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__
35 /** Helper class to initialize the library. There must be one static object
36 * of this class in every object file that makes use of our flyweights in
37 * order to guarantee proper initialization. Hence we put it into this
38 * file which is included by every relevant file anyways. This is modeled
39 * after section 27.4.2.1.6 of the C++ standard, where cout and friends are
50 /** For construction of flyweights, etc. */
51 static library_init library_initializer;
54 class scalar_products;
57 /** Lightweight wrapper for GiNaC's symbolic objects. Basically all it does is
58 * to hold a pointer to the other objects, manage the reference counting and
59 * provide methods for manipulation of these objects. (Some people call such
60 * a thing a proxy class.) */
63 friend class archive_node;
64 friend bool are_ex_trivially_equal(const ex &, const ex &);
65 template<class T> friend const T &ex_to(const ex &);
66 template<class T> friend bool is_a(const ex &);
67 template<class T> friend bool is_exactly_a(const ex &);
69 // default constructor, copy constructor and assignment operator
72 #ifdef OBSCURE_CINT_HACK
74 ex & operator=(const ex & other);
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);
92 // non-virtual functions in this class
94 /** Efficiently swap the contents of two expressions. */
97 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
98 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
103 ex eval(int level = 0) const { return bp->eval(level); }
104 ex evalf(int level = 0) const { return bp->evalf(level); }
105 ex evalm() const { return bp->evalm(); }
106 ex eval_ncmul(const exvector & v) const { return bp->eval_ncmul(v); }
109 void print(const print_context & c, unsigned level = 0) const;
110 void dbgprint() const;
111 void dbgprinttree() const;
114 bool info(unsigned inf) const { return bp->info(inf); }
117 size_t nops() const { return bp->nops(); }
118 ex op(size_t i) const { return bp->op(i); }
119 ex operator[](const ex & index) const { return (*bp)[index]; }
120 ex operator[](size_t i) const { return (*bp)[i]; }
121 ex & let_op(size_t i);
122 ex & operator[](const ex & index);
123 ex & operator[](size_t i);
128 bool has(const ex & pattern) const { return bp->has(pattern); }
129 bool find(const ex & pattern, lst & found) const;
130 bool match(const ex & pattern) const;
131 bool match(const ex & pattern, lst & repl_lst) const { return bp->match(pattern, repl_lst); }
134 ex subs(const lst & ls, const lst & lr, unsigned options = 0) const { return bp->subs(ls, lr, options); }
135 ex subs(const ex & e, unsigned options = 0) const { return bp->subs(e, options); }
138 ex map(map_function & f) const { return bp->map(f); }
139 ex map(ex (*f)(const ex & e)) const;
141 // visitors and tree traversal
142 void accept(visitor & v) const { bp->accept(v); }
143 void traverse_preorder(visitor & v) const;
144 void traverse_postorder(visitor & v) const;
145 void traverse(visitor & v) const { traverse_preorder(v); }
148 int degree(const ex & s) const { return bp->degree(s); }
149 int ldegree(const ex & s) const { return bp->ldegree(s); }
150 ex coeff(const ex & s, int n = 1) const { return bp->coeff(s, n); }
151 ex lcoeff(const ex & s) const { return coeff(s, degree(s)); }
152 ex tcoeff(const ex & s) const { return coeff(s, ldegree(s)); }
155 ex expand(unsigned options=0) const;
156 ex collect(const ex & s, bool distributed = false) const { return bp->collect(s, distributed); }
158 // differentiation and series expansion
159 ex diff(const symbol & s, unsigned nth = 1) const;
160 ex series(const ex & r, int order, unsigned options = 0) const;
