ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2002 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 "matrix.h"
  29 #include "archive.h"
  30 #include "utils.h"
  31
  32 namespace GiNaC {
  33
  34 GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
  35
  36 //////////
  37 // default ctor, dtor, copy ctor, assignment operator and helpers
  38 //////////
  39
  40 add::add()
  41 {
  42         tinfo_key = TINFO_add;
  43 }
  44
  45 DEFAULT_COPY(add)
  46 DEFAULT_DESTROY(add)
  47
  48 //////////
  49 // other constructors
  50 //////////
  51
  52 // public
  53
  54 add::add(const ex & lh, const ex & rh)
  55 {
  56         tinfo_key = TINFO_add;
  57         overall_coeff = _ex0;
  58         construct_from_2_ex(lh,rh);
  59         GINAC_ASSERT(is_canonical());
  60 }
  61
  62 add::add(const exvector & v)
  63 {
  64         tinfo_key = TINFO_add;
  65         overall_coeff = _ex0;
  66         construct_from_exvector(v);
  67         GINAC_ASSERT(is_canonical());
  68 }
  69
  70 add::add(const epvector & v)
  71 {
  72         tinfo_key = TINFO_add;
  73         overall_coeff = _ex0;
  74         construct_from_epvector(v);
  75         GINAC_ASSERT(is_canonical());
  76 }
  77
  78 add::add(const epvector & v, const ex & oc)
  79 {
  80         tinfo_key = TINFO_add;
  81         overall_coeff = oc;
  82         construct_from_epvector(v);
  83         GINAC_ASSERT(is_canonical());
  84 }
  85
  86 add::add(epvector * vp, const ex & oc)
  87 {
  88         tinfo_key = TINFO_add;
  89         GINAC_ASSERT(vp!=0);
  90         overall_coeff = oc;
  91         construct_from_epvector(*vp);
  92         delete vp;
  93         GINAC_ASSERT(is_canonical());
  94 }
  95
  96 //////////
  97 // archiving
  98 //////////
  99
 100 DEFAULT_ARCHIVING(add)
 101
 102 //////////
 103 // functions overriding virtual functions from base classes
 104 //////////
 105
 106 // public
 107
 108 void add::print(const print_context & c, unsigned level) const
 109 {
 110         if (is_a<print_tree>(c)) {
 111
 112                 inherited::print(c, level);
 113
 114         } else if (is_a<print_csrc>(c)) {
 115
 116                 if (precedence() <= level)
 117                         c.s << "(";
 118
 119                 // Print arguments, separated by "+"
 120                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 121                 while (it != itend) {
 122
 123                         // If the coefficient is -1, it is replaced by a single minus sign
 124                         if (it->coeff.is_equal(_ex1)) {
 125                                 it->rest.print(c, precedence());
 126                         } else if (it->coeff.is_equal(_ex_1)) {
 127                                 c.s << "-";
 128                                 it->rest.print(c, precedence());
 129                         } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num1)) {
 130                                 it->rest.print(c, precedence());
 131                                 c.s << "/";
 132                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 133                         } else if (ex_to<numeric>(it->coeff).numer().is_equal(_num_1)) {
 134                                 c.s << "-";
 135                                 it->rest.print(c, precedence());
 136                                 c.s << "/";
 137                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 138                         } else {
 139                                 it->coeff.print(c, precedence());
 140                                 c.s << "*";
 141                                 it->rest.print(c, precedence());
 142                         }
 143
 144                         // Separator is "+", except if the following expression would have a leading minus sign
 145                         ++it;
 146                         if (it != itend && !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative))))
 147                                 c.s << "+";
 148                 }
 149
 150                 if (!overall_coeff.is_zero()) {
 151                         if (overall_coeff.info(info_flags::positive))
 152                                 c.s << '+';
 153                         overall_coeff.print(c, precedence());
 154                 }
 155
 156                 if (precedence() <= level)
 157                         c.s << ")";
 158
 159         } else if (is_a<print_python_repr>(c)) {
 160
 161                 c.s << class_name() << '(';
 162                 op(0).print(c);
 163                 for (unsigned i=1; i<nops(); ++i) {
 164                         c.s << ',';
 165                         op(i).print(c);
 166                 }
 167                 c.s << ')';
 168
 169         } else {
 170
 171                 if (precedence() <= level) {
 172                         if (is_a<print_latex>(c))
 173                                 c.s << "{(";
 174                         else
 175                                 c.s << "(";
 176                 }
 177
 178                 numeric coeff;
 179                 bool first = true;
 180
 181                 // First print the overall numeric coefficient, if present
 182                 if (!overall_coeff.is_zero()) {
 183                         if (!is_a<print_tree>(c))
 184                                 overall_coeff.print(c, 0);
 185                         else
