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 "archive.h"
  29 #include "debugmsg.h"
  30 #include "utils.h"
  31
  32 namespace GiNaC {
  33
  34 GINAC_IMPLEMENT_REGISTERED_CLASS(add, expairseq)
  35
  36 //////////
  37 // default constructor, destructor, copy constructor assignment operator and helpers
  38 //////////
  39
  40 add::add()
  41 {
  42         debugmsg("add default constructor",LOGLEVEL_CONSTRUCT);
  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         debugmsg("add constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  58         tinfo_key = TINFO_add;
  59         overall_coeff = _ex0();
  60         construct_from_2_ex(lh,rh);
  61         GINAC_ASSERT(is_canonical());
  62 }
  63
  64 add::add(const exvector & v)
  65 {
  66         debugmsg("add constructor from exvector",LOGLEVEL_CONSTRUCT);
  67         tinfo_key = TINFO_add;
  68         overall_coeff = _ex0();
  69         construct_from_exvector(v);
  70         GINAC_ASSERT(is_canonical());
  71 }
  72
  73 add::add(const epvector & v)
  74 {
  75         debugmsg("add constructor from epvector",LOGLEVEL_CONSTRUCT);
  76         tinfo_key = TINFO_add;
  77         overall_coeff = _ex0();
  78         construct_from_epvector(v);
  79         GINAC_ASSERT(is_canonical());
  80 }
  81
  82 add::add(const epvector & v, const ex & oc)
  83 {
  84         debugmsg("add constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
  85         tinfo_key = TINFO_add;
  86         overall_coeff = oc;
  87         construct_from_epvector(v);
  88         GINAC_ASSERT(is_canonical());
  89 }
  90
  91 add::add(epvector * vp, const ex & oc)
  92 {
  93         debugmsg("add constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
  94         tinfo_key = TINFO_add;
  95         GINAC_ASSERT(vp!=0);
  96         overall_coeff = oc;
  97         construct_from_epvector(*vp);
  98         delete vp;
  99         GINAC_ASSERT(is_canonical());
 100 }
 101
 102 //////////
 103 // archiving
 104 //////////
 105
 106 DEFAULT_ARCHIVING(add)
 107
 108 //////////
 109 // functions overriding virtual functions from bases classes
 110 //////////
 111
 112 // public
 113
 114 void add::print(const print_context & c, unsigned level) const
 115 {
 116         debugmsg("add print", LOGLEVEL_PRINT);
 117
 118         if (is_of_type(c, print_tree)) {
 119
 120                 inherited::print(c, level);
 121
 122         } else if (is_of_type(c, print_csrc)) {
 123
 124                 if (precedence <= level)
 125                         c.s << "(";
 126
 127                 // Print arguments, separated by "+"
 128                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 129                 while (it != itend) {
 130
 131                         // If the coefficient is -1, it is replaced by a single minus sign
 132                         if (it->coeff.compare(_num1()) == 0) {
 133                                 it->rest.bp->print(c, precedence);
 134                         } else if (it->coeff.compare(_num_1()) == 0) {
 135                                 c.s << "-";
 136                                 it->rest.bp->print(c, precedence);
 137                         } else if (ex_to_numeric(it->coeff).numer().compare(_num1()) == 0) {
 138                                 it->rest.bp->print(c, precedence);
 139                                 c.s << "/";
 140                                 ex_to_numeric(it->coeff).denom().print(c, precedence);
 141                         } else if (ex_to_numeric(it->coeff).numer().compare(_num_1()) == 0) {
 142                                 c.s << "-";
 143                                 it->rest.bp->print(c, precedence);
 144                                 c.s << "/";
 145                                 ex_to_numeric(it->coeff).denom().print(c, precedence);
 146                         } else {
 147                                 it->coeff.bp->print(c, precedence);
 148                                 c.s << "*";
 149                                 it->rest.bp->print(c, precedence);
 150                         }
 151
 152                         // Separator is "+", except if the following expression would have a leading minus sign
 153                         it++;
 154                         if (it != itend && !(it->coeff.compare(_num0()) < 0 || (it->coeff.compare(_num1()) == 0 && is_ex_exactly_of_type(it->rest, numeric) && it->rest.compare(_num0()) < 0)))
 155                                 c.s << "+";
 156                 }
 157
 158                 if (!overall_coeff.is_zero()) {
 159                         if (overall_coeff.info(info_flags::positive))
 160                                 c.s << '+';
 161                         overall_coeff.bp->print(c, precedence);
 162                 }
 163
 164                 if (precedence <= level)
 165                         c.s << ")";
 166
 167         } else {
 168
 169                 if (precedence <= level)
 170                         c.s << "(";
 171
 172                 numeric coeff;
 173                 bool first = true;
 174
 175                 // First print the overall numeric coefficient, if present
 176                 if (!overall_coeff.is_zero()) {
 177                         if (!is_of_type(c, print_tree))
 178                                 overall_coeff.print(c, 0);
 179                         else
 180                                 overall_coeff.print(c, precedence);
 181                         first = false;
 182                 }
 183
 184                 // Then proceed with the remaining factors
 185                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 186                 while (it != itend) {
 187                         coeff = ex_to_numeric(it->coeff);
 188                         if (!first) {
 189                                 if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 190                         } else {
