ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2006 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
  26 #include "add.h"
  27 #include "mul.h"
  28 #include "archive.h"
  29 #include "operators.h"
  30 #include "matrix.h"
  31 #include "utils.h"
  32 #include "clifford.h"
  33 #include "ncmul.h"
  34
  35 namespace GiNaC {
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  38   print_func<print_context>(&add::do_print).
  39   print_func<print_latex>(&add::do_print_latex).
  40   print_func<print_csrc>(&add::do_print_csrc).
  41   print_func<print_tree>(&add::do_print_tree).
  42   print_func<print_python_repr>(&add::do_print_python_repr))
  43
  44 //////////
  45 // default constructor
  46 //////////
  47
  48 add::add()
  49 {
  50         tinfo_key = &add::tinfo_static;
  51 }
  52
  53 //////////
  54 // other constructors
  55 //////////
  56
  57 // public
  58
  59 add::add(const ex & lh, const ex & rh)
  60 {
  61         tinfo_key = &add::tinfo_static;
  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         tinfo_key = &add::tinfo_static;
  70         overall_coeff = _ex0;
  71         construct_from_exvector(v);
  72         GINAC_ASSERT(is_canonical());
  73 }
  74
  75 add::add(const epvector & v)
  76 {
  77         tinfo_key = &add::tinfo_static;
  78         overall_coeff = _ex0;
  79         construct_from_epvector(v);
  80         GINAC_ASSERT(is_canonical());
  81 }
  82
  83 add::add(const epvector & v, const ex & oc)
  84 {
  85         tinfo_key = &add::tinfo_static;
  86         overall_coeff = oc;
  87         construct_from_epvector(v);
  88         GINAC_ASSERT(is_canonical());
  89 }
  90
  91 add::add(std::auto_ptr<epvector> vp, const ex & oc)
  92 {
  93         tinfo_key = &add::tinfo_static;
  94         GINAC_ASSERT(vp.get()!=0);
  95         overall_coeff = oc;
  96         construct_from_epvector(*vp);
  97         GINAC_ASSERT(is_canonical());
  98 }
  99
 100 //////////
 101 // archiving
 102 //////////
 103
 104 DEFAULT_ARCHIVING(add)
 105
 106 //////////
 107 // functions overriding virtual functions from base classes
 108 //////////
 109
 110 // public
 111
 112 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 113 {
 114         if (precedence() <= level)
 115                 c.s << openbrace << '(';
 116
 117         numeric coeff;
 118         bool first = true;
 119
 120         // First print the overall numeric coefficient, if present
 121         if (!overall_coeff.is_zero()) {
 122                 overall_coeff.print(c, 0);
 123                 first = false;
 124         }
 125
 126         // Then proceed with the remaining factors
 127         epvector::const_iterator it = seq.begin(), itend = seq.end();
 128         while (it != itend) {
 129                 coeff = ex_to<numeric>(it->coeff);
 130                 if (!first) {
 131                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 132                 } else {
 133                         if (coeff.csgn() == -1) c.s << '-';
 134                         first = false;
 135                 }
 136                 if (!coeff.is_equal(*_num1_p) &&
 137                     !coeff.is_equal(*_num_1_p)) {
 138                         if (coeff.is_rational()) {
 139                                 if (coeff.is_negative())
 140                                         (-coeff).print(c);
 141                                 else
 142                                         coeff.print(c);
 143                         } else {
 144                                 if (coeff.csgn() == -1)
 145                                         (-coeff).print(c, precedence());
 146                                 else
 147                                         coeff.print(c, precedence());
 148                         }
 149                         c.s << mul_sym;
 150                 }
 151                 it->rest.print(c, precedence());
 152                 ++it;
 153         }
 154
 155         if (precedence() <= level)
 156                 c.s << ')' << closebrace;
 157 }
 158
 159 void add::do_print(const print_context & c, unsigned level) const
 160 {
 161         print_add(c, "", "", "*", level);
 162 }
 163
 164 void add::do_print_latex(const print_latex & c, unsigned level) const
 165 {
 166         print_add(c, "{", "}", " ", level);
 167 }
 168
 169 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 170 {
 171         if (precedence() <= level)
 172                 c.s << "(";
 173
 174         // Print arguments, separated by "+"
 175         epvector::const_iterator it = seq.begin(), itend = seq.end();
 176         while (it != itend) {
 177
 178                 // If the coefficient is -1, it is replaced by a single minus sign
 179                 if (it->coeff.is_equal(_ex1)) {
 180                         it->rest.print(c, precedence());
 181                 } else if (it->coeff.is_equal(_ex_1)) {
 182                         c.s << "-";
 183                         it->rest.print(c, precedence());
 184                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num1_p)) {
 185                         it->rest.print(c, precedence());
 186                         c.s << "/";
 187                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 188                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(*_num_1_p)) {
 189                         c.s << "-";
 190                         it->rest.print(c, precedence());
 191                         c.s << "/";
