ginac/add.cpp

   1 /** @file add.cpp
   2  *
   3  *  Implementation of GiNaC's sums of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2015 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  21  */
  22
  23 #include "add.h"
  24 #include "mul.h"
  25 #include "archive.h"
  26 #include "operators.h"
  27 #include "matrix.h"
  28 #include "utils.h"
  29 #include "clifford.h"
  30 #include "ncmul.h"
  31 #include "compiler.h"
  32
  33 #include <iostream>
  34 #include <limits>
  35 #include <stdexcept>
  36 #include <string>
  37
  38 namespace GiNaC {
  39
  40 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(add, expairseq,
  41   print_func<print_context>(&add::do_print).
  42   print_func<print_latex>(&add::do_print_latex).
  43   print_func<print_csrc>(&add::do_print_csrc).
  44   print_func<print_tree>(&add::do_print_tree).
  45   print_func<print_python_repr>(&add::do_print_python_repr))
  46
  47 //////////
  48 // default constructor
  49 //////////
  50
  51 add::add()
  52 {
  53 }
  54
  55 //////////
  56 // other constructors
  57 //////////
  58
  59 // public
  60
  61 add::add(const ex & lh, const ex & rh)
  62 {
  63         overall_coeff = _ex0;
  64         construct_from_2_ex(lh,rh);
  65         GINAC_ASSERT(is_canonical());
  66 }
  67
  68 add::add(const exvector & v)
  69 {
  70         overall_coeff = _ex0;
  71         construct_from_exvector(v);
  72         GINAC_ASSERT(is_canonical());
  73 }
  74
  75 add::add(const epvector & v)
  76 {
  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         overall_coeff = oc;
  85         construct_from_epvector(v);
  86         GINAC_ASSERT(is_canonical());
  87 }
  88
  89 add::add(epvector && vp)
  90 {
  91         overall_coeff = _ex0;
  92         construct_from_epvector(std::move(vp));
  93         GINAC_ASSERT(is_canonical());
  94 }
  95
  96 add::add(epvector && vp, const ex & oc)
  97 {
  98         overall_coeff = oc;
  99         construct_from_epvector(std::move(vp));
 100         GINAC_ASSERT(is_canonical());
 101 }
 102
 103 //////////
 104 // archiving
 105 //////////
 106
 107 GINAC_BIND_UNARCHIVER(add);
 108
 109 //////////
 110 // functions overriding virtual functions from base classes
 111 //////////
 112
 113 // public
 114
 115 void add::print_add(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, unsigned level) const
 116 {
 117         if (precedence() <= level)
 118                 c.s << openbrace << '(';
 119
 120         numeric coeff;
 121         bool first = true;
 122
 123         // First print the overall numeric coefficient, if present
 124         if (!overall_coeff.is_zero()) {
 125                 overall_coeff.print(c, 0);
 126                 first = false;
 127         }
 128
 129         // Then proceed with the remaining factors
 130         for (auto & it : seq) {
 131                 coeff = ex_to<numeric>(it.coeff);
 132                 if (!first) {
 133                         if (coeff.csgn() == -1) c.s << '-'; else c.s << '+';
 134                 } else {
 135                         if (coeff.csgn() == -1) c.s << '-';
 136                         first = false;
 137                 }
 138                 if (!coeff.is_equal(*_num1_p) &&
 139                     !coeff.is_equal(*_num_1_p)) {
 140                         if (coeff.is_rational()) {
 141                                 if (coeff.is_negative())
 142                                         (-coeff).print(c);
 143                                 else
 144                                         coeff.print(c);
 145                         } else {
 146                                 if (coeff.csgn() == -1)
 147                                         (-coeff).print(c, precedence());
 148                                 else
 149                                         coeff.print(c, precedence());
 150                         }
 151                         c.s << mul_sym;
 152                 }
 153                 it.rest.print(c, precedence());
 154         }
 155
 156         if (precedence() <= level)
 157                 c.s << ')' << closebrace;
 158 }
 159
 160 void add::do_print(const print_context & c, unsigned level) const
 161 {
 162         print_add(c, "", "", "*", level);
 163 }
 164
 165 void add::do_print_latex(const print_latex & c, unsigned level) const
 166 {
