ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products 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 <vector>
  25 #include <stdexcept>
  26 #include <limits>
  27
  28 #include "mul.h"
  29 #include "add.h"
  30 #include "power.h"
  31 #include "operators.h"
  32 #include "matrix.h"
  33 #include "lst.h"
  34 #include "archive.h"
  35 #include "utils.h"
  36
  37 namespace GiNaC {
  38
  39 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  40
  41 //////////
  42 // default ctor, dtor, copy ctor, assignment operator and helpers
  43 //////////
  44
  45 mul::mul()
  46 {
  47         tinfo_key = TINFO_mul;
  48 }
  49
  50 DEFAULT_COPY(mul)
  51 DEFAULT_DESTROY(mul)
  52
  53 //////////
  54 // other ctors
  55 //////////
  56
  57 // public
  58
  59 mul::mul(const ex & lh, const ex & rh)
  60 {
  61         tinfo_key = TINFO_mul;
  62         overall_coeff = _ex1;
  63         construct_from_2_ex(lh,rh);
  64         GINAC_ASSERT(is_canonical());
  65 }
  66
  67 mul::mul(const exvector & v)
  68 {
  69         tinfo_key = TINFO_mul;
  70         overall_coeff = _ex1;
  71         construct_from_exvector(v);
  72         GINAC_ASSERT(is_canonical());
  73 }
  74
  75 mul::mul(const epvector & v)
  76 {
  77         tinfo_key = TINFO_mul;
  78         overall_coeff = _ex1;
  79         construct_from_epvector(v);
  80         GINAC_ASSERT(is_canonical());
  81 }
  82
  83 mul::mul(const epvector & v, const ex & oc)
  84 {
  85         tinfo_key = TINFO_mul;
  86         overall_coeff = oc;
  87         construct_from_epvector(v);
  88         GINAC_ASSERT(is_canonical());
  89 }
  90
  91 mul::mul(epvector * vp, const ex & oc)
  92 {
  93         tinfo_key = TINFO_mul;
  94         GINAC_ASSERT(vp!=0);
  95         overall_coeff = oc;
  96         construct_from_epvector(*vp);
  97         delete vp;
  98         GINAC_ASSERT(is_canonical());
  99 }
 100
 101 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 102 {
 103         tinfo_key = TINFO_mul;
 104         exvector factors;
 105         factors.reserve(3);
 106         factors.push_back(lh);
 107         factors.push_back(mh);
 108         factors.push_back(rh);
 109         overall_coeff = _ex1;
 110         construct_from_exvector(factors);
 111         GINAC_ASSERT(is_canonical());
 112 }
 113
 114 //////////
 115 // archiving
 116 //////////
 117
 118 DEFAULT_ARCHIVING(mul)
 119
 120 //////////
 121 // functions overriding virtual functions from base classes
 122 //////////
 123
 124 // public
 125 void mul::print(const print_context & c, unsigned level) const
 126 {
 127         if (is_a<print_tree>(c)) {
 128
 129                 inherited::print(c, level);
 130
 131         } else if (is_a<print_csrc>(c)) {
 132
 133                 if (precedence() <= level)
 134                         c.s << "(";
 135
 136                 if (!overall_coeff.is_equal(_ex1)) {
 137                         overall_coeff.print(c, precedence());
 138                         c.s << "*";
 139                 }
 140
 141                 // Print arguments, separated by "*" or "/"
 142                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 143                 while (it != itend) {
 144
 145                         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 146                         bool needclosingparenthesis = false;
 147                         if (it == seq.begin() && it->coeff.info(info_flags::negint)) {
 148                                 if (is_a<print_csrc_cl_N>(c)) {
 149                                         c.s << "recip(";
 150                                         needclosingparenthesis = true;
 151                                 } else
 152                                         c.s << "1.0/";
 153                         }
 154
 155                         // If the exponent is 1 or -1, it is left out
 156                         if (it->coeff.is_equal(_ex1) || it->coeff.is_equal(_ex_1))
 157                                 it->rest.print(c, precedence());
 158                         else if (it->coeff.info(info_flags::negint))
 159                                 // Outer parens around ex needed for broken GCC parser:
 160                                 (ex(power(it->rest, -ex_to<numeric>(it->coeff)))).print(c, level);
 161                         else
 162                                 // Outer parens around ex needed for broken GCC parser:
 163                                 (ex(power(it->rest, ex_to<numeric>(it->coeff)))).print(c, level);
 164
 165                         if (needclosingparenthesis)
 166                                 c.s << ")";
 167
 168                         // Separator is "/" for negative integer powers, "*" otherwise
 169                         ++it;
 170                         if (it != itend) {
 171                                 if (it->coeff.info(info_flags::negint))
 172                                         c.s << "/";
 173                                 else
 174                                         c.s << "*";
 175                         }
 176                 }
 177
 178                 if (precedence() <= level)
 179                         c.s << ")";
 180
 181         } else if (is_a<print_python_repr>(c)) {
 182                 c.s << class_name() << '(';
