ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2007 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 <iostream>
  24 #include <stdexcept>
  25 #include <limits>
  26
  27 #include "add.h"
  28 #include "mul.h"
  29 #include "archive.h"
  30 #include "operators.h"
  31 #include "matrix.h"
  32 #include "utils.h"
  33 #include "clifford.h"
  34 #include "ncmul.h"
  35
  36 namespace GiNaC {
  37
  38 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  39   print_func<print_context>(&add::do_print).
  40   print_func<print_latex>(&add::do_print_latex).
  41   print_func<print_csrc>(&add::do_print_csrc).
  42   print_func<print_tree>(&add::do_print_tree).
  43   print_func<print_python_repr>(&add::do_print_python_repr))
  44
  45 //////////
  46 // default constructor
  47 //////////
  48
  49 add::add()
  50 {
  51         tinfo_key = &add::tinfo_static;
  52 }
  53
  54 //////////
  55 // other constructors
  56 //////////
  57
  58 // public
  59
  60 add::add(const ex & lh, const ex & rh)
  61 {
  62         tinfo_key = &add::tinfo_static;
  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         tinfo_key = &add::tinfo_static;
  71         overall_coeff = _ex0;
  72         construct_from_exvector(v);
  73         GINAC_ASSERT(is_canonical());
  74 }
  75
  76 add::add(const epvector & v)
  77 {
  78         tinfo_key = &add::tinfo_static;
  79         overall_coeff = _ex0;
  80         construct_from_epvector(v);
  81         GINAC_ASSERT(is_canonical());
  82 }
  83
  84 add::add(const epvector & v, const ex & oc)
  85 {
  86         tinfo_key = &add::tinfo_static;
  87         overall_coeff = oc;
  88         construct_from_epvector(v);
  89         GINAC_ASSERT(is_canonical());
  90 }
  91
  92 add::add(std::auto_ptr<epvector> vp, const ex & oc)
  93 {
  94         tinfo_key = &add::tinfo_static;
  95         GINAC_ASSERT(vp.get()!=0);
  96         overall_coeff = oc;
  97         construct_from_epvector(*vp);
  98         GINAC_ASSERT(is_canonical());
  99 }
 100
 101 //////////
 102 // archiving
 103 //////////
 104
 105 DEFAULT_ARCHIVING(add)
 106
 107 //////////
 108 // functions overriding virtual functions from base classes
 109 //////////
 110
 111 // public
 112
 113 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 114 {
 115         if (precedence() <= level)
 116                 c.s << openbrace << '(';
 117
 118         numeric coeff;
 119         bool first = true;
 120
 121         // First print the overall numeric coefficient, if present
 122         if (!overall_coeff.is_zero()) {
 123                 overall_coeff.print(c, 0);
 124                 first = false;
 125         }
 126
 127         // Then proceed with the remaining factors
 128         epvector::const_iterator it = seq.begin(), itend = seq.end();
 129         while (it != itend) {
 130                 coeff = ex_to<numeric>(it->coeff);
 131                 if (!first) {
 132                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 133                 } else {
 134                         if (coeff.csgn() == -1) c.s << '-';
 135                         first = false;
 136                 }
 137                 if (!coeff.is_equal(*_num1_p) &&
 138                     !coeff.is_equal(*_num_1_p)) {
 139                         if (coeff.is_rational()) {
 140                                 if (coeff.is_negative())
 141                                         (-coeff).print(c);
 142                                 else
 143                                         coeff.print(c);
 144                         } else {
 145                                 if (coeff.csgn() == -1)
 146                                         (-coeff).print(c, precedence());
 147                                 else
 148                                         coeff.print(c, precedence());
 149                         }
 150                         c.s << mul_sym;
 151                 }
 152                 it->rest.print(c, precedence());
 153                 ++it;
 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 "+"
 176         epvector::const_iterator it = seq.begin(), itend = seq.end();
 177         while (it != itend) {
 178
 179                 // If the coefficient is -1, it is replaced by a single minus sign
 180                 if (it->coeff.is_equal(_ex1)) {
 181                         it->rest.print(c, precedence());
 182                 } else if (it->coeff.is_equal(_ex_1)) {
 183                         c.s << "-";
 184                         it->rest.print(c, precedence());
 185                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p)) {
 186                         it->rest.print(c, precedence());
 187                         c.s << "/";
 188                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 189                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p)) {
 190                         c.s << "-";
 191                         it->rest.print(c, precedence());
 192                         c.s << "/";
 193                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 194                 } else {
 195                         it->coeff.print(c, precedence());
 196                         c.s << "*";
 197                         it->rest.print(c, precedence());
 198                 }
 199
 200                 // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
 201                 ++it;
 202                 if (it != itend
 203                  && (is_a<print_csrc_cl_N>(c) || !it->coeff.info(info_flags::real)  // sign inside ctor arguments
 204                   || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(*_num1_p) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