 167         print_add(c, "{", "}", " ", level);
 168 }
 169
 170 void add::do_print_csrc(const print_csrc & c, unsigned level) const
 171 {
 172         if (precedence() <= level)
 173                 c.s << "(";
 174
 175         // Print arguments, separated by "+" or "-"
 176         char separator = ' ';
 177         for (auto & it : seq) {
 178
 179                 // If the coefficient is negative, separator is "-"
 180                 if (it.coeff.is_equal(_ex_1) ||
 181                         ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
 182                         separator = '-';
 183                 c.s << separator;
 184                 if (it.coeff.is_equal(_ex1) || it.coeff.is_equal(_ex_1)) {
 185                         it.rest.print(c, precedence());
 186                 } else if (ex_to<numeric>(it.coeff).numer().is_equal(*_num1_p) ||
 187                                  ex_to<numeric>(it.coeff).numer().is_equal(*_num_1_p))
 188                 {
 189                         it.rest.print(c, precedence());
 190                         c.s << '/';
 191                         ex_to<numeric>(it.coeff).denom().print(c, precedence());
 192                 } else {
 193                         it.coeff.print(c, precedence());
 194                         c.s << '*';
 195                         it.rest.print(c, precedence());
 196                 }
 197
 198                 separator = '+';
 199         }
 200
 201         if (!overall_coeff.is_zero()) {
 202                 if (overall_coeff.info(info_flags::positive)
 203                  || is_a<print_csrc_cl_N>(c) || !overall_coeff.info(info_flags::real))  // sign inside ctor argument
 204                         c.s << '+';
 205                 overall_coeff.print(c, precedence());
 206         }
 207
 208         if (precedence() <= level)
 209                 c.s << ")";
 210 }
 211
 212 void add::do_print_python_repr(const print_python_repr & c, unsigned level) const
 213 {
 214         c.s << class_name() << '(';
 215         op(0).print(c);
 216         for (size_t i=1; i<nops(); ++i) {
 217                 c.s << ',';
 218                 op(i).print(c);
 219         }
 220         c.s << ')';
 221 }
 222
 223 bool add::info(unsigned inf) const
 224 {
 225         switch (inf) {
 226                 case info_flags::polynomial:
 227                 case info_flags::integer_polynomial:
 228                 case info_flags::cinteger_polynomial:
 229                 case info_flags::rational_polynomial:
 230                 case info_flags::real:
 231                 case info_flags::rational:
 232                 case info_flags::integer:
 233                 case info_flags::crational:
 234                 case info_flags::cinteger:
 235                 case info_flags::positive:
 236                 case info_flags::nonnegative:
 237                 case info_flags::posint:
 238                 case info_flags::nonnegint:
 239                 case info_flags::even:
 240                 case info_flags::crational_polynomial:
 241                 case info_flags::rational_function: {
 242                         for (auto & i : seq) {
 243                                 if (!(recombine_pair_to_ex(i).info(inf)))
 244                                         return false;
 245                         }
 246                         if (overall_coeff.is_zero() && (inf == info_flags::positive || inf == info_flags::posint))
 247                                 return true;
 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 bool add::is_polynomial(const ex & var) const
 264 {
 265         for (auto & i : seq) {
 266                 if (!i.rest.is_polynomial(var)) {
 267                         return false;
 268                 }
 269         }
 270         return true;
 271 }
 272
 273 int add::degree(const ex & s) const
 274 {
 275         int deg = std::numeric_limits<int>::min();
 276         if (!overall_coeff.is_zero())
 277                 deg = 0;
 278
 279         // Find maximum of degrees of individual terms
 280         for (auto & i : seq) {
 281                 int cur_deg = i.rest.degree(s);
 282                 if (cur_deg > deg)
 283                         deg = cur_deg;
 284         }
 285         return deg;
 286 }
 287
 288 int add::ldegree(const ex & s) const
 289 {
 290         int deg = std::numeric_limits<int>::max();