162 // rational functions
163 ex normal(int level = 0) const;
164 ex to_rational(lst &repl_lst) const;
165 ex to_polynomial(lst &repl_lst) const;
168 ex numer_denom() const;
170 // polynomial algorithms
171 ex unit(const symbol &x) const;
172 ex content(const symbol &x) const;
173 numeric integer_content() const;
174 ex primpart(const symbol &x) const;
175 ex primpart(const symbol &x, const ex &cont) const;
176 ex smod(const numeric &xi) const { return bp->smod(xi); }
177 numeric max_coefficient() const;
180 exvector get_free_indices() const { return bp->get_free_indices(); }
181 ex simplify_indexed() const;
182 ex simplify_indexed(const scalar_products & sp) const;
185 int compare(const ex & other) const;
186 bool is_equal(const ex & other) const;
187 bool is_zero() const { extern const ex _ex0; return is_equal(_ex0); }
190 ex symmetrize() const;
191 ex symmetrize(const lst & l) const;
192 ex antisymmetrize() const;
193 ex antisymmetrize(const lst & l) const;
194 ex symmetrize_cyclic() const;
195 ex symmetrize_cyclic(const lst & l) const;
198 unsigned return_type() const { return bp->return_type(); }
199 unsigned return_type_tinfo() const { return bp->return_type_tinfo(); }
201 unsigned gethash() const { return bp->gethash(); }
204 static ptr<basic> construct_from_basic(const basic & other);
205 static basic & construct_from_int(int i);
206 static basic & construct_from_uint(unsigned int i);
207 static basic & construct_from_long(long i);
208 static basic & construct_from_ulong(unsigned long i);
209 static basic & construct_from_double(double d);
210 static ptr<basic> construct_from_string_and_lst(const std::string &s, const ex &l);
211 void makewriteable();
213 #ifdef OBSCURE_CINT_HACK
215 static bool last_created_or_assigned_bp_can_be_converted_to_ex()
217 if (last_created_or_assigned_bp==0) return false;
218 if ((last_created_or_assigned_bp->flags &
219 status_flags::dynallocated)==0) return false;
220 if ((last_created_or_assigned_bp->flags &
221 status_flags::evaluated)==0) return false;
225 void update_last_created_or_assigned_bp()
227 last_created_or_assigned_bp = bp;
228 last_created_or_assigned_exp = (long)(void *)(this);
230 #endif // def OBSCURE_CINT_HACK
235 ptr<basic> bp; ///< pointer to basic object managed by this
237 #ifdef OBSCURE_CINT_HACK
239 static ptr<basic> last_created_or_assigned_bp;
240 static basic * dummy_bp;
241 static long last_created_or_assigned_exp;
242 #endif // def OBSCURE_CINT_HACK
246 // performance-critical inlined method implementations
248 // This needs to be a basic* because we don't know that numeric is derived
249 // from basic and we need a basic& for the ex default constructor
250 extern const basic *_num0_bp;
253 ex::ex() : bp(*const_cast<basic *>(_num0_bp))
255 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
256 #ifdef OBSCURE_CINT_HACK
257 update_last_created_or_assigned_bp();
258 #endif // def OBSCURE_CINT_HACK
261 #ifdef OBSCURE_CINT_HACK
263 ex::ex(const ex & other) : bp(other.bp)
265 GINAC_ASSERT((bp->flags) & status_flags::dynallocated);
266 update_last_created_or_assigned_bp();
270 ex & ex::operator=(const ex & other)
272 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
273 GINAC_ASSERT(other.bp->flags & status_flags::dynallocated);
275 update_last_created_or_assigned_bp();
278 #endif // def OBSCURE_CINT_HACK
281 ex::ex(const basic & other) : bp(construct_from_basic(other))
283 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
284 #ifdef OBSCURE_CINT_HACK
285 update_last_created_or_assigned_bp();
286 #endif // def OBSCURE_CINT_HACK
290 ex::ex(int i) : bp(construct_from_int(i))