 183                 op(0).print(c);
 184                 for (unsigned i=1; i<nops(); ++i) {
 185                         c.s << ',';
 186                         op(i).print(c);
 187                 }
 188                 c.s << ')';
 189         } else {
 190
 191                 if (precedence() <= level) {
 192                         if (is_a<print_latex>(c))
 193                                 c.s << "{(";
 194                         else
 195                                 c.s << "(";
 196                 }
 197
 198                 // First print the overall numeric coefficient
 199                 const numeric &coeff = ex_to<numeric>(overall_coeff);
 200                 if (coeff.csgn() == -1)
 201                         c.s << '-';
 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
 221                 // Then proceed with the remaining factors
 222                 epvector::const_iterator it = seq.begin(), itend = seq.end();
 223                 if (is_a<print_latex>(c)) {
 224
 225                         // Separate factors into those with negative numeric exponent
 226                         // and all others
 227                         exvector neg_powers, others;
 228                         while (it != itend) {
 229                                 GINAC_ASSERT(is_exactly_a<numeric>(it->coeff));
 230                                 if (ex_to<numeric>(it->coeff).is_negative())
 231                                         neg_powers.push_back(recombine_pair_to_ex(expair(it->rest, -(it->coeff))));
 232                                 else
 233                                         others.push_back(recombine_pair_to_ex(*it));
 234                                 ++it;
 235                         }
 236
 237                         if (!neg_powers.empty()) {
 238
 239                                 // Factors with negative exponent are printed as a fraction
 240                                 c.s << "\\frac{";
 241                                 mul(others).eval().print(c);
 242                                 c.s << "}{";
 243                                 mul(neg_powers).eval().print(c);
 244                                 c.s << "}";
 245
 246                         } else {
 247
 248                                 // All other factors are printed in the ordinary way
 249                                 exvector::const_iterator vit = others.begin(), vitend = others.end();
 250                                 while (vit != vitend) {
 251                                         c.s << ' ';
 252                                         vit->print(c, precedence());
 253                                         ++vit;
 254                                 }
 255                         }
 256
 257                 } else {
 258
 259                         bool first = true;
 260                         while (it != itend) {
 261                                 if (!first)
 262                                         c.s << '*';
 263                                 else
 264                                         first = false;
 265                                 recombine_pair_to_ex(*it).print(c, precedence());
 266                                 ++it;
 267                         }
 268                 }
 269
 270                 if (precedence() <= level) {
 271                         if (is_a<print_latex>(c))
 272                                 c.s << ")}";
 273                         else
 274                                 c.s << ")";
 275                 }
 276         }
 277 }
 278
 279 bool mul::info(unsigned inf) const
 280 {
 281         switch (inf) {
 282                 case info_flags::polynomial:
 283                 case info_flags::integer_polynomial:
 284                 case info_flags::cinteger_polynomial:
 285                 case info_flags::rational_polynomial:
 286                 case info_flags::crational_polynomial:
 287                 case info_flags::rational_function: {
 288                         epvector::const_iterator i = seq.begin(), end = seq.end();
 289                         while (i != end) {
 290                                 if (!(recombine_pair_to_ex(*i).info(inf)))
 291                                         return false;
 292                                 ++i;
 293                         }
 294                         return overall_coeff.info(inf);
 295                 }
 296                 case info_flags::algebraic: {
 297                         epvector::const_iterator i = seq.begin(), end = seq.end();
 298                         while (i != end) {
 299                                 if ((recombine_pair_to_ex(*i).info(inf)))
 300                                         return true;
 301                                 ++i;
 302                         }
 303                         return false;
 304                 }
 305         }
 306         return inherited::info(inf);
 307 }
 308
 309 int mul::degree(const ex & s) const
 310 {
 311         // Sum up degrees of factors
 312         int deg_sum = 0;
 313         epvector::const_iterator i = seq.begin(), end = seq.end();
 314         while (i != end) {
 315                 if (ex_to<numeric>(i->coeff).is_integer())