 205                         c.s << "+";
 206         }
 207
 208         if (!overall_coeff.is_zero()) {
 209                 if (overall_coeff.info(info_flags::positive)
 210                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 211                         c.s << '+';
 212                 overall_coeff.print(c, precedence());
 213         }
 214
 215         if (precedence() <= level)
 216                 c.s << ")";
 217 }
 218
 219 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 220 {
 221         c.s << class_name() << '(';
 222         op(0).print(c);
 223         for (size_t i=1; i<nops(); ++i) {
 224                 c.s << ',';
 225                 op(i).print(c);
 226         }
 227         c.s << ')';
 228 }
 229
 230 bool add::info(unsigned inf) const
 231 {
 232         switch (inf) {
 233                 case info_flags::polynomial:
 234                 case info_flags::integer_polynomial:
 235                 case info_flags::cinteger_polynomial:
 236                 case info_flags::rational_polynomial:
 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                         return overall_coeff.info(inf);
 246                 }
 247                 case info_flags::algebraic: {
 248                         epvector::const_iterator i = seq.begin(), end = seq.end();
 249                         while (i != end) {
 250                                 if ((recombine_pair_to_ex(*i).info(inf)))
 251                                         return true;
 252                                 ++i;
 253                         }
 254                         return false;
 255                 }
 256         }
 257         return inherited::info(inf);
 258 }
 259
 260 int add::degree(const ex & s) const
 261 {
 262         int deg = std::numeric_limits<int>::min();
 263         if (!overall_coeff.is_zero())
 264                 deg = 0;
 265
 266         // Find maximum of degrees of individual terms
 267         epvector::const_iterator i = seq.begin(), end = seq.end();
 268         while (i != end) {
 269                 int cur_deg = i->rest.degree(s);
 270                 if (cur_deg > deg)
 271                         deg = cur_deg;
 272                 ++i;
 273         }
 274         return deg;
 275 }
 276
 277 int add::ldegree(const ex & s) const
 278 {
 279         int deg = std::numeric_limits<int>::max();
 280         if (!overall_coeff.is_zero())
 281                 deg = 0;
 282
 283         // Find minimum of degrees of individual terms
 284         epvector::const_iterator i = seq.begin(), end = seq.end();
 285         while (i != end) {
 286                 int cur_deg = i->rest.ldegree(s);
 287                 if (cur_deg < deg)
 288                         deg = cur_deg;
 289                 ++i;
 290         }
 291         return deg;
 292 }
 293
 294 ex add::coeff(const ex & s, int n) const
 295 {
 296         std::auto_ptr<epvector> coeffseq(new epvector);
 297         std::auto_ptr<epvector> coeffseq_cliff(new epvector);
 298         char 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         epvector::const_iterator i = seq.begin(), end = seq.end();
 304         while (i != end) {
 305                 ex restcoeff = i->rest.coeff(s, n);
 306                 if (!restcoeff.is_zero()) {
 307                         if (do_clifford) {
 308                                 if (clifford_max_label(restcoeff) == -1) {
 309                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
 310                                 } else {
 311                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 312                                         nonscalar = true;
 313                                 }
 314                         }
 315                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 316                 }
 317                 ++i;
 318         }
 319
 320         return (new add(nonscalar ? coeffseq_cliff : 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         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 334         if (evaled_seqp.get()) {
 335                 // do more evaluation later
 336                 return (new add(evaled_seqp, overall_coeff))->
 337                        setflag(status_flags::dynallocated);
 338         }
 339
 340 #ifdef DO_GINAC_ASSERT
 341         epvector::const_iterator i = seq.begin(), end = seq.end();
 342         while (i != end) {
 343                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 344                 if (is_exactly_a<numeric>(i->rest))
 345                         dbgprint();
 346                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 347                 ++i;
 348         }
 349 #endif // def DO_GINAC_ASSERT
 350
 351         if (flags & status_flags::evaluated) {
 352                 GINAC_ASSERT(seq.size()>0);
 353                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 354                 return *this;
 355         }
 356
 357         int seq_size = seq.size();
 358         if (seq_size == 0) {
 359                 // +(;c) -> c
 360                 return overall_coeff;
 361         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 362                 // +(x;0) -> x
 363                 return recombine_pair_to_ex(*(seq.begin()));
 364         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 365                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 366         }
 367         return this->hold();
 368 }
 369
 370 ex add::evalm() const
 371 {
 372         // Evaluate children first and add up all matrices. Stop if there's one
 373         // term that is not a matrix.
