ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2003 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(add, expairseq)
  36
  37 //////////
  38 // default ctor, dtor, copy ctor, assignment operator and helpers
  39 //////////
  40
  41 add::add()
  42 {
  43         tinfo_key = TINFO_add;
  44 }
  45
  46 DEFAULT_COPY(add)
  47 DEFAULT_DESTROY(add)
  48
  49 //////////
  50 // other constructors
  51 //////////
  52
  53 // public
  54
  55 add::add(const ex & lh, const ex & rh)
  56 {
  57         tinfo_key = TINFO_add;
  58         overall_coeff = _ex0;
  59         construct_from_2_ex(lh,rh);
  60         GINAC_ASSERT(is_canonical());
  61 }
  62
  63 add::add(const exvector & v)
  64 {
  65         tinfo_key = TINFO_add;
  66         overall_coeff = _ex0;
  67         construct_from_exvector(v);
  68         GINAC_ASSERT(is_canonical());
  69 }
  70
  71 add::add(const epvector & v)
  72 {
  73         tinfo_key = TINFO_add;
  74         overall_coeff = _ex0;
  75         construct_from_epvector(v);
  76         GINAC_ASSERT(is_canonical());
  77 }
  78
  79 add::add(const epvector & v, const ex & oc)
  80 {
  81         tinfo_key = TINFO_add;
  82         overall_coeff = oc;
  83         construct_from_epvector(v);
  84         GINAC_ASSERT(is_canonical());
  85 }
  86
  87 add::add(epvector * vp, const ex & oc)
  88 {
  89         tinfo_key = TINFO_add;
  90         GINAC_ASSERT(vp!=0);
  91         overall_coeff = oc;
  92         construct_from_epvector(*vp);
  93         delete vp;
  94         GINAC_ASSERT(is_canonical());
  95 }
  96
  97 //////////
  98 // archiving
  99 //////////
 100
 101 DEFAULT_ARCHIVING(add)
 102
 103 //////////
 104 // functions overriding virtual functions from base classes
 105 //////////
 106
 107 // public
 108
 109 void add::print(const print_context & c, unsigned level) const
 110 {
 111         if (is_a<print_tree>(c)) {
 112
 113                 inherited::print(c, level);
 114
 115         } else if (is_a<print_csrc>(c)) {
 116
 117                 if (precedence() <= level)
 118                         c.s << "(";
 119
 120                 // Print arguments, separated by "+"
 121                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 122                 while (it != itend) {
 123
 124                         // If the coefficient is -1, it is replaced by a single minus sign
 125                         if (it->coeff.is_equal(_ex1)) {
 126                                 it->rest.print(c, precedence());
 127                         } else if (it->coeff.is_equal(_ex_1)) {
 128                                 c.s << "-";
 129                                 it->rest.print(c, precedence());
 130                         } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num1)) {
 131                                 it->rest.print(c, precedence());
 132                                 c.s << "/";
 133                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 134                         } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num_1)) {
 135                                 c.s << "-";
 136                                 it->rest.print(c, precedence());
 137                                 c.s << "/";
 138                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 139                         } else {
 140                                 it->coeff.print(c, precedence());
 141                                 c.s << "*";
 142                                 it->rest.print(c, precedence());
 143                         }
 144
 145                         // Separator is "+", except if the following expression would have a leading minus sign or the sign is sitting in parenthesis (as in a ctor)
 146                         ++it;
 147                         if (it != itend
 148                          && (is_a<print_csrc_cl_N>(c) || !it->coeff.info(info_flags::real)  // sign inside ctor arguments
 149                           || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
 150                                 c.s << "+";
 151                 }
 152
 153                 if (!overall_coeff.is_zero()) {
 154                         if (overall_coeff.info(info_flags::positive)
 155                          || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 156                                 c.s << '+';
 157                         overall_coeff.print(c, precedence());
 158                 }
 159
 160                 if (precedence() <= level)
 161                         c.s << ")";
 162
 163         } else if (is_a<print_python_repr>(c)) {
 164
 165                 c.s << class_name() << '(';
 166                 op(0).print(c);
 167                 for (size_t i=1; i<nops(); ++i) {
 168                         c.s << ',';
 169                         op(i).print(c);
 170                 }
 171                 c.s << ')';
 172
 173         } else {
 174
 175                 if (precedence() <= level) {
 176                         if (is_a<print_latex>(c))
 177                                 c.s << "{(";
 178                         else
 179                                 c.s << "(";
 180                 }
 181
 182                 numeric coeff;
 183                 bool first = true;
 184
 185                 // First print the overall numeric coefficient, if present
 186                 if (!overall_coeff.is_zero()) {
 187                         if (!is_a<print_tree>(c))
 188                                 overall_coeff.print(c, 0);
 189                         else
 190                                 overall_coeff.print(c, precedence());
 191                         first = false;
 192                 }
 193
 194                 // Then proceed with the remaining factors
 195                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 196                 while (it != itend) {
 197                         coeff = ex_to<numeric>(it->coeff);
 198                         if (!first) {
 199                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 200                         } else {
 201                                 if (coeff.csgn() == -1) c.s << '-';
 202                                 first = false;
 203                         }
