ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2001 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 "debugmsg.h"
  31 #include "utils.h"
  32
  33 namespace GiNaC {
  34
  35 GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
  36
  37 //////////
  38 // default constructor, destructor, copy constructor assignment operator and helpers
  39 //////////
  40
  41 add::add()
  42 {
  43         debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
  44         tinfo_key = TINFO_add;
  45 }
  46
  47 DEFAULT_COPY(add)
  48 DEFAULT_DESTROY(add)
  49
  50 //////////
  51 // other constructors
  52 //////////
  53
  54 // public
  55
  56 add::add(const ex & lh, const ex & rh)
  57 {
  58         debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  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         debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
  68         tinfo_key = TINFO_add;
  69         overall_coeff = _ex0();
  70         construct_from_exvector(v);
  71         GINAC_ASSERT(is_canonical());
  72 }
  73
  74 add::add(const epvector & v)
  75 {
  76         debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
  77         tinfo_key = TINFO_add;
  78         overall_coeff = _ex0();
  79         construct_from_epvector(v);
  80         GINAC_ASSERT(is_canonical());
  81 }
  82
  83 add::add(const epvector & v, const ex & oc)
  84 {
  85         debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
  86         tinfo_key = TINFO_add;
  87         overall_coeff = oc;
  88         construct_from_epvector(v);
  89         GINAC_ASSERT(is_canonical());
  90 }
  91
  92 add::add(epvector * vp, const ex & oc)
  93 {
  94         debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
  95         tinfo_key = TINFO_add;
  96         GINAC_ASSERT(vp!=0);
  97         overall_coeff = oc;
  98         construct_from_epvector(*vp);
  99         delete vp;
 100         GINAC_ASSERT(is_canonical());
 101 }
 102
 103 //////////
 104 // archiving
 105 //////////
 106
 107 DEFAULT_ARCHIVING(add)
 108
 109 //////////
 110 // functions overriding virtual functions from bases classes
 111 //////////
 112
 113 // public
 114
 115 void add::print(const print_context & c, unsigned level) const
 116 {
 117         debugmsg("add print", LOGLEVEL_PRINT);
 118
 119         if (is_a<print_tree>(c)) {
 120
 121                 inherited::print(c, level);
 122
 123         } else if (is_a<print_csrc>(c)) {
 124
 125                 if (precedence() <= level)
 126                         c.s << "(";
 127
 128                 // Print arguments, separated by "+"
 129                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 130                 while (it != itend) {
 131
 132                         // If the coefficient is -1, it is replaced by a single minus sign
 133                         if (it->coeff.compare(_num1()) == 0) {
 134                                 it->rest.bp->print(c, precedence());
 135                         } else if (it->coeff.compare(_num_1()) == 0) {
 136                                 c.s << "-";
 137                                 it->rest.bp->print(c, precedence());
 138                         } else if (ex_to<numeric>(it->coeff).numer().compare(_num1()) == 0) {
 139                                 it->rest.bp->print(c, precedence());
 140                                 c.s << "/";
 141                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 142                         } else if (ex_to<numeric>(it->coeff).numer().compare(_num_1()) == 0) {
 143                                 c.s << "-";
 144                                 it->rest.bp->print(c, precedence());
 145                                 c.s << "/";
 146                                 ex_to<numeric>(it->coeff).denom().print(c, precedence());
 147                         } else {
 148                                 it->coeff.bp->print(c, precedence());
 149                                 c.s << "*";
 150                                 it->rest.bp->print(c, precedence());
 151                         }
 152
 153                         // Separator is "+", except if the following expression would have a leading minus sign
 154                         it++;
 155                         if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_exactly_a<numeric>(it->rest) && it->rest.compare(_num0()) < 0)))
 156                                 c.s << "+";
 157                 }
 158
 159                 if (!overall_coeff.is_zero()) {
 160                         if (overall_coeff.info(info_flags::positive))
 161                                 c.s << '+';
 162                         overall_coeff.bp->print(c, precedence());
 163                 }
 164
 165                 if (precedence() <= level)
 166                         c.s << ")";
 167
 168         } else {
 169
 170                 if (precedence() <= level) {
 171                         if (is_a<print_latex>(c))
 172                                 c.s << "{(";
 173                         else
 174                                 c.s << "(";
 175                 }
 176
 177                 numeric coeff;
 178                 bool first = true;
 179
 180                 // First print the overall numeric coefficient, if present
 181                 if (!overall_coeff.is_zero()) {
 182                         if (!is_a<print_tree>(c))
 183                                 overall_coeff.print(c, 0);
 184                         else
 185                                 overall_coeff.print(c, precedence());
 186                         first = false;
 187                 }
 188
 189                 // Then proceed with the remaining factors
 190                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 191                 while (it != itend) {
 192                         coeff = ex_to<numeric>(it->coeff);
 193                         if (!first) {