 186                                 overall_coeff.print(c, precedence());
 187                         first = false;
 188                 }
 189
 190                 // Then proceed with the remaining factors
 191                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 192                 while (it != itend) {
 193                         coeff = ex_to<numeric>(it->coeff);
 194                         if (!first) {
 195                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 196                         } else {
 197                                 if (coeff.csgn() == -1) c.s << '-';
 198                                 first = false;
 199                         }
 200                         if (!coeff.is_equal(_num1) &&
 201                             !coeff.is_equal(_num_1)) {
 202                                 if (coeff.is_rational()) {
 203                                         if (coeff.is_negative())
 204                                                 (-coeff).print(c);
 205                                         else
 206                                                 coeff.print(c);
 207                                 } else {
 208                                         if (coeff.csgn() == -1)
 209                                                 (-coeff).print(c, precedence());
 210                                         else
 211                                                 coeff.print(c, precedence());
 212                                 }
 213                                 if (is_a<print_latex>(c))
 214                                         c.s << ' ';
 215                                 else
 216                                         c.s << '*';
 217                         }
 218                         it->rest.print(c, precedence());
 219                         ++it;
 220                 }
 221
 222                 if (precedence() <= level) {
 223                         if (is_a<print_latex>(c))
 224                                 c.s << ")}";
 225                         else
 226                                 c.s << ")";
 227                 }
 228         }
 229 }
 230
 231 bool add::info(unsigned inf) const
 232 {
 233         switch (inf) {
 234                 case info_flags::polynomial:
 235                 case info_flags::integer_polynomial:
 236                 case info_flags::cinteger_polynomial:
 237                 case info_flags::rational_polynomial:
 238                 case info_flags::crational_polynomial:
 239                 case info_flags::rational_function: {
 240                         epvector::const_iterator i = seq.begin(), end = seq.end();
 241                         while (i != end) {
 242                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 243                                         return false;
 244                                 ++i;
 245                         }
 246                         return overall_coeff.info(inf);
 247                 }
 248                 case info_flags::algebraic: {
 249                         epvector::const_iterator i = seq.begin(), end = seq.end();
 250                         while (i != end) {
 251                                 if ((recombine_pair_to_ex(*i).info(inf)))
 252                                         return true;
 253                                 ++i;
 254                         }
 255                         return false;
 256                 }
 257         }
 258         return inherited::info(inf);
 259 }
 260
 261 int add::degree(const ex & s) const
 262 {
 263         int deg = INT_MIN;
 264         if (!overall_coeff.is_zero())
 265                 deg = 0;
 266
 267         // Find maximum of degrees of individual terms
 268         epvector::const_iterator i = seq.begin(), end = seq.end();
 269         while (i != end) {
 270                 int cur_deg = i->rest.degree(s);
 271                 if (cur_deg > deg)
 272                         deg = cur_deg;
 273                 ++i;
 274         }
 275         return deg;
 276 }
 277
 278 int add::ldegree(const ex & s) const
 279 {
 280         int deg = INT_MAX;
 281         if (!overall_coeff.is_zero())
 282                 deg = 0;
 283
 284         // Find minimum of degrees of individual terms
 285         epvector::const_iterator i = seq.begin(), end = seq.end();
 286         while (i != end) {
 287                 int cur_deg = i->rest.ldegree(s);
 288                 if (cur_deg < deg)
 289                         deg = cur_deg;
 290                 ++i;
 291         }
 292         return deg;
 293 }
 294
 295 ex add::coeff(const ex & s, int n) const
 296 {
 297         epvector *coeffseq = new epvector();
 298
 299         // Calculate sum of coefficients in each term
 300         epvector::const_iterator i = seq.begin(), end = seq.end();
 301         while (i != end) {
 302                 ex restcoeff = i->rest.coeff(s, n);
 303                 if (!restcoeff.is_zero())
 304                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 305                 ++i;
 306         }
 307
 308         return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 309 }
 310
 311 /** Perform automatic term rewriting rules in this class.  In the following
 312  *  x stands for a symbolic variables of type ex and c stands for such
 313  *  an expression that contain a plain number.