 191                                 if (coeff.csgn() == -1) c.s << '-';
 192                                 first = false;
 193                         }
 194                         if (!coeff.is_equal(_num1()) &&
 195                             !coeff.is_equal(_num_1())) {
 196                                 if (coeff.is_rational()) {
 197                                         if (coeff.is_negative())
 198                                                 (-coeff).print(c);
 199                                         else
 200                                                 coeff.print(c);
 201                                 } else {
 202                                         if (coeff.csgn() == -1)
 203                                                 (-coeff).print(c, precedence);
 204                                         else
 205                                                 coeff.print(c, precedence);
 206                                 }
 207                                 c.s << '*';
 208                         }
 209                         it->rest.print(c, precedence);
 210                         it++;
 211                 }
 212
 213                 if (precedence <= level)
 214                         c.s << ")";
 215         }
 216 }
 217
 218 bool add::info(unsigned inf) const
 219 {
 220         switch (inf) {
 221                 case info_flags::polynomial:
 222                 case info_flags::integer_polynomial:
 223                 case info_flags::cinteger_polynomial:
 224                 case info_flags::rational_polynomial:
 225                 case info_flags::crational_polynomial:
 226                 case info_flags::rational_function: {
 227                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 228                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 229                                         return false;
 230                         }
 231                         return overall_coeff.info(inf);
 232                 }
 233                 case info_flags::algebraic: {
 234                         for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 235                                 if ((recombine_pair_to_ex(*i).info(inf)))
 236                                         return true;
 237                         }
 238                         return false;
 239                 }
 240         }
 241         return inherited::info(inf);
 242 }
 243
 244 int add::degree(const ex & s) const
 245 {
 246         int deg = INT_MIN;
 247         if (!overall_coeff.is_equal(_ex0()))
 248                 deg = 0;
 249
 250         int cur_deg;
 251         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 252                 cur_deg = (*cit).rest.degree(s);
 253                 if (cur_deg>deg)
 254                         deg = cur_deg;
 255         }
 256         return deg;
 257 }
 258
 259 int add::ldegree(const ex & s) const
 260 {
 261         int deg = INT_MAX;
 262         if (!overall_coeff.is_equal(_ex0()))
 263                 deg = 0;
 264
 265         int cur_deg;
 266         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 267                 cur_deg = (*cit).rest.ldegree(s);
 268                 if (cur_deg<deg) deg=cur_deg;
 269         }
 270         return deg;
 271 }
 272
 273 ex add::coeff(const ex & s, int n) const
 274 {
 275         epvector coeffseq;
 276         coeffseq.reserve(seq.size());
 277
 278         epvector::const_iterator it=seq.begin();
 279         while (it!=seq.end()) {
 280                 coeffseq.push_back(combine_ex_with_coeff_to_pair((*it).rest.coeff(s,n),
 281                                                                  (*it).coeff));
 282                 ++it;
 283         }
 284         if (n==0) {
 285                 return (new add(coeffseq,overall_coeff))->setflag(status_flags::dynallocated);
 286         }
 287         return (new add(coeffseq))->setflag(status_flags::dynallocated);
 288 }
 289
 290 ex add::eval(int level) const
 291 {
 292         // simplifications: +(;c) -> c
 293         //                  +(x;1) -> x
 294
 295         debugmsg("add eval",LOGLEVEL_MEMBER_FUNCTION);
 296
 297         epvector * evaled_seqp = evalchildren(level);
 298         if (evaled_seqp!=0) {
 299                 // do more evaluation later
 300                 return (new add(evaled_seqp,overall_coeff))->
 301                        setflag(status_flags::dynallocated);
 302         }
 303
 304 #ifdef DO_GINAC_ASSERT
 305         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 306                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,add));
 307                 if (is_ex_exactly_of_type((*cit).rest,numeric))
 308                         dbgprint();
 309                 GINAC_ASSERT(!is_ex_exactly_of_type((*cit).rest,numeric));
 310         }
 311 #endif // def DO_GINAC_ASSERT
 312
 313         if (flags & status_flags::evaluated) {
 314                 GINAC_ASSERT(seq.size()>0);
 315                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 316                 return *this;
 317         }
 318
 319         int seq_size = seq.size();
 320         if (seq_size==0) {
 321                 // +(;c) -> c
 322                 return overall_coeff;
 323         } else if ((seq_size==1) && overall_coeff.is_equal(_ex0())) {
 324                 // +(x;0) -> x
 325                 return recombine_pair_to_ex(*(seq.begin()));
 326         }
 327         return this->hold();
 328 }
 329
 330 ex add::simplify_ncmul(const exvector & v) const
 331 {
 332         if (seq.size()==0) {
 333                 return inherited::simplify_ncmul(v);
 334         }
 335         return (*seq.begin()).rest.simplify_ncmul(v);
 336 }
 337
 338 // protected
 339
 340 /** Implementation of ex::diff() for a sum. It differentiates each term.