 291         if (!overall_coeff.is_zero())
 292                 deg = 0;
 293
 294         // Find minimum of degrees of individual terms
 295         for (auto & i : seq) {
 296                 int cur_deg = i.rest.ldegree(s);
 297                 if (cur_deg < deg)
 298                         deg = cur_deg;
 299         }
 300         return deg;
 301 }
 302
 303 ex add::coeff(const ex & s, int n) const
 304 {
 305         epvector coeffseq;
 306         epvector coeffseq_cliff;
 307         int rl = clifford_max_label(s);
 308         bool do_clifford = (rl != -1);
 309         bool nonscalar = false;
 310
 311         // Calculate sum of coefficients in each term
 312         for (auto & i : seq) {
 313                 ex restcoeff = i.rest.coeff(s, n);
 314                 if (!restcoeff.is_zero()) {
 315                         if (do_clifford) {
 316                                 if (clifford_max_label(restcoeff) == -1) {
 317                                         coeffseq_cliff.push_back(expair(ncmul(restcoeff, dirac_ONE(rl)), i.coeff));
 318                                 } else {
 319                                         coeffseq_cliff.push_back(expair(restcoeff, i.coeff));
 320                                         nonscalar = true;
 321                                 }
 322                         }
 323                         coeffseq.push_back(expair(restcoeff, i.coeff));
 324                 }
 325         }
 326
 327         return dynallocate<add>(nonscalar ? std::move(coeffseq_cliff) : std::move(coeffseq),
 328                                 n==0 ? overall_coeff : _ex0);
 329 }
 330
 331 /** Perform automatic term rewriting rules in this class.  In the following
 332  *  x stands for a symbolic variables of type ex and c stands for such
 333  *  an expression that contain a plain number.
 334  *  - +(;c) -> c
 335  *  - +(x;0) -> x
 336  */
 337 ex add::eval() const
 338 {
 339         if (flags & status_flags::evaluated) {
 340                 GINAC_ASSERT(seq.size()>0);
 341                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_zero());
 342                 return *this;
 343         }
 344
 345         const epvector evaled = evalchildren();
 346         if (unlikely(!evaled.empty())) {
 347                 // start over evaluating a new object
 348                 return dynallocate<add>(std::move(evaled), overall_coeff);
 349         }
 350
 351 #ifdef DO_GINAC_ASSERT
 352         for (auto & i : seq) {
 353                 GINAC_ASSERT(!is_exactly_a<add>(i.rest));
 354         }
 355 #endif // def DO_GINAC_ASSERT
 356
 357         int seq_size = seq.size();
 358         if (seq_size == 0) {
 359                 // +(;c) -> c
 360                 return overall_coeff;
 361         } else if (seq_size == 1 && overall_coeff.is_zero()) {
 362                 // +(x;0) -> x
 363                 return recombine_pair_to_ex(*(seq.begin()));
 364         } else if (!overall_coeff.is_zero() && seq[0].rest.return_type() != return_types::commutative) {
 365                 throw (std::logic_error("add::eval(): sum of non-commutative objects has non-zero numeric term"));
 366         }
 367
 368         // if any terms in the sum still are purely numeric, then they are more
 369         // appropriately collected into the overall coefficient
 370         int terms_to_collect = 0;
 371         for (auto & it : seq) {
 372                 if (unlikely(is_a<numeric>(it.rest)))
 373                         ++terms_to_collect;
 374         }
 375         if (terms_to_collect) {
 376                 epvector s;
 377                 s.reserve(seq_size - terms_to_collect);
 378                 numeric oc = *_num1_p;
 379                 for (auto & it : seq) {
 380                         if (unlikely(is_a<numeric>(it.rest)))
 381                                 oc = oc.mul(ex_to<numeric>(it.rest)).mul(ex_to<numeric>(it.coeff));
 382                         else
 383                                 s.push_back(it);
 384                 }
 385                 return dynallocate<add>(std::move(s), ex_to<numeric>(overall_coeff).add_dyn(oc));
 386         }
 387
 388         return this->hold();
 389 }
 390
 391 ex add::evalm() const
 392 {
 393         // Evaluate children first and add up all matrices. Stop if there's one
 394         // term that is not a matrix.
