ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2008 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 #include <string>
  27
  28 #include "add.h"
  29 #include "mul.h"
  30 #include "archive.h"
  31 #include "operators.h"
  32 #include "matrix.h"
  33 #include "utils.h"
  34 #include "clifford.h"
  35 #include "ncmul.h"
  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         tinfo_key = &add::tinfo_static;
  53 }
  54
  55 //////////
  56 // other constructors
  57 //////////
  58
  59 // public
  60
  61 add::add(const ex & lh, const ex & rh)
  62 {
  63         tinfo_key = &add::tinfo_static;
  64         overall_coeff = _ex0;
  65         construct_from_2_ex(lh,rh);
  66         GINAC_ASSERT(is_canonical());
  67 }
  68
  69 add::add(const exvector & v)
  70 {
  71         tinfo_key = &add::tinfo_static;
  72         overall_coeff = _ex0;
  73         construct_from_exvector(v);
  74         GINAC_ASSERT(is_canonical());
  75 }
  76
  77 add::add(const epvector & v)
  78 {
  79         tinfo_key = &add::tinfo_static;
  80         overall_coeff = _ex0;
  81         construct_from_epvector(v);
  82         GINAC_ASSERT(is_canonical());
  83 }
  84
  85 add::add(const epvector & v, const ex & oc)
  86 {
  87         tinfo_key = &add::tinfo_static;
  88         overall_coeff = oc;
  89         construct_from_epvector(v);
  90         GINAC_ASSERT(is_canonical());
  91 }
  92
  93 add::add(std::auto_ptr<epvector> vp, const ex & oc)
  94 {
  95         tinfo_key = &add::tinfo_static;
  96         GINAC_ASSERT(vp.get()!=0);
  97         overall_coeff = oc;
  98         construct_from_epvector(*vp);
  99         GINAC_ASSERT(is_canonical());
 100 }
 101
 102 //////////
 103 // archiving
 104 //////////
 105
 106 DEFAULT_ARCHIVING(add)
 107
 108 //////////
 109 // functions overriding virtual functions from base classes
 110 //////////
 111
 112 // public
 113
 114 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 115 {
 116         if (precedence() <= level)
 117                 c.s << openbrace << '(';
 118
 119         numeric coeff;
 120         bool first = true;
 121
 122         // First print the overall numeric coefficient, if present
 123         if (!overall_coeff.is_zero()) {
 124                 overall_coeff.print(c, 0);
 125                 first = false;
 126         }
 127
 128         // Then proceed with the remaining factors
 129         epvector::const_iterator it = seq.begin(), itend = seq.end();
 130         while (it != itend) {
 131                 coeff = ex_to<numeric>(it->coeff);
 132                 if (!first) {
 133                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 134                 } else {
 135                         if (coeff.csgn() == -1) c.s << '-';
 136                         first = false;
 137                 }
 138                 if (!coeff.is_equal(*_num1_p) &&
 139                     !coeff.is_equal(*_num_1_p)) {
 140                         if (coeff.is_rational()) {
 141                                 if (coeff.is_negative())
 142                                         (-coeff).print(c);
 143                                 else
 144                                         coeff.print(c);
 145                         } else {
 146                                 if (coeff.csgn() == -1)
 147                                         (-coeff).print(c, precedence());
 148                                 else
 149                                         coeff.print(c, precedence());
 150                         }
 151                         c.s << mul_sym;
 152                 }
 153                 it->rest.print(c, precedence());
 154                 ++it;
 155         }
 156
 157         if (precedence() <= level)
 158                 c.s << ')' << closebrace;
 159 }
 160
 161 void add::do_print(const print_context & c, unsigned level) const
 162 {
 163         print_add(c, "", "", "*", level);
 164 }
 165
 166 void add::do_print_latex(const print_latex & c, unsigned level) const
 167 {
 168         print_add(c, "{", "}", " ", level);
 169 }
 170
 171 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 172 {
 173         if (precedence() <= level)
 174                 c.s << "(";
 175
 176         // Print arguments, separated by "+" or "-"
 177         epvector::const_iterator it = seq.begin(), itend = seq.end();
 178         char separator = ' ';
 179         while (it != itend) {
 180
 181                 // If the coefficient is negative, separator is "-"
 182                 if (it->coeff.is_equal(_ex_1) ||