 316                         deg_sum += i->rest.degree(s) * ex_to<numeric>(i->coeff).to_int();
 317                 ++i;
 318         }
 319         return deg_sum;
 320 }
 321
 322 int mul::ldegree(const ex & s) const
 323 {
 324         // Sum up degrees of factors
 325         int deg_sum = 0;
 326         epvector::const_iterator i = seq.begin(), end = seq.end();
 327         while (i != end) {
 328                 if (ex_to<numeric>(i->coeff).is_integer())
 329                         deg_sum += i->rest.ldegree(s) * ex_to<numeric>(i->coeff).to_int();
 330                 ++i;
 331         }
 332         return deg_sum;
 333 }
 334
 335 ex mul::coeff(const ex & s, int n) const
 336 {
 337         exvector coeffseq;
 338         coeffseq.reserve(seq.size()+1);
 339
 340         if (n==0) {
 341                 // product of individual coeffs
 342                 // if a non-zero power of s is found, the resulting product will be 0
 343                 epvector::const_iterator i = seq.begin(), end = seq.end();
 344                 while (i != end) {
 345                         coeffseq.push_back(recombine_pair_to_ex(*i).coeff(s,n));
 346                         ++i;
 347                 }
 348                 coeffseq.push_back(overall_coeff);
 349                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 350         }
 351
 352         epvector::const_iterator i = seq.begin(), end = seq.end();
 353         bool coeff_found = false;
 354         while (i != end) {
 355                 ex t = recombine_pair_to_ex(*i);
 356                 ex c = t.coeff(s, n);
 357                 if (!c.is_zero()) {
 358                         coeffseq.push_back(c);
 359                         coeff_found = 1;
 360                 } else {
 361                         coeffseq.push_back(t);
 362                 }
 363                 ++i;
 364         }
 365         if (coeff_found) {
 366                 coeffseq.push_back(overall_coeff);
 367                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 368         }
 369
 370         return _ex0;
 371 }
 372
 373 /** Perform automatic term rewriting rules in this class.  In the following
 374  *  x, x1, x2,... stand for a symbolic variables of type ex and c, c1, c2...
 375  *  stand for such expressions that contain a plain number.
 376  *  - *(...,x;0) -> 0
 377  *  - *(+(x1,x2,...);c) -> *(+(*(x1,c),*(x2,c),...))
 378  *  - *(x;1) -> x
 379  *  - *(;c) -> c
 380  *
 381  *  @param level cut-off in recursive evaluation */
 382 ex mul::eval(int level) const
 383 {
 384         epvector *evaled_seqp = evalchildren(level);
 385         if (evaled_seqp) {
 386                 // do more evaluation later
 387                 return (new mul(evaled_seqp,overall_coeff))->
 388                            setflag(status_flags::dynallocated);
 389         }
 390
 391 #ifdef DO_GINAC_ASSERT
 392         epvector::const_iterator i = seq.begin(), end = seq.end();
 393         while (i != end) {
 394                 GINAC_ASSERT((!is_exactly_a<mul>(i->rest)) ||
 395                              (!(ex_to<numeric>(i->coeff).is_integer())));
 396                 GINAC_ASSERT(!(i->is_canonical_numeric()));
 397                 if (is_exactly_a<numeric>(recombine_pair_to_ex(*i)))
 398                     print(print_tree(std::cerr));
 399                 GINAC_ASSERT(!is_exactly_a<numeric>(recombine_pair_to_ex(*i)));
 400                 /* for paranoia */
 401                 expair p = split_ex_to_pair(recombine_pair_to_ex(*i));
 402                 GINAC_ASSERT(p.rest.is_equal(i->rest));
 403                 GINAC_ASSERT(p.coeff.is_equal(i->coeff));
 404                 /* end paranoia */
 405                 ++i;
 406         }
 407 #endif // def DO_GINAC_ASSERT
 408
 409         if (flags & status_flags::evaluated) {
 410                 GINAC_ASSERT(seq.size()>0);
 411                 GINAC_ASSERT(seq.size()>1 || !overall_coeff.is_equal(_ex1));
 412                 return *this;
 413         }
 414
 415         int seq_size = seq.size();
 416         if (overall_coeff.is_zero()) {
 417                 // *(...,x;0) -> 0
 418                 return _ex0;
 419         } else if (seq_size==0) {
 420                 // *(;c) -> c
 421                 return overall_coeff;
 422         } else if (seq_size==1 && overall_coeff.is_equal(_ex1)) {
 423                 // *(x;1) -> x
 424                 return recombine_pair_to_ex(*(seq.begin()));
 425         } else if ((seq_size==1) &&
 426                    is_exactly_a<add>((*seq.begin()).rest) &&
 427                    ex_to<numeric>((*seq.begin()).coeff).is_equal(_num1)) {
 428                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 429                 const add & addref = ex_to<add>((*seq.begin()).rest);
 430                 epvector *distrseq = new epvector();
 431                 distrseq->reserve(addref.seq.size());
 432                 epvector::const_iterator i = addref.seq.begin(), end = addref.seq.end();
 433                 while (i != end) {
 434                         distrseq->push_back(addref.combine_pair_with_coeff_to_pair(*i, overall_coeff));
 435                         ++i;
 436                 }
 437                 return (new add(distrseq,
 438                                 ex_to<numeric>(addref.overall_coeff).
