ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 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, const ex & oc)
  90 {
  91         overall_coeff = oc;
  92         construct_from_epvector(std::move(vp));
  93         GINAC_ASSERT(is_canonical());
  94 }
  95
  96 //////////
  97 // archiving
  98 //////////
  99
 100 GINAC_BIND_UNARCHIVER(add);
 101
 102 //////////
 103 // functions overriding virtual functions from base classes
 104 //////////
 105
 106 // public
 107
 108 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 109 {
 110         if (precedence() <= level)
 111                 c.s << openbrace << '(';
 112
 113         numeric coeff;
 114         bool first = true;
 115
 116         // First print the overall numeric coefficient, if present
 117         if (!overall_coeff.is_zero()) {
 118                 overall_coeff.print(c, 0);
 119                 first = false;
 120         }
 121
 122         // Then proceed with the remaining factors
 123         for (auto & it : seq) {
 124                 coeff = ex_to<numeric>(it.coeff);
 125                 if (!first) {
 126                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 127                 } else {
 128                         if (coeff.csgn() == -1) c.s << '-';
 129                         first = false;
 130                 }
 131                 if (!coeff.is_equal(*_num1_p) &&
 132                     !coeff.is_equal(*_num_1_p)) {
 133                         if (coeff.is_rational()) {
 134                                 if (coeff.is_negative())
 135                                         (-coeff).print(c);
 136                                 else
 137                                         coeff.print(c);
 138                         } else {
 139                                 if (coeff.csgn() == -1)
 140                                         (-coeff).print(c, precedence());
 141                                 else
 142                                         coeff.print(c, precedence());
 143                         }
 144                         c.s << mul_sym;
 145                 }
 146                 it.rest.print(c, precedence());
 147         }
 148
 149         if (precedence() <= level)
 150                 c.s << ')' << closebrace;
 151 }
 152
 153 void add::do_print(const print_context & c, unsigned level) const
 154 {
 155         print_add(c, "", "", "*", level);
 156 }
 157
 158 void add::do_print_latex(const print_latex & c, unsigned level) const
 159 {
 160         print_add(c, "{", "}", " ", level);
 161 }
 162
 163 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 164 {
 165         if (precedence() <= level)
 166                 c.s << "(";
 167
 168         // Print arguments, separated by "+" or "-"
 169         char separator = ' ';
 170         for (auto & it : seq) {
 171
 172                 // If the coefficient is negative, separator is "-"
 173                 if (it.coeff.is_equal(_ex_1) ||
 174                         ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
 175                         separator = '-';
 176                 c.s << separator;
 177                 if (it.coeff.is_equal(_ex1) || it.coeff.is_equal(_ex_1)) {
 178                         it.rest.print(c, precedence());
 179                 } else if (ex_to<numeric>(it.coeff).numer().is_equal(*_num1_p) ||
 180                                  ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
 181                 {
 182                         it.rest.print(c, precedence());
 183                         c.s << '/';
 184                         ex_to<numeric>(it.coeff).denom().print(c, precedence());
 185                 } else {
 186                         it.coeff.print(c, precedence());
 187                         c.s << '*';
 188                         it.rest.print(c, precedence());
 189                 }
 190
 191                 separator = '+';
 192         }
 193
 194         if (!overall_coeff.is_zero()) {
 195                 if (overall_coeff.info(info_flags::positive)
 196                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 197                         c.s << '+';
 198                 overall_coeff.print(c, precedence());
 199         }
 200
 201         if (precedence() <= level)
 202                 c.s << ")";
 203 }
 204
 205 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 206 {
 207         c.s << class_name() << '(';
 208         op(0).print(c);
 209         for (size_t i=1; i<nops(); ++i) {
 210                 c.s << ',';
 211                 op(i).print(c);
 212         }
 213         c.s << ')';
 214 }
 215
 216 bool add::info(unsigned inf) const
 217 {
 218         switch (inf) {
 219                 case info_flags::polynomial:
 220                 case info_flags::integer_polynomial:
 221                 case info_flags::cinteger_polynomial:
 222                 case info_flags::rational_polynomial:
 223                 case info_flags::real:
 224                 case info_flags::rational:
 225                 case info_flags::integer:
 226                 case info_flags::crational:
 227                 case info_flags::cinteger:
 228                 case info_flags::positive:
 229                 case info_flags::nonnegative:
 230                 case info_flags::posint:
 231                 case info_flags::nonnegint:
 232                 case info_flags::even:
 233                 case info_flags::crational_polynomial:
 234                 case info_flags::rational_function: {
 235                         for (auto & i : seq) {
 236                                 if (!(recombine_pair_to_ex(i).info(inf)))
 237                                         return false;
 238                         }
 239                         if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
 240                                 return true;
