ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2010 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
  32 #include <iostream>
  33 #include <limits>
  34 #include <stdexcept>
  35 #include <string>
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  40   print_func<print_context>(&add::do_print).
  41   print_func<print_latex>(&add::do_print_latex).
  42   print_func<print_csrc>(&add::do_print_csrc).
  43   print_func<print_tree>(&add::do_print_tree).
  44   print_func<print_python_repr>(&add::do_print_python_repr))
  45
  46 //////////
  47 // default constructor
  48 //////////
  49
  50 add::add()
  51 {
  52 }
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 add::add(const ex & lh, const ex & rh)
  61 {
  62         overall_coeff = _ex0;
  63         construct_from_2_ex(lh,rh);
  64         GINAC_ASSERT(is_canonical());
  65 }
  66
  67 add::add(const exvector & v)
  68 {
  69         overall_coeff = _ex0;
  70         construct_from_exvector(v);
  71         GINAC_ASSERT(is_canonical());
  72 }
  73
  74 add::add(const epvector & v)
  75 {
  76         overall_coeff = _ex0;
  77         construct_from_epvector(v);
  78         GINAC_ASSERT(is_canonical());
  79 }
  80
  81 add::add(const epvector & v, const ex & oc)
  82 {
  83         overall_coeff = oc;
  84         construct_from_epvector(v);
  85         GINAC_ASSERT(is_canonical());
  86 }
  87
  88 add::add(std::auto_ptr<epvector> vp, const ex & oc)
  89 {
  90         GINAC_ASSERT(vp.get()!=0);
  91         overall_coeff = oc;
  92         construct_from_epvector(*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         epvector::const_iterator it = seq.begin(), itend = seq.end();
 124         while (it != itend) {
 125                 coeff = ex_to<numeric>(it->coeff);
 126                 if (!first) {
 127                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 128                 } else {
 129                         if (coeff.csgn() == -1) c.s << '-';
 130                         first = false;
 131                 }
 132                 if (!coeff.is_equal(*_num1_p) &&
 133                     !coeff.is_equal(*_num_1_p)) {
 134                         if (coeff.is_rational()) {
 135                                 if (coeff.is_negative())
 136                                         (-coeff).print(c);
 137                                 else
 138                                         coeff.print(c);
 139                         } else {
 140                                 if (coeff.csgn() == -1)
 141                                         (-coeff).print(c, precedence());
 142                                 else
 143                                         coeff.print(c, precedence());
 144                         }
 145                         c.s << mul_sym;
 146                 }
 147                 it->rest.print(c, precedence());
 148                 ++it;
 149         }
 150
 151         if (precedence() <= level)
 152                 c.s << ')' << closebrace;
 153 }
 154
 155 void add::do_print(const print_context & c, unsigned level) const
 156 {
 157         print_add(c, "", "", "*", level);
 158 }
 159
 160 void add::do_print_latex(const print_latex & c, unsigned level) const
 161 {
 162         print_add(c, "{", "}", " ", level);
 163 }
 164
 165 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 166 {
 167         if (precedence() <= level)
 168                 c.s << "(";
 169
 170         // Print arguments, separated by "+" or "-"
 171         epvector::const_iterator it = seq.begin(), itend = seq.end();
 172         char separator = ' ';
 173         while (it != itend) {
 174
 175                 // If the coefficient is negative, separator is "-"
 176                 if (it->coeff.is_equal(_ex_1) ||
 177                         ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 178                         separator = '-';
 179                 c.s << separator;
 180                 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
 181                         it->rest.print(c, precedence());
 182                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
 183                                  ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 184                 {
 185                         it->rest.print(c, precedence());
 186                         c.s << '/';
 187                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 188                 } else {
 189                         it->coeff.print(c, precedence());
 190                         c.s << '*';
 191                         it->rest.print(c, precedence());
 192                 }
 193
 194                 ++it;
 195                 separator = '+';
 196         }
 197
 198         if (!overall_coeff.is_zero()) {
 199                 if (overall_coeff.info(info_flags::positive)
