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 or the sign is sitting in parenthesis (as in a ctor)
 145                         ++it;
 146                         if (it != itend
 147                                 && (is_a<print_csrc_cl_N>(c)  // sign inside ctor arguments
 148                                         || !(it->coeff.info(info_flags::negative) || (it->coeff.is_equal(_num1) && is_exactly_a<numeric>(it->rest) && it->rest.info(info_flags::negative)))))
 149                                 c.s << "+";
 150                 }
 151
 152                 if (!overall_coeff.is_zero()) {
 153                         if (overall_coeff.info(info_flags::positive))
 154                                 c.s << '+';
 155                         overall_coeff.print(c, precedence());
 156                 }
 157
 158                 if (precedence() <= level)
 159                         c.s << ")";
 160
 161         } else if (is_a<print_python_repr>(c)) {
 162
 163                 c.s << class_name() << '(';
 164                 op(0).print(c);
 165                 for (unsigned i=1; i<nops(); ++i) {
 166                         c.s << ',';
 167                         op(i).print(c);
 168                 }
 169                 c.s << ')';
 170
 171         } else {
 172
 173                 if (precedence() <= level) {
 174                         if (is_a<print_latex>(c))
 175                                 c.s << "{(";
 176                         else
 177                                 c.s << "(";
 178                 }
 179
 180                 numeric coeff;
 181                 bool first = true;
 182
 183                 // First print the overall numeric coefficient, if present
 184                 if (!overall_coeff.is_zero()) {
 185                         if (!is_a<print_tree>(c))
 186                                 overall_coeff.print(c, 0);
 187                         else
 188                                 overall_coeff.print(c, precedence());
 189                         first = false;
 190                 }
 191
 192                 // Then proceed with the remaining factors
 193                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 194                 while (it != itend) {
 195                         coeff = ex_to<numeric>(it->coeff);
 196                         if (!first) {
 197                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 198                         } else {
 199                                 if (coeff.csgn() == -1) c.s << '-';
 200                                 first = false;
 201                         }
 202                         if (!coeff.is_equal(_num1) &&
 203                             !coeff.is_equal(_num_1)) {
 204                                 if (coeff.is_rational()) {
 205                                         if (coeff.is_negative())
 206                                                 (-coeff).print(c);
 207                                         else
 208                                                 coeff.print(c);
 209                                 } else {
 210                                         if (coeff.csgn() == -1)
 211                                                 (-coeff).print(c, precedence());
 212                                         else
 213                                                 coeff.print(c, precedence());
 214                                 }
 215                                 if (is_a<print_latex>(c))
 216                                         c.s << ' ';
 217                                 else
 218                                         c.s << '*';
 219                         }
 220                         it->rest.print(c, precedence());
 221                         ++it;
 222                 }
 223
 224                 if (precedence() <= level) {
 225                         if (is_a<print_latex>(c))
 226                                 c.s << ")}";
 227                         else
 228                                 c.s << ")";
 229                 }
 230         }
 231 }
 232
 233 bool add::info(unsigned inf) const
 234 {
 235         switch (inf) {
 236                 case info_flags::polynomial:
 237                 case info_flags::integer_polynomial:
 238                 case info_flags::cinteger_polynomial:
 239                 case info_flags::rational_polynomial:
 240                 case info_flags::crational_polynomial:
 241                 case info_flags::rational_function: {
 242                         epvector::const_iterator i = seq.begin(), end = seq.end();
 243                         while (i != end) {
 244                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 245                                         return false;
 246                                 ++i;
 247                         }
 248                         return overall_coeff.info(inf);
 249                 }
 250                 case info_flags::algebraic: {
 251                         epvector::const_iterator i = seq.begin(), end = seq.end();
 252                         while (i != end) {
 253                                 if ((recombine_pair_to_ex(*i).info(inf)))
