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(exmap & repl) const;
174 ex to_rational(lst & repl_lst) const;
175 ex to_polynomial(exmap & repl) const;
176 ex to_polynomial(lst & repl_lst) const;
179 ex numer_denom() const;
181 // polynomial algorithms
182 ex unit(const ex &x) const;
183 ex content(const ex &x) const;
184 numeric integer_content() const;
185 ex primpart(const ex &x) const;
186 ex primpart(const ex &x, const ex &cont) const;
187 ex smod(const numeric &xi) const { return bp->smod(xi); }
188 numeric max_coefficient() const;
191 exvector get_free_indices() const { return bp->get_free_indices(); }
192 ex simplify_indexed(unsigned options = 0) const;
193 ex simplify_indexed(const scalar_products & sp, unsigned options = 0) const;
196 int compare(const ex & other) const;
197 bool is_equal(const ex & other) const;
198 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
201 ex symmetrize() const;
202 ex symmetrize(const lst & l) const;
203 ex antisymmetrize() const;
204 ex antisymmetrize(const lst & l) const;
205 ex symmetrize_cyclic() const;
206 ex symmetrize_cyclic(const lst & l) const;
209 unsigned return_type() const { return bp->return_type(); }
210 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
212 unsigned gethash() const { return bp->gethash(); }
215 static ptr<basic> construct_from_basic(const basic & other);
216 static basic & construct_from_int(int i);
217 static basic & construct_from_uint(unsigned int i);
218 static basic & construct_from_long(long i);
219 static basic & construct_from_ulong(unsigned long i);
220 static basic & construct_from_double(double d);
221 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
222 void makewriteable();
223 void share(const ex & other) const;
225 #ifdef OBSCURE_CINT_HACK
227 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
229 if (last_created_or_assigned_bp==0) return false;
230 if ((last_created_or_assigned_bp->flags &
231 status_flags::dynallocated)==0) return false;
232 if ((last_created_or_assigned_bp->flags &
233 status_flags::evaluated)==0) return false;
237 void update_last_created_or_assigned_bp()
239 last_created_or_assigned_bp = bp;
240 last_created_or_assigned_exp = (long)(void *)(this);
242 #endif // def OBSCURE_CINT_HACK
247 mutable ptr<basic> bp; ///< pointer to basic object managed by this
249 #ifdef OBSCURE_CINT_HACK
251 static ptr<basic> last_created_or_assigned_bp;
252 static basic * dummy_bp;
253 static long last_created_or_assigned_exp;
254 #endif // def OBSCURE_CINT_HACK
258 // performance-critical inlined method implementations
260 // This needs to be a basic* because we don't know that numeric is derived
261 // from basic and we need a basic& for the ex default constructor
262 extern const basic *_num0_bp;
265 ex::ex() throw() : bp(*const_cast<basic *>(_num0_bp))
267 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
268 #ifdef OBSCURE_CINT_HACK
269 update_last_created_or_assigned_bp();
270 #endif // def OBSCURE_CINT_HACK
273 #ifdef OBSCURE_CINT_HACK
275 ex::ex(const ex & other) : bp(other.bp)
277 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
278 update_last_created_or_assigned_bp();
282 ex & ex::operator=(const ex & other)
284 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
285 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
287 update_last_created_or_assigned_bp();
290 #endif // def OBSCURE_CINT_HACK
293 ex::ex(const basic & other) : bp(construct_from_basic(other))
295 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
296 #ifdef OBSCURE_CINT_HACK
297 update_last_created_or_assigned_bp();
298 #endif // def OBSCURE_CINT_HACK
302 ex::ex(int i) : bp(construct_from_int(i))
304 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
305 #ifdef OBSCURE_CINT_HACK
306 update_last_created_or_assigned_bp();
307 #endif // def OBSCURE_CINT_HACK
311 ex::ex(unsigned int i) : bp(construct_from_uint(i))
313 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
314 #ifdef OBSCURE_CINT_HACK
315 update_last_created_or_assigned_bp();
316 #endif // def OBSCURE_CINT_HACK
320 ex::ex(long i) : bp(construct_from_long(i))
322 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
323 #ifdef OBSCURE_CINT_HACK
324 update_last_created_or_assigned_bp();
325 #endif // def OBSCURE_CINT_HACK
329 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
331 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
332 #ifdef OBSCURE_CINT_HACK
333 update_last_created_or_assigned_bp();
334 #endif // def OBSCURE_CINT_HACK
338 ex::ex(double const d) : bp(construct_from_double(d))
340 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
341 #ifdef OBSCURE_CINT_HACK
342 update_last_created_or_assigned_bp();
343 #endif // def OBSCURE_CINT_HACK
347 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
349 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
350 #ifdef OBSCURE_CINT_HACK
351 update_last_created_or_assigned_bp();
352 #endif // def OBSCURE_CINT_HACK
356 int ex::compare(const ex & other) const
358 if (bp == other.bp) // trivial case: both expressions point to same basic
360 const int cmpval = bp->compare(*other.bp);
362 // Expressions point to different, but equal, trees: conserve
363 // memory and make subsequent compare() operations faster by
364 // making both expression point to the same tree.