 439                                 mul_dyn(ex_to<numeric>(overall_coeff))))
 440                       ->setflag(status_flags::dynallocated | status_flags::evaluated);
 441         }
 442         return this->hold();
 443 }
 444
 445 ex mul::evalf(int level) const
 446 {
 447         if (level==1)
 448                 return mul(seq,overall_coeff);
 449
 450         if (level==-max_recursion_level)
 451                 throw(std::runtime_error("max recursion level reached"));
 452
 453         epvector *s = new epvector();
 454         s->reserve(seq.size());
 455
 456         --level;
 457         epvector::const_iterator i = seq.begin(), end = seq.end();
 458         while (i != end) {
 459                 s->push_back(combine_ex_with_coeff_to_pair(i->rest.evalf(level),
 460                                                            i->coeff));
 461                 ++i;
 462         }
 463         return mul(s, overall_coeff.evalf(level));
 464 }
 465
 466 ex mul::evalm(void) const
 467 {
 468         // numeric*matrix
 469         if (seq.size() == 1 && seq[0].coeff.is_equal(_ex1)
 470          && is_a<matrix>(seq[0].rest))
 471                 return ex_to<matrix>(seq[0].rest).mul(ex_to<numeric>(overall_coeff));
 472
 473         // Evaluate children first, look whether there are any matrices at all
 474         // (there can be either no matrices or one matrix; if there were more
 475         // than one matrix, it would be a non-commutative product)
 476         epvector *s = new epvector;
 477         s->reserve(seq.size());
 478
 479         bool have_matrix = false;
 480         epvector::iterator the_matrix;
 481
 482         epvector::const_iterator i = seq.begin(), end = seq.end();
 483         while (i != end) {
 484                 const ex &m = recombine_pair_to_ex(*i).evalm();
 485                 s->push_back(split_ex_to_pair(m));
 486                 if (is_a<matrix>(m)) {
 487                         have_matrix = true;
 488                         the_matrix = s->end() - 1;
 489                 }
 490                 ++i;
 491         }
 492
 493         if (have_matrix) {
 494
 495                 // The product contained a matrix. We will multiply all other factors
 496                 // into that matrix.
 497                 matrix m = ex_to<matrix>(the_matrix->rest);
 498                 s->erase(the_matrix);
 499                 ex scalar = (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 500                 return m.mul_scalar(scalar);
 501
 502         } else
 503                 return (new mul(s, overall_coeff))->setflag(status_flags::dynallocated);
 504 }
 505
 506 ex mul::eval_ncmul(const exvector & v) const
 507 {
 508         if (seq.empty())
 509                 return inherited::eval_ncmul(v);
 510
 511         // Find first noncommutative element and call its eval_ncmul()
 512         epvector::const_iterator i = seq.begin(), end = seq.end();
 513         while (i != end) {
 514                 if (i->rest.return_type() == return_types::noncommutative)
 515                         return i->rest.eval_ncmul(v);
 516                 ++i;
 517         }
 518         return inherited::eval_ncmul(v);
 519 }
 520
 521 bool tryfactsubs(const ex & origfactor, const ex & patternfactor, unsigned & nummatches, lst & repls)
 522 {
 523         ex origbase;
 524         int origexponent;
 525         int origexpsign;
 526
 527         if (is_exactly_a<power>(origfactor) && origfactor.op(1).info(info_flags::integer)) {
 528                 origbase = origfactor.op(0);
 529                 int expon = ex_to<numeric>(origfactor.op(1)).to_int();
 530                 origexponent = expon > 0 ? expon : -expon;
 531                 origexpsign = expon > 0 ? 1 : -1;
 532         } else {
 533                 origbase = origfactor;
 534                 origexponent = 1;
 535                 origexpsign = 1;
 536         }
 537
 538         ex patternbase;
 539         int patternexponent;
 540         int patternexpsign;
 541
 542         if (is_exactly_a<power>(patternfactor) && patternfactor.op(1).info(info_flags::integer)) {
 543                 patternbase = patternfactor.op(0);
 544                 int expon = ex_to<numeric>(patternfactor.op(1)).to_int();
 545                 patternexponent = expon > 0 ? expon : -expon;
 546                 patternexpsign = expon > 0 ? 1 : -1;
 547         } else {
 548                 patternbase = patternfactor;
 549                 patternexponent = 1;
 550                 patternexpsign = 1;