 254                                         return true;
 255                                 ++i;
 256                         }
 257                         return false;
 258                 }
 259         }
 260         return inherited::info(inf);
 261 }
 262
 263 int add::degree(const ex & s) const
 264 {
 265         int deg = INT_MIN;
 266         if (!overall_coeff.is_zero())
 267                 deg = 0;
 268
 269         // Find maximum of degrees of individual terms
 270         epvector::const_iterator i = seq.begin(), end = seq.end();
 271         while (i != end) {
 272                 int cur_deg = i->rest.degree(s);
 273                 if (cur_deg > deg)
 274                         deg = cur_deg;
 275                 ++i;
 276         }
 277         return deg;
 278 }
 279
 280 int add::ldegree(const ex & s) const
 281 {
 282         int deg = INT_MAX;
 283         if (!overall_coeff.is_zero())
 284                 deg = 0;
 285
 286         // Find minimum of degrees of individual terms
 287         epvector::const_iterator i = seq.begin(), end = seq.end();
 288         while (i != end) {
 289                 int cur_deg = i->rest.ldegree(s);
 290                 if (cur_deg < deg)
 291                         deg = cur_deg;
 292                 ++i;
 293         }
 294         return deg;
 295 }
 296
 297 ex add::coeff(const ex & s, int n) const
 298 {
 299         epvector *coeffseq = new epvector();
 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                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 307                 ++i;
 308         }
 309
 310         return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 311 }
 312
 313 /** Perform automatic term rewriting rules in this class.  In the following
 314  *  x stands for a symbolic variables of type ex and c stands for such
 315  *  an expression that contain a plain number.
 316  *  - +(;c) -> c
 317  *  - +(x;1) -> x
 318  *
 319  *  @param level cut-off in recursive evaluation */
 320 ex add::eval(int level) const
 321 {
 322         epvector *evaled_seqp = evalchildren(level);
 323         if (evaled_seqp) {
 324                 // do more evaluation later
 325                 return (new add(evaled_seqp, overall_coeff))->
 326                        setflag(status_flags::dynallocated);
 327         }
 328
 329 #ifdef DO_GINAC_ASSERT
 330         epvector::const_iterator i = seq.begin(), end = seq.end();
 331         while (i != end) {
 332                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 333                 if (is_ex_exactly_of_type(i->rest,numeric))
 334                         dbgprint();
 335                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 336                 ++i;
 337         }
 338 #endif // def DO_GINAC_ASSERT
 339
 340         if (flags & status_flags::evaluated) {
 341                 GINAC_ASSERT(seq.size()>0);
 342                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 343                 return *this;
 344         }
 345
 346         int seq_size = seq.size();
 347         if (seq_size == 0) {
 348                 // +(;c) -> c
 349                 return overall_coeff;
 350         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 351                 // +(x;0) -> x
 352                 return recombine_pair_to_ex(*(seq.begin()));
 353         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 354                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 355         }
 356         return this->hold();
 357 }
 358
 359 ex add::evalm(void) const
 360 {
 361         // Evaluate children first and add up all matrices. Stop if there's one
 362         // term that is not a matrix.
 363         epvector *s = new epvector;
 364         s->reserve(seq.size());
 365
 366         bool all_matrices = true;
 367         bool first_term = true;
 368         matrix sum;
 369
 370         epvector::const_iterator it = seq.begin(), itend = seq.end();
 371         while (it != itend) {
 372                 const ex &m = recombine_pair_to_ex(*it).evalm();
 373                 s->push_back(split_ex_to_pair(m));
 374                 if (is_ex_of_type(m, matrix)) {
 375                         if (first_term) {
 376                                 sum = ex_to<matrix>(m);
 377                                 first_term = false;
 378                         } else
 379                                 sum = sum.add(ex_to<matrix>(m));
 380                 } else
 381                         all_matrices = false;
 382                 ++it;
 383         }
 384
 385         if (all_matrices) {
 386                 delete s;
 387                 return sum + overall_coeff;
 388         } else
 389                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 390 }
 391
 392 ex add::simplify_ncmul(const exvector & v) const
 393 {
 394         if (seq.empty())
 395                 return inherited::simplify_ncmul(v);
 396         else
 397                 return seq.begin()->rest.simplify_ncmul(v);
 398 }
 399
 400 // protected
 401
 402 /** Implementation of ex::diff() for a sum. It differentiates each term.