 241                         return overall_coeff.info(inf);
 242                 }
 243                 case info_flags::algebraic: {
 244                         epvector::const_iterator i = seq.begin(), end = seq.end();
 245                         while (i != end) {
 246                                 if ((recombine_pair_to_ex(*i).info(inf)))
 247                                         return true;
 248                                 ++i;
 249                         }
 250                         return false;
 251                 }
 252         }
 253         return inherited::info(inf);
 254 }
 255
 256 bool add::is_polynomial(const ex & var) const
 257 {
 258         for (auto & i : seq) {
 259                 if (!i.rest.is_polynomial(var)) {
 260                         return false;
 261                 }
 262         }
 263         return true;
 264 }
 265
 266 int add::degree(const ex & s) const
 267 {
 268         int deg = std::numeric_limits<int>::min();
 269         if (!overall_coeff.is_zero())
 270                 deg = 0;
 271
 272         // Find maximum of degrees of individual terms
 273         for (auto & i : seq) {
 274                 int cur_deg = i.rest.degree(s);
 275                 if (cur_deg > deg)
 276                         deg = cur_deg;
 277         }
 278         return deg;
 279 }
 280
 281 int add::ldegree(const ex & s) const
 282 {
 283         int deg = std::numeric_limits<int>::max();
 284         if (!overall_coeff.is_zero())
 285                 deg = 0;
 286
 287         // Find minimum of degrees of individual terms
 288         for (auto & i : seq) {
 289                 int cur_deg = i.rest.ldegree(s);
 290                 if (cur_deg < deg)
 291                         deg = cur_deg;
 292         }
 293         return deg;
 294 }
 295
 296 ex add::coeff(const ex & s, int n) const
 297 {
 298         epvector coeffseq;
 299         epvector coeffseq_cliff;
 300         int rl = clifford_max_label(s);
 301         bool do_clifford = (rl != -1);
 302         bool nonscalar = false;
 303
 304         // Calculate sum of coefficients in each term
 305         for (auto & i : seq) {
 306                 ex restcoeff = i.rest.coeff(s, n);
 307                 if (!restcoeff.is_zero()) {
 308                         if (do_clifford) {
 309                                 if (clifford_max_label(restcoeff) == -1) {
 310                                         coeffseq_cliff.push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i.coeff));
 311                                 } else {
 312                                         coeffseq_cliff.push_back(combine_ex_with_coeff_to_pair(restcoeff, i.coeff));
 313                                         nonscalar = true;
 314                                 }
 315                         }
 316                         coeffseq.push_back(combine_ex_with_coeff_to_pair(restcoeff, i.coeff));
 317                 }
 318         }
 319
 320         return (new add(nonscalar ? std::move(coeffseq_cliff) : std::move(coeffseq),
 321                         n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 322 }
 323
 324 /** Perform automatic term rewriting rules in this class.  In the following
 325  *  x stands for a symbolic variables of type ex and c stands for such
 326  *  an expression that contain a plain number.
 327  *  - +(;c) -> c
 328  *  - +(x;0) -> x
 329  *
 330  *  @param level cut-off in recursive evaluation */
 331 ex add::eval(int level) const
 332 {
 333         epvector evaled = evalchildren(level);
 334         if (unlikely(!evaled.empty())) {
 335                 // do more evaluation later
 336                 return (new add(std::move(evaled), overall_coeff))->
 337                         setflag(status_flags::dynallocated);
 338         }
 339
 340 #ifdef DO_GINAC_ASSERT
 341         for (auto & i : seq) {
 342                 GINAC_ASSERT(!is_exactly_a<add>(i.rest));
 343         }
 344 #endif // def DO_GINAC_ASSERT
 345
 346         if (flags & status_flags::evaluated) {
 347                 GINAC_ASSERT(seq.size()>0);
 348                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 349                 return *this;
 350         }
 351
 352         int seq_size = seq.size();
 353         if (seq_size == 0) {
 354                 // +(;c) -> c
 355                 return overall_coeff;
 356         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 357                 // +(x;0) -> x
 358                 return recombine_pair_to_ex(*(seq.begin()));
 359         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 360                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 361         }
 362
 363         // if any terms in the sum still are purely numeric, then they are more
 364         // appropriately collected into the overall coefficient
 365         int terms_to_collect = 0;
 366         for (auto & it : seq) {
 367                 if (unlikely(is_a<numeric>(it.rest)))
 368                         ++terms_to_collect;
 369         }
 370         if (terms_to_collect) {
 371                 epvector s;
 372                 s.reserve(seq_size - terms_to_collect);
 373                 numeric oc = *_num1_p;
 374                 for (auto & it : seq) {
 375                         if (unlikely(is_a<numeric>(it.rest)))
 376                                 oc = oc.mul(ex_to<numeric>(it.rest)).mul(ex_to<numeric>(it.coeff));
 377                         else
 378                                 s.push_back(it);
 379                 }
 380                 return (new add(std::move(s), ex_to<numeric>(overall_coeff).add_dyn(oc)))
 381                         ->setflag(status_flags::dynallocated);
 382         }
 383
 384         return this->hold();
 385 }
 386
 387 ex add::evalm() const
 388 {
 389         // Evaluate children first and add up all matrices. Stop if there's one
 390         // term that is not a matrix.
