ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2004 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  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
  33 namespace GiNaC {
  34
  35 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  36   print_func<print_context>(&add::do_print).
  37   print_func<print_latex>(&add::do_print_latex).
  38   print_func<print_csrc>(&add::do_print_csrc).
  39   print_func<print_tree>(&add::do_print_tree).
  40   print_func<print_python_repr>(&add::do_print_python_repr))
  41
  42 //////////
  43 // default constructor
  44 //////////
  45
  46 add::add()
  47 {
  48         tinfo_key = TINFO_add;
  49 }
  50
  51 //////////
  52 // other constructors
  53 //////////
  54
  55 // public
  56
  57 add::add(const ex & lh, const ex & rh)
  58 {
  59         tinfo_key = TINFO_add;
  60         overall_coeff = _ex0;
  61         construct_from_2_ex(lh,rh);
  62         GINAC_ASSERT(is_canonical());
  63 }
  64
  65 add::add(const exvector & v)
  66 {
  67         tinfo_key = TINFO_add;
  68         overall_coeff = _ex0;
  69         construct_from_exvector(v);
  70         GINAC_ASSERT(is_canonical());
  71 }
  72
  73 add::add(const epvector & v)
  74 {
  75         tinfo_key = TINFO_add;
  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         tinfo_key = TINFO_add;
  84         overall_coeff = oc;
  85         construct_from_epvector(v);
  86         GINAC_ASSERT(is_canonical());
  87 }
  88
  89 add::add(std::auto_ptr<epvector> vp, const ex & oc)
  90 {
  91         tinfo_key = TINFO_add;
  92         GINAC_ASSERT(vp.get()!=0);
  93         overall_coeff = oc;
  94         construct_from_epvector(*vp);
  95         GINAC_ASSERT(is_canonical());
  96 }
  97
  98 //////////
  99 // archiving
 100 //////////
 101
 102 DEFAULT_ARCHIVING(add)
 103
 104 //////////
 105 // functions overriding virtual functions from base classes
 106 //////////
 107
 108 // public
 109
 110 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 111 {
 112         if (precedence() <= level)
 113                 c.s << openbrace << '(';
 114
 115         numeric coeff;
 116         bool first = true;
 117
 118         // First print the overall numeric coefficient, if present
 119         if (!overall_coeff.is_zero()) {
 120                 overall_coeff.print(c, 0);
 121                 first = false;
 122         }
 123
 124         // Then proceed with the remaining factors
 125         epvector::const_iterator it = seq.begin(), itend = seq.end();
 126         while (it != itend) {
 127                 coeff = ex_to<numeric>(it->coeff);
 128                 if (!first) {
 129                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 130                 } else {
 131                         if (coeff.csgn() == -1) c.s << '-';
 132                         first = false;
 133                 }
 134                 if (!coeff.is_equal(_num1) &&
 135                     !coeff.is_equal(_num_1)) {
 136                         if (coeff.is_rational()) {
 137                                 if (coeff.is_negative())
 138                                         (-coeff).print(c);
 139                                 else
 140                                         coeff.print(c);
 141                         } else {
 142                                 if (coeff.csgn() == -1)
 143                                         (-coeff).print(c, precedence());
 144                                 else
 145                                         coeff.print(c, precedence());
 146                         }
 147                         c.s << mul_sym;
 148                 }
 149                 it->rest.print(c, precedence());
 150                 ++it;
 151         }
 152
 153         if (precedence() <= level)
 154                 c.s << ')' << closebrace;
 155 }
 156
 157 void add::do_print(const print_context & c, unsigned level) const
 158 {
 159         print_add(c, "", "", "*", level);
 160 }
 161
 162 void add::do_print_latex(const print_latex & c, unsigned level) const
 163 {
 164         print_add(c, "{", "}", " ", level);
 165 }
 166
 167 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 168 {
 169         if (precedence() <= level)
 170                 c.s << "(";
 171
 172         // Print arguments, separated by "+"
 173         epvector::const_iterator it = seq.begin(), itend = seq.end();
 174         while (it != itend) {
 175
 176                 // If the coefficient is -1, it is replaced by a single minus sign
 177                 if (it->coeff.is_equal(_ex1)) {
 178                         it->rest.print(c, precedence());
 179                 } else if (it->coeff.is_equal(_ex_1)) {
 180                         c.s << "-";
 181                         it->rest.print(c, precedence());
 182                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num1)) {
 183                         it->rest.print(c, precedence());
