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 "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)  // 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                                 c.s << '+';
 156                         overall_coeff.print(c, precedence());
 157                 }
 158
 159                 if (precedence() <= level)
 160                         c.s << ")";
 161
 162         } else if (is_a<print_python_repr>(c)) {
 163
 164                 c.s << class_name() << '(';
 165                 op(0).print(c);
 166                 for (unsigned i=1; i<nops(); ++i) {
 167                         c.s << ',';
 168                         op(i).print(c);
 169                 }
 170                 c.s << ')';
 171
 172         } else {
 173
 174                 if (precedence() <= level) {
 175                         if (is_a<print_latex>(c))
 176                                 c.s << "{(";
 177                         else
 178                                 c.s << "(";
 179                 }
 180
 181                 numeric coeff;
 182                 bool first = true;
 183
 184                 // First print the overall numeric coefficient, if present
 185                 if (!overall_coeff.is_zero()) {
 186                         if (!is_a<print_tree>(c))
 187                                 overall_coeff.print(c, 0);
 188                         else
 189                                 overall_coeff.print(c, precedence());
 190                         first = false;
 191                 }
 192
 193                 // Then proceed with the remaining factors
 194                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 195                 while (it != itend) {
 196                         coeff = ex_to<numeric>(it->coeff);
 197                         if (!first) {
 198                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 199                         } else {
 200                                 if (coeff.csgn() == -1) c.s << '-';
 201                                 first = false;
 202                         }
 203                         if (!coeff.is_equal(_num1) &&
 204                             !coeff.is_equal(_num_1)) {
 205                                 if (coeff.is_rational()) {
 206                                         if (coeff.is_negative())
 207                                                 (-coeff).print(c);
 208                                         else
 209                                                 coeff.print(c);
 210                                 } else {
 211                                         if (coeff.csgn() == -1)
 212                                                 (-coeff).print(c, precedence());
 213                                         else
 214                                                 coeff.print(c, precedence());
 215                                 }
 216                                 if (is_a<print_latex>(c))
 217                                         c.s << ' ';
 218                                 else
 219                                         c.s << '*';
 220                         }
 221                         it->rest.print(c, precedence());
 222                         ++it;
 223                 }
 224
 225                 if (precedence() <= level) {
 226                         if (is_a<print_latex>(c))
 227                                 c.s << ")}";
 228                         else
 229                                 c.s << ")";
 230                 }
 231         }
 232 }
 233
 234 bool add::info(unsigned inf) const
 235 {
 236         switch (inf) {
 237                 case info_flags::polynomial:
 238                 case info_flags::integer_polynomial:
 239                 case info_flags::cinteger_polynomial:
 240                 case info_flags::rational_polynomial:
 241                 case info_flags::crational_polynomial:
 242                 case info_flags::rational_function: {
 243                         epvector::const_iterator i = seq.begin(), end = seq.end();
 244                         while (i != end) {
 245                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 246                                         return false;
 247                                 ++i;
 248                         }
 249                         return overall_coeff.info(inf);
 250                 }
 251                 case info_flags::algebraic: {
 252                         epvector::const_iterator i = seq.begin(), end = seq.end();
 253                         while (i != end) {
 254                                 if ((recombine_pair_to_ex(*i).info(inf)))
 255                                         return true;
 256                                 ++i;
 257                         }
 258                         return false;
 259                 }
 260         }
 261         return inherited::info(inf);
 262 }
 263
 264 int add::degree(const ex & s) const
 265 {
 266         int deg = INT_MIN;