 374         std::auto_ptr<epvector> s(new epvector);
 375         s->reserve(seq.size());
 376
 377         bool all_matrices = true;
 378         bool first_term = true;
 379         matrix sum;
 380
 381         epvector::const_iterator it = seq.begin(), itend = seq.end();
 382         while (it != itend) {
 383                 const ex &m = recombine_pair_to_ex(*it).evalm();
 384                 s->push_back(split_ex_to_pair(m));
 385                 if (is_a<matrix>(m)) {
 386                         if (first_term) {
 387                                 sum = ex_to<matrix>(m);
 388                                 first_term = false;
 389                         } else
 390                                 sum = sum.add(ex_to<matrix>(m));
 391                 } else
 392                         all_matrices = false;
 393                 ++it;
 394         }
 395
 396         if (all_matrices)
 397                 return sum + overall_coeff;
 398         else
 399                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 400 }
 401
 402 ex add::conjugate() const
 403 {
 404         exvector *v = 0;
 405         for (size_t i=0; i<nops(); ++i) {
 406                 if (v) {
 407                         v->push_back(op(i).conjugate());
 408                         continue;
 409                 }
 410                 ex term = op(i);
 411                 ex ccterm = term.conjugate();
 412                 if (are_ex_trivially_equal(term, ccterm))
 413                         continue;
 414                 v = new exvector;
 415                 v->reserve(nops());
 416                 for (size_t j=0; j<i; ++j)
 417                         v->push_back(op(j));
 418                 v->push_back(ccterm);
 419         }
 420         if (v) {
 421                 ex result = add(*v);
 422                 delete v;
 423                 return result;
 424         }
 425         return *this;
 426 }
 427
 428 ex add::real_part() const
 429 {
 430         epvector v;
 431         v.reserve(seq.size());
 432         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 433                 if ((i->coeff).info(info_flags::real)) {
 434                         ex rp = (i->rest).real_part();
 435                         if (!rp.is_zero())
 436                                 v.push_back(expair(rp, i->coeff));
 437                 } else {
 438                         ex rp=recombine_pair_to_ex(*i).real_part();
 439                         if (!rp.is_zero())
 440                                 v.push_back(split_ex_to_pair(rp));
 441                 }
 442         return (new add(v, overall_coeff.real_part()))
 443                 -> setflag(status_flags::dynallocated);
 444 }
 445
 446 ex add::imag_part() const
 447 {
 448         epvector v;
 449         v.reserve(seq.size());
 450         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 451                 if ((i->coeff).info(info_flags::real)) {
 452                         ex ip = (i->rest).imag_part();
 453                         if (!ip.is_zero())
 454                                 v.push_back(expair(ip, i->coeff));
 455                 } else {
 456                         ex ip=recombine_pair_to_ex(*i).imag_part();
 457                         if (!ip.is_zero())
 458                                 v.push_back(split_ex_to_pair(ip));
 459                 }
 460         return (new add(v, overall_coeff.imag_part()))
 461                 -> setflag(status_flags::dynallocated);
 462 }
 463
 464 ex add::eval_ncmul(const exvector & v) const
 465 {
 466         if (seq.empty())
 467                 return inherited::eval_ncmul(v);
 468         else
 469                 return seq.begin()->rest.eval_ncmul(v);
 470 }
 471
 472 // protected
 473
 474 /** Implementation of ex::diff() for a sum. It differentiates each term.