 551         }
 552
 553         lst saverepls = repls;
 554         if (origexponent < patternexponent || origexpsign != patternexpsign || !origbase.match(patternbase,saverepls))
 555                 return false;
 556         repls = saverepls;
 557
 558         int newnummatches = origexponent / patternexponent;
 559         if (newnummatches < nummatches)
 560                 nummatches = newnummatches;
 561         return true;
 562 }
 563
 564 ex mul::algebraic_subs_mul(const lst & ls, const lst & lr, unsigned options) const
 565 {
 566         std::vector<bool> subsed(seq.size(), false);
 567         exvector subsresult(seq.size());
 568
 569         for (int i=0; i<ls.nops(); i++) {
 570
 571                 if (is_exactly_a<mul>(ls.op(i))) {
 572
 573                         unsigned nummatches = std::numeric_limits<unsigned>::max();
 574                         std::vector<bool> currsubsed(seq.size(), false);
 575                         bool succeed = true;
 576                         lst repls;
 577
 578                         for (int j=0; j<ls.op(i).nops(); j++) {
 579                                 bool found=false;
 580                                 for (int k=0; k<nops(); k++) {
 581                                         if (currsubsed[k] || subsed[k])
 582                                                 continue;
 583                                         if (tryfactsubs(op(k), ls.op(i).op(j), nummatches, repls)) {
 584                                                 currsubsed[k] = true;
 585                                                 found = true;
 586                                                 break;
 587                                         }
 588                                 }
 589                                 if (!found) {
 590                                         succeed = false;
 591                                         break;
 592                                 }
 593                         }
 594                         if (!succeed)
 595                                 continue;
 596
 597                         bool foundfirstsubsedfactor = false;
 598                         for (int j=0; j<subsed.size(); j++) {
 599                                 if (currsubsed[j]) {
 600                                         if (foundfirstsubsedfactor)
 601                                                 subsresult[j] = op(j);
 602                                         else {
 603                                                 foundfirstsubsedfactor = true;
 604                                                 subsresult[j] = op(j) * power(lr.op(i).subs(ex(repls), subs_options::subs_no_pattern) / ls.op(i).subs(ex(repls), subs_options::subs_no_pattern), nummatches);
 605                                         }
 606                                         subsed[j] = true;
 607                                 }
 608                         }
 609
 610                 } else {
 611
 612                         unsigned nummatches = std::numeric_limits<unsigned>::max();
 613                         lst repls;
 614
 615                         for (int j=0; j<this->nops(); j++) {
 616                                 if (!subsed[j] && tryfactsubs(op(j), ls.op(i), nummatches, repls)) {
 617                                         subsed[j] = true;
 618                                         subsresult[j] = op(j) * power(lr.op(i).subs(ex(repls), subs_options::subs_no_pattern) / ls.op(i).subs(ex(repls), subs_options::subs_no_pattern), nummatches);
 619                                 }
 620                         }
 621                 }
 622         }
 623
 624         bool subsfound = false;
 625         for (int i=0; i<subsed.size(); i++) {
 626                 if (subsed[i]) {
 627                         subsfound = true;
 628                         break;
 629                 }
 630         }
 631         if (!subsfound)
 632                 return basic::subs(ls, lr, options | subs_options::subs_algebraic);
 633
 634         exvector ev; ev.reserve(nops());
 635         for (int i=0; i<nops(); i++) {
 636                 if (subsed[i])
 637                         ev.push_back(subsresult[i]);
 638                 else
 639                         ev.push_back(op(i));
 640         }
 641
 642         return (new mul(ev))->setflag(status_flags::dynallocated);
 643 }
 644
 645 // protected
 646
 647 /** Implementation of ex::diff() for a product.  It applies the product rule.