 267         if (!overall_coeff.is_zero())
 268                 deg = 0;
 269
 270         // Find maximum of degrees of individual terms
 271         epvector::const_iterator i = seq.begin(), end = seq.end();
 272         while (i != end) {
 273                 int cur_deg = i->rest.degree(s);
 274                 if (cur_deg > deg)
 275                         deg = cur_deg;
 276                 ++i;
 277         }
 278         return deg;
 279 }
 280
 281 int add::ldegree(const ex & s) const
 282 {
 283         int deg = INT_MAX;
 284         if (!overall_coeff.is_zero())
 285                 deg = 0;
 286
 287         // Find minimum of degrees of individual terms
 288         epvector::const_iterator i = seq.begin(), end = seq.end();
 289         while (i != end) {
 290                 int cur_deg = i->rest.ldegree(s);
 291                 if (cur_deg < deg)
 292                         deg = cur_deg;
 293                 ++i;
 294         }
 295         return deg;
 296 }
 297
 298 ex add::coeff(const ex & s, int n) const
 299 {
 300         epvector *coeffseq = new epvector();
 301
 302         // Calculate sum of coefficients in each term
 303         epvector::const_iterator i = seq.begin(), end = seq.end();
 304         while (i != end) {
 305                 ex restcoeff = i->rest.coeff(s, n);
 306                 if (!restcoeff.is_zero())
 307                         coeffseq->push_back(combine_ex_with_coeff_to_pair(restcoeff, i->coeff));
 308                 ++i;
 309         }
 310
 311         return (new add(coeffseq, n==0 ? overall_coeff : _ex0))->setflag(status_flags::dynallocated);
 312 }
 313
 314 /** Perform automatic term rewriting rules in this class.  In the following
 315  *  x stands for a symbolic variables of type ex and c stands for such
 316  *  an expression that contain a plain number.
 317  *  - +(;c) -> c
 318  *  - +(x;1) -> x
 319  *
 320  *  @param level cut-off in recursive evaluation */
 321 ex add::eval(int level) const
 322 {
 323         epvector *evaled_seqp = evalchildren(level);
 324         if (evaled_seqp) {
 325                 // do more evaluation later
 326                 return (new add(evaled_seqp, overall_coeff))->
 327                        setflag(status_flags::dynallocated);
 328         }
 329
 330 #ifdef DO_GINAC_ASSERT
 331         epvector::const_iterator i = seq.begin(), end = seq.end();
 332         while (i != end) {
 333                 GINAC_ASSERT(!is_exactly_a<add>(i->rest));
 334                 if (is_exactly_a<numeric>(i->rest))
 335                         dbgprint();
 336                 GINAC_ASSERT(!is_exactly_a<numeric>(i->rest));
 337                 ++i;
 338         }
 339 #endif // def DO_GINAC_ASSERT
 340
 341         if (flags & status_flags::evaluated) {
 342                 GINAC_ASSERT(seq.size()>0);
 343                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 344                 return *this;
 345         }
 346
 347         int seq_size = seq.size();
 348         if (seq_size == 0) {
 349                 // +(;c) -> c
 350                 return overall_coeff;
 351         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 352                 // +(x;0) -> x
 353                 return recombine_pair_to_ex(*(seq.begin()));
 354         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 355                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 356         }
 357         return this->hold();
 358 }
 359
 360 ex add::evalm(void) const
 361 {
 362         // Evaluate children first and add up all matrices. Stop if there's one
 363         // term that is not a matrix.
 364         epvector *s = new epvector;
 365         s->reserve(seq.size());
 366
 367         bool all_matrices = true;
 368         bool first_term = true;
 369         matrix sum;
 370
 371         epvector::const_iterator it = seq.begin(), itend = seq.end();
 372         while (it != itend) {
 373                 const ex &m = recombine_pair_to_ex(*it).evalm();
 374                 s->push_back(split_ex_to_pair(m));
 375                 if (is_a<matrix>(m)) {
 376                         if (first_term) {
 377                                 sum = ex_to<matrix>(m);
 378                                 first_term = false;
 379                         } else
 380                                 sum = sum.add(ex_to<matrix>(m));
 381                 } else
 382                         all_matrices = false;
 383                 ++it;
 384         }
 385
 386         if (all_matrices) {
 387                 delete s;
 388                 return sum + overall_coeff;
 389         } else
 390                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 391 }
 392
 393 ex add::simplify_ncmul(const exvector & v) const
 394 {
 395         if (seq.empty())
 396                 return inherited::simplify_ncmul(v);
 397         else
 398                 return seq.begin()->rest.simplify_ncmul(v);
 399 }
 400
 401 // protected
 402
 403 /** Implementation of ex::diff() for a sum. It differentiates each term.
