- replaced the Derivative() function by a more resonable fderivative class;
[ginac.git] / ginac / add.cpp
1 /** @file add.cpp
2  *
3  *  Implementation of GiNaC's sums of expressions. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
7  *
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.
12  *
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.
17  *
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
21  */
22
23 #include <iostream>
24 #include <stdexcept>
25
26 #include "add.h"
27 #include "mul.h"
28 #include "matrix.h"
29 #include "archive.h"
30 #include "debugmsg.h"
31 #include "utils.h"
32
33 namespace GiNaC {
34
35 GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
36
37 //////////
38 // default constructor, destructor, copy constructor assignment operator and helpers
39 //////////
40
41 add::add()
42 {
43         debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
44         tinfo_key = TINFO_add;
45 }
46
47 DEFAULT_COPY(add)
48 DEFAULT_DESTROY(add)
49
50 //////////
51 // other constructors
52 //////////
53
54 // public
55
56 add::add(const ex & lh, const ex & rh)
57 {
58         debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
59         tinfo_key = TINFO_add;
60         overall_coeff = _ex0();
61         construct_from_2_ex(lh,rh);
62         GINAC_ASSERT(is_canonical());
63 }
64
65 add::add(const exvector & v)
66 {
67         debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
68         tinfo_key = TINFO_add;
69         overall_coeff = _ex0();
70         construct_from_exvector(v);
71         GINAC_ASSERT(is_canonical());
72 }
73
74 add::add(const epvector & v)
75 {
76         debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
77         tinfo_key = TINFO_add;
78         overall_coeff = _ex0();
79         construct_from_epvector(v);
80         GINAC_ASSERT(is_canonical());
81 }
82
83 add::add(const epvector & v, const ex & oc)
84 {
85         debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
86         tinfo_key = TINFO_add;
87         overall_coeff = oc;
88         construct_from_epvector(v);
89         GINAC_ASSERT(is_canonical());
90 }
91
92 add::add(epvector * vp, const ex & oc)
93 {
94         debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
95         tinfo_key = TINFO_add;
96         GINAC_ASSERT(vp!=0);
97         overall_coeff = oc;
98         construct_from_epvector(*vp);
99         delete vp;
100         GINAC_ASSERT(is_canonical());
101 }
102
103 //////////
104 // archiving
105 //////////
106
107 DEFAULT_ARCHIVING(add)
108
109 //////////
110 // functions overriding virtual functions from base classes
111 //////////
112
113 // public
114
115 void add::print(const print_context & c, unsigned level) const
116 {
117         debugmsg("add print", LOGLEVEL_PRINT);
118
119         if (is_a<print_tree>(c)) {
120
121                 inherited::print(c, level);
122
123         } else if (is_a<print_csrc>(c)) {
124
125                 if (precedence() <= level)
126                         c.s << "(";
127         
128                 // Print arguments, separated by "+"
129                 epvector::const_iterator it = seq.begin(), itend = seq.end();
130                 while (it != itend) {
131                 
132                         // If the coefficient is -1, it is replaced by a single minus sign
133                         if (it->coeff.compare(_num1()) == 0) {
134                                 it->rest.bp->print(c, precedence());
135                         } else if (it->coeff.compare(_num_1()) == 0) {
136                                 c.s << "-";
137                                 it->rest.bp->print(c, precedence());
138                         } else if (ex_to<numeric>(it->coeff).numer().compare(_num1()) == 0) {
139                                 it->rest.bp->print(c, precedence());
140                                 c.s << "/";
141                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
142                         } else if (ex_to<numeric>(it->coeff).numer().compare(_num_1()) == 0) {
143                                 c.s << "-";
144                                 it->rest.bp->print(c, precedence());
145                                 c.s << "/";
146                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
147                         } else {
148                                 it->coeff.bp->print(c, precedence());
149                                 c.s << "*";
150                                 it->rest.bp->print(c, precedence());
151                         }
152                 
153                         // Separator is "+", except if the following expression would have a leading minus sign
154                         ++it;
155                         if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_exactly_a<numeric>(it->rest) && it->rest.compare(_num0()) < 0)))
156                                 c.s << "+";
157                 }