 184                         c.s << "/";
 185                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 186                 } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num_1)) {
 187                         c.s << "-";
 188                         it->rest.print(c, precedence());
 189                         c.s << "/";
 190                         ex_to<numeric>(it->coeff).denom().print(c, precedence());
 191                 } else {
 192                         it->coeff.print(c, precedence());
 193                         c.s << "*";
 194                         it->rest.print(c, precedence());
 195                 }
 196
 197                 // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
 198                 ++it;
 199                 if (it != itend
 200                  && (is_a<print_csrc_cl_N>(c) || !it->coeff.info(info_flags::real)  // sign inside ctor arguments
 201                   || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
 202                         c.s << "+";
 203         }
 204
 205         if (!overall_coeff.is_zero()) {
 206                 if (overall_coeff.info(info_flags::positive)
 207                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 208                         c.s << '+';
 209                 overall_coeff.print(c, precedence());
 210         }
 211
 212         if (precedence() <= level)
 213                 c.s << ")";
 214 }
 215
 216 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 217 {
 218         c.s << class_name() << '(';
 219         op(0).print(c);
 220         for (size_t i=1; i<nops(); ++i) {
 221                 c.s << ',';
 222                 op(i).print(c);
 223         }
 224         c.s << ')';
 225 }
 226
 227 bool add::info(unsigned inf) const
 228 {
 229         switch (inf) {
 230                 case info_flags::polynomial:
 231                 case info_flags::integer_polynomial:
 232                 case info_flags::cinteger_polynomial:
 233                 case info_flags::rational_polynomial:
 234                 case info_flags::crational_polynomial:
 235                 case info_flags::rational_function: {
 236                         epvector::const_iterator i = seq.begin(), end = seq.end();
 237                         while (i != end) {
 238                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 239                                         return false;
 240                                 ++i;
 241                         }
 242                         return overall_coeff.info(inf);
 243                 }
 244                 case info_flags::algebraic: {
 245                         epvector::const_iterator i = seq.begin(), end = seq.end();
 246                         while (i != end) {
 247                                 if ((recombine_pair_to_ex(*i).info(inf)))
 248                                         return true;
 249                                 ++i;
 250                         }
 251                         return false;
 252                 }
 253         }
 254         return inherited::info(inf);
 255 }
 256
 257 int add::degree(const ex & s) const
 258 {
 259         int deg = INT_MIN;
 260         if (!overall_coeff.is_zero())
 261                 deg = 0;
 262
 263         // Find maximum of degrees of individual terms
 264         epvector::const_iterator i = seq.begin(), end = seq.end();
 265         while (i != end) {
 266                 int cur_deg = i->rest.degree(s);
 267                 if (cur_deg > deg)
 268                         deg = cur_deg;
 269                 ++i;
 270         }
 271         return deg;
 272 }
 273
 274 int add::ldegree(const ex & s) const
 275 {
 276         int deg = INT_MAX;
 277         if (!overall_coeff.is_zero())
 278                 deg = 0;
 279
 280         // Find minimum of degrees of individual terms
 281         epvector::const_iterator i = seq.begin(), end = seq.end();
 282         while (i != end) {
 283                 int cur_deg = i->rest.ldegree(s);
 284                 if (cur_deg < deg)
 285                         deg = cur_deg;
 286                 ++i;
 287         }
 288         return deg;
 289 }
 290
 291 ex add::coeff(const ex & s, int n) const
 292 {
 293         std::auto_ptr<epvector> coeffseq(new epvector);
 294
 295         // Calculate sum of coefficients in each term
 296         epvector::const_iterator i = seq.begin(), end = seq.end();
 297         while (i != end) {
 298                 ex restcoeff = i->rest.coeff(s, n);
 299                 if (!restcoeff.is_zero())
 300                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 301                 ++i;
 302         }
 303
 304         return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 305 }
 306
 307 /** Perform automatic term rewriting rules in this class.  In the following
 308  *  x stands for a symbolic variables of type ex and c stands for such
 309  *  an expression that contain a plain number.