 391         epvector s;
 392         s.reserve(seq.size());
 393
 394         bool all_matrices = true;
 395         bool first_term = true;
 396         matrix sum;
 397
 398         for (auto & it : seq) {
 399                 const ex &m = recombine_pair_to_ex(it).evalm();
 400                 s.push_back(split_ex_to_pair(m));
 401                 if (is_a<matrix>(m)) {
 402                         if (first_term) {
 403                                 sum = ex_to<matrix>(m);
 404                                 first_term = false;
 405                         } else
 406                                 sum = sum.add(ex_to<matrix>(m));
 407                 } else
 408                         all_matrices = false;
 409         }
 410
 411         if (all_matrices)
 412                 return sum + overall_coeff;
 413         else
 414                 return (new add(std::move(s), overall_coeff))->setflag(status_flags::dynallocated);
 415 }
 416
 417 ex add::conjugate() const
 418 {
 419         std::unique_ptr<exvector> v(nullptr);
 420         for (size_t i=0; i<nops(); ++i) {
 421                 if (v) {
 422                         v->push_back(op(i).conjugate());
 423                         continue;
 424                 }
 425                 ex term = op(i);
 426                 ex ccterm = term.conjugate();
 427                 if (are_ex_trivially_equal(term, ccterm))
 428                         continue;
 429                 v.reset(new exvector);
 430                 v->reserve(nops());
 431                 for (size_t j=0; j<i; ++j)
 432                         v->push_back(op(j));
 433                 v->push_back(ccterm);
 434         }
 435         if (v) {
 436                 return add(std::move(*v));
 437         }
 438         return *this;
 439 }
 440
 441 ex add::real_part() const
 442 {
 443         epvector v;
 444         v.reserve(seq.size());
 445         for (auto & it : seq)
 446                 if (it.coeff.info(info_flags::real)) {
 447                         ex rp = it.rest.real_part();
 448                         if (!rp.is_zero())
 449                                 v.push_back(expair(rp, it.coeff));
 450                 } else {
 451                         ex rp = recombine_pair_to_ex(it).real_part();
 452                         if (!rp.is_zero())
 453                                 v.push_back(split_ex_to_pair(rp));
 454                 }
 455         return (new add(std::move(v), overall_coeff.real_part()))
 456                 -> setflag(status_flags::dynallocated);
 457 }
 458
 459 ex add::imag_part() const
 460 {
 461         epvector v;
 462         v.reserve(seq.size());
 463         for (auto & it : seq)
 464                 if (it.coeff.info(info_flags::real)) {
 465                         ex ip = it.rest.imag_part();
 466                         if (!ip.is_zero())
 467                                 v.push_back(expair(ip, it.coeff));
 468                 } else {
 469                         ex ip = recombine_pair_to_ex(it).imag_part();
 470                         if (!ip.is_zero())
 471                                 v.push_back(split_ex_to_pair(ip));
 472                 }
 473         return (new add(std::move(v), overall_coeff.imag_part()))
 474                 -> setflag(status_flags::dynallocated);
 475 }
 476
 477 ex add::eval_ncmul(const exvector & v) const
 478 {
 479         if (seq.empty())
 480                 return inherited::eval_ncmul(v);
 481         else
 482                 return seq.begin()->rest.eval_ncmul(v);
 483 }
 484
 485 // protected
 486
 487 /** Implementation of ex::diff() for a sum. It differentiates each term.