158         
159                 if (!overall_coeff.is_zero()) {
160                         if (overall_coeff.info(info_flags::positive))
161                                 c.s << '+';
162                         overall_coeff.bp->print(c, precedence());
163                 }
164         
165                 if (precedence() <= level)
166                         c.s << ")";
167
168         } else {
169
170                 if (precedence() <= level) {
171                         if (is_a<print_latex>(c))
172                                 c.s << "{(";
173                         else
174                                 c.s << "(";
175                 }
176
177                 numeric coeff;
178                 bool first = true;
179
180                 // First print the overall numeric coefficient, if present
181                 if (!overall_coeff.is_zero()) {
182                         if (!is_a<print_tree>(c))
183                                 overall_coeff.print(c, 0);
184                         else
185                                 overall_coeff.print(c, precedence());
186                         first = false;
187                 }
188
189                 // Then proceed with the remaining factors
190                 epvector::const_iterator it = seq.begin(), itend = seq.end();
191                 while (it != itend) {
192                         coeff = ex_to<numeric>(it->coeff);
193                         if (!first) {
194                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
195                         } else {
196                                 if (coeff.csgn() == -1) c.s << '-';
197                                 first = false;
198                         }
199                         if (!coeff.is_equal(_num1()) &&
200                             !coeff.is_equal(_num_1())) {
201                                 if (coeff.is_rational()) {
202                                         if (coeff.is_negative())
203                                                 (-coeff).print(c);
204                                         else
205                                                 coeff.print(c);
206                                 } else {
207                                         if (coeff.csgn() == -1)
208                                                 (-coeff).print(c, precedence());
209                                         else
210                                                 coeff.print(c, precedence());
211                                 }
212                                 if (is_a<print_latex>(c))
213                                         c.s << ' ';
214                                 else
215                                         c.s << '*';
216                         }
217                         it->rest.print(c, precedence());
218                         ++it;
219                 }
220
221                 if (precedence() <= level) {
222                         if (is_a<print_latex>(c))
223                                 c.s << ")}";
224                         else
225                                 c.s << ")";
226                 }
227         }
228 }
229
230 bool add::info(unsigned inf) const
231 {
232         switch (inf) {
233                 case info_flags::polynomial:
234                 case info_flags::integer_polynomial:
235                 case info_flags::cinteger_polynomial:
236                 case info_flags::rational_polynomial:
237                 case info_flags::crational_polynomial:
238                 case info_flags::rational_function: {
239                         epvector::const_iterator i = seq.begin(), end = seq.end();
240                         while (i != end) {
241                                 if (!(recombine_pair_to_ex(*i).info(inf)))
242                                         return false;
243                                 ++i;
244                         }
245                         return overall_coeff.info(inf);
246                 }
247                 case info_flags::algebraic: {
248                         epvector::const_iterator i = seq.begin(), end = seq.end();
249                         while (i != end) {
250                                 if ((recombine_pair_to_ex(*i).info(inf)))
251                                         return true;
252                                 ++i;
253                         }
254                         return false;
255                 }
256         }
257         return inherited::info(inf);
258 }
259
260 int add::degree(const ex & s) const
261 {
262         int deg = INT_MIN;
263         if (!overall_coeff.is_zero())
264                 deg = 0;
265         
266         // Find maximum of degrees of individual terms
267         epvector::const_iterator i = seq.begin(), end = seq.end();
268         while (i != end) {
269                 int cur_deg = i->rest.degree(s);
270                 if (cur_deg > deg)