 310  *  - +(;c) -> c
 311  *  - +(x;0) -> x
 312  *
 313  *  @param level cut-off in recursive evaluation */
 314 ex add::eval(int level) const
 315 {
 316         std::auto_ptr<epvector> evaled_seqp = evalchildren(level);
 317         if (evaled_seqp.get()) {
 318                 // do more evaluation later
 319                 return (new add(evaled_seqp, overall_coeff))->
 320                        setflag(status_flags::dynallocated);
 321         }
 322
 323 #ifdef DO_GINAC_ASSERT
 324         epvector::const_iterator i = seq.begin(), end = seq.end();
 325         while (i != end) {
 326                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 327                 if (is_exactly_a<numeric>(i->rest))
 328                         dbgprint();
 329                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 330                 ++i;
 331         }
 332 #endif // def DO_GINAC_ASSERT
 333
 334         if (flags & status_flags::evaluated) {
 335                 GINAC_ASSERT(seq.size()>0);
 336                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 337                 return *this;
 338         }
 339
 340         int seq_size = seq.size();
 341         if (seq_size == 0) {
 342                 // +(;c) -> c
 343                 return overall_coeff;
 344         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 345                 // +(x;0) -> x
 346                 return recombine_pair_to_ex(*(seq.begin()));
 347         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 348                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 349         }
 350         return this->hold();
 351 }
 352
 353 ex add::evalm() const
 354 {
 355         // Evaluate children first and add up all matrices. Stop if there's one
 356         // term that is not a matrix.
 357         std::auto_ptr<epvector> s(new epvector);
 358         s->reserve(seq.size());
 359
 360         bool all_matrices = true;
 361         bool first_term = true;
 362         matrix sum;
 363
 364         epvector::const_iterator it = seq.begin(), itend = seq.end();
 365         while (it != itend) {
 366                 const ex &m = recombine_pair_to_ex(*it).evalm();
 367                 s->push_back(split_ex_to_pair(m));
 368                 if (is_a<matrix>(m)) {
 369                         if (first_term) {
 370                                 sum = ex_to<matrix>(m);
 371                                 first_term = false;
 372                         } else
 373                                 sum = sum.add(ex_to<matrix>(m));
 374                 } else
 375                         all_matrices = false;
 376                 ++it;
 377         }
 378
 379         if (all_matrices)
 380                 return sum + overall_coeff;
 381         else
 382                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 383 }
 384
 385 ex add::conjugate() const
 386 {
 387         exvector *v = 0;
 388         for (int i=0; i<nops(); ++i) {
 389                 if (v) {
 390                         v->push_back(op(i).conjugate());
 391                         continue;
 392                 }
 393                 ex term = op(i);
 394                 ex ccterm = term.conjugate();
 395                 if (are_ex_trivially_equal(term, ccterm))
 396                         continue;
 397                 v = new exvector;
 398                 v->reserve(nops());
 399                 for (int j=0; j<i; ++j)
 400                         v->push_back(op(j));
 401                 v->push_back(ccterm);
 402         }
 403         if (v) {
 404                 ex result = add(*v);
 405                 delete v;
 406                 return result;
 407         }
 408         return *this;
 409 }
 410
 411 ex add::eval_ncmul(const exvector & v) const
 412 {
 413         if (seq.empty())
 414                 return inherited::eval_ncmul(v);
 415         else
 416                 return seq.begin()->rest.eval_ncmul(v);
 417 }
 418
 419 // protected
 420
 421 /** Implementation of ex::diff() for a sum. It differentiates each term.
