ginac/mul.cpp

   1 /** @file mul.cpp
   2  *
   3  *  Implementation of GiNaC's products of expressions. */
   4
   5 /*
   6  *  GiNaC Copyright (C) 1999-2000 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 <vector>
  24 #include <stdexcept>
  25
  26 #include "mul.h"
  27 #include "add.h"
  28 #include "power.h"
  29 #include "archive.h"
  30 #include "debugmsg.h"
  31 #include "utils.h"
  32
  33 #ifndef NO_NAMESPACE_GINAC
  34 namespace GiNaC {
  35 #endif // ndef NO_NAMESPACE_GINAC
  36
  37 GINAC_IMPLEMENT_REGISTERED_CLASS(mul, expairseq)
  38
  39 //////////
  40 // default constructor, destructor, copy constructor assignment operator and helpers
  41 //////////
  42
  43 // public
  44
  45 mul::mul()
  46 {
  47     debugmsg("mul default constructor",LOGLEVEL_CONSTRUCT);
  48     tinfo_key = TINFO_mul;
  49 }
  50
  51 mul::~mul()
  52 {
  53     debugmsg("mul destructor",LOGLEVEL_DESTRUCT);
  54     destroy(0);
  55 }
  56
  57 mul::mul(const mul & other)
  58 {
  59     debugmsg("mul copy constructor",LOGLEVEL_CONSTRUCT);
  60     copy(other);
  61 }
  62
  63 const mul & mul::operator=(const mul & other)
  64 {
  65     debugmsg("mul operator=",LOGLEVEL_ASSIGNMENT);
  66     if (this != &other) {
  67         destroy(1);
  68         copy(other);
  69     }
  70     return *this;
  71 }
  72
  73 // protected
  74
  75 void mul::copy(const mul & other)
  76 {
  77     inherited::copy(other);
  78 }
  79
  80 void mul::destroy(bool call_parent)
  81 {
  82     if (call_parent) inherited::destroy(call_parent);
  83 }
  84
  85 //////////
  86 // other constructors
  87 //////////
  88
  89 // public
  90
  91 mul::mul(const ex & lh, const ex & rh)
  92 {
  93     debugmsg("mul constructor from ex,ex",LOGLEVEL_CONSTRUCT);
  94     tinfo_key = TINFO_mul;
  95     overall_coeff = _ex1();
  96     construct_from_2_ex(lh,rh);
  97     GINAC_ASSERT(is_canonical());
  98 }
  99
 100 mul::mul(const exvector & v)
 101 {
 102     debugmsg("mul constructor from exvector",LOGLEVEL_CONSTRUCT);
 103     tinfo_key = TINFO_mul;
 104     overall_coeff = _ex1();
 105     construct_from_exvector(v);
 106     GINAC_ASSERT(is_canonical());
 107 }
 108
 109 mul::mul(const epvector & v)
 110 {
 111     debugmsg("mul constructor from epvector",LOGLEVEL_CONSTRUCT);
 112     tinfo_key = TINFO_mul;
 113     overall_coeff = _ex1();
 114     construct_from_epvector(v);
 115     GINAC_ASSERT(is_canonical());
 116 }
 117
 118 mul::mul(const epvector & v, const ex & oc)
 119 {
 120     debugmsg("mul constructor from epvector,ex",LOGLEVEL_CONSTRUCT);
 121     tinfo_key = TINFO_mul;
 122     overall_coeff = oc;
 123     construct_from_epvector(v);
 124     GINAC_ASSERT(is_canonical());
 125 }
 126
 127 mul::mul(epvector * vp, const ex & oc)
 128 {
 129     debugmsg("mul constructor from epvector *,ex",LOGLEVEL_CONSTRUCT);
 130     tinfo_key = TINFO_mul;
 131     GINAC_ASSERT(vp!=0);
 132     overall_coeff = oc;
 133     construct_from_epvector(*vp);
 134     delete vp;
 135     GINAC_ASSERT(is_canonical());
 136 }
 137
 138 mul::mul(const ex & lh, const ex & mh, const ex & rh)
 139 {
 140     debugmsg("mul constructor from ex,ex,ex",LOGLEVEL_CONSTRUCT);
 141     tinfo_key = TINFO_mul;
 142     exvector factors;
 143     factors.reserve(3);
 144     factors.push_back(lh);
 145     factors.push_back(mh);
 146     factors.push_back(rh);
 147     overall_coeff = _ex1();
 148     construct_from_exvector(factors);
 149     GINAC_ASSERT(is_canonical());
 150 }
 151
 152 //////////
 153 // archiving
 154 //////////
 155
 156 /** Construct object from archive_node. */
 157 mul::mul(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
 158 {
 159     debugmsg("mul constructor from archive_node", LOGLEVEL_CONSTRUCT);
 160 }
 161
 162 /** Unarchive the object. */
 163 ex mul::unarchive(const archive_node &n, const lst &sym_lst)
 164 {
 165     return (new mul(n, sym_lst))->setflag(status_flags::dynallocated);
 166 }
 167
 168 /** Archive the object. */
 169 void mul::archive(archive_node &n) const
 170 {
 171     inherited::archive(n);
 172 }
 173
 174 //////////
 175 // functions overriding virtual functions from bases classes
 176 //////////
 177
 178 // public
 179
 180 basic * mul::duplicate() const
 181 {
 182     debugmsg("mul duplicate",LOGLEVEL_ASSIGNMENT);
 183     return new mul(*this);
 184 }
 185
 186 void mul::print(ostream & os, unsigned upper_precedence) const
 187 {
 188     debugmsg("mul print",LOGLEVEL_PRINT);
 189     if (precedence<=upper_precedence) os << "(";
