- The default implementations of evalf(), diff(), normal() and expand() use
[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 bases 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                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
240                                 if (!(recombine_pair_to_ex(*i).info(inf)))
241                                         return false;
242                         }
243                         return overall_coeff.info(inf);
244                 }
245                 case info_flags::algebraic: {
246                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
247                                 if ((recombine_pair_to_ex(*i).info(inf)))
248                                         return true;
249                         }
250                         return false;
251                 }
252         }
253         return inherited::info(inf);
254 }
255
256 int add::degree(const ex & s) const
257 {
258         int deg = INT_MIN;
259         if (!overall_coeff.is_equal(_ex0()))
260                 deg = 0;
261         
262         int cur_deg;
263         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
264                 cur_deg = (*cit).rest.degree(s);
265                 if (cur_deg>deg)
266                         deg = cur_deg;
267         }
268         return deg;
269 }
270
271 int add::ldegree(const ex & s) const
272 {
273         int deg = INT_MAX;
274         if (!overall_coeff.is_equal(_ex0()))
275                 deg = 0;
276         
277         int cur_deg;
278         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
279                 cur_deg = (*cit).rest.ldegree(s);
280                 if (cur_deg<deg) deg=cur_deg;
281         }
282         return deg;
283 }
284
285 ex add::coeff(const ex & s, int n) const
286 {
287         epvector coeffseq;
288         
289         epvector::const_iterator it=seq.begin();
290         while (it!=seq.end()) {
291                 ex restcoeff = it->rest.coeff(s,n);
292                 if (!restcoeff.is_zero())
293                         coeffseq.push_back(combine_ex_with_coeff_to_pair(restcoeff,it->coeff));
294                 ++it;
295         }
296         
297         return (new add(coeffseq, n==0 ? overall_coeff : default_overall_coeff()))->setflag(status_flags::dynallocated);
298 }
299
300 ex add::eval(int level) const
301 {
302         // simplifications: +(;c) -> c
303         //                  +(x;1) -> x
304         
305         debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
306         
307         epvector * evaled_seqp = evalchildren(level);
308         if (evaled_seqp!=0) {
309                 // do more evaluation later
310                 return (new add(evaled_seqp,overall_coeff))->
311                        setflag(status_flags::dynallocated);
312         }
313         
314 #ifdef DO_GINAC_ASSERT
315         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
316                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
317                 if (is_ex_exactly_of_type((*cit).rest,numeric))
318                         dbgprint();
319                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
320         }
321 #endif // def DO_GINAC_ASSERT
322         
323         if (flags & status_flags::evaluated) {
324                 GINAC_ASSERT(seq.size()>0);
325                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
326                 return *this;
327         }
328         
329         int seq_size = seq.size();
330         if (seq_size==0) {
331                 // +(;c) -> c
332                 return overall_coeff;
333         } else if ((seq_size==1) && overall_coeff.is_equal(_ex0())) {
334                 // +(x;0) -> x
335                 return recombine_pair_to_ex(*(seq.begin()));
336         }
337         return this->hold();
338 }
339
340 ex add::evalm(void) const
341 {
342         // Evaluate children first and add up all matrices. Stop if there's one
343         // term that is not a matrix.
344         epvector *s = new epvector;
345         s->reserve(seq.size());
346
347         bool all_matrices = true;
348         bool first_term = true;
349         matrix sum;
350
351         epvector::const_iterator it = seq.begin(), itend = seq.end();
352         while (it != itend) {
353                 const ex &m = recombine_pair_to_ex(*it).evalm();
354                 s->push_back(split_ex_to_pair(m));
355                 if (is_ex_of_type(m, matrix)) {
356                         if (first_term) {
357                                 sum = ex_to<matrix>(m);
358                                 first_term = false;
359                         } else
360                                 sum = sum.add(ex_to<matrix>(m));
361                 } else
362                         all_matrices = false;
363                 it++;
364         }
365
366         if (all_matrices)
367                 return sum + overall_coeff;
368         else
369                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
370 }
371
372 ex add::simplify_ncmul(const exvector & v) const
373 {
374         if (seq.size()==0) {
375                 return inherited::simplify_ncmul(v);
376         }
377         return (*seq.begin()).rest.simplify_ncmul(v);
378 }    
379
380 // protected
381
382 /** Implementation of ex::diff() for a sum. It differentiates each term.
