ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2011 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(std::auto_ptr<epvector> vp, const ex & oc)
  90 {
  91         GINAC_ASSERT(vp.get()!=0);
  92         overall_coeff = oc;
  93         construct_from_epvector(*vp);
  94         GINAC_ASSERT(is_canonical());
  95 }
  96
  97 //////////
  98 // archiving
  99 //////////
 100
 101 GINAC_BIND_UNARCHIVER(add);
 102
 103 //////////
 104 // functions overriding virtual functions from base classes
 105 //////////
 106
 107 // public
 108
 109 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 110 {
 111         if (precedence() <= level)
 112                 c.s << openbrace << '(';
 113
 114         numeric coeff;
 115         bool first = true;
 116
 117         // First print the overall numeric coefficient, if present
 118         if (!overall_coeff.is_zero()) {
 119                 overall_coeff.print(c, 0);
 120                 first = false;
 121         }
 122
 123         // Then proceed with the remaining factors
 124         epvector::const_iterator it = seq.begin(), itend = seq.end();
 125         while (it != itend) {
 126                 coeff = ex_to<numeric>(it->coeff);
 127                 if (!first) {
 128                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 129                 } else {
 130                         if (coeff.csgn() == -1) c.s << '-';
 131                         first = false;
 132                 }
 133                 if (!coeff.is_equal(*_num1_p) &&
 134                     !coeff.is_equal(*_num_1_p)) {
 135                         if (coeff.is_rational()) {
 136                                 if (coeff.is_negative())
 137                                         (-coeff).print(c);
 138                                 else
 139                                         coeff.print(c);
 140                         } else {
 141                                 if (coeff.csgn() == -1)
 142                                         (-coeff).print(c, precedence());
 143                                 else
 144                                         coeff.print(c, precedence());
 145                         }
 146                         c.s << mul_sym;
 147                 }
 148                 it->rest.print(c, precedence());
 149                 ++it;
 150         }
 151
 152         if (precedence() <= level)
 153                 c.s << ')' << closebrace;
 154 }
 155
 156 void add::do_print(const print_context & c, unsigned level) const
 157 {
 158         print_add(c, "", "", "*", level);
 159 }
 160
 161 void add::do_print_latex(const print_latex & c, unsigned level) const
 162 {
 163         print_add(c, "{", "}", " ", level);
 164 }
 165
 166 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 167 {
 168         if (precedence() <= level)
 169                 c.s << "(";
 170
 171         // Print arguments, separated by "+" or "-"
 172         epvector::const_iterator it = seq.begin(), itend = seq.end();
 173         char separator = ' ';
 174         while (it != itend) {
 175
 176                 // If the coefficient is negative, separator is "-"
 177                 if (it->coeff.is_equal(_ex_1) ||
 178                         ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 179                         separator = '-';
 180                 c.s << separator;
 181                 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
 182                         it->rest.print(c, precedence());
 183                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
 184                                  ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 185                 {
 186                         it->rest.print(c, precedence());
 187                         c.s << '/';
 188                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 189                 } else {
 190                         it->coeff.print(c, precedence());
 191                         c.s << '*';
 192                         it->rest.print(c, precedence());
 193                 }
 194
 195                 ++it;
 196                 separator = '+';
 197         }
 198
 199         if (!overall_coeff.is_zero()) {
 200                 if (overall_coeff.info(info_flags::positive)
 201                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 202                         c.s << '+';
 203                 overall_coeff.print(c, precedence());
 204         }
 205
 206         if (precedence() <= level)
 207                 c.s << ")";
 208 }
 209
 210 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 211 {
 212         c.s << class_name() << '(';
 213         op(0).print(c);
 214         for (size_t i=1; i<nops(); ++i) {
 215                 c.s << ',';
 216                 op(i).print(c);