 395         epvector s;
 396         s.reserve(seq.size());
 397
 398         bool all_matrices = true;
 399         bool first_term = true;
 400         matrix sum;
 401
 402         for (auto & it : seq) {
 403                 const ex &m = recombine_pair_to_ex(it).evalm();
 404                 s.push_back(split_ex_to_pair(m));
 405                 if (is_a<matrix>(m)) {
 406                         if (first_term) {
 407                                 sum = ex_to<matrix>(m);
 408                                 first_term = false;
 409                         } else
 410                                 sum = sum.add(ex_to<matrix>(m));
 411                 } else
 412                         all_matrices = false;
 413         }
 414
 415         if (all_matrices)
 416                 return sum + overall_coeff;
 417         else
 418                 return dynallocate<add>(std::move(s), overall_coeff);
 419 }
 420
 421 ex add::conjugate() const
 422 {
 423         std::unique_ptr<exvector> v(nullptr);
 424         for (size_t i=0; i<nops(); ++i) {
 425                 if (v) {
 426                         v->push_back(op(i).conjugate());
 427                         continue;
 428                 }
 429                 ex term = op(i);
 430                 ex ccterm = term.conjugate();
 431                 if (are_ex_trivially_equal(term, ccterm))
 432                         continue;
 433                 v.reset(new exvector);
 434                 v->reserve(nops());
 435                 for (size_t j=0; j<i; ++j)
 436                         v->push_back(op(j));
 437                 v->push_back(ccterm);
 438         }
 439         if (v) {
 440                 return add(std::move(*v));
 441         }
 442         return *this;
 443 }
 444
 445 ex add::real_part() const
 446 {
 447         epvector v;
 448         v.reserve(seq.size());
 449         for (auto & it : seq)
 450                 if (it.coeff.info(info_flags::real)) {
 451                         ex rp = it.rest.real_part();
 452                         if (!rp.is_zero())
 453                                 v.push_back(expair(rp, it.coeff));
 454                 } else {
 455                         ex rp = recombine_pair_to_ex(it).real_part();
 456                         if (!rp.is_zero())
 457                                 v.push_back(split_ex_to_pair(rp));
 458                 }
 459         return dynallocate<add>(std::move(v), overall_coeff.real_part());
 460 }
 461
 462 ex add::imag_part() const
 463 {
 464         epvector v;
 465         v.reserve(seq.size());
 466         for (auto & it : seq)
 467                 if (it.coeff.info(info_flags::real)) {
 468                         ex ip = it.rest.imag_part();
 469                         if (!ip.is_zero())
 470                                 v.push_back(expair(ip, it.coeff));
 471                 } else {
 472                         ex ip = recombine_pair_to_ex(it).imag_part();
 473                         if (!ip.is_zero())
 474                                 v.push_back(split_ex_to_pair(ip));
 475                 }
 476         return dynallocate<add>(std::move(v), overall_coeff.imag_part());
 477 }
 478
 479 ex add::eval_ncmul(const exvector & v) const
 480 {
 481         if (seq.empty())
 482                 return inherited::eval_ncmul(v);
 483         else
 484                 return seq.begin()->rest.eval_ncmul(v);
 485 }
 486
 487 // protected
 488
 489 /** Implementation of ex::diff() for a sum. It differentiates each term.
 490  *  @see ex::diff */
 491 ex add::derivative(const symbol & y) const
 492 {
 493         epvector s;
 494         s.reserve(seq.size());
 495
 496         // Only differentiate the "rest" parts of the expairs. This is faster
 497         // than the default implementation in basic::derivative() although
 498         // if performs the same function (differentiate each term).
 499         for (auto & it : seq)
 500                 s.push_back(expair(it.rest.diff(y), it.coeff));
 501
 502         return dynallocate<add>(std::move(s));
 503 }
 504
 505 int add::compare_same_type(const basic & other) const
 506 {
 507         return inherited::compare_same_type(other);
 508 }
 509
 510 unsigned add::return_type() const
 511 {
 512         if (seq.empty())
 513                 return return_types::commutative;
 514         else
 515                 return seq.begin()->rest.return_type();
 516 }
 517
 518 return_type_t add::return_type_tinfo() const
 519 {
 520         if (seq.empty())
 521                 return make_return_type_t<add>();
 522         else
 523                 return seq.begin()->rest.return_type_tinfo();
 524 }
 525
 526 // Note: do_index_renaming is ignored because it makes no sense for an add.