 422  *  @see ex::diff */
 423 ex add::derivative(const symbol & y) const
 424 {
 425         std::auto_ptr<epvector> s(new epvector);
 426         s->reserve(seq.size());
 427
 428         // Only differentiate the "rest" parts of the expairs. This is faster
 429         // than the default implementation in basic::derivative() although
 430         // if performs the same function (differentiate each term).
 431         epvector::const_iterator i = seq.begin(), end = seq.end();
 432         while (i != end) {
 433                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 434                 ++i;
 435         }
 436         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 437 }
 438
 439 int add::compare_same_type(const basic & other) const
 440 {
 441         return inherited::compare_same_type(other);
 442 }
 443
 444 unsigned add::return_type() const
 445 {
 446         if (seq.empty())
 447                 return return_types::commutative;
 448         else
 449                 return seq.begin()->rest.return_type();
 450 }
 451
 452 unsigned add::return_type_tinfo() const
 453 {
 454         if (seq.empty())
 455                 return tinfo_key;
 456         else
 457                 return seq.begin()->rest.return_type_tinfo();
 458 }
 459
 460 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 461 {
 462         return (new add(v,oc))->setflag(status_flags::dynallocated);
 463 }
 464
 465 ex add::thisexpairseq(std::auto_ptr<epvector> vp, const ex & oc) const
 466 {
 467         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 468 }
 469
 470 expair add::split_ex_to_pair(const ex & e) const
 471 {
 472         if (is_exactly_a<mul>(e)) {
 473                 const mul &mulref(ex_to<mul>(e));
 474                 const ex &numfactor = mulref.overall_coeff;
 475                 mul *mulcopyp = new mul(mulref);
 476                 mulcopyp->overall_coeff = _ex1;
 477                 mulcopyp->clearflag(status_flags::evaluated);
 478                 mulcopyp->clearflag(status_flags::hash_calculated);
 479                 mulcopyp->setflag(status_flags::dynallocated);
 480                 return expair(*mulcopyp,numfactor);
 481         }
 482         return expair(e,_ex1);
 483 }
 484
 485 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 486                                                                                   const ex & c) const
 487 {
 488         GINAC_ASSERT(is_exactly_a<numeric>(c));
 489         if (is_exactly_a<mul>(e)) {
 490                 const mul &mulref(ex_to<mul>(e));
 491                 const ex &numfactor = mulref.overall_coeff;
 492                 mul *mulcopyp = new mul(mulref);
 493                 mulcopyp->overall_coeff = _ex1;
 494                 mulcopyp->clearflag(status_flags::evaluated);
 495                 mulcopyp->clearflag(status_flags::hash_calculated);
 496                 mulcopyp->setflag(status_flags::dynallocated);
 497                 if (c.is_equal(_ex1))
 498                         return expair(*mulcopyp, numfactor);
 499                 else if (numfactor.is_equal(_ex1))
 500                         return expair(*mulcopyp, c);
 501                 else
 502                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 503         } else if (is_exactly_a<numeric>(e)) {
 504                 if (c.is_equal(_ex1))
 505                         return expair(e, _ex1);
 506                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 507         }
 508         return expair(e, c);
 509 }
 510
 511 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 512                                                                                         const ex & c) const
 513 {
 514         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 515         GINAC_ASSERT(is_exactly_a<numeric>(c));
 516
 517         if (is_exactly_a<numeric>(p.rest)) {
 518                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
 519                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 520         }
 521
 522         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 523 }
 524
 525 ex add::recombine_pair_to_ex(const expair & p) const
 526 {
 527         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 528                 return p.rest;
 529         else
 530                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 531 }
 532
 533 ex add::expand(unsigned options) const
 534 {
 535         std::auto_ptr<epvector> vp = expandchildren(options);
 536         if (vp.get() == 0) {
 537                 // the terms have not changed, so it is safe to declare this expanded
 538                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 539         }
 540
 541         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 542 }
 543
 544 } // namespace GiNaC