383  *  @see ex::diff */
384 ex add::derivative(const symbol & y) const
385 {
386         epvector *s = new epvector();
387         s->reserve(seq.size());
388         
389         // Only differentiate the "rest" parts of the expairs. This is faster
390         // than the default implementation in basic::derivative() although
391         // if performs the same function (differentiate each term).
392         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
393                 s->push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
394                                                            (*it).coeff));
395         }
396         return (new add(s, _ex0()))->setflag(status_flags::dynallocated);
397 }
398
399 int add::compare_same_type(const basic & other) const
400 {
401         return inherited::compare_same_type(other);
402 }
403
404 bool add::is_equal_same_type(const basic & other) const
405 {
406         return inherited::is_equal_same_type(other);
407 }
408
409 unsigned add::return_type(void) const
410 {
411         if (seq.size()==0) {
412                 return return_types::commutative;
413         }
414         return (*seq.begin()).rest.return_type();
415 }
416    
417 unsigned add::return_type_tinfo(void) const
418 {
419         if (seq.size()==0) {
420                 return tinfo_key;
421         }
422         return (*seq.begin()).rest.return_type_tinfo();
423 }
424
425 ex add::thisexpairseq(const epvector & v, const ex & oc) const
426 {
427         return (new add(v,oc))->setflag(status_flags::dynallocated);
428 }
429
430 ex add::thisexpairseq(epvector * vp, const ex & oc) const
431 {
432         return (new add(vp,oc))->setflag(status_flags::dynallocated);
433 }
434
435 expair add::split_ex_to_pair(const ex & e) const
436 {
437         if (is_ex_exactly_of_type(e,mul)) {
438                 const mul &mulref(ex_to<mul>(e));
439                 ex numfactor = mulref.overall_coeff;
440                 mul *mulcopyp = new mul(mulref);
441                 mulcopyp->overall_coeff = _ex1();
442                 mulcopyp->clearflag(status_flags::evaluated);
443                 mulcopyp->clearflag(status_flags::hash_calculated);
444                 mulcopyp->setflag(status_flags::dynallocated);
445                 return expair(*mulcopyp,numfactor);
446         }
447         return expair(e,_ex1());
448 }
449
450 expair add::combine_ex_with_coeff_to_pair(const ex & e,
451                                                                                   const ex & c) const
452 {
453         GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
454         if (is_ex_exactly_of_type(e, mul)) {
455                 const mul &mulref(ex_to<mul>(e));
456                 ex numfactor = mulref.overall_coeff;
457                 mul *mulcopyp = new mul(mulref);
458                 mulcopyp->overall_coeff = _ex1();
459                 mulcopyp->clearflag(status_flags::evaluated);
460                 mulcopyp->clearflag(status_flags::hash_calculated);
461                 mulcopyp->setflag(status_flags::dynallocated);
462                 if (are_ex_trivially_equal(c, _ex1()))
463                         return expair(*mulcopyp, numfactor);
464                 else if (are_ex_trivially_equal(numfactor, _ex1()))
465                         return expair(*mulcopyp, c);
466                 else
467                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
468         } else if (is_ex_exactly_of_type(e, numeric)) {
469                 if (are_ex_trivially_equal(c, _ex1()))
470                         return expair(e, _ex1());
471                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1());
472         }
473         return expair(e, c);
474 }
475
476 expair add::combine_pair_with_coeff_to_pair(const expair & p,
477                                                                                         const ex & c) const
478 {
479         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
480         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
481
482         if (is_ex_exactly_of_type(p.rest,numeric)) {
483                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1())); // should be normalized
484                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1());
485         }
486
487         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
488 }
489         
490 ex add::recombine_pair_to_ex(const expair & p) const
491 {
492         if (ex_to<numeric>(p.coeff).is_equal(_num1()))
493                 return p.rest;
494         else
495                 return p.rest*p.coeff;
496 }
497
498 ex add::expand(unsigned options) const
499 {
500         if (flags & status_flags::expanded)
501                 return *this;
502         
503         epvector * vp = expandchildren(options);
504         if (vp == NULL) {
505                 // the terms have not changed, so it is safe to declare this expanded
506                 return this->setflag(status_flags::expanded);
507         }
508         
509         return (new add(vp,overall_coeff))->setflag(status_flags::expanded | status_flags::dynallocated);
510 }
511
512 } // namespace GiNaC