 314  *  - +(;c) -> c
 315  *  - +(x;1) -> x
 316  *
 317  *  @param level cut-off in recursive evaluation */
 318 ex add::eval(int level) const
 319 {
 320         epvector *evaled_seqp = evalchildren(level);
 321         if (evaled_seqp) {
 322                 // do more evaluation later
 323                 return (new add(evaled_seqp, overall_coeff))->
 324                        setflag(status_flags::dynallocated);
 325         }
 326
 327 #ifdef DO_GINAC_ASSERT
 328         epvector::const_iterator i = seq.begin(), end = seq.end();
 329         while (i != end) {
 330                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 331                 if (is_ex_exactly_of_type(i->rest,numeric))
 332                         dbgprint();
 333                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 334                 ++i;
 335         }
 336 #endif // def DO_GINAC_ASSERT
 337
 338         if (flags & status_flags::evaluated) {
 339                 GINAC_ASSERT(seq.size()>0);
 340                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 341                 return *this;
 342         }
 343
 344         int seq_size = seq.size();
 345         if (seq_size == 0) {
 346                 // +(;c) -> c
 347                 return overall_coeff;
 348         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 349                 // +(x;0) -> x
 350                 return recombine_pair_to_ex(*(seq.begin()));
 351         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 352                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 353         }
 354         return this->hold();
 355 }
 356
 357 ex add::evalm(void) const
 358 {
 359         // Evaluate children first and add up all matrices. Stop if there's one
 360         // term that is not a matrix.
 361         epvector *s = new epvector;
 362         s->reserve(seq.size());
 363
 364         bool all_matrices = true;
 365         bool first_term = true;
 366         matrix sum;
 367
 368         epvector::const_iterator it = seq.begin(), itend = seq.end();
 369         while (it != itend) {
 370                 const ex &m = recombine_pair_to_ex(*it).evalm();
 371                 s->push_back(split_ex_to_pair(m));
 372                 if (is_ex_of_type(m, matrix)) {
 373                         if (first_term) {
 374                                 sum = ex_to<matrix>(m);
 375                                 first_term = false;
 376                         } else
 377                                 sum = sum.add(ex_to<matrix>(m));
 378                 } else
 379                         all_matrices = false;
 380                 ++it;
 381         }
 382
 383         if (all_matrices) {
 384                 delete s;
 385                 return sum + overall_coeff;
 386         } else
 387                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 388 }
 389
 390 ex add::simplify_ncmul(const exvector & v) const
 391 {
 392         if (seq.empty())
 393                 return inherited::simplify_ncmul(v);
 394         else
 395                 return seq.begin()->rest.simplify_ncmul(v);
 396 }
 397
 398 // protected
 399
 400 /** Implementation of ex::diff() for a sum. It differentiates each term.