 648  *  @see ex::diff */
 649 ex mul::derivative(const symbol & s) const
 650 {
 651         unsigned num = seq.size();
 652         exvector addseq;
 653         addseq.reserve(num);
 654
 655         // D(a*b*c) = D(a)*b*c + a*D(b)*c + a*b*D(c)
 656         epvector mulseq = seq;
 657         epvector::const_iterator i = seq.begin(), end = seq.end();
 658         epvector::iterator i2 = mulseq.begin();
 659         while (i != end) {
 660                 expair ep = split_ex_to_pair(power(i->rest, i->coeff - _ex1) *
 661                                              i->rest.diff(s));
 662                 ep.swap(*i2);
 663                 addseq.push_back((new mul(mulseq, overall_coeff * i->coeff))->setflag(status_flags::dynallocated));
 664                 ep.swap(*i2);
 665                 ++i; ++i2;
 666         }
 667         return (new add(addseq))->setflag(status_flags::dynallocated);
 668 }
 669
 670 int mul::compare_same_type(const basic & other) const
 671 {
 672         return inherited::compare_same_type(other);
 673 }
 674
 675 unsigned mul::return_type(void) const
 676 {
 677         if (seq.empty()) {
 678                 // mul without factors: should not happen, but commutes
 679                 return return_types::commutative;
 680         }
 681
 682         bool all_commutative = true;
 683         epvector::const_iterator noncommutative_element; // point to first found nc element
 684
 685         epvector::const_iterator i = seq.begin(), end = seq.end();
 686         while (i != end) {
 687                 unsigned rt = i->rest.return_type();
 688                 if (rt == return_types::noncommutative_composite)
 689                         return rt; // one ncc -> mul also ncc
 690                 if ((rt == return_types::noncommutative) && (all_commutative)) {
 691                         // first nc element found, remember position
 692                         noncommutative_element = i;
 693                         all_commutative = false;
 694                 }
 695                 if ((rt == return_types::noncommutative) && (!all_commutative)) {
 696                         // another nc element found, compare type_infos
 697                         if (noncommutative_element->rest.return_type_tinfo() != i->rest.return_type_tinfo()) {
 698                                 // diffent types -> mul is ncc
 699                                 return return_types::noncommutative_composite;
 700                         }
 701                 }
 702                 ++i;
 703         }
 704         // all factors checked
 705         return all_commutative ? return_types::commutative : return_types::noncommutative;
 706 }
 707
 708 unsigned mul::return_type_tinfo(void) const
 709 {
 710         if (seq.empty())
 711                 return tinfo_key;  // mul without factors: should not happen
 712
 713         // return type_info of first noncommutative element
 714         epvector::const_iterator i = seq.begin(), end = seq.end();
 715         while (i != end) {
 716                 if (i->rest.return_type() == return_types::noncommutative)
 717                         return i->rest.return_type_tinfo();
 718                 ++i;
 719         }
 720         // no noncommutative element found, should not happen
 721         return tinfo_key;
 722 }
 723
 724 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 725 {
 726         return (new mul(v, oc))->setflag(status_flags::dynallocated);
 727 }
 728
 729 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 730 {
 731         return (new mul(vp, oc))->setflag(status_flags::dynallocated);
 732 }
 733
 734 expair mul::split_ex_to_pair(const ex & e) const
 735 {
 736         if (is_exactly_a<power>(e)) {
 737                 const power & powerref = ex_to<power>(e);
 738                 if (is_exactly_a<numeric>(powerref.exponent))
 739                         return expair(powerref.basis,powerref.exponent);
 740         }
 741         return expair(e,_ex1);
 742 }
 743
 744 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 745                                           const ex & c) const
 746 {
 747         // to avoid duplication of power simplification rules,
 748         // we create a temporary power object
 749         // otherwise it would be hard to correctly evaluate
 750         // expression like (4^(1/3))^(3/2)
 751         if (c.is_equal(_ex1))
 752                 return split_ex_to_pair(e);
 753
 754         return split_ex_to_pair(power(e,c));
 755 }
 756
 757 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 758                                             const ex & c) const
 759 {
 760         // to avoid duplication of power simplification rules,
 761         // we create a temporary power object
 762         // otherwise it would be hard to correctly evaluate
 763         // expression like (4^(1/3))^(3/2)
 764         if (c.is_equal(_ex1))
 765                 return p;
 766
 767         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 768 }
 769
 770 ex mul::recombine_pair_to_ex(const expair & p) const
 771 {
 772         if (ex_to<numeric>(p.coeff).is_equal(_num1))
 773                 return p.rest;
 774         else
 775                 return (new power(p.rest,p.coeff))->setflag(status_flags::dynallocated);
 776 }
 777
 778 bool mul::expair_needs_further_processing(epp it)
 779 {
 780         if (is_exactly_a<mul>(it->rest) &&
 781                 ex_to<numeric>(it->coeff).is_integer()) {
 782                 // combined pair is product with integer power -> expand it
 783                 *it = split_ex_to_pair(recombine_pair_to_ex(*it));
 784                 return true;
 785         }
 786         if (is_exactly_a<numeric>(it->rest)) {
 787                 expair ep = split_ex_to_pair(recombine_pair_to_ex(*it));
 788                 if (!ep.is_equal(*it)) {
 789                         // combined pair is a numeric power which can be simplified
 790                         *it = ep;
 791                         return true;
 792                 }
 793                 if (it->coeff.is_equal(_ex1)) {
 794                         // combined pair has coeff 1 and must be moved to the end
 795                         return true;
 796                 }
 797         }
 798         return false;
 799 }
 800
 801 ex mul::default_overall_coeff(void) const
 802 {
 803         return _ex1;
 804 }
 805
 806 void mul::combine_overall_coeff(const ex & c)
 807 {
 808         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 809         GINAC_ASSERT(is_exactly_a<numeric>(c));