 217         }
 218         c.s << ')';
 219 }
 220
 221 bool add::info(unsigned inf) const
 222 {
 223         switch (inf) {
 224                 case info_flags::polynomial:
 225                 case info_flags::integer_polynomial:
 226                 case info_flags::cinteger_polynomial:
 227                 case info_flags::rational_polynomial:
 228                 case info_flags::real:
 229                 case info_flags::rational:
 230                 case info_flags::integer:
 231                 case info_flags::crational:
 232                 case info_flags::cinteger:
 233                 case info_flags::positive:
 234                 case info_flags::nonnegative:
 235                 case info_flags::posint:
 236                 case info_flags::nonnegint:
 237                 case info_flags::even:
 238                 case info_flags::crational_polynomial:
 239                 case info_flags::rational_function: {
 240                         epvector::const_iterator i = seq.begin(), end = seq.end();
 241                         while (i != end) {
 242                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 243                                         return false;
 244                                 ++i;
 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                 case info_flags::algebraic: {
 251                         epvector::const_iterator i = seq.begin(), end = seq.end();
 252                         while (i != end) {
 253                                 if ((recombine_pair_to_ex(*i).info(inf)))
 254                                         return true;
 255                                 ++i;
 256                         }
 257                         return false;
 258                 }
 259         }
 260         return inherited::info(inf);
 261 }
 262
 263 bool add::is_polynomial(const ex & var) const
 264 {
 265         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 266                 if (!(i->rest).is_polynomial(var)) {
 267                         return false;
 268                 }
 269         }
 270         return true;
 271 }
 272
 273 int add::degree(const ex & s) const
 274 {
 275         int deg = std::numeric_limits<int>::min();
 276         if (!overall_coeff.is_zero())
 277                 deg = 0;
 278
 279         // Find maximum of degrees of individual terms
 280         epvector::const_iterator i = seq.begin(), end = seq.end();
 281         while (i != end) {
 282                 int cur_deg = i->rest.degree(s);
 283                 if (cur_deg > deg)
 284                         deg = cur_deg;
 285                 ++i;
 286         }
 287         return deg;
 288 }
 289
 290 int add::ldegree(const ex & s) const
 291 {
 292         int deg = std::numeric_limits<int>::max();
 293         if (!overall_coeff.is_zero())
 294                 deg = 0;
 295
 296         // Find minimum of degrees of individual terms
 297         epvector::const_iterator i = seq.begin(), end = seq.end();
 298         while (i != end) {
 299                 int cur_deg = i->rest.ldegree(s);
 300                 if (cur_deg < deg)
 301                         deg = cur_deg;
 302                 ++i;
 303         }
 304         return deg;
 305 }
 306
 307 ex add::coeff(const ex & s, int n) const
 308 {
 309         std::auto_ptr<epvector> coeffseq(new epvector);
 310         std::auto_ptr<epvector> coeffseq_cliff(new epvector);
 311         int rl = clifford_max_label(s);
 312         bool do_clifford = (rl != -1);
 313         bool nonscalar = false;
 314
 315         // Calculate sum of coefficients in each term
 316         epvector::const_iterator i = seq.begin(), end = seq.end();
 317         while (i != end) {
 318                 ex restcoeff = i->rest.coeff(s, n);
 319                 if (!restcoeff.is_zero()) {
 320                         if (do_clifford) {
 321                                 if (clifford_max_label(restcoeff) == -1) {
 322                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
 323                                 } else {
 324                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 325                                         nonscalar = true;
 326                                 }
 327                         }
 328                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 329                 }
 330                 ++i;
 331         }
 332
 333         return (new add(nonscalar ? coeffseq_cliff : coeffseq,
 334                         n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 335 }
 336
 337 /** Perform automatic term rewriting rules in this class.  In the following
 338  *  x stands for a symbolic variables of type ex and c stands for such
 339  *  an expression that contain a plain number.