271                         deg = cur_deg;
272                 ++i;
273         }
274         return deg;
275 }
276
277 int add::ldegree(const ex & s) const
278 {
279         int deg = INT_MAX;
280         if (!overall_coeff.is_zero())
281                 deg = 0;
282         
283         // Find minimum of degrees of individual terms
284         epvector::const_iterator i = seq.begin(), end = seq.end();
285         while (i != end) {
286                 int cur_deg = i->rest.ldegree(s);
287                 if (cur_deg < deg)
288                         deg = cur_deg;
289                 ++i;
290         }
291         return deg;
292 }
293
294 ex add::coeff(const ex & s, int n) const
295 {
296         epvector *coeffseq = new epvector();
297
298         // Calculate sum of coefficients in each term
299         epvector::const_iterator i = seq.begin(), end = seq.end();
300         while (i != end) {
301                 ex restcoeff = i->rest.coeff(s, n);
302                 if (!restcoeff.is_zero())
303                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
304                 ++i;
305         }
306
307         return (new add(coeffseq, n==0 ? overall_coeff : _ex0()))->setflag(status_flags::dynallocated);
308 }
309
310 ex add::eval(int level) const
311 {
312         // simplifications: +(;c) -> c
313         //                  +(x;1) -> x
314         
315         debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
316         
317         epvector *evaled_seqp = evalchildren(level);
318         if (evaled_seqp) {
319                 // do more evaluation later
320                 return (new add(evaled_seqp, overall_coeff))->
321                        setflag(status_flags::dynallocated);
322         }
323         
324 #ifdef DO_GINAC_ASSERT
325         epvector::const_iterator i = seq.begin(), end = seq.end();
326         while (i != end) {
327                 GINAC_ASSERT(!is_ex_exactly_of_type(i->rest,add));
328                 if (is_ex_exactly_of_type(i->rest,numeric))
329                         dbgprint();
330                 GINAC_ASSERT(!is_ex_exactly_of_type(i->rest,numeric));
331                 ++i;
332         }
333 #endif // def DO_GINAC_ASSERT
334         
335         if (flags & status_flags::evaluated) {
336                 GINAC_ASSERT(seq.size()>0);
337                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
338                 return *this;
339         }
340         
341         int seq_size = seq.size();
342         if (seq_size == 0) {
343                 // +(;c) -> c
344                 return overall_coeff;
345         } else if (seq_size == 1 && overall_coeff.is_zero()) {
346                 // +(x;0) -> x
347                 return recombine_pair_to_ex(*(seq.begin()));
348         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
349                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
350         }
351         return this->hold();
352 }
353
354 ex add::evalm(void) const
355 {
356         // Evaluate children first and add up all matrices. Stop if there's one
357         // term that is not a matrix.
358         epvector *s = new epvector;
359         s->reserve(seq.size());
360
361         bool all_matrices = true;
362         bool first_term = true;
363         matrix sum;
364
365         epvector::const_iterator it = seq.begin(), itend = seq.end();
366         while (it != itend) {
367                 const ex &m = recombine_pair_to_ex(*it).evalm();
368                 s->push_back(split_ex_to_pair(m));
369                 if (is_ex_of_type(m, matrix)) {
370                         if (first_term) {
371                                 sum = ex_to<matrix>(m);
372                                 first_term = false;
373                         } else
374                                 sum = sum.add(ex_to<matrix>(m));
375                 } else
376                         all_matrices = false;
377                 it++;
378         }
379
380         if (all_matrices) {
381                 delete s;
382                 return sum + overall_coeff;
383         } else
384                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
385 }
386
387 ex add::simplify_ncmul(const exvector & v) const
388 {
389         if (seq.empty())
390                 return inherited::simplify_ncmul(v);
391         else
392                 return seq.begin()->rest.simplify_ncmul(v);
393 }    
394
395 // protected
396
397 /** Implementation of ex::diff() for a sum. It differentiates each term.
398  *  @see ex::diff */
399 ex add::derivative(const symbol & y) const
400 {
401         epvector *s = new epvector();
402         s->reserve(seq.size());
403         
404         // Only differentiate the "rest" parts of the expairs. This is faster
405         // than the default implementation in basic::derivative() although
406         // if performs the same function (differentiate each term).