 810         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c));
 811 }
 812
 813 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 814 {
 815         GINAC_ASSERT(is_exactly_a<numeric>(overall_coeff));
 816         GINAC_ASSERT(is_exactly_a<numeric>(c1));
 817         GINAC_ASSERT(is_exactly_a<numeric>(c2));
 818         overall_coeff = ex_to<numeric>(overall_coeff).mul_dyn(ex_to<numeric>(c1).power(ex_to<numeric>(c2)));
 819 }
 820
 821 bool mul::can_make_flat(const expair & p) const
 822 {
 823         GINAC_ASSERT(is_exactly_a<numeric>(p.coeff));
 824         // this assertion will probably fail somewhere
 825         // it would require a more careful make_flat, obeying the power laws
 826         // probably should return true only if p.coeff is integer
 827         return ex_to<numeric>(p.coeff).is_equal(_num1);
 828 }
 829
 830 ex mul::expand(unsigned options) const
 831 {
 832         // First, expand the children
 833         epvector * expanded_seqp = expandchildren(options);
 834         const epvector & expanded_seq = (expanded_seqp == NULL) ? seq : *expanded_seqp;
 835
 836         // Now, look for all the factors that are sums and multiply each one out
 837         // with the next one that is found while collecting the factors which are
 838         // not sums
 839         int number_of_adds = 0;
 840         ex last_expanded = _ex1;
 841         epvector non_adds;
 842         non_adds.reserve(expanded_seq.size());
 843         epvector::const_iterator cit = expanded_seq.begin(), last = expanded_seq.end();
 844         while (cit != last) {
 845                 if (is_exactly_a<add>(cit->rest) &&
 846                         (cit->coeff.is_equal(_ex1))) {
 847                         ++number_of_adds;
 848                         if (is_exactly_a<add>(last_expanded)) {
 849 #if 0
 850                                 // Expand a product of two sums, simple and robust version.
 851                                 const add & add1 = ex_to<add>(last_expanded);
 852                                 const add & add2 = ex_to<add>(cit->rest);
 853                                 const int n1 = add1.nops();
 854                                 const int n2 = add2.nops();
 855                                 ex tmp_accu;
 856                                 exvector distrseq;
 857                                 distrseq.reserve(n2);
 858                                 for (int i1=0; i1<n1; ++i1) {
 859                                         distrseq.clear();
 860                                         // cache the first operand (for efficiency):
 861                                         const ex op1 = add1.op(i1);
 862                                         for (int i2=0; i2<n2; ++i2)
 863                                                 distrseq.push_back(op1 * add2.op(i2));
 864                                         tmp_accu += (new add(distrseq))->
 865                                                      setflag(status_flags::dynallocated);
 866                                 }
 867                                 last_expanded = tmp_accu;
 868 #else
 869                                 // Expand a product of two sums, aggressive version.
 870                                 // Caring for the overall coefficients in separate loops can
 871                                 // sometimes give a performance gain of up to 15%!
 872
 873                                 const int sizedifference = ex_to<add>(last_expanded).seq.size()-ex_to<add>(cit->rest).seq.size();
 874                                 // add2 is for the inner loop and should be the bigger of the two sums
 875                                 // in the presence of asymptotically good sorting:
 876                                 const add& add1 = (sizedifference<0 ? ex_to<add>(last_expanded) : ex_to<add>(cit->rest));
 877                                 const add& add2 = (sizedifference<0 ? ex_to<add>(cit->rest) : ex_to<add>(last_expanded));
 878                                 const epvector::const_iterator add1begin = add1.seq.begin();
 879                                 const epvector::const_iterator add1end   = add1.seq.end();
 880                                 const epvector::const_iterator add2begin = add2.seq.begin();
 881                                 const epvector::const_iterator add2end   = add2.seq.end();
 882                                 epvector distrseq;
 883                                 distrseq.reserve(add1.seq.size()+add2.seq.size());
 884                                 // Multiply add2 with the overall coefficient of add1 and append it to distrseq:
 885                                 if (!add1.overall_coeff.is_zero()) {
 886                                         if (add1.overall_coeff.is_equal(_ex1))
 887                                                 distrseq.insert(distrseq.end(),add2begin,add2end);
 888                                         else
 889                                                 for (epvector::const_iterator i=add2begin; i!=add2end; ++i)
 890                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add1.overall_coeff))));
 891                                 }
 892                                 // Multiply add1 with the overall coefficient of add2 and append it to distrseq:
 893                                 if (!add2.overall_coeff.is_zero()) {
 894                                         if (add2.overall_coeff.is_equal(_ex1))
 895                                                 distrseq.insert(distrseq.end(),add1begin,add1end);
 896                                         else
 897                                                 for (epvector::const_iterator i=add1begin; i!=add1end; ++i)
 898                                                         distrseq.push_back(expair(i->rest, ex_to<numeric>(i->coeff).mul_dyn(ex_to<numeric>(add2.overall_coeff))));
 899                                 }
 900                                 // Compute the new overall coefficient and put it together:
 901                                 ex tmp_accu = (new add(distrseq, add1.overall_coeff*add2.overall_coeff))->setflag(status_flags::dynallocated);
 902                                 // Multiply explicitly all non-numeric terms of add1 and add2:
 903                                 for (epvector::const_iterator i1=add1begin; i1!=add1end; ++i1) {
 904                                         // We really have to combine terms here in order to compactify
 905                                         // the result.  Otherwise it would become waayy tooo bigg.