 340  *  - +(;c) -> c
 341  *  - +(x;0) -> x
 342  *
 343  *  @param level cut-off in recursive evaluation */
 344 ex add::eval(int level) const
 345 {
 346         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 347         if (evaled_seqp.get()) {
 348                 // do more evaluation later
 349                 return (new add(evaled_seqp, overall_coeff))->
 350                        setflag(status_flags::dynallocated);
 351         }
 352
 353 #ifdef DO_GINAC_ASSERT
 354         epvector::const_iterator i = seq.begin(), end = seq.end();
 355         while (i != end) {
 356                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 357                 ++i;
 358         }
 359 #endif // def DO_GINAC_ASSERT
 360
 361         if (flags & status_flags::evaluated) {
 362                 GINAC_ASSERT(seq.size()>0);
 363                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 364                 return *this;
 365         }
 366
 367         int seq_size = seq.size();
 368         if (seq_size == 0) {
 369                 // +(;c) -> c
 370                 return overall_coeff;
 371         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 372                 // +(x;0) -> x
 373                 return recombine_pair_to_ex(*(seq.begin()));
 374         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 375                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 376         }
 377
 378         // if any terms in the sum still are purely numeric, then they are more
 379         // appropriately collected into the overall coefficient
 380         epvector::const_iterator last = seq.end();
 381         epvector::const_iterator j = seq.begin();
 382         int terms_to_collect = 0;
 383         while (j != last) {
 384                 if (unlikely(is_a<numeric>(j->rest)))
 385                         ++terms_to_collect;
 386                 ++j;
 387         }
 388         if (terms_to_collect) {
 389                 std::auto_ptr<epvector> s(new epvector);
 390                 s->reserve(seq_size - terms_to_collect);
 391                 numeric oc = *_num1_p;
 392                 j = seq.begin();
 393                 while (j != last) {
 394                         if (unlikely(is_a<numeric>(j->rest)))
 395                                 oc = oc.mul(ex_to<numeric>(j->rest)).mul(ex_to<numeric>(j->coeff));
 396                         else
 397                                 s->push_back(*j);
 398                         ++j;
 399                 }
 400                 return (new add(s, ex_to<numeric>(overall_coeff).add_dyn(oc)))
 401                         ->setflag(status_flags::dynallocated);
 402         }
 403
 404         return this->hold();
 405 }
 406
 407 ex add::evalm() const
 408 {
 409         // Evaluate children first and add up all matrices. Stop if there's one
 410         // term that is not a matrix.
 411         std::auto_ptr<epvector> s(new epvector);
 412         s->reserve(seq.size());
 413
 414         bool all_matrices = true;
 415         bool first_term = true;
 416         matrix sum;
 417
 418         epvector::const_iterator it = seq.begin(), itend = seq.end();
 419         while (it != itend) {
 420                 const ex &m = recombine_pair_to_ex(*it).evalm();
 421                 s->push_back(split_ex_to_pair(m));
 422                 if (is_a<matrix>(m)) {
 423                         if (first_term) {
 424                                 sum = ex_to<matrix>(m);
 425                                 first_term = false;
 426                         } else
 427                                 sum = sum.add(ex_to<matrix>(m));
 428                 } else
 429                         all_matrices = false;
 430                 ++it;
 431         }
 432
 433         if (all_matrices)
 434                 return sum + overall_coeff;
 435         else
 436                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 437 }
 438
 439 ex add::conjugate() const
 440 {
 441         exvector *v = 0;
 442         for (size_t i=0; i<nops(); ++i) {
 443                 if (v) {
 444                         v->push_back(op(i).conjugate());
 445                         continue;
 446                 }
 447                 ex term = op(i);
 448                 ex ccterm = term.conjugate();
 449                 if (are_ex_trivially_equal(term, ccterm))
 450                         continue;
 451                 v = new exvector;
 452                 v->reserve(nops());
 453                 for (size_t j=0; j<i; ++j)
 454                         v->push_back(op(j));
 455                 v->push_back(ccterm);
 456         }
 457         if (v) {
 458                 ex result = add(*v);
 459                 delete v;
 460                 return result;
 461         }
 462         return *this;
 463 }
 464
 465 ex add::real_part() const
 466 {
 467         epvector v;
 468         v.reserve(seq.size());
 469         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 470                 if ((i->coeff).info(info_flags::real)) {
 471                         ex rp = (i->rest).real_part();
 472                         if (!rp.is_zero())
 473                                 v.push_back(expair(rp, i->coeff));
 474                 } else {
 475                         ex rp=recombine_pair_to_ex(*i).real_part();
 476                         if (!rp.is_zero())
 477                                 v.push_back(split_ex_to_pair(rp));
 478                 }
 479         return (new add(v, overall_coeff.real_part()))
 480                 -> setflag(status_flags::dynallocated);
 481 }
 482
 483 ex add::imag_part() const
 484 {
 485         epvector v;
 486         v.reserve(seq.size());
 487         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 488                 if ((i->coeff).info(info_flags::real)) {
 489                         ex ip = (i->rest).imag_part();
 490                         if (!ip.is_zero())
 491                                 v.push_back(expair(ip, i->coeff));
 492                 } else {
 493                         ex ip=recombine_pair_to_ex(*i).imag_part();
 494                         if (!ip.is_zero())
 495                                 v.push_back(split_ex_to_pair(ip));
 496                 }
 497         return (new add(v, overall_coeff.imag_part()))
 498                 -> setflag(status_flags::dynallocated);
 499 }
 500
 501 ex add::eval_ncmul(const exvector & v) const
 502 {
 503         if (seq.empty())
 504                 return inherited::eval_ncmul(v);
 505         else
 506                 return seq.begin()->rest.eval_ncmul(v);
 507 }
 508
 509 // protected
 510
 511 /** Implementation of ex::diff() for a sum. It differentiates each term.