 200                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 201                         c.s << '+';
 202                 overall_coeff.print(c, precedence());
 203         }
 204
 205         if (precedence() <= level)
 206                 c.s << ")";
 207 }
 208
 209 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 210 {
 211         c.s << class_name() << '(';
 212         op(0).print(c);
 213         for (size_t i=1; i<nops(); ++i) {
 214                 c.s << ',';
 215                 op(i).print(c);
 216         }
 217         c.s << ')';
 218 }
 219
 220 bool add::info(unsigned inf) const
 221 {
 222         switch (inf) {
 223                 case info_flags::polynomial:
 224                 case info_flags::integer_polynomial:
 225                 case info_flags::cinteger_polynomial:
 226                 case info_flags::rational_polynomial:
 227                 case info_flags::real:
 228                 case info_flags::rational:
 229                 case info_flags::integer:
 230                 case info_flags::crational:
 231                 case info_flags::cinteger:
 232                 case info_flags::positive:
 233                 case info_flags::nonnegative:
 234                 case info_flags::posint:
 235                 case info_flags::nonnegint:
 236                 case info_flags::even:
 237                 case info_flags::crational_polynomial:
 238                 case info_flags::rational_function: {
 239                         epvector::const_iterator i = seq.begin(), end = seq.end();
 240                         while (i != end) {
 241                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 242                                         return false;
 243                                 ++i;
 244                         }
 245                         if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
 246                                 return true;
 247                         return overall_coeff.info(inf);
 248                 }
 249                 case info_flags::algebraic: {
 250                         epvector::const_iterator i = seq.begin(), end = seq.end();
 251                         while (i != end) {
 252                                 if ((recombine_pair_to_ex(*i).info(inf)))
 253                                         return true;
 254                                 ++i;
 255                         }
 256                         return false;
 257                 }
 258         }
 259         return inherited::info(inf);
 260 }
 261
 262 int add::degree(const ex & s) const
 263 {
 264         int deg = std::numeric_limits<int>::min();
 265         if (!overall_coeff.is_zero())
 266                 deg = 0;
 267
 268         // Find maximum of degrees of individual terms
 269         epvector::const_iterator i = seq.begin(), end = seq.end();
 270         while (i != end) {
 271                 int cur_deg = i->rest.degree(s);
 272                 if (cur_deg > deg)
 273                         deg = cur_deg;
 274                 ++i;
 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         epvector::const_iterator i = seq.begin(), end = seq.end();
 287         while (i != end) {
 288                 int cur_deg = i->rest.ldegree(s);
 289                 if (cur_deg < deg)
 290                         deg = cur_deg;
 291                 ++i;
 292         }
 293         return deg;
 294 }
 295
 296 ex add::coeff(const ex & s, int n) const
 297 {
 298         std::auto_ptr<epvector> coeffseq(new epvector);
 299         std::auto_ptr<epvector> coeffseq_cliff(new epvector);
 300         char 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         epvector::const_iterator i = seq.begin(), end = seq.end();
 306         while (i != end) {
 307                 ex restcoeff = i->rest.coeff(s, n);
 308                 if (!restcoeff.is_zero()) {
 309                         if (do_clifford) {
 310                                 if (clifford_max_label(restcoeff) == -1) {
 311                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
 312                                 } else {
 313                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 314                                         nonscalar = true;
 315                                 }
 316                         }
 317                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 318                 }
 319                 ++i;
 320         }
 321
 322         return (new add(nonscalar ? coeffseq_cliff : coeffseq,
 323                         n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 324 }
 325
 326 /** Perform automatic term rewriting rules in this class.  In the following
 327  *  x stands for a symbolic variables of type ex and c stands for such
 328  *  an expression that contain a plain number.