407         epvector::const_iterator i = seq.begin(), end = seq.end();
408         while (i != end) {
409                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
410                 ++i;
411         }
412         return (new add(s, _ex0()))->setflag(status_flags::dynallocated);
413 }
414
415 int add::compare_same_type(const basic & other) const
416 {
417         return inherited::compare_same_type(other);
418 }
419
420 bool add::is_equal_same_type(const basic & other) const
421 {
422         return inherited::is_equal_same_type(other);
423 }
424
425 unsigned add::return_type(void) const
426 {
427         if (seq.empty())
428                 return return_types::commutative;
429         else
430                 return seq.begin()->rest.return_type();
431 }
432    
433 unsigned add::return_type_tinfo(void) const
434 {
435         if (seq.empty())
436                 return tinfo_key;
437         else
438                 return seq.begin()->rest.return_type_tinfo();
439 }
440
441 ex add::thisexpairseq(const epvector & v, const ex & oc) const
442 {
443         return (new add(v,oc))->setflag(status_flags::dynallocated);
444 }
445
446 ex add::thisexpairseq(epvector * vp, const ex & oc) const
447 {
448         return (new add(vp,oc))->setflag(status_flags::dynallocated);
449 }
450
451 expair add::split_ex_to_pair(const ex & e) const
452 {
453         if (is_ex_exactly_of_type(e,mul)) {
454                 const mul &mulref(ex_to<mul>(e));
455                 ex numfactor = mulref.overall_coeff;
456                 mul *mulcopyp = new mul(mulref);
457                 mulcopyp->overall_coeff = _ex1();
458                 mulcopyp->clearflag(status_flags::evaluated);
459                 mulcopyp->clearflag(status_flags::hash_calculated);
460                 mulcopyp->setflag(status_flags::dynallocated);
461                 return expair(*mulcopyp,numfactor);
462         }
463         return expair(e,_ex1());
464 }
465
466 expair add::combine_ex_with_coeff_to_pair(const ex & e,
467                                                                                   const ex & c) const
468 {
469         GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
470         if (is_ex_exactly_of_type(e, mul)) {
471                 const mul &mulref(ex_to<mul>(e));
472                 ex numfactor = mulref.overall_coeff;
473                 mul *mulcopyp = new mul(mulref);
474                 mulcopyp->overall_coeff = _ex1();
475                 mulcopyp->clearflag(status_flags::evaluated);
476                 mulcopyp->clearflag(status_flags::hash_calculated);
477                 mulcopyp->setflag(status_flags::dynallocated);
478                 if (are_ex_trivially_equal(c, _ex1()))
479                         return expair(*mulcopyp, numfactor);
480                 else if (are_ex_trivially_equal(numfactor, _ex1()))
481                         return expair(*mulcopyp, c);
482                 else
483                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
484         } else if (is_ex_exactly_of_type(e, numeric)) {
485                 if (are_ex_trivially_equal(c, _ex1()))
486                         return expair(e, _ex1());
487                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1());
488         }
489         return expair(e, c);
490 }
491
492 expair add::combine_pair_with_coeff_to_pair(const expair & p,
493                                                                                         const ex & c) const
494 {
495         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
496         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
497
498         if (is_ex_exactly_of_type(p.rest,numeric)) {
499                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1())); // should be normalized
500                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1());
501         }
502
503         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
504 }
505         
506 ex add::recombine_pair_to_ex(const expair & p) const
507 {
508         if (ex_to<numeric>(p.coeff).is_equal(_num1()))
509                 return p.rest;
510         else
511                 return p.rest*p.coeff;
512 }
513
514 ex add::expand(unsigned options) const
515 {
516         epvector *vp = expandchildren(options);
517         if (vp == NULL) {
518                 // the terms have not changed, so it is safe to declare this expanded
519                 return (options == 0) ? setflag(status_flags::expanded) : *this;
520         }
521         
522         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
523 }
524
525 } // namespace GiNaC