 906                                         numeric oc;
 907                                         distrseq.clear();
 908                                         for (epvector::const_iterator i2=add2begin; i2!=add2end; ++i2) {
 909                                                 // Don't push_back expairs which might have a rest that evaluates to a numeric,
 910                                                 // since that would violate an invariant of expairseq:
 911                                                 const ex rest = (new mul(i1->rest, i2->rest))->setflag(status_flags::dynallocated);
 912                                                 if (is_exactly_a<numeric>(rest))
 913                                                         oc += ex_to<numeric>(rest).mul(ex_to<numeric>(i1->coeff).mul(ex_to<numeric>(i2->coeff)));
 914                                                 else
 915                                                         distrseq.push_back(expair(rest, ex_to<numeric>(i1->coeff).mul_dyn(ex_to<numeric>(i2->coeff))));
 916                                         }
 917                                         tmp_accu += (new add(distrseq, oc))->setflag(status_flags::dynallocated);
 918                                 }
 919                                 last_expanded = tmp_accu;
 920 #endif
 921                         } else {
 922                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 923                                 last_expanded = cit->rest;
 924                         }
 925                 } else {
 926                         non_adds.push_back(*cit);
 927                 }
 928                 ++cit;
 929         }
 930         if (expanded_seqp)
 931                 delete expanded_seqp;
 932
 933         // Now the only remaining thing to do is to multiply the factors which
 934         // were not sums into the "last_expanded" sum
 935         if (is_exactly_a<add>(last_expanded)) {
 936                 const add & finaladd = ex_to<add>(last_expanded);
 937                 exvector distrseq;
 938                 int n = finaladd.nops();
 939                 distrseq.reserve(n);
 940                 for (int i=0; i<n; ++i) {
 941                         epvector factors = non_adds;
 942                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 943                         distrseq.push_back((new mul(factors, overall_coeff))->
 944                                             setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 945                 }
 946                 return ((new add(distrseq))->
 947                         setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0)));
 948         }
 949         non_adds.push_back(split_ex_to_pair(last_expanded));
 950         return (new mul(non_adds, overall_coeff))->
 951                 setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
 952 }
 953
 954
 955 //////////
 956 // new virtual functions which can be overridden by derived classes
 957 //////////
 958
 959 // none
 960
 961 //////////
 962 // non-virtual functions in this class
 963 //////////
 964
 965
 966 /** Member-wise expand the expairs representing this sequence.  This must be
 967  *  overridden from expairseq::expandchildren() and done iteratively in order
 968  *  to allow for early cancallations and thus safe memory.
 969  *
 970  *  @see mul::expand()
 971  *  @return pointer to epvector containing expanded representation or zero
 972  *  pointer, if sequence is unchanged. */
 973 epvector * mul::expandchildren(unsigned options) const
 974 {
 975         const epvector::const_iterator last = seq.end();
 976         epvector::const_iterator cit = seq.begin();
 977         while (cit!=last) {
 978                 const ex & factor = recombine_pair_to_ex(*cit);
 979                 const ex & expanded_factor = factor.expand(options);
 980                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 981
 982                         // something changed, copy seq, eval and return it
 983                         epvector *s = new epvector;
 984                         s->reserve(seq.size());
 985
 986                         // copy parts of seq which are known not to have changed
 987                         epvector::const_iterator cit2 = seq.begin();
 988                         while (cit2!=cit) {
 989                                 s->push_back(*cit2);
 990                                 ++cit2;
 991                         }
 992                         // copy first changed element
 993                         s->push_back(split_ex_to_pair(expanded_factor));
 994                         ++cit2;
 995                         // copy rest
 996                         while (cit2!=last) {
 997                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 998                                 ++cit2;
 999                         }
1000                         return s;
1001                 }
1002                 ++cit;
1003         }
1004
1005         return 0; // nothing has changed
1006 }
1007
1008 } // namespace GiNaC