 403  *  @see ex::diff */
 404 ex add::derivative(const symbol & y) const
 405 {
 406         epvector *s = new epvector();
 407         s->reserve(seq.size());
 408
 409         // Only differentiate the "rest" parts of the expairs. This is faster
 410         // than the default implementation in basic::derivative() although
 411         // if performs the same function (differentiate each term).
 412         epvector::const_iterator i = seq.begin(), end = seq.end();
 413         while (i != end) {
 414                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 415                 ++i;
 416         }
 417         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 418 }
 419
 420 int add::compare_same_type(const basic & other) const
 421 {
 422         return inherited::compare_same_type(other);
 423 }
 424
 425 bool add::is_equal_same_type(const basic & other) const
 426 {
 427         return inherited::is_equal_same_type(other);
 428 }
 429
 430 unsigned add::return_type(void) const
 431 {
 432         if (seq.empty())
 433                 return return_types::commutative;
 434         else
 435                 return seq.begin()->rest.return_type();
 436 }
 437
 438 unsigned add::return_type_tinfo(void) const
 439 {
 440         if (seq.empty())
 441                 return tinfo_key;
 442         else
 443                 return seq.begin()->rest.return_type_tinfo();
 444 }
 445
 446 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 447 {
 448         return (new add(v,oc))->setflag(status_flags::dynallocated);
 449 }
 450
 451 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 452 {
 453         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 454 }
 455
 456 expair add::split_ex_to_pair(const ex & e) const
 457 {
 458         if (is_ex_exactly_of_type(e,mul)) {
 459                 const mul &mulref(ex_to<mul>(e));
 460                 const ex &numfactor = mulref.overall_coeff;
 461                 mul *mulcopyp = new mul(mulref);
 462                 mulcopyp->overall_coeff = _ex1;
 463                 mulcopyp->clearflag(status_flags::evaluated);
 464                 mulcopyp->clearflag(status_flags::hash_calculated);
 465                 mulcopyp->setflag(status_flags::dynallocated);
 466                 return expair(*mulcopyp,numfactor);
 467         }
 468         return expair(e,_ex1);
 469 }
 470
 471 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 472                                                                                   const ex & c) const
 473 {
 474         GINAC_ASSERT(is_exactly_a<numeric>(c));
 475         if (is_ex_exactly_of_type(e, mul)) {
 476                 const mul &mulref(ex_to<mul>(e));
 477                 const ex &numfactor = mulref.overall_coeff;
 478                 mul *mulcopyp = new mul(mulref);
 479                 mulcopyp->overall_coeff = _ex1;
 480                 mulcopyp->clearflag(status_flags::evaluated);
 481                 mulcopyp->clearflag(status_flags::hash_calculated);
 482                 mulcopyp->setflag(status_flags::dynallocated);
 483                 if (are_ex_trivially_equal(c, _ex1))
 484                         return expair(*mulcopyp, numfactor);
 485                 else if (are_ex_trivially_equal(numfactor, _ex1))
 486                         return expair(*mulcopyp, c);
 487                 else
 488                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 489         } else if (is_ex_exactly_of_type(e, numeric)) {
 490                 if (are_ex_trivially_equal(c, _ex1))
 491                         return expair(e, _ex1);
 492                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 493         }
 494         return expair(e, c);
 495 }
 496
 497 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 498                                                                                         const ex & c) const
 499 {
 500         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 501         GINAC_ASSERT(is_exactly_a<numeric>(c));
 502
 503         if (is_ex_exactly_of_type(p.rest,numeric)) {
 504                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
 505                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 506         }
 507
 508         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 509 }
 510
 511 ex add::recombine_pair_to_ex(const expair & p) const
 512 {
 513         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 514                 return p.rest;
 515         else
 516                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 517 }
 518
 519 ex add::expand(unsigned options) const
 520 {
 521         epvector *vp = expandchildren(options);
 522         if (vp == NULL) {
 523                 // the terms have not changed, so it is safe to declare this expanded
 524                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 525         }
 526
 527         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 528 }
 529
 530 } // namespace GiNaC