 512  *  @see ex::diff */
 513 ex add::derivative(const symbol & y) const
 514 {
 515         std::auto_ptr<epvector> s(new epvector);
 516         s->reserve(seq.size());
 517
 518         // Only differentiate the "rest" parts of the expairs. This is faster
 519         // than the default implementation in basic::derivative() although
 520         // if performs the same function (differentiate each term).
 521         epvector::const_iterator i = seq.begin(), end = seq.end();
 522         while (i != end) {
 523                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 524                 ++i;
 525         }
 526         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 527 }
 528
 529 int add::compare_same_type(const basic & other) const
 530 {
 531         return inherited::compare_same_type(other);
 532 }
 533
 534 unsigned add::return_type() const
 535 {
 536         if (seq.empty())
 537                 return return_types::commutative;
 538         else
 539                 return seq.begin()->rest.return_type();
 540 }
 541
 542 return_type_t add::return_type_tinfo() const
 543 {
 544         if (seq.empty())
 545                 return make_return_type_t<add>();
 546         else
 547                 return seq.begin()->rest.return_type_tinfo();
 548 }
 549
 550 // Note: do_index_renaming is ignored because it makes no sense for an add.
 551 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 552 {
 553         return (new add(v,oc))->setflag(status_flags::dynallocated);
 554 }
 555
 556 // Note: do_index_renaming is ignored because it makes no sense for an add.
 557 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 558 {
 559         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 560 }
 561
 562 expair add::split_ex_to_pair(const ex & e) const
 563 {
 564         if (is_exactly_a<mul>(e)) {
 565                 const mul &mulref(ex_to<mul>(e));
 566                 const ex &numfactor = mulref.overall_coeff;
 567                 mul *mulcopyp = new mul(mulref);
 568                 mulcopyp->overall_coeff = _ex1;
 569                 mulcopyp->clearflag(status_flags::evaluated);
 570                 mulcopyp->clearflag(status_flags::hash_calculated);
 571                 mulcopyp->setflag(status_flags::dynallocated);
 572                 return expair(*mulcopyp,numfactor);
 573         }
 574         return expair(e,_ex1);
 575 }
 576
 577 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 578                                                                                   const ex & c) const
 579 {
 580         GINAC_ASSERT(is_exactly_a<numeric>(c));
 581         if (is_exactly_a<mul>(e)) {
 582                 const mul &mulref(ex_to<mul>(e));
 583                 const ex &numfactor = mulref.overall_coeff;
 584                 mul *mulcopyp = new mul(mulref);
 585                 mulcopyp->overall_coeff = _ex1;
 586                 mulcopyp->clearflag(status_flags::evaluated);
 587                 mulcopyp->clearflag(status_flags::hash_calculated);
 588                 mulcopyp->setflag(status_flags::dynallocated);
 589                 if (c.is_equal(_ex1))
 590                         return expair(*mulcopyp, numfactor);
 591                 else if (numfactor.is_equal(_ex1))
 592                         return expair(*mulcopyp, c);
 593                 else
 594                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 595         } else if (is_exactly_a<numeric>(e)) {
 596                 if (c.is_equal(_ex1))
 597                         return expair(e, _ex1);
 598                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 599         }
 600         return expair(e, c);
 601 }
 602
 603 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 604                                                                                         const ex & c) const
 605 {
 606         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 607         GINAC_ASSERT(is_exactly_a<numeric>(c));
 608
 609         if (is_exactly_a<numeric>(p.rest)) {
 610                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 611                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 612         }
 613
 614         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 615 }
 616
 617 ex add::recombine_pair_to_ex(const expair & p) const
 618 {
 619         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 620                 return p.rest;
 621         else
 622                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 623 }
 624
 625 ex add::expand(unsigned options) const
 626 {
 627         std::auto_ptr<epvector> vp = expandchildren(options);
 628         if (vp.get() == 0) {
 629                 // the terms have not changed, so it is safe to declare this expanded
 630                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 631         }
 632
 633         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 634 }
 635
 636 } // namespace GiNaC