 194                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 195                         } else {
 196                                 if (coeff.csgn() == -1) c.s << '-';
 197                                 first = false;
 198                         }
 199                         if (!coeff.is_equal(_num1()) &&
 200                             !coeff.is_equal(_num_1())) {
 201                                 if (coeff.is_rational()) {
 202                                         if (coeff.is_negative())
 203                                                 (-coeff).print(c);
 204                                         else
 205                                                 coeff.print(c);
 206                                 } else {
 207                                         if (coeff.csgn() == -1)
 208                                                 (-coeff).print(c, precedence());
 209                                         else
 210                                                 coeff.print(c, precedence());
 211                                 }
 212                                 if (is_a<print_latex>(c))
 213                                         c.s << ' ';
 214                                 else
 215                                         c.s << '*';
 216                         }
 217                         it->rest.print(c, precedence());
 218                         it++;
 219                 }
 220
 221                 if (precedence() <= level) {
 222                         if (is_a<print_latex>(c))
 223                                 c.s << ")}";
 224                         else
 225                                 c.s << ")";
 226                 }
 227         }
 228 }
 229
 230 bool add::info(unsigned inf) const
 231 {
 232         switch (inf) {
 233                 case info_flags::polynomial:
 234                 case info_flags::integer_polynomial:
 235                 case info_flags::cinteger_polynomial:
 236                 case info_flags::rational_polynomial:
 237                 case info_flags::crational_polynomial:
 238                 case info_flags::rational_function: {
 239                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 240                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 241                                         return false;
 242                         }
 243                         return overall_coeff.info(inf);
 244                 }
 245                 case info_flags::algebraic: {
 246                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 247                                 if ((recombine_pair_to_ex(*i).info(inf)))
 248                                         return true;
 249                         }
 250                         return false;
 251                 }
 252         }
 253         return inherited::info(inf);
 254 }
 255
 256 int add::degree(const ex & s) const
 257 {
 258         int deg = INT_MIN;
 259         if (!overall_coeff.is_equal(_ex0()))
 260                 deg = 0;
 261
 262         int cur_deg;
 263         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 264                 cur_deg = (*cit).rest.degree(s);
 265                 if (cur_deg>deg)
 266                         deg = cur_deg;
 267         }
 268         return deg;
 269 }
 270
 271 int add::ldegree(const ex & s) const
 272 {
 273         int deg = INT_MAX;
 274         if (!overall_coeff.is_equal(_ex0()))
 275                 deg = 0;
 276
 277         int cur_deg;
 278         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 279                 cur_deg = (*cit).rest.ldegree(s);
 280                 if (cur_deg<deg) deg=cur_deg;
 281         }
 282         return deg;
 283 }
 284
 285 ex add::coeff(const ex & s, int n) const
 286 {
 287         epvector coeffseq;
 288
 289         epvector::const_iterator it=seq.begin();
 290         while (it!=seq.end()) {
 291                 ex restcoeff = it->rest.coeff(s,n);
 292                 if (!restcoeff.is_zero())
 293                         coeffseq.push_back(combine_ex_with_coeff_to_pair(restcoeff,it->coeff));
 294                 ++it;
 295         }
 296
 297         return (new add(coeffseq, n==0 ? overall_coeff : default_overall_coeff()))->setflag(status_flags::dynallocated);
 298 }
 299
 300 ex add::eval(int level) const
 301 {
 302         // simplifications: +(;c) -> c
 303         //                  +(x;1) -> x
 304
 305         debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
 306
 307         epvector * evaled_seqp = evalchildren(level);
 308         if (evaled_seqp!=0) {
 309                 // do more evaluation later
 310                 return (new add(evaled_seqp,overall_coeff))->
 311                        setflag(status_flags::dynallocated);
 312         }
 313
 314 #ifdef DO_GINAC_ASSERT
 315         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 316                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
 317                 if (is_ex_exactly_of_type((*cit).rest,numeric))
 318                         dbgprint();
 319                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
 320         }
 321 #endif // def DO_GINAC_ASSERT
 322
 323         if (flags & status_flags::evaluated) {
 324                 GINAC_ASSERT(seq.size()>0);
 325                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 326                 return *this;
 327         }
 328
 329         int seq_size = seq.size();
 330         if (seq_size==0) {
 331                 // +(;c) -> c
 332                 return overall_coeff;
 333         } else if ((seq_size==1) && overall_coeff.is_equal(_ex0())) {
 334                 // +(x;0) -> x
 335                 return recombine_pair_to_ex(*(seq.begin()));
 336         }
 337         return this->hold();
 338 }
 339
 340 ex add::evalm(void) const
 341 {
 342         // Evaluate children first and add up all matrices. Stop if there's one
 343         // term that is not a matrix.