 192                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 193                 } else {
 194                         it->coeff.print(c, precedence());
 195                         c.s << "*";
 196                         it->rest.print(c, precedence());
 197                 }
 198
 199                 // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
 200                 ++it;
 201                 if (it != itend
 202                  && (is_a<print_csrc_cl_N>(c) || !it->coeff.info(info_flags::real)  // sign inside ctor arguments
 203                   || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(*_num1_p) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
 204                         c.s << "+";
 205         }
 206
 207         if (!overall_coeff.is_zero()) {
 208                 if (overall_coeff.info(info_flags::positive)
 209                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 210                         c.s << '+';
 211                 overall_coeff.print(c, precedence());
 212         }
 213
 214         if (precedence() <= level)
 215                 c.s << ")";
 216 }
 217
 218 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 219 {
 220         c.s << class_name() << '(';
 221         op(0).print(c);
 222         for (size_t i=1; i<nops(); ++i) {
 223                 c.s << ',';
 224                 op(i).print(c);
 225         }
 226         c.s << ')';
 227 }
 228
 229 bool add::info(unsigned inf) const
 230 {
 231         switch (inf) {
 232                 case info_flags::polynomial:
 233                 case info_flags::integer_polynomial:
 234                 case info_flags::cinteger_polynomial:
 235                 case info_flags::rational_polynomial:
 236                 case info_flags::crational_polynomial:
 237                 case info_flags::rational_function: {
 238                         epvector::const_iterator i = seq.begin(), end = seq.end();
 239                         while (i != end) {
 240                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 241                                         return false;
 242                                 ++i;
 243                         }
 244                         return overall_coeff.info(inf);
 245                 }
 246                 case info_flags::algebraic: {
 247                         epvector::const_iterator i = seq.begin(), end = seq.end();
 248                         while (i != end) {
 249                                 if ((recombine_pair_to_ex(*i).info(inf)))
 250                                         return true;
 251                                 ++i;
 252                         }
 253                         return false;
 254                 }
 255         }
 256         return inherited::info(inf);
 257 }
 258
 259 int add::degree(const ex & s) const
 260 {
 261         int deg = INT_MIN;
 262         if (!overall_coeff.is_zero())
 263                 deg = 0;
 264
 265         // Find maximum of degrees of individual terms
 266         epvector::const_iterator i = seq.begin(), end = seq.end();
 267         while (i != end) {
 268                 int cur_deg = i->rest.degree(s);
 269                 if (cur_deg > deg)
 270                         deg = cur_deg;
 271                 ++i;
 272         }
 273         return deg;
 274 }
 275
 276 int add::ldegree(const ex & s) const
 277 {
 278         int deg = INT_MAX;
 279         if (!overall_coeff.is_zero())
 280                 deg = 0;
 281
 282         // Find minimum of degrees of individual terms
 283         epvector::const_iterator i = seq.begin(), end = seq.end();
 284         while (i != end) {
 285                 int cur_deg = i->rest.ldegree(s);
 286                 if (cur_deg < deg)
 287                         deg = cur_deg;
 288                 ++i;
 289         }
 290         return deg;
 291 }
 292
 293 ex add::coeff(const ex & s, int n) const
 294 {
 295         std::auto_ptr<epvector> coeffseq(new epvector);
 296         std::auto_ptr<epvector> coeffseq_cliff(new epvector);
 297         char rl = clifford_max_label(s);
 298         bool do_clifford = (rl != -1);
 299         bool nonscalar = false;
 300
 301         // Calculate sum of coefficients in each term
 302         epvector::const_iterator i = seq.begin(), end = seq.end();
 303         while (i != end) {
 304                 ex restcoeff = i->rest.coeff(s, n);
 305                 if (!restcoeff.is_zero()) {
 306                         if (do_clifford) {
 307                                 if (clifford_max_label(restcoeff) == -1) {
 308                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(ncmul(restcoeff, dirac_ONE(rl)), i->coeff));
 309                                 } else {
 310                                         coeffseq_cliff->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 311                                         nonscalar = true;
 312                                 }
 313                         }
 314                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 315                 }
 316                 ++i;
 317         }
 318
 319         return (new add(nonscalar ? coeffseq_cliff : coeffseq,
 320                         n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 321 }
 322
 323 /** Perform automatic term rewriting rules in this class.  In the following
 324  *  x stands for a symbolic variables of type ex and c stands for such
 325  *  an expression that contain a plain number.
