Happy New Year!
[ginac.git] / ginac / add.cpp
1 /** @file add.cpp
2  *
3  *  Implementation of GiNaC's sums of expressions. */
4
5 /*
6  *  GiNaC Copyright (C) 1999-2019 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
21  */
22
23 #include "add.h"
24 #include "mul.h"
25 #include "archive.h"
26 #include "operators.h"
27 #include "matrix.h"
28 #include "utils.h"
29 #include "clifford.h"
30 #include "ncmul.h"
31 #include "compiler.h"
32
33 #include <iostream>
34 #include <limits>
35 #include <stdexcept>
36 #include <string>
37
38 namespace GiNaC {
39
40 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
41   print_func<print_context>(&add::do_print).
42   print_func<print_latex>(&add::do_print_latex).
43   print_func<print_csrc>(&add::do_print_csrc).
44   print_func<print_tree>(&add::do_print_tree).
45   print_func<print_python_repr>(&add::do_print_python_repr))
46
47 //////////
48 // default constructor
49 //////////
50
51 add::add()
52 {
53 }
54
55 //////////
56 // other constructors
57 //////////
58
59 // public
60
61 add::add(const ex & lh, const ex & rh)
62 {
63         overall_coeff = _ex0;
64         construct_from_2_ex(lh,rh);
65         GINAC_ASSERT(is_canonical());
66 }
67
68 add::add(const exvector & v)
69 {
70         overall_coeff = _ex0;
71         construct_from_exvector(v);
72         GINAC_ASSERT(is_canonical());
73 }
74
75 add::add(const epvector & v)
76 {
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         overall_coeff = oc;
85         construct_from_epvector(v);
86         GINAC_ASSERT(is_canonical());
87 }
88
89 add::add(epvector && vp)
90 {
91         overall_coeff = _ex0;
92         construct_from_epvector(std::move(vp));
93         GINAC_ASSERT(is_canonical());
94 }
95
96 add::add(epvector && vp, const ex & oc)
97 {
98         overall_coeff = oc;
99         construct_from_epvector(std::move(vp));
100         GINAC_ASSERT(is_canonical());
101 }
102
103 //////////
104 // archiving
105 //////////
106
107 GINAC_BIND_UNARCHIVER(add);
108
109 //////////
110 // functions overriding virtual functions from base classes
111 //////////
112
113 // public
114
115 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
116 {
117         if (precedence() <= level)
118                 c.s << openbrace << '(';
119
120         numeric coeff;
121         bool first = true;
122
123         // First print the overall numeric coefficient, if present
124         if (!overall_coeff.is_zero()) {
125                 overall_coeff.print(c, 0);
126                 first = false;
127         }
128
129         // Then proceed with the remaining factors
130         for (auto & it : seq) {
131                 coeff = ex_to<numeric>(it.coeff);
132                 if (!first) {
133                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
134                 } else {
135                         if (coeff.csgn() == -1) c.s << '-';
136                         first = false;
137                 }
138                 if (!coeff.is_equal(*_num1_p) &&
139                     !coeff.is_equal(*_num_1_p)) {
140                         if (coeff.is_rational()) {
141                                 if (coeff.is_negative())
142                                         (-coeff).print(c);
143                                 else
144                                         coeff.print(c);
145                         } else {
146                                 if (coeff.csgn() == -1)
147                                         (-coeff).print(c, precedence());
148                                 else
149                                         coeff.print(c, precedence());
150                         }
151                         c.s << mul_sym;
152                 }
153                 it.rest.print(c, precedence());
154         }
155
156         if (precedence() <= level)
157                 c.s << ')' << closebrace;
158 }
159
160 void add::do_print(const print_context & c, unsigned level) const
161 {
162         print_add(c, "", "", "*", level);
163 }
164
165 void add::do_print_latex(const print_latex & c, unsigned level) const
166 {
167         print_add(c, "{", "}", " ", level);
168 }
169
170 void add::do_print_csrc(const print_csrc & c, unsigned level) const
171 {
172         if (precedence() <= level)
173                 c.s << "(";
174         
175         // Print arguments, separated by "+" or "-"
176         char separator = ' ';
177         for (auto & it : seq) {
178                 
179                 // If the coefficient is negative, separator is "-"
180                 if (it.coeff.is_equal(_ex_1) ||
181                         ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
182                         separator = '-';
183                 c.s << separator;
184                 if (it.coeff.is_equal(_ex1) || it.coeff.is_equal(_ex_1)) {
185                         it.rest.print(c, precedence());
186                 } else if (ex_to<numeric>(it.coeff).numer().is_equal(*_num1_p) ||
187                                  ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
188                 {
189                         it.rest.print(c, precedence());