 204                         if (!coeff.is_equal(_num1) &&
 205                             !coeff.is_equal(_num_1)) {
 206                                 if (coeff.is_rational()) {
 207                                         if (coeff.is_negative())
 208                                                 (-coeff).print(c);
 209                                         else
 210                                                 coeff.print(c);
 211                                 } else {
 212                                         if (coeff.csgn() == -1)
 213                                                 (-coeff).print(c, precedence());
 214                                         else
 215                                                 coeff.print(c, precedence());
 216                                 }
 217                                 if (is_a<print_latex>(c))
 218                                         c.s << ' ';
 219                                 else
 220                                         c.s << '*';
 221                         }
 222                         it->rest.print(c, precedence());
 223                         ++it;
 224                 }
 225
 226                 if (precedence() <= level) {
 227                         if (is_a<print_latex>(c))
 228                                 c.s << ")}";
 229                         else
 230                                 c.s << ")";
 231                 }
 232         }
 233 }
 234
 235 bool add::info(unsigned inf) const
 236 {
 237         switch (inf) {
 238                 case info_flags::polynomial:
 239                 case info_flags::integer_polynomial:
 240                 case info_flags::cinteger_polynomial:
 241                 case info_flags::rational_polynomial:
 242                 case info_flags::crational_polynomial:
 243                 case info_flags::rational_function: {
 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 false;
 248                                 ++i;
 249                         }
 250                         return overall_coeff.info(inf);
 251                 }
 252                 case info_flags::algebraic: {
 253                         epvector::const_iterator i = seq.begin(), end = seq.end();
 254                         while (i != end) {
 255                                 if ((recombine_pair_to_ex(*i).info(inf)))
 256                                         return true;
 257                                 ++i;
 258                         }
 259                         return false;
 260                 }
 261         }
 262         return inherited::info(inf);
 263 }
 264
 265 int add::degree(const ex & s) const
 266 {
 267         int deg = INT_MIN;
 268         if (!overall_coeff.is_zero())
 269                 deg = 0;
 270
 271         // Find maximum of degrees of individual terms
 272         epvector::const_iterator i = seq.begin(), end = seq.end();
 273         while (i != end) {
 274                 int cur_deg = i->rest.degree(s);
 275                 if (cur_deg > deg)
 276                         deg = cur_deg;
 277                 ++i;
 278         }
 279         return deg;
 280 }
 281
 282 int add::ldegree(const ex & s) const
 283 {
 284         int deg = INT_MAX;
 285         if (!overall_coeff.is_zero())
 286                 deg = 0;
 287
 288         // Find minimum of degrees of individual terms
 289         epvector::const_iterator i = seq.begin(), end = seq.end();
 290         while (i != end) {
 291                 int cur_deg = i->rest.ldegree(s);
 292                 if (cur_deg < deg)
 293                         deg = cur_deg;
 294                 ++i;
 295         }
 296         return deg;
 297 }
 298
 299 ex add::coeff(const ex & s, int n) const
 300 {
 301         epvector *coeffseq = new epvector();
 302
 303         // Calculate sum of coefficients in each term
 304         epvector::const_iterator i = seq.begin(), end = seq.end();
 305         while (i != end) {
 306                 ex restcoeff = i->rest.coeff(s, n);
 307                 if (!restcoeff.is_zero())
 308                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 309                 ++i;
 310         }
 311
 312         return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 313 }
 314
 315 /** Perform automatic term rewriting rules in this class.  In the following
 316  *  x stands for a symbolic variables of type ex and c stands for such
 317  *  an expression that contain a plain number.
 318  *  - +(;c) -> c
 319  *  - +(x;0) -> x
 320  *
 321  *  @param level cut-off in recursive evaluation */
 322 ex add::eval(int level) const
 323 {
 324         epvector *evaled_seqp = evalchildren(level);
 325         if (evaled_seqp) {
 326                 // do more evaluation later
 327                 return (new add(evaled_seqp, overall_coeff))->
 328                        setflag(status_flags::dynallocated);
 329         }
 330
 331 #ifdef DO_GINAC_ASSERT
 332         epvector::const_iterator i = seq.begin(), end = seq.end();
 333         while (i != end) {
 334                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 335                 if (is_exactly_a<numeric>(i->rest))
 336                         dbgprint();
 337                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 338                 ++i;
 339         }
 340 #endif // def DO_GINAC_ASSERT
 341
 342         if (flags & status_flags::evaluated) {
 343                 GINAC_ASSERT(seq.size()>0);
 344                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 345                 return *this;
 346         }
 347
 348         int seq_size = seq.size();
 349         if (seq_size == 0) {
 350                 // +(;c) -> c
 351                 return overall_coeff;
 352         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 353                 // +(x;0) -> x
 354                 return recombine_pair_to_ex(*(seq.begin()));
 355         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 356                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 357         }
 358         return this->hold();
 359 }
 360
 361 ex add::evalm(void) const
 362 {
 363         // Evaluate children first and add up all matrices. Stop if there's one
 364         // term that is not a matrix.