 527 ex add::thisexpairseq(const epvector & v, const ex & oc, bool do_index_renaming) const
 528 {
 529         return dynallocate<add>(v, oc);
 530 }
 531
 532 // Note: do_index_renaming is ignored because it makes no sense for an add.
 533 ex add::thisexpairseq(epvector && vp, const ex & oc, bool do_index_renaming) const
 534 {
 535         return dynallocate<add>(std::move(vp), oc);
 536 }
 537
 538 expair add::split_ex_to_pair(const ex & e) const
 539 {
 540         if (is_exactly_a<mul>(e)) {
 541                 const mul &mulref(ex_to<mul>(e));
 542                 const ex &numfactor = mulref.overall_coeff;
 543                 if (numfactor.is_equal(_ex1))
 544                         return expair(e, _ex1);
 545                 mul & mulcopy = dynallocate<mul>(mulref);
 546                 mulcopy.overall_coeff = _ex1;
 547                 mulcopy.clearflag(status_flags::evaluated | status_flags::hash_calculated);
 548                 return expair(mulcopy, numfactor);
 549         }
 550         return expair(e,_ex1);
 551 }
 552
 553 expair add::combine_ex_with_coeff_to_pair(const ex & e,
 554                                           const ex & c) const
 555 {
 556         GINAC_ASSERT(is_exactly_a<numeric>(c));
 557         if (is_exactly_a<mul>(e)) {
 558                 const mul &mulref(ex_to<mul>(e));
 559                 const ex &numfactor = mulref.overall_coeff;
 560                 if (likely(numfactor.is_equal(_ex1)))
 561                         return expair(e, c);
 562                 mul & mulcopy = dynallocate<mul>(mulref);
 563                 mulcopy.overall_coeff = _ex1;
 564                 mulcopy.clearflag(status_flags::evaluated | status_flags::hash_calculated);
 565                 if (c.is_equal(_ex1))
 566                         return expair(mulcopy, numfactor);
 567                 else
 568                         return expair(mulcopy, ex_to<numeric>(numfactor).mul_dyn(ex_to<numeric>(c)));
 569         } else if (is_exactly_a<numeric>(e)) {
 570                 if (c.is_equal(_ex1))
 571                         return expair(e, _ex1);
 572                 if (e.is_equal(_ex1))
 573                         return expair(c, _ex1);
 574                 return expair(ex_to<numeric>(e).mul_dyn(ex_to<numeric>(c)), _ex1);
 575         }
 576         return expair(e, c);
 577 }
 578
 579 expair add::combine_pair_with_coeff_to_pair(const expair & p,
 580                                             const ex & c) const
 581 {
 582         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 583         GINAC_ASSERT(is_exactly_a<numeric>(c));
 584
 585         if (is_exactly_a<numeric>(p.rest)) {
 586                 GINAC_ASSERT(ex_to<numeric>(p.coeff).is_equal(*_num1_p)); // should be normalized
 587                 return expair(ex_to<numeric>(p.rest).mul_dyn(ex_to<numeric>(c)),_ex1);
 588         }
 589
 590         return expair(p.rest,ex_to<numeric>(p.coeff).mul_dyn(ex_to<numeric>(c)));
 591 }
 592
 593 ex add::recombine_pair_to_ex(const expair & p) const
 594 {
 595         if (ex_to<numeric>(p.coeff).is_equal(*_num1_p))
 596                 return p.rest;
 597         else
 598                 return dynallocate<mul>(p.rest, p.coeff);
 599 }
 600
 601 ex add::expand(unsigned options) const
 602 {
 603         epvector expanded = expandchildren(options);
 604         if (expanded.empty())
 605                 return (options == 0) ? setflag(status_flags::expanded) : *this;
 606
 607         return dynallocate<add>(std::move(expanded), overall_coeff).setflag(options == 0 ? status_flags::expanded : 0);
 608 }
 609
 610 } // namespace GiNaC