE_CINT_HACK
318 update_last_created_or_assigned_bp();
319 #endif // def OBSCURE_CINT_HACK
323 ex::ex(long i) : bp(construct_from_long(i))
325 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
326 #ifdef OBSCURE_CINT_HACK
327 update_last_created_or_assigned_bp();
328 #endif // def OBSCURE_CINT_HACK
332 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
334 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
335 #ifdef OBSCURE_CINT_HACK
336 update_last_created_or_assigned_bp();
337 #endif // def OBSCURE_CINT_HACK
341 ex::ex(double const d) : bp(construct_from_double(d))
343 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
344 #ifdef OBSCURE_CINT_HACK
345 update_last_created_or_assigned_bp();
346 #endif // def OBSCURE_CINT_HACK
350 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
352 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
353 #ifdef OBSCURE_CINT_HACK
354 update_last_created_or_assigned_bp();
355 #endif // def OBSCURE_CINT_HACK
359 int ex::compare(const ex & other) const
361 if (bp == other.bp) // trivial case: both expressions point to same basic
363 const int cmpval = bp->compare(*other.bp);
365 // Expressions point to different, but equal, trees: conserve
366 // memory and make subsequent compare() operations faster by
367 // making both expression point to the same tree.
374 bool ex::is_equal(const ex & other) const
376 if (bp == other.bp) // trivial case: both expressions point to same basic
378 return bp->is_equal(*other.bp);
384 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
387 friend class const_preorder_iterator;
388 friend class const_postorder_iterator;
391 const_iterator() throw() {}
394 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
397 // This should return an ex&, but that would be a reference to a
404 // This should return an ex*, but that would be a pointer to a
406 std::auto_ptr<ex> operator->() const
408 return std::auto_ptr<ex>(new ex(operator*()));
411 ex operator[](difference_type n) const
416 const_iterator &operator++() throw()
422 const_iterator operator++(int) throw()
424 const_iterator tmp = *this;
429 const_iterator &operator+=(difference_type n) throw()
435 const_iterator operator+(difference_type n) const throw()
437 return const_iterator(e, i + n);
440 inline friend const_iterator operator+(difference_type n, const const_iterator &it) throw()
442 return const_iterator(it.e, it.i + n);
445 const_iterator &operator--() throw()
451 const_iterator operator--(int) throw()
453 const_iterator tmp = *this;
458 const_iterator &operator-=(difference_type n) throw()
464 const_iterator operator-(difference_type n) const throw()
466 return const_iterator(e, i - n);
469 inline friend difference_type operator-(const const_iterator &lhs, const const_iterator &rhs) throw()
471 return lhs.i - rhs.i;
474 bool operator==(const const_iterator &other) const throw()
476 return are_ex_trivially_equal(e, other.e) && i == other.i;
479 bool operator!=(const const_iterator &other) const throw()
481 return !(*this == other);
484 bool operator<(const const_iterator &other) const throw()
489 bool operator>(const const_iterator &other) const throw()
491 return other < *this;
494 bool operator<=(const const_iterator &other) const throw()
496 return !(other < *this);
499 bool operator>=(const const_iterator &other) const throw()
501 return !(*this < other);
505 ex e; // this used to be a "const basic *", but in view of object fusion that wouldn't be safe
512 _iter_rep(const ex &e_, size_t i_, size_t i_end_) : e(e_), i(i_), i_end(i_end_) {}
514 bool operator==(const _iter_rep &other) const throw()
516 return are_ex_trivially_equal(e, other.e) && i == other.i;
519 bool operator!=(const _iter_rep &other) const throw()
521 return !(*this == other);
529 } // namespace internal
531 class const_preorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
534 const_preorder_iterator() throw() {}
536 // Provide implicit conversion from const_iterator, so ex::begin() and
537 // ex::end() can be used to create const_preorder_iterators
538 const_preorder_iterator(const const_iterator & cit)
540 s.push(internal::_iter_rep(cit.e, cit.i, cit.e.nops()));
549 std::auto_ptr<ex> operator->() const
551 return std::auto_ptr<ex>(new ex(operator*()));
554 const_preorder_iterator &operator++()
560 const_preorder_iterator operator++(int)
562 const_preorder_iterator tmp = *this;