190                         c.s << '/';
191                         ex_to<numeric>(it.coeff).denom().print(c, precedence());
192                 } else {
193                         it.coeff.print(c, precedence());
194                         c.s << '*';
195                         it.rest.print(c, precedence());
196                 }
197                 
198                 separator = '+';
199         }
200         
201         if (!overall_coeff.is_zero()) {
202                 if (overall_coeff.info(info_flags::positive)
203                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
204                         c.s << '+';
205                 overall_coeff.print(c, precedence());
206         }
207                 
208         if (precedence() <= level)
209                 c.s << ")";
210 }
211
212 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
213 {
214         c.s << class_name() << '(';
215         op(0).print(c);
216         for (size_t i=1; i<nops(); ++i) {
217                 c.s << ',';
218                 op(i).print(c);
219         }
220         c.s << ')';
221 }
222
223 bool add::info(unsigned inf) const
224 {
225         switch (inf) {
226                 case info_flags::polynomial:
227                 case info_flags::integer_polynomial:
228                 case info_flags::cinteger_polynomial:
229                 case info_flags::rational_polynomial:
230                 case info_flags::real:
231                 case info_flags::rational:
232                 case info_flags::integer:
233                 case info_flags::crational:
234                 case info_flags::cinteger:
235                 case info_flags::positive:
236                 case info_flags::nonnegative:
237                 case info_flags::posint:
238                 case info_flags::nonnegint:
239                 case info_flags::even:
240                 case info_flags::crational_polynomial:
241                 case info_flags::rational_function: {
242                         for (auto & i : seq) {
243                                 if (!(recombine_pair_to_ex(i).info(inf)))
244                                         return false;
245                         }
246                         if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
247                                 return true;
248                         return overall_coeff.info(inf);
249                 }
250         }
251         return inherited::info(inf);
252 }
253
254 bool add::is_polynomial(const ex & var) const
255 {
256         for (auto & i : seq) {
257                 if (!i.rest.is_polynomial(var)) {
258                         return false;
259                 }
260         }
261         return true;
262 }
263
264 int add::degree(const ex & s) const
265 {
266         int deg = std::numeric_limits<int>::min();
267         if (!overall_coeff.is_zero())
268                 deg = 0;
269         
270         // Find maximum of degrees of individual terms
271         for (auto & i : seq) {
272                 int cur_deg = i.rest.degree(s);
273                 if (cur_deg > deg)
274                         deg = cur_deg;
275         }
276         return deg;
277 }
278
279 int add::ldegree(const ex & s) const
280 {
281         int deg = std::numeric_limits<int>::max();
282         if (!overall_coeff.is_zero())
283                 deg = 0;
284         
285         // Find minimum of degrees of individual terms
286         for (auto & i : seq) {
287                 int cur_deg = i.rest.ldegree(s);
288                 if (cur_deg < deg)
289                         deg = cur_deg;
290         }
291         return deg;
292 }
293
294 ex add::coeff(const ex & s, int n) const
295 {
296         epvector coeffseq;
297         epvector coeffseq_cliff;
298         int rl = clifford_max_label(s);
299         bool do_clifford = (rl != -1);
300         bool nonscalar = false;
301
302         // Calculate sum of coefficients in each term
303         for (auto & i : seq) {
304                 ex restcoeff = i.rest.coeff(s, n);
305                 if (!restcoeff.is_zero()) {
306                         if (do_clifford) {
307                                 if (clifford_max_label(restcoeff) == -1) {
308                                         coeffseq_cliff.push_back(expair(ncmul(restcoeff, dirac_ONE(rl)), i.coeff));
309                                 } else {
310                                         coeffseq_cliff.push_back(expair(restcoeff, i.coeff));
311                                         nonscalar = true;
312                                 }
313                         }
314                         coeffseq.push_back(expair(restcoeff, i.coeff));
315                 }
316         }
317
318         return dynallocate<add>(nonscalar ? std::move(coeffseq_cliff) : std::move(coeffseq),
319                                 n==0 ? overall_coeff : _ex0);
320 }
321
322 /** Perform automatic term rewriting rules in this class.  In the following
323  *  x stands for a symbolic variables of type ex and c stands for such
324  *  an expression that contain a plain number.