 183                         ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 184                         separator = '-';
 185                 c.s << separator;
 186                 if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1)) {
 187                         it->rest.print(c, precedence());
 188                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p) ||
 189                                  ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p))
 190                 {
 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                 ++it;
 201                 separator = '+';
 202         }
 203
 204         if (!overall_coeff.is_zero()) {
 205                 if (overall_coeff.info(info_flags::positive)
 206                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 207                         c.s << '+';
 208                 overall_coeff.print(c, precedence());
 209         }
 210
 211         if (precedence() <= level)
 212                 c.s << ")";
 213 }
 214
 215 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 216 {
 217         c.s << class_name() << '(';
 218         op(0).print(c);
 219         for (size_t i=1; i<nops(); ++i) {
 220                 c.s << ',';
 221                 op(i).print(c);
 222         }
 223         c.s << ')';
 224 }
 225
 226 bool add::info(unsigned inf) const
 227 {
 228         switch (inf) {
 229                 case info_flags::polynomial:
 230                 case info_flags::integer_polynomial:
 231                 case info_flags::cinteger_polynomial:
 232                 case info_flags::rational_polynomial:
 233                 case info_flags::crational_polynomial:
 234                 case info_flags::rational_function: {
 235                         epvector::const_iterator i = seq.begin(), end = seq.end();
 236                         while (i != end) {
 237                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 238                                         return false;
 239                                 ++i;
 240                         }
 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 int add::degree(const ex & s) const
 257 {
 258         int deg = std::numeric_limits<int>::min();
 259         if (!overall_coeff.is_zero())
 260                 deg = 0;
 261
 262         // Find maximum of degrees of individual terms
 263         epvector::const_iterator i = seq.begin(), end = seq.end();
 264         while (i != end) {
 265                 int cur_deg = i->rest.degree(s);
 266                 if (cur_deg > deg)
 267                         deg = cur_deg;
 268                 ++i;
 269         }
 270         return deg;
 271 }
 272
 273 int add::ldegree(const ex & s) const
 274 {
 275         int deg = std::numeric_limits<int>::max();
 276         if (!overall_coeff.is_zero())
 277                 deg = 0;
 278
 279         // Find minimum 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.ldegree(s);
 283                 if (cur_deg < deg)
 284                         deg = cur_deg;
 285                 ++i;
 286         }
 287         return deg;
 288 }
 289
 290 ex add::coeff(const ex & s, int n) const
 291 {
 292         std::auto_ptr<epvector> coeffseq(new epvector);
 293         std::auto_ptr<epvector> coeffseq_cliff(new epvector);
 294         char rl = clifford_max_label(s);
 295         bool do_clifford = (rl != -1);
 296         bool nonscalar = false;
 297
 298         // Calculate sum of coefficients in each term
 299         epvector::const_iterator i = seq.begin(), end = seq.end();
 300         while (i != end) {
 301                 ex restcoeff = i->rest.coeff(s, n);
 302                 if (!restcoeff.is_zero()) {
 303                         if (do_clifford) {
 304                                 if (clifford_max_label(restcoeff) == -1) {
 305                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
 306                                 } else {
 307                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 308                                         nonscalar = true;
 309                                 }
 310                         }
 311                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 312                 }
 313                 ++i;
 314         }
 315
 316         return (new add(nonscalar ? coeffseq_cliff : coeffseq,
 317                         n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 318 }
 319
 320 /** Perform automatic term rewriting rules in this class.  In the following
 321  *  x stands for a symbolic variables of type ex and c stands for such
 322  *  an expression that contain a plain number.