 404  *  @see ex::diff */
 405 ex add::derivative(const symbol & y) const
 406 {
 407         epvector *s = new epvector();
 408         s->reserve(seq.size());
 409
 410         // Only differentiate the "rest" parts of the expairs. This is faster
 411         // than the default implementation in basic::derivative() although
 412         // if performs the same function (differentiate each term).
 413         epvector::const_iterator i = seq.begin(), end = seq.end();
 414         while (i != end) {
 415                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.diff(y), i->coeff));
 416                 ++i;
 417         }
 418         return (new add(s, _ex0))->setflag(status_flags::dynallocated);
 419 }
 420
 421 int add::compare_same_type(const basic & other) const
 422 {
 423         return inherited::compare_same_type(other);
 424 }
 425
 426 unsigned add::return_type(void) const
 427 {
 428         if (seq.empty())
 429                 return return_types::commutative;
 430         else
 431                 return seq.begin()->rest.return_type();
 432 }
 433
 434 unsigned add::return_type_tinfo(void) const
 435 {
 436         if (seq.empty())
 437                 return tinfo_key;
 438         else
 439                 return seq.begin()->rest.return_type_tinfo();
 440 }
 441
 442 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 443 {
 444         return (new add(v,oc))->setflag(status_flags::dynallocated);
 445 }
 446
 447 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 448 {
 449         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 450 }
 451
 452 expair add::split_ex_to_pair(const ex & e) const
 453 {
 454         if (is_exactly_a<mul>(e)) {
 455                 const mul &mulref(ex_to<mul>(e));
 456                 const ex &numfactor = mulref.overall_coeff;
 457                 mul *mulcopyp = new mul(mulref);
 458                 mulcopyp->overall_coeff = _ex1;
 459                 mulcopyp->clearflag(status_flags::evaluated);
 460                 mulcopyp->clearflag(status_flags::hash_calculated);
 461                 mulcopyp->setflag(status_flags::dynallocated);
 462                 return expair(*mulcopyp,numfactor);
 463         }
 464         return expair(e,_ex1);
 465 }
 466
 467 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 468                                                                                   const ex & c) const
 469 {
 470         GINAC_ASSERT(is_exactly_a<numeric>(c));
 471         if (is_exactly_a<mul>(e)) {
 472                 const mul &mulref(ex_to<mul>(e));
 473                 const ex &numfactor = mulref.overall_coeff;
 474                 mul *mulcopyp = new mul(mulref);
 475                 mulcopyp->overall_coeff = _ex1;
 476                 mulcopyp->clearflag(status_flags::evaluated);
 477                 mulcopyp->clearflag(status_flags::hash_calculated);
 478                 mulcopyp->setflag(status_flags::dynallocated);
 479                 if (c.is_equal(_ex1))
 480                         return expair(*mulcopyp, numfactor);
 481                 else if (numfactor.is_equal(_ex1))
 482                         return expair(*mulcopyp, c);
 483                 else
 484                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 485         } else if (is_exactly_a<numeric>(e)) {
 486                 if (c.is_equal(_ex1))
 487                         return expair(e, _ex1);
 488                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 489         }
 490         return expair(e, c);
 491 }
 492
 493 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 494                                                                                         const ex & c) const
 495 {
 496         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 497         GINAC_ASSERT(is_exactly_a<numeric>(c));
 498
 499         if (is_exactly_a<numeric>(p.rest)) {
 500                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1)); // should be normalized
 501                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 502         }
 503
 504         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 505 }
 506
 507 ex add::recombine_pair_to_ex(const expair & p) const
 508 {
 509         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 510                 return p.rest;
 511         else
 512                 return (new mul(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 513 }
 514
 515 ex add::expand(unsigned options) const
 516 {
 517         epvector *vp = expandchildren(options);
 518         if (vp == NULL) {
 519                 // the terms have not changed, so it is safe to declare this expanded
 520                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 521         }
 522
 523         return (new add(vp, overall_coeff))->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 524 }
 525
 526 } // namespace GiNaC