292 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
293 #ifdef OBSCURE_CINT_HACK
294 update_last_created_or_assigned_bp();
295 #endif // def OBSCURE_CINT_HACK
299 ex::ex(unsigned int i) : bp(construct_from_uint(i))
301 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
302 #ifdef OBSCURE_CINT_HACK
303 update_last_created_or_assigned_bp();
304 #endif // def OBSCURE_CINT_HACK
308 ex::ex(long i) : bp(construct_from_long(i))
310 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
311 #ifdef OBSCURE_CINT_HACK
312 update_last_created_or_assigned_bp();
313 #endif // def OBSCURE_CINT_HACK
317 ex::ex(unsigned long i) : bp(construct_from_ulong(i))
319 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
320 #ifdef OBSCURE_CINT_HACK
321 update_last_created_or_assigned_bp();
322 #endif // def OBSCURE_CINT_HACK
326 ex::ex(double const d) : bp(construct_from_double(d))
328 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
329 #ifdef OBSCURE_CINT_HACK
330 update_last_created_or_assigned_bp();
331 #endif // def OBSCURE_CINT_HACK
335 ex::ex(const std::string &s, const ex &l) : bp(construct_from_string_and_lst(s, l))
337 GINAC_ASSERT(bp->flags & status_flags::dynallocated);
338 #ifdef OBSCURE_CINT_HACK
339 update_last_created_or_assigned_bp();
340 #endif // def OBSCURE_CINT_HACK
344 int ex::compare(const ex & other) const
346 if (bp == other.bp) // trivial case: both expressions point to same basic
348 return bp->compare(*other.bp);
352 bool ex::is_equal(const ex & other) const
354 if (bp == other.bp) // trivial case: both expressions point to same basic
356 return bp->is_equal(*other.bp);
362 /** Compare two objects of class quickly without doing a deep tree traversal.
363 * @return "true" if they are equal
364 * "false" if equality cannot be established quickly (e1 and e2 may
365 * still be equal, in this case. */
366 inline bool are_ex_trivially_equal(const ex &e1, const ex &e2)
368 return e1.bp == e2.bp;
371 // wrapper functions around member functions
372 inline size_t nops(const ex & thisex)
373 { return thisex.nops(); }
375 inline ex expand(const ex & thisex, unsigned options = 0)
376 { return thisex.expand(options); }
378 inline bool has(const ex & thisex, const ex & pattern)
379 { return thisex.has(pattern); }
381 inline bool find(const ex & thisex, const ex & pattern, lst & found)
382 { return thisex.find(pattern, found); }
384 inline int degree(const ex & thisex, const ex & s)
385 { return thisex.degree(s); }
387 inline int ldegree(const ex & thisex, const ex & s)
388 { return thisex.ldegree(s); }
390 inline ex coeff(const ex & thisex, const ex & s, int n=1)
391 { return thisex.coeff(s, n); }
393 inline ex numer(const ex & thisex)
394 { return thisex.numer(); }
396 inline ex denom(const ex & thisex)
397 { return thisex.denom(); }
399 inline ex numer_denom(const ex & thisex)
400 { return thisex.numer_denom(); }
402 inline ex normal(const ex & thisex, int level=0)
403 { return thisex.normal(level); }
405 inline ex to_rational(const ex & thisex, lst & repl_lst)
406 { return thisex.to_rational(repl_lst); }
408 inline ex to_polynomial(const ex & thisex, lst & repl_lst)
409 { return thisex.to_polynomial(repl_lst); }
411 inline ex collect(const ex & thisex, const ex & s, bool distributed = false)
412 { return thisex.collect(s, distributed); }
414 inline ex eval(const ex & thisex, int level = 0)
415 { return thisex.eval(level); }
417 inline ex evalf(const ex & thisex, int level = 0)
418 { return thisex.evalf(level); }
420 inline ex evalm(const ex & thisex)
421 { return thisex.evalm(); }
423 inline ex diff(const ex & thisex, const symbol & s, unsigned nth = 1)
424 { return thisex.diff(s, nth); }