 326  *  - +(;c) -> c
 327  *  - +(x;0) -> x
 328  *
 329  *  @param level cut-off in recursive evaluation */
 330 ex add::eval(int level) const
 331 {
 332         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 333         if (evaled_seqp.get()) {
 334                 // do more evaluation later
 335                 return (new add(evaled_seqp, overall_coeff))->
 336                        setflag(status_flags::dynallocated);
 337         }
 338
 339 #ifdef DO_GINAC_ASSERT
 340         epvector::const_iterator i = seq.begin(), end = seq.end();
 341         while (i != end) {
 342                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 343                 if (is_exactly_a<numeric>(i->rest))
 344                         dbgprint();
 345                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 346                 ++i;
 347         }
 348 #endif // def DO_GINAC_ASSERT
 349
 350         if (flags & status_flags::evaluated) {
 351                 GINAC_ASSERT(seq.size()>0);
 352                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 353                 return *this;
 354         }
 355
 356         int seq_size = seq.size();
 357         if (seq_size == 0) {
 358                 // +(;c) -> c
 359                 return overall_coeff;
 360         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 361                 // +(x;0) -> x
 362                 return recombine_pair_to_ex(*(seq.begin()));
 363         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 364                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 365         }
 366         return this->hold();
 367 }
 368
 369 ex add::evalm() const
 370 {
 371         // Evaluate children first and add up all matrices. Stop if there's one
 372         // term that is not a matrix.
 373         std::auto_ptr<epvector> s(new epvector);
 374         s->reserve(seq.size());
 375
 376         bool all_matrices = true;
 377         bool first_term = true;
 378         matrix sum;
 379
 380         epvector::const_iterator it = seq.begin(), itend = seq.end();
 381         while (it != itend) {
 382                 const ex &m = recombine_pair_to_ex(*it).evalm();
 383                 s->push_back(split_ex_to_pair(m));
 384                 if (is_a<matrix>(m)) {
 385                         if (first_term) {
 386                                 sum = ex_to<matrix>(m);
 387                                 first_term = false;
 388                         } else
 389                                 sum = sum.add(ex_to<matrix>(m));
 390                 } else
 391                         all_matrices = false;
 392                 ++it;
 393         }
 394
 395         if (all_matrices)
 396                 return sum + overall_coeff;
 397         else
 398                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 399 }
 400
 401 ex add::conjugate() const
 402 {
 403         exvector *v = 0;
 404         for (size_t i=0; i<nops(); ++i) {
 405                 if (v) {
 406                         v->push_back(op(i).conjugate());
 407                         continue;
 408                 }
 409                 ex term = op(i);
 410                 ex ccterm = term.conjugate();
 411                 if (are_ex_trivially_equal(term, ccterm))
 412                         continue;
 413                 v = new exvector;
 414                 v->reserve(nops());
 415                 for (size_t j=0; j<i; ++j)
 416                         v->push_back(op(j));
 417                 v->push_back(ccterm);
 418         }
 419         if (v) {
 420                 ex result = add(*v);
 421                 delete v;
 422                 return result;
 423         }
 424         return *this;
 425 }
 426
 427 ex add::real_part() const
 428 {
 429         epvector v;
 430         v.reserve(seq.size());
 431         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
 432                 if ((i->coeff).info(info_flags::real))
 433                         v.push_back(expair((i->rest).real_part(), i->coeff));
 434                 else {
 435                         ex rp=recombine_pair_to_ex(*i).real_part();
 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                         v.push_back(expair((i->rest).imag_part(), i->coeff));
 449                 else {
 450                         ex ip=recombine_pair_to_ex(*i).imag_part();
 451                         v.push_back(split_ex_to_pair(ip));
 452                 }
 453         return (new add(v, overall_coeff.imag_part()))
 454                 -> setflag(status_flags::dynallocated);
 455 }
 456
 457 ex add::eval_ncmul(const exvector & v) const
 458 {
 459         if (seq.empty())
 460                 return inherited::eval_ncmul(v);
 461         else
 462                 return seq.begin()->rest.eval_ncmul(v);
 463 }
 464
 465 // protected
 466
 467 /** Implementation of ex::diff() for a sum. It differentiates each term.