567 bool operator==(const const_preorder_iterator &other) const throw()
569 return s.top() == other.s.top();
572 bool operator!=(const const_preorder_iterator &other) const throw()
574 return !(*this == other);
578 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
582 while (s.top().i == s.top().i_end && s.size() > 1) {
587 internal::_iter_rep & current = s.top();
589 if (current.i != current.i_end) {
590 const ex & child = current.e.op(current.i);
591 s.push(internal::_iter_rep(child, 0, child.nops()));
596 class const_postorder_iterator : public std::iterator<std::forward_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
599 const_postorder_iterator() throw() {}
601 // Provide implicit conversion from const_iterator, so ex::begin() and
602 // ex::end() can be used to create const_postorder_iterators
603 const_postorder_iterator(const const_iterator & cit)
605 size_t n = cit.e.nops();
607 s.push(internal::_iter_rep(cit.e, cit.i, n));
618 std::auto_ptr<ex> operator->() const
620 return std::auto_ptr<ex>(new ex(operator*()));
623 const_postorder_iterator &operator++()
629 const_postorder_iterator operator++(int)
631 const_postorder_iterator tmp = *this;
636 bool operator==(const const_postorder_iterator &other) const throw()
641 bool operator!=(const const_postorder_iterator &other) const throw()
643 return !(*this == other);
647 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
651 while (s.top().i != s.top().i_end) {
652 internal::_iter_rep & current = s.top();
653 const ex & child = current.e.op(current.i);
654 s.push(internal::_iter_rep(child, 0, child.nops()));
660 if (s.top().i == s.top().i_end)
669 inline const_iterator ex::begin() const throw()
671 return const_iterator(*this, 0);
674 inline const_iterator ex::end() const throw()
676 return const_iterator(*this, nops());
682 /** Compare two objects of class quickly without doing a deep tree traversal.
683 * @return "true" if they are equal
684 * "false" if equality cannot be established quickly (e1 and e2 may
685 * still be equal, in this case. */
686 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
688 return e1.bp == e2.bp;
691 /* Function objects for STL sort() etc. */
692 struct ex_is_less : public std::binary_function<ex, ex, bool> {
693 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
696 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
697 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
700 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
701 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
704 struct ex_swap : public std::binary_function<ex, ex, void> {
705 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
708 // wrapper functions around member functions
709 inline size_t nops(const ex & thisex)
710 { return thisex.nops(); }
712 inline ex expand(const ex & thisex, unsigned options = 0)
713 { return thisex.expand(options); }
715 inline bool has(const ex & thisex, const ex & pattern)
716 { return thisex.has(pattern); }
718 inline bool find(const ex & thisex, const ex & pattern, lst & found)
719 { return thisex.find(pattern, found); }
721 inline int degree(const ex & thisex, const ex & s)
722 { return thisex.degree(s); }
724 inline int ldegree(const ex & thisex, const ex & s)
725 { return thisex.ldegree(s); }
727 inline ex coeff(const ex & thisex, const ex & s, int n=1)
728 { return thisex.coeff(s, n); }
730 inline ex numer(const ex & thisex)
731 { return thisex.numer(); }
733 inline ex denom(const ex & thisex)
734 { return thisex.denom(); }
736 inline ex numer_denom(const ex & thisex)
737 { return thisex.numer_denom(); }
739 inline ex normal(const ex & thisex, int level=0)
740 { return thisex.normal(level); }
742 inline ex to_rational(const ex & thisex, lst & repl_lst)
743 { return thisex.to_rational(repl_lst); }
745 inline ex to_rational(const ex & thisex, exmap & repl)
746 { return thisex.to_rational(repl); }
748 inline ex to_polynomial(const ex & thisex, exmap & repl)
749 { return thisex.to_polynomial(repl); }
751 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
752 { return thisex.to_polynomial(repl_lst); }
754 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
755 { return thisex.collect(s, distributed); }
757 inline ex eval(const ex & thisex, int level = 0)
758 { return thisex.eval(level); }
760 inline ex evalf(const ex & thisex, int level = 0)
761 { return thisex.evalf(level); }
763 inline ex evalm(const ex & thisex)
