ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2018 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