 323  *  - +(;c) -> c
 324  *  - +(x;0) -> x
 325  *
 326  *  @param level cut-off in recursive evaluation */
 327 ex add::eval(int level) const
 328 {
 329         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 330         if (evaled_seqp.get()) {
 331                 // do more evaluation later
 332                 return (new add(evaled_seqp, overall_coeff))->
 333                        setflag(status_flags::dynallocated);
 334         }
 335
 336 #ifdef DO_GINAC_ASSERT
 337         epvector::const_iterator i = seq.begin(), end = seq.end();
 338         while (i != end) {
 339                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 340                 if (is_exactly_a<numeric>(i->rest))
 341                         dbgprint();
 342                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 343                 ++i;
 344         }
 345 #endif // def DO_GINAC_ASSERT
 346
 347         if (flags & status_flags::evaluated) {
 348                 GINAC_ASSERT(seq.size()>0);
 349                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 350                 return *this;
 351         }
 352
 353         int seq_size = seq.size();
 354         if (seq_size == 0) {
 355                 // +(;c) -> c
 356                 return overall_coeff;
 357         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 358                 // +(x;0) -> x
 359                 return recombine_pair_to_ex(*(seq.begin()));
 360         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 361                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 362         }
 363         return this->hold();
 364 }
 365
 366 ex add::evalm() const
 367 {
 368         // Evaluate children first and add up all matrices. Stop if there's one
 369         // term that is not a matrix.
 370         std::auto_ptr<epvector> s(new epvector);
 371         s->reserve(seq.size());
 372
 373         bool all_matrices = true;
 374         bool first_term = true;
 375         matrix sum;
 376
 377         epvector::const_iterator it = seq.begin(), itend = seq.end();
 378         while (it != itend) {
 379                 const ex &m = recombine_pair_to_ex(*it).evalm();
 380                 s->push_back(split_ex_to_pair(m));
 381                 if (is_a<matrix>(m)) {
 382                         if (first_term) {
 383                                 sum = ex_to<matrix>(m);
 384                                 first_term = false;
 385                         } else
 386                                 sum = sum.add(ex_to<matrix>(m));
 387                 } else
 388                         all_matrices = false;
 389                 ++it;
 390         }
 391
 392         if (all_matrices)
 393                 return sum + overall_coeff;
 394         else
 395                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 396 }
 397
 398 ex add::conjugate() const
 399 {
 400         exvector *v = 0;
 401         for (size_t i=0; i<nops(); ++i) {
 402                 if (v) {
 403                         v->push_back(op(i).conjugate());
 404                         continue;
 405                 }
 406                 ex term = op(i);
 407                 ex ccterm = term.conjugate();
 408                 if (are_ex_trivially_equal(term, ccterm))
 409                         continue;
 410                 v = new exvector;
 411                 v->reserve(nops());
 412                 for (size_t j=0; j<i; ++j)
 413                         v->push_back(op(j));
 414                 v->push_back(ccterm);
 415         }
 416         if (v) {
 417                 ex result = add(*v);
 418                 delete v;
 419                 return result;
 420         }
 421         return *this;
 422 }
 423
 424 ex add::real_part() const
 425 {
 426         epvector v;
 427         v.reserve(seq.size());
 428         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 429                 if ((i->coeff).info(info_flags::real)) {
 430                         ex rp = (i->rest).real_part();
 431                         if (!rp.is_zero())
 432                                 v.push_back(expair(rp, i->coeff));
 433                 } else {
 434                         ex rp=recombine_pair_to_ex(*i).real_part();
 435                         if (!rp.is_zero())
 436                                 v.push_back(split_ex_to_pair(rp));
 437                 }
 438         return (new add(v, overall_coeff.real_part()))
 439                 -> setflag(status_flags::dynallocated);
 440 }
 441
 442 ex add::imag_part() const
 443 {
 444         epvector v;
 445         v.reserve(seq.size());
 446         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 447                 if ((i->coeff).info(info_flags::real)) {
 448                         ex ip = (i->rest).imag_part();
 449                         if (!ip.is_zero())
 450                                 v.push_back(expair(ip, i->coeff));
 451                 } else {
 452                         ex ip=recombine_pair_to_ex(*i).imag_part();
 453                         if (!ip.is_zero())
 454                                 v.push_back(split_ex_to_pair(ip));
 455                 }
 456         return (new add(v, overall_coeff.imag_part()))
 457                 -> setflag(status_flags::dynallocated);
 458 }
 459
 460 ex add::eval_ncmul(const exvector & v) const
 461 {
 462         if (seq.empty())
 463                 return inherited::eval_ncmul(v);
 464         else
 465                 return seq.begin()->rest.eval_ncmul(v);
 466 }
 467
 468 // protected
 469
 470 /** Implementation of ex::diff() for a sum. It differentiates each term.