 475  *  @see ex::diff */
 476 ex add::derivative(const symbol & y) const
 477 {
 478         std::auto_ptr<epvector> s(new epvector);
 479         s->reserve(seq.size());
 480
 481         // Only differentiate the "rest" parts of the expairs. This is faster
 482         // than the default implementation in basic::derivative() although
 483         // if performs the same function (differentiate each term).
 484         epvector::const_iterator i = seq.begin(), end = seq.end();
 485         while (i != end) {
 486                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 487                 ++i;
 488         }
 489         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 490 }
 491
 492 int add::compare_same_type(const basic & other) const
 493 {
 494         return inherited::compare_same_type(other);
 495 }
 496
 497 unsigned add::return_type() const
 498 {
 499         if (seq.empty())
 500                 return return_types::commutative;
 501         else
 502                 return seq.begin()->rest.return_type();
 503 }
 504
 505 tinfo_t add::return_type_tinfo() const
 506 {
 507         if (seq.empty())
 508                 return this;
 509         else
 510                 return seq.begin()->rest.return_type_tinfo();
 511 }
 512
 513 // Note: do_index_renaming is ignored because it makes no sense for an add.
 514 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 515 {
 516         return (new add(v,oc))->setflag(status_flags::dynallocated);
 517 }
 518
 519 // Note: do_index_renaming is ignored because it makes no sense for an add.
 520 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 521 {
 522         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 523 }
 524
 525 expair add::split_ex_to_pair(const ex & e) const
 526 {
 527         if (is_exactly_a<mul>(e)) {
 528                 const mul &mulref(ex_to<mul>(e));
 529                 const ex &numfactor = mulref.overall_coeff;
 530                 mul *mulcopyp = new mul(mulref);
 531                 mulcopyp->overall_coeff = _ex1;
 532                 mulcopyp->clearflag(status_flags::evaluated);
 533                 mulcopyp->clearflag(status_flags::hash_calculated);
 534                 mulcopyp->setflag(status_flags::dynallocated);
 535                 return expair(*mulcopyp,numfactor);
 536         }
 537         return expair(e,_ex1);
 538 }
 539
 540 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 541                                                                                   const ex & c) const
 542 {
 543         GINAC_ASSERT(is_exactly_a<numeric>(c));
 544         if (is_exactly_a<mul>(e)) {
 545                 const mul &mulref(ex_to<mul>(e));
 546                 const ex &numfactor = mulref.overall_coeff;
 547                 mul *mulcopyp = new mul(mulref);
 548                 mulcopyp->overall_coeff = _ex1;
 549                 mulcopyp->clearflag(status_flags::evaluated);
 550                 mulcopyp->clearflag(status_flags::hash_calculated);
 551                 mulcopyp->setflag(status_flags::dynallocated);
 552                 if (c.is_equal(_ex1))
 553                         return expair(*mulcopyp, numfactor);
 554                 else if (numfactor.is_equal(_ex1))
 555                         return expair(*mulcopyp, c);
 556                 else
 557                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 558         } else if (is_exactly_a<numeric>(e)) {
 559                 if (c.is_equal(_ex1))
 560                         return expair(e, _ex1);
 561                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 562         }
 563         return expair(e, c);
 564 }
 565
 566 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 567                                                                                         const ex & c) const
 568 {
 569         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 570         GINAC_ASSERT(is_exactly_a<numeric>(c));
 571
 572         if (is_exactly_a<numeric>(p.rest)) {
 573                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 574                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 575         }
 576
 577         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 578 }
 579
 580 ex add::recombine_pair_to_ex(const expair & p) const
 581 {
 582         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 583                 return p.rest;
 584         else
 585                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 586 }
 587
 588 ex add::expand(unsigned options) const
 589 {
 590         std::auto_ptr<epvector> vp = expandchildren(options);
 591         if (vp.get() == 0) {
 592                 // the terms have not changed, so it is safe to declare this expanded
 593                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 594         }
 595
 596         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 597 }
 598
 599 } // namespace GiNaC