764 { return thisex.evalm(); }
766 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
767 { return thisex.diff(s, nth); }
769 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
770 { return thisex.series(r, order, options); }
772 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
773 { return thisex.match(pattern, repl_lst); }
775 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
776 { return thisex.simplify_indexed(options); }
778 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
779 { return thisex.simplify_indexed(sp, options); }
781 inline ex symmetrize(const ex & thisex)
782 { return thisex.symmetrize(); }
784 inline ex symmetrize(const ex & thisex, const lst & l)
785 { return thisex.symmetrize(l); }
787 inline ex antisymmetrize(const ex & thisex)
788 { return thisex.antisymmetrize(); }
790 inline ex antisymmetrize(const ex & thisex, const lst & l)
791 { return thisex.antisymmetrize(l); }
793 inline ex symmetrize_cyclic(const ex & thisex)
794 { return thisex.symmetrize_cyclic(); }
796 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
797 { return thisex.symmetrize_cyclic(l); }
799 inline ex op(const ex & thisex, size_t i)
800 { return thisex.op(i); }
802 inline ex lhs(const ex & thisex)
803 { return thisex.lhs(); }
805 inline ex rhs(const ex & thisex)
806 { return thisex.rhs(); }
808 inline bool is_zero(const ex & thisex)
809 { return thisex.is_zero(); }
811 inline void swap(ex & e1, ex & e2)
814 inline ex ex::subs(const exmap & m, unsigned options) const
816 return bp->subs(m, options);
819 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
820 { return thisex.subs(m, options); }
822 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
823 { return thisex.subs(ls, lr, options); }
825 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
826 { return thisex.subs(e, options); }
829 /* Convert function pointer to function object suitable for map(). */
830 class pointer_to_map_function : public map_function {
832 ex (*ptr)(const ex &);
834 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
835 ex operator()(const ex & e) { return ptr(e); }
839 class pointer_to_map_function_1arg : public map_function {
841 ex (*ptr)(const ex &, T1);
844 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
845 ex operator()(const ex & e) { return ptr(e, arg1); }
848 template<class T1, class T2>
849 class pointer_to_map_function_2args : public map_function {
851 ex (*ptr)(const ex &, T1, T2);
855 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
856 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
859 template<class T1, class T2, class T3>
860 class pointer_to_map_function_3args : public map_function {
862 ex (*ptr)(const ex &, T1, T2, T3);
867 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) {}
868 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
871 inline ex ex::map(ex f(const ex &)) const
873 pointer_to_map_function fcn(f);
877 // convenience type checker template functions
879 /** Check if ex is a handle to a T, including base classes. */
881 inline bool is_a(const ex &obj)
883 return is_a<T>(*obj.bp);
886 /** Check if ex is a handle to a T, not including base classes. */
888 inline bool is_exactly_a(const ex &obj)
890 return is_exactly_a<T>(*obj.bp);
893 /** Return a reference to the basic-derived class T object embedded in an
894 * expression. This is fast but unsafe: the result is undefined if the
895 * expression does not contain a T object at its top level. Hence, you
896 * should generally check the type of e first. Also, you shouldn't cache
897 * the returned reference because GiNaC's garbage collector may destroy
898 * the referenced object any time it's used in another expression.
900 * @param e expression
901 * @return reference to object of class T
902 * @see is_exactly_a<class T>() */
904 inline const T &ex_to(const ex &e)
906 GINAC_ASSERT(is_a<T>(e));
907 return static_cast<const T &>(*e.bp);
913 // Specializations of Standard Library algorithms
916 /** Specialization of std::swap() for ex objects. */
918 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
923 /** Specialization of std::iter_swap() for vector<ex> iterators. */
925 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
930 /** Specialization of std::iter_swap() for list<ex> iterators. */
932 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
939 #endif // ndef __GINAC_EX_H__