 341  *  @see ex::diff */
 342 ex add::derivative(const symbol & s) const
 343 {
 344         // D(a+b+c)=D(a)+D(b)+D(c)
 345         return (new add(diffchildren(s)))->setflag(status_flags::dynallocated);
 346 }
 347
 348 int add::compare_same_type(const basic & other) const
 349 {
 350         return inherited::compare_same_type(other);
 351 }
 352
 353 bool add::is_equal_same_type(const basic & other) const
 354 {
 355         return inherited::is_equal_same_type(other);
 356 }
 357
 358 unsigned add::return_type(void) const
 359 {
 360         if (seq.size()==0) {
 361                 return return_types::commutative;
 362         }
 363         return (*seq.begin()).rest.return_type();
 364 }
 365
 366 unsigned add::return_type_tinfo(void) const
 367 {
 368         if (seq.size()==0) {
 369                 return tinfo_key;
 370         }
 371         return (*seq.begin()).rest.return_type_tinfo();
 372 }
 373
 374 ex add::thisexpairseq(const epvector & v, const ex & oc) const
 375 {
 376         return (new add(v,oc))->setflag(status_flags::dynallocated);
 377 }
 378
 379 ex add::thisexpairseq(epvector * vp, const ex & oc) const
 380 {
 381         return (new add(vp,oc))->setflag(status_flags::dynallocated);
 382 }
 383
 384 expair add::split_ex_to_pair(const ex & e) const
 385 {
 386         if (is_ex_exactly_of_type(e,mul)) {
 387                 const mul &mulref = ex_to_mul(e);
 388                 ex numfactor = mulref.overall_coeff;
 389                 mul *mulcopyp = new mul(mulref);
 390                 mulcopyp->overall_coeff = _ex1();
 391                 mulcopyp->clearflag(status_flags::evaluated);
 392                 mulcopyp->clearflag(status_flags::hash_calculated);
 393                 mulcopyp->setflag(status_flags::dynallocated);
 394                 return expair(*mulcopyp,numfactor);
 395         }
 396         return expair(e,_ex1());
 397 }
 398
 399 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 400                                                                                   const ex & c) const
 401 {
 402         GINAC_ASSERT(is_ex_exactly_of_type(c, numeric));
 403         if (is_ex_exactly_of_type(e, mul)) {
 404                 const mul &mulref = ex_to_mul(e);
 405                 ex numfactor = mulref.overall_coeff;
 406                 mul *mulcopyp = new mul(mulref);
 407                 mulcopyp->overall_coeff = _ex1();
 408                 mulcopyp->clearflag(status_flags::evaluated);
 409                 mulcopyp->clearflag(status_flags::hash_calculated);
 410                 mulcopyp->setflag(status_flags::dynallocated);
 411                 if (are_ex_trivially_equal(c, _ex1()))
 412                         return expair(*mulcopyp, numfactor);
 413                 else if (are_ex_trivially_equal(numfactor, _ex1()))
 414                         return expair(*mulcopyp, c);
 415                 else
 416                         return expair(*mulcopyp, ex_to_numeric(numfactor).mul_dyn(ex_to_numeric(c)));
 417         } else if (is_ex_exactly_of_type(e, numeric)) {
 418                 if (are_ex_trivially_equal(c, _ex1()))
 419                         return expair(e, _ex1());
 420                 return expair(ex_to_numeric(e).mul_dyn(ex_to_numeric(c)), _ex1());
 421         }
 422         return expair(e, c);
 423 }
 424
 425 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 426                                                                                         const ex & c) const
 427 {
 428         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 429         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 430
 431         if (is_ex_exactly_of_type(p.rest,numeric)) {
 432                 GINAC_ASSERT(ex_to_numeric(p.coeff).is_equal(_num1())); // should be normalized
 433                 return expair(ex_to_numeric(p.rest).mul_dyn(ex_to_numeric(c)),_ex1());
 434         }
 435
 436         return expair(p.rest,ex_to_numeric(p.coeff).mul_dyn(ex_to_numeric(c)));
 437 }
 438
 439 ex add::recombine_pair_to_ex(const expair & p) const
 440 {
 441         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 442                 return p.rest;
 443         else
 444                 return p.rest*p.coeff;
 445 }
 446
 447 ex add::expand(unsigned options) const
 448 {
 449         if (flags & status_flags::expanded)
 450                 return *this;
 451
 452         epvector * vp = expandchildren(options);
 453         if (vp==0) {
 454                 // the terms have not changed, so it is safe to declare this expanded
 455                 setflag(status_flags::expanded);
 456                 return *this;
 457         }
 458
 459         return (new add(vp,overall_coeff))->setflag(status_flags::expanded | status_flags::dynallocated);
 460 }
 461
 462 //////////
 463 // static member variables
 464 //////////
 465
 466 // protected
 467
 468 unsigned add::precedence = 40;
 469
 470 } // namespace GiNaC