325  *  - +(;c) -> c
326  *  - +(x;0) -> x
327  */
328 ex add::eval() const
329 {
330         if (flags & status_flags::evaluated) {
331                 GINAC_ASSERT(seq.size()>0);
332                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
333                 return *this;
334         }
335
336         const epvector evaled = evalchildren();
337         if (unlikely(!evaled.empty())) {
338                 // start over evaluating a new object
339                 return dynallocate<add>(std::move(evaled), overall_coeff);
340         }
341
342 #ifdef DO_GINAC_ASSERT
343         for (auto & i : seq) {
344                 GINAC_ASSERT(!is_exactly_a<add>(i.rest));
345         }
346 #endif // def DO_GINAC_ASSERT
347
348         size_t seq_size = seq.size();
349         if (seq_size == 0) {
350                 // +(;c) -> c
351                 return overall_coeff;
352         } else if (seq_size == 1 && overall_coeff.is_zero()) {
353                 // +(x;0) -> x
354                 return recombine_pair_to_ex(*(seq.begin()));
355         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
356                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
357         }
358
359         return this->hold();
360 }
361
362 ex add::evalm() const
363 {
364         // Evaluate children first and add up all matrices. Stop if there's one
365         // term that is not a matrix.
366         epvector s;
367         s.reserve(seq.size());
368
369         bool all_matrices = true;
370         bool first_term = true;
371         matrix sum;
372
373         for (auto & it : seq) {
374                 const ex &m = recombine_pair_to_ex(it).evalm();
375                 s.push_back(split_ex_to_pair(m));
376                 if (is_a<matrix>(m)) {
377                         if (first_term) {
378                                 sum = ex_to<matrix>(m);
379                                 first_term = false;
380                         } else
381                                 sum = sum.add(ex_to<matrix>(m));
382                 } else
383                         all_matrices = false;
384         }
385
386         if (all_matrices)
387                 return sum + overall_coeff;
388         else
389                 return dynallocate<add>(std::move(s), overall_coeff);
390 }
391
392 ex add::conjugate() const
393 {
394         std::unique_ptr<exvector> v(nullptr);
395         for (size_t i=0; i<nops(); ++i) {
396                 if (v) {
397                         v->push_back(op(i).conjugate());
398                         continue;
399                 }
400                 ex term = op(i);
401                 ex ccterm = term.conjugate();
402                 if (are_ex_trivially_equal(term, ccterm))
403                         continue;
404                 v.reset(new exvector);
405                 v->reserve(nops());
406                 for (size_t j=0; j<i; ++j)
407                         v->push_back(op(j));
408                 v->push_back(ccterm);
409         }
410         if (v) {
411                 return add(std::move(*v));
412         }
413         return *this;
414 }
415
416 ex add::real_part() const
417 {
418         epvector v;
419         v.reserve(seq.size());
420         for (auto & it : seq)
421                 if (it.coeff.info(info_flags::real)) {
422                         ex rp = it.rest.real_part();
423                         if (!rp.is_zero())
424                                 v.push_back(expair(rp, it.coeff));
425                 } else {
426                         ex rp = recombine_pair_to_ex(it).real_part();
427                         if (!rp.is_zero())
428                                 v.push_back(split_ex_to_pair(rp));
429                 }
430         return dynallocate<add>(std::move(v), overall_coeff.real_part());
431 }
432
433 ex add::imag_part() const
434 {
435         epvector v;
436         v.reserve(seq.size());
437         for (auto & it : seq)
438                 if (it.coeff.info(info_flags::real)) {
439                         ex ip = it.rest.imag_part();
440                         if (!ip.is_zero())
441                                 v.push_back(expair(ip, it.coeff));
442                 } else {
443                         ex ip = recombine_pair_to_ex(it).imag_part();
444                         if (!ip.is_zero())
445                                 v.push_back(split_ex_to_pair(ip));
446                 }
447         return dynallocate<add>(std::move(v), overall_coeff.imag_part());
448 }
449
450 ex add::eval_ncmul(const exvector & v) const
451 {
452         if (seq.empty())
453                 return inherited::eval_ncmul(v);
454         else
455                 return seq.begin()->rest.eval_ncmul(v);
456 }    
457
458 // protected
459
460 /** Implementation of ex::diff() for a sum. It differentiates each term.
