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