 468  *  @see ex::diff */
 469 ex add::derivative(const symbol & y) const
 470 {
 471         std::auto_ptr<epvector> s(new epvector);
 472         s->reserve(seq.size());
 473
 474         // Only differentiate the "rest" parts of the expairs. This is faster
 475         // than the default implementation in basic::derivative() although
 476         // if performs the same function (differentiate each term).
 477         epvector::const_iterator i = seq.begin(), end = seq.end();
 478         while (i != end) {
 479                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 480                 ++i;
 481         }
 482         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 483 }
 484
 485 int add::compare_same_type(const basic & other) const
 486 {
 487         return inherited::compare_same_type(other);
 488 }
 489
 490 unsigned add::return_type() const
 491 {
 492         if (seq.empty())
 493                 return return_types::commutative;
 494         else
 495                 return seq.begin()->rest.return_type();
 496 }
 497
 498 tinfo_t add::return_type_tinfo() const
 499 {
 500         if (seq.empty())
 501                 return this;
 502         else
 503                 return seq.begin()->rest.return_type_tinfo();
 504 }
 505
 506 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 507 {
 508         return (new add(v,oc))->setflag(status_flags::dynallocated);
 509 }
 510
 511 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc) const
 512 {
 513         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 514 }
 515
 516 expair add::split_ex_to_pair(const ex & e) const
 517 {
 518         if (is_exactly_a<mul>(e)) {
 519                 const mul &mulref(ex_to<mul>(e));
 520                 const ex &numfactor = mulref.overall_coeff;
 521                 mul *mulcopyp = new mul(mulref);
 522                 mulcopyp->overall_coeff = _ex1;
 523                 mulcopyp->clearflag(status_flags::evaluated);
 524                 mulcopyp->clearflag(status_flags::hash_calculated);
 525                 mulcopyp->setflag(status_flags::dynallocated);
 526                 return expair(*mulcopyp,numfactor);
 527         }
 528         return expair(e,_ex1);
 529 }
 530
 531 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 532                                                                                   const ex & c) const
 533 {
 534         GINAC_ASSERT(is_exactly_a<numeric>(c));
 535         if (is_exactly_a<mul>(e)) {
 536                 const mul &mulref(ex_to<mul>(e));
 537                 const ex &numfactor = mulref.overall_coeff;
 538                 mul *mulcopyp = new mul(mulref);
 539                 mulcopyp->overall_coeff = _ex1;
 540                 mulcopyp->clearflag(status_flags::evaluated);
 541                 mulcopyp->clearflag(status_flags::hash_calculated);
 542                 mulcopyp->setflag(status_flags::dynallocated);
 543                 if (c.is_equal(_ex1))
 544                         return expair(*mulcopyp, numfactor);
 545                 else if (numfactor.is_equal(_ex1))
 546                         return expair(*mulcopyp, c);
 547                 else
 548                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 549         } else if (is_exactly_a<numeric>(e)) {
 550                 if (c.is_equal(_ex1))
 551                         return expair(e, _ex1);
 552                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 553         }
 554         return expair(e, c);
 555 }
 556
 557 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 558                                                                                         const ex & c) const
 559 {
 560         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 561         GINAC_ASSERT(is_exactly_a<numeric>(c));
 562
 563         if (is_exactly_a<numeric>(p.rest)) {
 564                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 565                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 566         }
 567
 568         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 569 }
 570
 571 ex add::recombine_pair_to_ex(const expair & p) const
 572 {
 573         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 574                 return p.rest;
 575         else
 576                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 577 }
 578
 579 ex add::expand(unsigned options) const
 580 {
 581         std::auto_ptr<epvector> vp = expandchildren(options);
 582         if (vp.get() == 0) {
 583                 // the terms have not changed, so it is safe to declare this expanded
 584                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 585         }
 586
 587         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 588 }
 589
 590 } // namespace GiNaC