 488  *  @see ex::diff */
 489 ex add::derivative(const symbol & y) const
 490 {
 491         epvector s;
 492         s.reserve(seq.size());
 493
 494         // Only differentiate the "rest" parts of the expairs. This is faster
 495         // than the default implementation in basic::derivative() although
 496         // if performs the same function (differentiate each term).
 497         for (auto & it : seq)
 498                 s.push_back(combine_ex_with_coeff_to_pair(it.rest.diff(y), it.coeff));
 499
 500         return (new add(std::move(s), _ex0))->setflag(status_flags::dynallocated);
 501 }
 502
 503 int add::compare_same_type(const basic & other) const
 504 {
 505         return inherited::compare_same_type(other);
 506 }
 507
 508 unsigned add::return_type() const
 509 {
 510         if (seq.empty())
 511                 return return_types::commutative;
 512         else
 513                 return seq.begin()->rest.return_type();
 514 }
 515
 516 return_type_t add::return_type_tinfo() const
 517 {
 518         if (seq.empty())
 519                 return make_return_type_t<add>();
 520         else
 521                 return seq.begin()->rest.return_type_tinfo();
 522 }
 523
 524 // Note: do_index_renaming is ignored because it makes no sense for an add.
 525 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 526 {
 527         return (new add(v,oc))->setflag(status_flags::dynallocated);
 528 }
 529
 530 // Note: do_index_renaming is ignored because it makes no sense for an add.
 531 ex add::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const
 532 {
 533         return (new add(std::move(vp), oc))->setflag(status_flags::dynallocated);
 534 }
 535
 536 expair add::split_ex_to_pair(const ex & e) const
 537 {
 538         if (is_exactly_a<mul>(e)) {
 539                 const mul &mulref(ex_to<mul>(e));
 540                 const ex &numfactor = mulref.overall_coeff;
 541                 if (numfactor.is_equal(_ex1))
 542                         return expair(e, _ex1);
 543                 mul *mulcopyp = new mul(mulref);
 544                 mulcopyp->overall_coeff = _ex1;
 545                 mulcopyp->clearflag(status_flags::evaluated);
 546                 mulcopyp->clearflag(status_flags::hash_calculated);
 547                 mulcopyp->setflag(status_flags::dynallocated);
 548                 return expair(*mulcopyp,numfactor);
 549         }
 550         return expair(e,_ex1);
 551 }
 552
 553 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 554                                           const ex & c) const
 555 {
 556         GINAC_ASSERT(is_exactly_a<numeric>(c));
 557         if (is_exactly_a<mul>(e)) {
 558                 const mul &mulref(ex_to<mul>(e));
 559                 const ex &numfactor = mulref.overall_coeff;
 560                 if (numfactor.is_equal(_ex1))
 561                         return expair(e, c);
 562                 mul *mulcopyp = new mul(mulref);
 563                 mulcopyp->overall_coeff = _ex1;
 564                 mulcopyp->clearflag(status_flags::evaluated);
 565                 mulcopyp->clearflag(status_flags::hash_calculated);
 566                 mulcopyp->setflag(status_flags::dynallocated);
 567                 if (c.is_equal(_ex1))
 568                         return expair(*mulcopyp, numfactor);
 569                 else
 570                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 571         } else if (is_exactly_a<numeric>(e)) {
 572                 if (c.is_equal(_ex1))
 573                         return expair(e, _ex1);
 574                 if (e.is_equal(_ex1))
 575                         return expair(c, _ex1);
 576                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 577         }
 578         return expair(e, c);
 579 }
 580
 581 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 582                                             const ex & c) const
 583 {
 584         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 585         GINAC_ASSERT(is_exactly_a<numeric>(c));
 586
 587         if (is_exactly_a<numeric>(p.rest)) {
 588                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 589                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 590         }
 591
 592         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 593 }
 594
 595 ex add::recombine_pair_to_ex(const expair & p) const
 596 {
 597         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 598                 return p.rest;
 599         else
 600                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 601 }
 602
 603 ex add::expand(unsigned options) const
 604 {
 605         epvector expanded = expandchildren(options);
 606         if (expanded.empty())
 607                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 608
 609         return (new add(std::move(expanded), overall_coeff))->setflag(status_flags::dynallocated |
 610                                                                       (options == 0 ? status_flags::expanded : 0));
 611 }
 612
 613 } // namespace GiNaC