371 bool ex::is_equal(const ex & other) const
373 if (bp == other.bp) // trivial case: both expressions point to same basic
375 return bp->is_equal(*other.bp);
381 class const_iterator : public std::iterator<std::random_access_iterator_tag, ex, ptrdiff_t, const ex *, const ex &>
384 friend class const_preorder_iterator;
385 friend class const_postorder_iterator;
388 const_iterator() throw() {}
391 const_iterator(const ex &e_, size_t i_) throw() : e(e_), i(i_) {}
394 // This should return an ex&, but that would be a reference to a
401 // This should return an ex*, but that would be a pointer to a
403 std::auto_ptr<ex> operator->() const
405 return std::auto_ptr<ex>(new ex(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 ex::begin() and
534 // ex::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()));
546 std::auto_ptr<ex> operator->() const
548 return std::auto_ptr<ex>(new ex(operator*()));
551 const_preorder_iterator &operator++()
557 const_preorder_iterator operator++(int)
559 const_preorder_iterator tmp = *this;
564 bool operator==(const const_preorder_iterator &other) const throw()
566 return s.top() == other.s.top();
569 bool operator!=(const const_preorder_iterator &other) const throw()
571 return !(*this == other);
575 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
579 while (s.top().i == s.top().i_end && s.size() > 1) {
584 internal::_iter_rep & current = s.top();
586 if (current.i != current.i_end) {
587 const ex & child = current.e.op(current.i);
588 s.push(internal::_iter_rep(child, 0, child.nops()));
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 ex::begin() and
599 // ex::end() can be used to create const_postorder_iterators
600 const_postorder_iterator(const const_iterator & cit)
602 size_t n = cit.e.nops();
604 s.push(internal::_iter_rep(cit.e, cit.i, n));
615 std::auto_ptr<ex> operator->() const
617 return std::auto_ptr<ex>(new ex(operator*()));
620 const_postorder_iterator &operator++()
626 const_postorder_iterator operator++(int)
628 const_postorder_iterator tmp = *this;
633 bool operator==(const const_postorder_iterator &other) const throw()
638 bool operator!=(const const_postorder_iterator &other) const throw()
640 return !(*this == other);
644 std::stack<internal::_iter_rep, std::vector<internal::_iter_rep> > s;
648 while (s.top().i != s.top().i_end) {
649 internal::_iter_rep & current = s.top();
650 const ex & child = current.e.op(current.i);
651 s.push(internal::_iter_rep(child, 0, child.nops()));
657 if (s.top().i == s.top().i_end)
666 inline const_iterator ex::begin() const throw()
668 return const_iterator(*this, 0);
671 inline const_iterator ex::end() const throw()
673 return const_iterator(*this, nops());
679 /** Compare two objects of class quickly without doing a deep tree traversal.
680 * @return "true" if they are equal
681 * "false" if equality cannot be established quickly (e1 and e2 may
682 * still be equal, in this case. */
683 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
685 return e1.bp == e2.bp;
688 /* Function objects for STL sort() etc. */
689 struct ex_is_less : public std::binary_function<ex, ex, bool> {
690 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
693 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
694 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
697 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
698 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
701 struct ex_swap : public std::binary_function<ex, ex, void> {
702 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
705 // wrapper functions around member functions
706 inline size_t nops(const ex & thisex)
707 { return thisex.nops(); }
709 inline ex expand(const ex & thisex, unsigned options = 0)
710 { return thisex.expand(options); }
712 inline bool has(const ex & thisex, const ex & pattern)
713 { return thisex.has(pattern); }
715 inline bool find(const ex & thisex, const ex & pattern, lst & found)
716 { return thisex.find(pattern, found); }
718 inline int degree(const ex & thisex, const ex & s)
719 { return thisex.degree(s); }
721 inline int ldegree(const ex & thisex, const ex & s)
722 { return thisex.ldegree(s); }
724 inline ex coeff(const ex & thisex, const ex & s, int n=1)
725 { return thisex.coeff(s, n); }
727 inline ex numer(const ex & thisex)
728 { return thisex.numer(); }
730 inline ex denom(const ex & thisex)
731 { return thisex.denom(); }
733 inline ex numer_denom(const ex & thisex)
734 { return thisex.numer_denom(); }
736 inline ex normal(const ex & thisex, int level=0)
737 { return thisex.normal(level); }
739 inline ex to_rational(const ex & thisex, lst & repl_lst)
740 { return thisex.to_rational(repl_lst); }
742 inline ex to_rational(const ex & thisex, exmap & repl)
743 { return thisex.to_rational(repl); }
745 inline ex to_polynomial(const ex & thisex, exmap & repl)
746 { return thisex.to_polynomial(repl); }
748 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