 365         epvector *s = new epvector;
 366         s->reserve(seq.size());
 367
 368         bool all_matrices = true;
 369         bool first_term = true;
 370         matrix sum;
 371
 372         epvector::const_iterator it = seq.begin(), itend = seq.end();
 373         while (it != itend) {
 374                 const ex &m = recombine_pair_to_ex(*it).evalm();
 375                 s->push_back(split_ex_to_pair(m));
 376                 if (is_a<matrix>(m)) {
 377                         if (first_term) {
 378                                 sum = ex_to<matrix>(m);
 379                                 first_term = false;
 380                         } else
 381                                 sum = sum.add(ex_to<matrix>(m));
 382                 } else
 383                         all_matrices = false;
 384                 ++it;
 385         }
 386
 387         if (all_matrices) {
 388                 delete s;
 389                 return sum + overall_coeff;
 390         } else
 391                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 392 }
 393
 394 ex add::eval_ncmul(const exvector & v) const
 395 {
 396         if (seq.empty())
 397                 return inherited::eval_ncmul(v);
 398         else
 399                 return seq.begin()->rest.eval_ncmul(v);
 400 }
 401
 402 // protected
 403
 404 /** Implementation of ex::diff() for a sum. It differentiates each term.
 405  *  @see ex::diff */
 406 ex add::derivative(const symbol & y) const
 407 {
 408         epvector *s = new epvector();
 409         s->reserve(seq.size());
 410
 411         // Only differentiate the "rest" parts of the expairs. This is faster
 412         // than the default implementation in basic::derivative() although
 413         // if performs the same function (differentiate each term).
 414         epvector::const_iterator i = seq.begin(), end = seq.end();
 415         while (i != end) {
 416                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 417                 ++i;
 418         }
 419         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 420 }
 421
 422 int add::compare_same_type(const basic & other) const
 423 {
 424         return inherited::compare_same_type(other);
 425 }
 426
 427 unsigned add::return_type(void) const
 428 {
 429         if (seq.empty())
 430                 return return_types::commutative;
 431         else
 432                 return seq.begin()->rest.return_type();
 433 }
 434
 435 unsigned add::return_type_tinfo(void) const
 436 {
 437         if (seq.empty())
 438                 return tinfo_key;
 439         else
 440                 return seq.begin()->rest.return_type_tinfo();
 441 }
 442
 443 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 444 {
 445         return (new add(v,oc))->setflag(status_flags::dynallocated);
 446 }
 447
 448 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 449 {
 450         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 451 }
 452
 453 expair add::split_ex_to_pair(const ex & e) const
 454 {
 455         if (is_exactly_a<mul>(e)) {
 456                 const mul &mulref(ex_to<mul>(e));
 457                 const ex &numfactor = mulref.overall_coeff;
 458                 mul *mulcopyp = new mul(mulref);
 459                 mulcopyp->overall_coeff = _ex1;
 460                 mulcopyp->clearflag(status_flags::evaluated);
 461                 mulcopyp->clearflag(status_flags::hash_calculated);
 462                 mulcopyp->setflag(status_flags::dynallocated);
 463                 return expair(*mulcopyp,numfactor);
 464         }
 465         return expair(e,_ex1);
 466 }
 467
 468 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 469                                                                                   const ex & c) const
 470 {
 471         GINAC_ASSERT(is_exactly_a<numeric>(c));
 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                 if (c.is_equal(_ex1))
 481                         return expair(*mulcopyp, numfactor);
 482                 else if (numfactor.is_equal(_ex1))
 483                         return expair(*mulcopyp, c);
 484                 else
 485                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 486         } else if (is_exactly_a<numeric>(e)) {
 487                 if (c.is_equal(_ex1))
 488                         return expair(e, _ex1);
 489                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 490         }
 491         return expair(e, c);
 492 }
 493
 494 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 495                                                                                         const ex & c) const
 496 {
 497         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 498         GINAC_ASSERT(is_exactly_a<numeric>(c));
 499
 500         if (is_exactly_a<numeric>(p.rest)) {
 501                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
 502                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 503         }
 504
 505         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 506 }
 507
 508 ex add::recombine_pair_to_ex(const expair & p) const
 509 {
 510         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 511                 return p.rest;
 512         else
 513                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 514 }
 515
 516 ex add::expand(unsigned options) const
 517 {
 518         epvector *vp = expandchildren(options);
 519         if (vp == NULL) {
 520                 // the terms have not changed, so it is safe to declare this expanded
 521                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 522         }
 523
 524         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 525 }
 526
 527 } // namespace GiNaC