 329  *  - +(;c) -> c
 330  *  - +(x;0) -> x
 331  *
 332  *  @param level cut-off in recursive evaluation */
 333 ex add::eval(int level) const
 334 {
 335         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 336         if (evaled_seqp.get()) {
 337                 // do more evaluation later
 338                 return (new add(evaled_seqp, overall_coeff))->
 339                        setflag(status_flags::dynallocated);
 340         }
 341
 342 #ifdef DO_GINAC_ASSERT
 343         epvector::const_iterator i = seq.begin(), end = seq.end();
 344         while (i != end) {
 345                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 346                 if (is_exactly_a<numeric>(i->rest))
 347                         dbgprint();
 348                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 349                 ++i;
 350         }
 351 #endif // def DO_GINAC_ASSERT
 352
 353         if (flags & status_flags::evaluated) {
 354                 GINAC_ASSERT(seq.size()>0);
 355                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 356                 return *this;
 357         }
 358
 359         int seq_size = seq.size();
 360         if (seq_size == 0) {
 361                 // +(;c) -> c
 362                 return overall_coeff;
 363         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 364                 // +(x;0) -> x
 365                 return recombine_pair_to_ex(*(seq.begin()));
 366         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 367                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 368         }
 369         return this->hold();
 370 }
 371
 372 ex add::evalm() const
 373 {
 374         // Evaluate children first and add up all matrices. Stop if there's one
 375         // term that is not a matrix.
 376         std::auto_ptr<epvector> s(new epvector);
 377         s->reserve(seq.size());
 378
 379         bool all_matrices = true;
 380         bool first_term = true;
 381         matrix sum;
 382
 383         epvector::const_iterator it = seq.begin(), itend = seq.end();
 384         while (it != itend) {
 385                 const ex &m = recombine_pair_to_ex(*it).evalm();
 386                 s->push_back(split_ex_to_pair(m));
 387                 if (is_a<matrix>(m)) {
 388                         if (first_term) {
 389                                 sum = ex_to<matrix>(m);
 390                                 first_term = false;
 391                         } else
 392                                 sum = sum.add(ex_to<matrix>(m));
 393                 } else
 394                         all_matrices = false;
 395                 ++it;
 396         }
 397
 398         if (all_matrices)
 399                 return sum + overall_coeff;
 400         else
 401                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 402 }
 403
 404 ex add::conjugate() const
 405 {
 406         exvector *v = 0;
 407         for (size_t i=0; i<nops(); ++i) {
 408                 if (v) {
 409                         v->push_back(op(i).conjugate());
 410                         continue;
 411                 }
 412                 ex term = op(i);
 413                 ex ccterm = term.conjugate();
 414                 if (are_ex_trivially_equal(term, ccterm))
 415                         continue;
 416                 v = new exvector;
 417                 v->reserve(nops());
 418                 for (size_t j=0; j<i; ++j)
 419                         v->push_back(op(j));
 420                 v->push_back(ccterm);
 421         }
 422         if (v) {
 423                 ex result = add(*v);
 424                 delete v;
 425                 return result;
 426         }
 427         return *this;
 428 }
 429
 430 ex add::real_part() const
 431 {
 432         epvector v;
 433         v.reserve(seq.size());
 434         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 435                 if ((i->coeff).info(info_flags::real)) {
 436                         ex rp = (i->rest).real_part();
 437                         if (!rp.is_zero())
 438                                 v.push_back(expair(rp, i->coeff));
 439                 } else {
 440                         ex rp=recombine_pair_to_ex(*i).real_part();
 441                         if (!rp.is_zero())
 442                                 v.push_back(split_ex_to_pair(rp));
 443                 }
 444         return (new add(v, overall_coeff.real_part()))
 445                 -> setflag(status_flags::dynallocated);
 446 }
 447
 448 ex add::imag_part() const
 449 {
 450         epvector v;
 451         v.reserve(seq.size());
 452         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 453                 if ((i->coeff).info(info_flags::real)) {
 454                         ex ip = (i->rest).imag_part();
 455                         if (!ip.is_zero())
 456                                 v.push_back(expair(ip, i->coeff));
 457                 } else {
 458                         ex ip=recombine_pair_to_ex(*i).imag_part();
 459                         if (!ip.is_zero())
 460                                 v.push_back(split_ex_to_pair(ip));
 461                 }
 462         return (new add(v, overall_coeff.imag_part()))
 463                 -> setflag(status_flags::dynallocated);
 464 }
 465
 466 ex add::eval_ncmul(const exvector & v) const
 467 {
 468         if (seq.empty())
 469                 return inherited::eval_ncmul(v);
 470         else
 471                 return seq.begin()->rest.eval_ncmul(v);
 472 }
 473
 474 // protected
 475
 476 /** Implementation of ex::diff() for a sum. It differentiates each term.