749 { return thisex.to_polynomial(repl_lst); }
751 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
752 { return thisex.collect(s, distributed); }
754 inline ex eval(const ex & thisex, int level = 0)
755 { return thisex.eval(level); }
757 inline ex evalf(const ex & thisex, int level = 0)
758 { return thisex.evalf(level); }
760 inline ex evalm(const ex & thisex)
761 { return thisex.evalm(); }
763 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
764 { return thisex.diff(s, nth); }
766 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
767 { return thisex.series(r, order, options); }
769 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
770 { return thisex.match(pattern, repl_lst); }
772 inline ex simplify_indexed(const ex & thisex, unsigned options = 0)
773 { return thisex.simplify_indexed(options); }
775 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp, unsigned options = 0)
776 { return thisex.simplify_indexed(sp, options); }
778 inline ex symmetrize(const ex & thisex)
779 { return thisex.symmetrize(); }
781 inline ex symmetrize(const ex & thisex, const lst & l)
782 { return thisex.symmetrize(l); }
784 inline ex antisymmetrize(const ex & thisex)
785 { return thisex.antisymmetrize(); }
787 inline ex antisymmetrize(const ex & thisex, const lst & l)
788 { return thisex.antisymmetrize(l); }
790 inline ex symmetrize_cyclic(const ex & thisex)
791 { return thisex.symmetrize_cyclic(); }
793 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
794 { return thisex.symmetrize_cyclic(l); }
796 inline ex op(const ex & thisex, size_t i)
797 { return thisex.op(i); }
799 inline ex lhs(const ex & thisex)
800 { return thisex.lhs(); }
802 inline ex rhs(const ex & thisex)
803 { return thisex.rhs(); }
805 inline bool is_zero(const ex & thisex)
806 { return thisex.is_zero(); }
808 inline void swap(ex & e1, ex & e2)
811 inline ex ex::subs(const exmap & m, unsigned options) const
813 return bp->subs(m, options);
816 inline ex subs(const ex & thisex, const exmap & m, unsigned options = 0)
817 { return thisex.subs(m, options); }
819 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
820 { return thisex.subs(ls, lr, options); }
822 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
823 { return thisex.subs(e, options); }
826 /* Convert function pointer to function object suitable for map(). */
827 class pointer_to_map_function : public map_function {
829 ex (*ptr)(const ex &);
831 explicit pointer_to_map_function(ex x(const ex &)) : ptr(x) {}
832 ex operator()(const ex & e) { return ptr(e); }
836 class pointer_to_map_function_1arg : public map_function {
838 ex (*ptr)(const ex &, T1);
841 explicit pointer_to_map_function_1arg(ex x(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
842 ex operator()(const ex & e) { return ptr(e, arg1); }
845 template<class T1, class T2>
846 class pointer_to_map_function_2args : public map_function {
848 ex (*ptr)(const ex &, T1, T2);
852 explicit pointer_to_map_function_2args(ex x(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
853 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
856 template<class T1, class T2, class T3>
857 class pointer_to_map_function_3args : public map_function {
859 ex (*ptr)(const ex &, T1, T2, T3);
864 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) {}
865 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
868 inline ex ex::map(ex f(const ex &)) const
870 pointer_to_map_function fcn(f);
874 // convenience type checker template functions
876 /** Check if ex is a handle to a T, including base classes. */
878 inline bool is_a(const ex &obj)
880 return is_a<T>(*obj.bp);
883 /** Check if ex is a handle to a T, not including base classes. */
885 inline bool is_exactly_a(const ex &obj)
887 return is_exactly_a<T>(*obj.bp);
890 /** Return a reference to the basic-derived class T object embedded in an
891 * expression. This is fast but unsafe: the result is undefined if the
892 * expression does not contain a T object at its top level. Hence, you
893 * should generally check the type of e first. Also, you shouldn't cache
894 * the returned reference because GiNaC's garbage collector may destroy
895 * the referenced object any time it's used in another expression.
897 * @param e expression
898 * @return reference to object of class T
899 * @see is_exactly_a<class T>() */
901 inline const T &ex_to(const ex &e)
903 GINAC_ASSERT(is_a<T>(e));
904 return static_cast<const T &>(*e.bp);
910 // Specializations of Standard Library algorithms
913 /** Specialization of std::swap() for ex objects. */
915 inline void swap(GiNaC::ex &a, GiNaC::ex &b)
920 /** Specialization of std::iter_swap() for vector<ex> iterators. */
922 inline void iter_swap(vector<GiNaC::ex>::iterator i1, vector<GiNaC::ex>::iterator i2)
927 /** Specialization of std::iter_swap() for list<ex> iterators. */
929 inline void iter_swap(list<GiNaC::ex>::iterator i1, list<GiNaC::ex>::iterator i2)
936 #endif // ndef __GINAC_EX_H__