 401  *  @see ex::diff */
 402 ex add::derivative(const symbol & y) const
 403 {
 404         epvector *s = new epvector();
 405         s->reserve(seq.size());
 406
 407         // Only differentiate the "rest" parts of the expairs. This is faster
 408         // than the default implementation in basic::derivative() although
 409         // if performs the same function (differentiate each term).
 410         epvector::const_iterator i = seq.begin(), end = seq.end();
 411         while (i != end) {
 412                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 413                 ++i;
 414         }
 415         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 416 }
 417
 418 int add::compare_same_type(const basic & other) const
 419 {
 420         return inherited::compare_same_type(other);
 421 }
 422
 423 bool add::is_equal_same_type(const basic & other) const
 424 {
 425         return inherited::is_equal_same_type(other);
 426 }
 427
 428 unsigned add::return_type(void) const
 429 {
 430         if (seq.empty())
 431                 return return_types::commutative;
 432         else
 433                 return seq.begin()->rest.return_type();
 434 }
 435
 436 unsigned add::return_type_tinfo(void) const
 437 {
 438         if (seq.empty())
 439                 return tinfo_key;
 440         else
 441                 return seq.begin()->rest.return_type_tinfo();
 442 }
 443
 444 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 445 {
 446         return (new add(v,oc))->setflag(status_flags::dynallocated);
 447 }
 448
 449 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 450 {
 451         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 452 }
 453
 454 expair add::split_ex_to_pair(const ex & e) const
 455 {
 456         if (is_ex_exactly_of_type(e,mul)) {
 457                 const mul &mulref(ex_to<mul>(e));
 458                 const ex &numfactor = mulref.overall_coeff;
 459                 mul *mulcopyp = new mul(mulref);
 460                 mulcopyp->overall_coeff = _ex1;
 461                 mulcopyp->clearflag(status_flags::evaluated);
 462                 mulcopyp->clearflag(status_flags::hash_calculated);
 463                 mulcopyp->setflag(status_flags::dynallocated);
 464                 return expair(*mulcopyp,numfactor);
 465         }
 466         return expair(e,_ex1);
 467 }
 468
 469 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 470                                                                                   const ex & c) const
 471 {
 472         GINAC_ASSERT(is_exactly_a<numeric>(c));
 473         if (is_ex_exactly_of_type(e, mul)) {
 474                 const mul &mulref(ex_to<mul>(e));
 475                 const ex &numfactor = mulref.overall_coeff;
 476                 mul *mulcopyp = new mul(mulref);
 477                 mulcopyp->overall_coeff = _ex1;
 478                 mulcopyp->clearflag(status_flags::evaluated);
 479                 mulcopyp->clearflag(status_flags::hash_calculated);
 480                 mulcopyp->setflag(status_flags::dynallocated);
 481                 if (are_ex_trivially_equal(c, _ex1))
 482                         return expair(*mulcopyp, numfactor);
 483                 else if (are_ex_trivially_equal(numfactor, _ex1))
 484                         return expair(*mulcopyp, c);
 485                 else
 486                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 487         } else if (is_ex_exactly_of_type(e, numeric)) {
 488                 if (are_ex_trivially_equal(c, _ex1))
 489                         return expair(e, _ex1);
 490                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 491         }
 492         return expair(e, c);
 493 }
 494
 495 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 496                                                                                         const ex & c) const
 497 {
 498         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 499         GINAC_ASSERT(is_exactly_a<numeric>(c));
 500
 501         if (is_ex_exactly_of_type(p.rest,numeric)) {
 502                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
 503                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 504         }
 505
 506         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 507 }
 508
 509 ex add::recombine_pair_to_ex(const expair & p) const
 510 {
 511         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 512                 return p.rest;
 513         else
 514                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 515 }
 516
 517 ex add::expand(unsigned options) const
 518 {
 519         epvector *vp = expandchildren(options);
 520         if (vp == NULL) {
 521                 // the terms have not changed, so it is safe to declare this expanded
 522                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 523         }
 524
 525         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 526 }
 527
 528 } // namespace GiNaC