 477  *  @see ex::diff */
 478 ex add::derivative(const symbol & y) const
 479 {
 480         std::auto_ptr<epvector> s(new epvector);
 481         s->reserve(seq.size());
 482
 483         // Only differentiate the "rest" parts of the expairs. This is faster
 484         // than the default implementation in basic::derivative() although
 485         // if performs the same function (differentiate each term).
 486         epvector::const_iterator i = seq.begin(), end = seq.end();
 487         while (i != end) {
 488                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 489                 ++i;
 490         }
 491         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 492 }
 493
 494 int add::compare_same_type(const basic & other) const
 495 {
 496         return inherited::compare_same_type(other);
 497 }
 498
 499 unsigned add::return_type() const
 500 {
 501         if (seq.empty())
 502                 return return_types::commutative;
 503         else
 504                 return seq.begin()->rest.return_type();
 505 }
 506
 507 return_type_t add::return_type_tinfo() const
 508 {
 509         if (seq.empty())
 510                 return make_return_type_t<add>();
 511         else
 512                 return seq.begin()->rest.return_type_tinfo();
 513 }
 514
 515 // Note: do_index_renaming is ignored because it makes no sense for an add.
 516 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 517 {
 518         return (new add(v,oc))->setflag(status_flags::dynallocated);
 519 }
 520
 521 // Note: do_index_renaming is ignored because it makes no sense for an add.
 522 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 523 {
 524         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 525 }
 526
 527 expair add::split_ex_to_pair(const ex & e) const
 528 {
 529         if (is_exactly_a<mul>(e)) {
 530                 const mul &mulref(ex_to<mul>(e));
 531                 const ex &numfactor = mulref.overall_coeff;
 532                 mul *mulcopyp = new mul(mulref);
 533                 mulcopyp->overall_coeff = _ex1;
 534                 mulcopyp->clearflag(status_flags::evaluated);
 535                 mulcopyp->clearflag(status_flags::hash_calculated);
 536                 mulcopyp->setflag(status_flags::dynallocated);
 537                 return expair(*mulcopyp,numfactor);
 538         }
 539         return expair(e,_ex1);
 540 }
 541
 542 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 543                                                                                   const ex & c) const
 544 {
 545         GINAC_ASSERT(is_exactly_a<numeric>(c));
 546         if (is_exactly_a<mul>(e)) {
 547                 const mul &mulref(ex_to<mul>(e));
 548                 const ex &numfactor = mulref.overall_coeff;
 549                 mul *mulcopyp = new mul(mulref);
 550                 mulcopyp->overall_coeff = _ex1;
 551                 mulcopyp->clearflag(status_flags::evaluated);
 552                 mulcopyp->clearflag(status_flags::hash_calculated);
 553                 mulcopyp->setflag(status_flags::dynallocated);
 554                 if (c.is_equal(_ex1))
 555                         return expair(*mulcopyp, numfactor);
 556                 else if (numfactor.is_equal(_ex1))
 557                         return expair(*mulcopyp, c);
 558                 else
 559                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 560         } else if (is_exactly_a<numeric>(e)) {
 561                 if (c.is_equal(_ex1))
 562                         return expair(e, _ex1);
 563                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 564         }
 565         return expair(e, c);
 566 }
 567
 568 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 569                                                                                         const ex & c) const
 570 {
 571         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 572         GINAC_ASSERT(is_exactly_a<numeric>(c));
 573
 574         if (is_exactly_a<numeric>(p.rest)) {
 575                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 576                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 577         }
 578
 579         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 580 }
 581
 582 ex add::recombine_pair_to_ex(const expair & p) const
 583 {
 584         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 585                 return p.rest;
 586         else
 587                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 588 }
 589
 590 ex add::expand(unsigned options) const
 591 {
 592         std::auto_ptr<epvector> vp = expandchildren(options);
 593         if (vp.get() == 0) {
 594                 // the terms have not changed, so it is safe to declare this expanded
 595                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 596         }
 597
 598         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 599 }
 600
 601 } // namespace GiNaC