 344         epvector *s = new epvector;
 345         s->reserve(seq.size());
 346
 347         bool all_matrices = true;
 348         bool first_term = true;
 349         matrix sum;
 350
 351         epvector::const_iterator it = seq.begin(), itend = seq.end();
 352         while (it != itend) {
 353                 const ex &m = recombine_pair_to_ex(*it).evalm();
 354                 s->push_back(split_ex_to_pair(m));
 355                 if (is_ex_of_type(m, matrix)) {
 356                         if (first_term) {
 357                                 sum = ex_to<matrix>(m);
 358                                 first_term = false;
 359                         } else
 360                                 sum = sum.add(ex_to<matrix>(m));
 361                 } else
 362                         all_matrices = false;
 363                 it++;
 364         }
 365
 366         if (all_matrices)
 367                 return sum + overall_coeff;
 368         else
 369                 return (new add(s, overall_coeff))->setflag(status_flags::dynallocated);
 370 }
 371
 372 ex add::simplify_ncmul(const exvector & v) const
 373 {
 374         if (seq.size()==0) {
 375                 return inherited::simplify_ncmul(v);
 376         }
 377         return (*seq.begin()).rest.simplify_ncmul(v);
 378 }
 379
 380 // protected
 381
 382 /** Implementation of ex::diff() for a sum. It differentiates each term.
 383  *  @see ex::diff */
 384 ex add::derivative(const symbol & y) const
 385 {
 386         epvector *s = new epvector();
 387         s->reserve(seq.size());
 388
 389         // Only differentiate the "rest" parts of the expairs. This is faster
 390         // than the default implementation in basic::derivative() although
 391         // if performs the same function (differentiate each term).
 392         for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 393                 s->push_back(combine_ex_with_coeff_to_pair((*it).rest.diff(y),
 394                                                            (*it).coeff));
 395         }
 396         return (new add(s, _ex0()))->setflag(status_flags::dynallocated);
 397 }
 398
 399 int add::compare_same_type(const basic & other) const
 400 {
 401         return inherited::compare_same_type(other);
 402 }
 403
 404 bool add::is_equal_same_type(const basic & other) const
 405 {
 406         return inherited::is_equal_same_type(other);
 407 }
 408
 409 unsigned add::return_type(void) const
 410 {
 411         if (seq.size()==0) {
 412                 return return_types::commutative;
 413         }
 414         return (*seq.begin()).rest.return_type();
 415 }
 416
 417 unsigned add::return_type_tinfo(void) const
 418 {
 419         if (seq.size()==0) {
 420                 return tinfo_key;
 421         }
 422         return (*seq.begin()).rest.return_type_tinfo();
 423 }
 424
 425 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 426 {
 427         return (new add(v,oc))->setflag(status_flags::dynallocated);
 428 }
 429
 430 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 431 {
 432         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 433 }
 434
 435 expair add::split_ex_to_pair(const ex & e) const
 436 {
 437         if (is_ex_exactly_of_type(e,mul)) {
 438                 const mul &mulref(ex_to<mul>(e));
 439                 ex numfactor = mulref.overall_coeff;
 440                 mul *mulcopyp = new mul(mulref);
 441                 mulcopyp->overall_coeff = _ex1();
 442                 mulcopyp->clearflag(status_flags::evaluated);
 443                 mulcopyp->clearflag(status_flags::hash_calculated);
 444                 mulcopyp->setflag(status_flags::dynallocated);
 445                 return expair(*mulcopyp,numfactor);
 446         }
 447         return expair(e,_ex1());
 448 }
 449
 450 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 451                                                                                   const ex & c) const
 452 {
 453         GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
 454         if (is_ex_exactly_of_type(e, mul)) {
 455                 const mul &mulref(ex_to<mul>(e));
 456                 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                 if (are_ex_trivially_equal(c, _ex1()))
 463                         return expair(*mulcopyp, numfactor);
 464                 else if (are_ex_trivially_equal(numfactor, _ex1()))
 465                         return expair(*mulcopyp, c);
 466                 else
 467                         return expair(*mulcopyp, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 468         } else if (is_ex_exactly_of_type(e, numeric)) {
 469                 if (are_ex_trivially_equal(c, _ex1()))
 470                         return expair(e, _ex1());
 471                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1());
 472         }
 473         return expair(e, c);
 474 }
 475
 476 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 477                                                                                         const ex & c) const
 478 {
 479         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 480         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 481
 482         if (is_ex_exactly_of_type(p.rest,numeric)) {
 483                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(_num1())); // should be normalized
 484                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1());
 485         }
 486
 487         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 488 }
 489
 490 ex add::recombine_pair_to_ex(const expair & p) const
 491 {
 492         if (ex_to<numeric>(p.coeff).is_equal(_num1()))
 493                 return p.rest;
 494         else
 495                 return p.rest*p.coeff;
 496 }
 497
 498 ex add::expand(unsigned options) const
 499 {
 500         if (flags & status_flags::expanded)
 501                 return *this;
 502
 503         epvector * vp = expandchildren(options);
 504         if (vp == NULL) {
 505                 // the terms have not changed, so it is safe to declare this expanded
 506                 return this->setflag(status_flags::expanded);
 507         }
 508
 509         return (new add(vp,overall_coeff))->setflag(status_flags::expanded | status_flags::dynallocated);
 510 }
 511
 512 } // namespace GiNaC