426 inline ex series(const ex & thisex, const ex & r, int order, unsigned options = 0)
427 { return thisex.series(r, order, options); }
429 inline bool match(const ex & thisex, const ex & pattern, lst & repl_lst)
430 { return thisex.match(pattern, repl_lst); }
432 inline ex subs(const ex & thisex, const ex & e, unsigned options = 0)
433 { return thisex.subs(e, options); }
435 inline ex subs(const ex & thisex, const lst & ls, const lst & lr, unsigned options = 0)
436 { return thisex.subs(ls, lr, options); }
438 inline ex simplify_indexed(const ex & thisex)
439 { return thisex.simplify_indexed(); }
441 inline ex simplify_indexed(const ex & thisex, const scalar_products & sp)
442 { return thisex.simplify_indexed(sp); }
444 inline ex symmetrize(const ex & thisex)
445 { return thisex.symmetrize(); }
447 inline ex symmetrize(const ex & thisex, const lst & l)
448 { return thisex.symmetrize(l); }
450 inline ex antisymmetrize(const ex & thisex)
451 { return thisex.antisymmetrize(); }
453 inline ex antisymmetrize(const ex & thisex, const lst & l)
454 { return thisex.antisymmetrize(l); }
456 inline ex symmetrize_cyclic(const ex & thisex)
457 { return thisex.symmetrize_cyclic(); }
459 inline ex symmetrize_cyclic(const ex & thisex, const lst & l)
460 { return thisex.symmetrize_cyclic(l); }
462 inline ex op(const ex & thisex, size_t i)
463 { return thisex.op(i); }
465 inline ex lhs(const ex & thisex)
466 { return thisex.lhs(); }
468 inline ex rhs(const ex & thisex)
469 { return thisex.rhs(); }
471 inline bool is_zero(const ex & thisex)
472 { return thisex.is_zero(); }
474 inline void swap(ex & e1, ex & e2)
478 // This makes STL algorithms use the more efficient swap operation for ex objects
479 inline void iter_swap(std::vector<ex>::iterator i1, std::vector<ex>::iterator i2)
483 /* Function objects for STL sort() etc. */
484 struct ex_is_less : public std::binary_function<ex, ex, bool> {
485 bool operator() (const ex &lh, const ex &rh) const { return lh.compare(rh) < 0; }
488 struct ex_is_equal : public std::binary_function<ex, ex, bool> {
489 bool operator() (const ex &lh, const ex &rh) const { return lh.is_equal(rh); }
492 struct op0_is_equal : public std::binary_function<ex, ex, bool> {
493 bool operator() (const ex &lh, const ex &rh) const { return lh.op(0).is_equal(rh.op(0)); }
496 struct ex_swap : public std::binary_function<ex, ex, void> {
497 void operator() (ex &lh, ex &rh) const { lh.swap(rh); }
501 /* Convert function pointer to function object suitable for map(). */
502 class pointer_to_map_function : public map_function {
504 ex (*ptr)(const ex &);
506 explicit pointer_to_map_function(ex (*x)(const ex &)) : ptr(x) {}
507 ex operator()(const ex & e) { return ptr(e); }
511 class pointer_to_map_function_1arg : public map_function {
513 ex (*ptr)(const ex &, T1);
516 explicit pointer_to_map_function_1arg(ex (*x)(const ex &, T1), T1 a1) : ptr(x), arg1(a1) {}
517 ex operator()(const ex & e) { return ptr(e, arg1); }
520 template<class T1, class T2>
521 class pointer_to_map_function_2args : public map_function {
523 ex (*ptr)(const ex &, T1, T2);
527 explicit pointer_to_map_function_2args(ex (*x)(const ex &, T1, T2), T1 a1, T2 a2) : ptr(x), arg1(a1), arg2(a2) {}
528 ex operator()(const ex & e) { return ptr(e, arg1, arg2); }
531 template<class T1, class T2, class T3>
532 class pointer_to_map_function_3args : public map_function {
534 ex (*ptr)(const ex &, T1, T2, T3);
539 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) {}
540 ex operator()(const ex & e) { return ptr(e, arg1, arg2, arg3); }
543 inline ex ex::map(ex (*f)(const ex & e)) const
545 pointer_to_map_function fcn(f);
552 #endif // ndef __GINAC_EX_H__