 471  *  @see ex::diff */
 472 ex add::derivative(const symbol & y) const
 473 {
 474         std::auto_ptr<epvector> s(new epvector);
 475         s->reserve(seq.size());
 476
 477         // Only differentiate the "rest" parts of the expairs. This is faster
 478         // than the default implementation in basic::derivative() although
 479         // if performs the same function (differentiate each term).
 480         epvector::const_iterator i = seq.begin(), end = seq.end();
 481         while (i != end) {
 482                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 483                 ++i;
 484         }
 485         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 486 }
 487
 488 int add::compare_same_type(const basic & other) const
 489 {
 490         return inherited::compare_same_type(other);
 491 }
 492
 493 unsigned add::return_type() const
 494 {
 495         if (seq.empty())
 496                 return return_types::commutative;
 497         else
 498                 return seq.begin()->rest.return_type();
 499 }
 500
 501 tinfo_t add::return_type_tinfo() const
 502 {
 503         if (seq.empty())
 504                 return this;
 505         else
 506                 return seq.begin()->rest.return_type_tinfo();
 507 }
 508
 509 // Note: do_index_renaming is ignored because it makes no sense for an add.
 510 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 511 {
 512         return (new add(v,oc))->setflag(status_flags::dynallocated);
 513 }
 514
 515 // Note: do_index_renaming is ignored because it makes no sense for an add.
 516 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc, bool do_index_renaming) const
 517 {
 518         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 519 }
 520
 521 expair add::split_ex_to_pair(const ex & e) const
 522 {
 523         if (is_exactly_a<mul>(e)) {
 524                 const mul &mulref(ex_to<mul>(e));
 525                 const ex &numfactor = mulref.overall_coeff;
 526                 mul *mulcopyp = new mul(mulref);
 527                 mulcopyp->overall_coeff = _ex1;
 528                 mulcopyp->clearflag(status_flags::evaluated);
 529                 mulcopyp->clearflag(status_flags::hash_calculated);
 530                 mulcopyp->setflag(status_flags::dynallocated);
 531                 return expair(*mulcopyp,numfactor);
 532         }
 533         return expair(e,_ex1);
 534 }
 535
 536 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 537                                                                                   const ex & c) const
 538 {
 539         GINAC_ASSERT(is_exactly_a<numeric>(c));
 540         if (is_exactly_a<mul>(e)) {
 541                 const mul &mulref(ex_to<mul>(e));
 542                 const ex &numfactor = mulref.overall_coeff;
 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                 if (c.is_equal(_ex1))
 549                         return expair(*mulcopyp, numfactor);
 550                 else if (numfactor.is_equal(_ex1))
 551                         return expair(*mulcopyp, c);
 552                 else
 553                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 554         } else if (is_exactly_a<numeric>(e)) {
 555                 if (c.is_equal(_ex1))
 556                         return expair(e, _ex1);
 557                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 558         }
 559         return expair(e, c);
 560 }
 561
 562 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 563                                                                                         const ex & c) const
 564 {
 565         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 566         GINAC_ASSERT(is_exactly_a<numeric>(c));
 567
 568         if (is_exactly_a<numeric>(p.rest)) {
 569                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 570                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 571         }
 572
 573         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 574 }
 575
 576 ex add::recombine_pair_to_ex(const expair & p) const
 577 {
 578         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 579                 return p.rest;
 580         else
 581                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 582 }
 583
 584 ex add::expand(unsigned options) const
 585 {
 586         std::auto_ptr<epvector> vp = expandchildren(options);
 587         if (vp.get() == 0) {
 588                 // the terms have not changed, so it is safe to declare this expanded
 589                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 590         }
 591
 592         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 593 }
 594
 595 } // namespace GiNaC