461  *  @see ex::diff */
462 ex add::derivative(const symbol & y) const
463 {
464         epvector s;
465         s.reserve(seq.size());
466         
467         // Only differentiate the "rest" parts of the expairs. This is faster
468         // than the default implementation in basic::derivative() although
469         // if performs the same function (differentiate each term).
470         for (auto & it : seq)
471                 s.push_back(expair(it.rest.diff(y), it.coeff));
472
473         return dynallocate<add>(std::move(s));
474 }
475
476 int add::compare_same_type(const basic & other) const
477 {
478         return inherited::compare_same_type(other);
479 }
480
481 unsigned add::return_type() const
482 {
483         if (seq.empty())
484                 return return_types::commutative;
485         else
486                 return seq.begin()->rest.return_type();
487 }
488
489 return_type_t add::return_type_tinfo() const
490 {
491         if (seq.empty())
492                 return make_return_type_t<add>();
493         else
494                 return seq.begin()->rest.return_type_tinfo();
495 }
496
497 // Note: do_index_renaming is ignored because it makes no sense for an add.
498 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
499 {
500         return dynallocate<add>(v, oc);
501 }
502
503 // Note: do_index_renaming is ignored because it makes no sense for an add.
504 ex add::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const
505 {
506         return dynallocate<add>(std::move(vp), oc);
507 }
508
509 expair add::split_ex_to_pair(const ex & e) const
510 {
511         if (is_exactly_a<mul>(e)) {
512                 const mul &mulref(ex_to<mul>(e));
513                 const ex &numfactor = mulref.overall_coeff;
514                 if (numfactor.is_equal(_ex1))
515                         return expair(e, _ex1);
516                 mul & mulcopy = dynallocate<mul>(mulref);
517                 mulcopy.overall_coeff = _ex1;
518                 mulcopy.clearflag(status_flags::evaluated | status_flags::hash_calculated);
519                 return expair(mulcopy, numfactor);
520         }
521         return expair(e,_ex1);
522 }
523
524 expair add::combine_ex_with_coeff_to_pair(const ex & e,
525                                           const ex & c) const
526 {
527         GINAC_ASSERT(is_exactly_a<numeric>(c));
528         if (is_exactly_a<mul>(e)) {
529                 const mul &mulref(ex_to<mul>(e));
530                 const ex &numfactor = mulref.overall_coeff;
531                 if (likely(numfactor.is_equal(_ex1)))
532                         return expair(e, c);
533                 mul & mulcopy = dynallocate<mul>(mulref);
534                 mulcopy.overall_coeff = _ex1;
535                 mulcopy.clearflag(status_flags::evaluated | status_flags::hash_calculated);
536                 if (c.is_equal(_ex1))
537                         return expair(mulcopy, numfactor);
538                 else
539                         return expair(mulcopy, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
540         } else if (is_exactly_a<numeric>(e)) {
541                 if (c.is_equal(_ex1))
542                         return expair(e, _ex1);
543                 if (e.is_equal(_ex1))
544                         return expair(c, _ex1);
545                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
546         }
547         return expair(e, c);
548 }
549
550 expair add::combine_pair_with_coeff_to_pair(const expair & p,
551                                             const ex & c) const
552 {
553         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
554         GINAC_ASSERT(is_exactly_a<numeric>(c));
555
556         if (is_exactly_a<numeric>(p.rest)) {
557                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
558                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
559         }
560
561         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
562 }
563
564 ex add::recombine_pair_to_ex(const expair & p) const
565 {
566         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
567                 return p.rest;
568         else
569                 return dynallocate<mul>(p.rest, p.coeff);
570 }
571
572 ex add::expand(unsigned options) const
573 {
574         epvector expanded = expandchildren(options);
575         if (expanded.empty())
576                 return (options == 0) ? setflag(status_flags::expanded) : *this;
577
578         return dynallocate<add>(std::move(expanded), overall_coeff).setflag(options == 0 ? status_flags::expanded : 0);
579 }
580
581 } // namespace GiNaC