 190     bool first=true;
 191     // first print the overall numeric coefficient:
 192     numeric coeff = ex_to_numeric(overall_coeff);
 193     if (coeff.csgn()==-1) os << '-';
 194     if (!coeff.is_equal(_num1()) &&
 195         !coeff.is_equal(_num_1())) {
 196         if (coeff.is_rational()) {
 197             if (coeff.is_negative())
 198                 os << -coeff;
 199             else
 200                 os << coeff;
 201         } else {
 202             if (coeff.csgn()==-1)
 203                 (-coeff).print(os, precedence);
 204             else
 205                 coeff.print(os, precedence);
 206         }
 207         os << '*';
 208     }
 209     // then proceed with the remaining factors:
 210     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 211         if (!first) {
 212             os << '*';
 213         } else {
 214             first=false;
 215         }
 216         recombine_pair_to_ex(*cit).print(os,precedence);
 217     }
 218     if (precedence<=upper_precedence) os << ")";
 219 }
 220
 221 void mul::printraw(ostream & os) const
 222 {
 223     debugmsg("mul printraw",LOGLEVEL_PRINT);
 224
 225     os << "*(";
 226     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 227         os << "(";
 228         (*it).rest.bp->printraw(os);
 229         os << ",";
 230         (*it).coeff.bp->printraw(os);
 231         os << "),";
 232     }
 233     os << ",hash=" << hashvalue << ",flags=" << flags;
 234     os << ")";
 235 }
 236
 237 void mul::printcsrc(ostream & os, unsigned type, unsigned upper_precedence) const
 238 {
 239     debugmsg("mul print csrc", LOGLEVEL_PRINT);
 240     if (precedence <= upper_precedence)
 241         os << "(";
 242
 243     if (!overall_coeff.is_equal(_ex1())) {
 244         overall_coeff.bp->printcsrc(os,type,precedence);
 245         os << "*";
 246     }
 247
 248     // Print arguments, separated by "*" or "/"
 249     epvector::const_iterator it = seq.begin();
 250     epvector::const_iterator itend = seq.end();
 251     while (it != itend) {
 252
 253         // If the first argument is a negative integer power, it gets printed as "1.0/<expr>"
 254         if (it == seq.begin() && ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0) {
 255             if (type == csrc_types::ctype_cl_N)
 256                 os << "recip(";
 257             else
 258                 os << "1.0/";
 259         }
 260
 261         // If the exponent is 1 or -1, it is left out
 262         if (it->coeff.compare(_ex1()) == 0 || it->coeff.compare(_num_1()) == 0)
 263             it->rest.bp->printcsrc(os, type, precedence);
 264         else
 265             // outer parens around ex needed for broken gcc-2.95 parser:
 266             (ex(power(it->rest, abs(ex_to_numeric(it->coeff))))).bp->printcsrc(os, type, upper_precedence);
 267
 268         // Separator is "/" for negative integer powers, "*" otherwise
 269         it++;
 270         if (it != itend) {
 271             if (ex_to_numeric(it->coeff).is_integer() && it->coeff.compare(_num0()) < 0)
 272                 os << "/";
 273             else
 274                 os << "*";
 275         }
 276     }
 277     if (precedence <= upper_precedence)
 278         os << ")";
 279 }
 280
 281 bool mul::info(unsigned inf) const
 282 {
 283     switch (inf) {
 284         case info_flags::polynomial:
 285         case info_flags::integer_polynomial:
 286         case info_flags::cinteger_polynomial:
 287         case info_flags::rational_polynomial:
 288         case info_flags::crational_polynomial:
 289         case info_flags::rational_function: {
 290             for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 291                 if (!(recombine_pair_to_ex(*i).info(inf)))
 292                     return false;
 293             }
 294             return overall_coeff.info(inf);
 295         }
 296         case info_flags::algebraic: {
 297             for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
 298                 if ((recombine_pair_to_ex(*i).info(inf)))
 299                     return true;
 300             }
 301             return false;
 302         }
 303     }
 304     return inherited::info(inf);
 305 }
 306
 307 typedef vector<int> intvector;
 308
 309 int mul::degree(const symbol & s) const
 310 {
 311     int deg_sum = 0;
 312     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 313         deg_sum+=(*cit).rest.degree(s) * ex_to_numeric((*cit).coeff).to_int();
 314     }
 315     return deg_sum;
 316 }
 317
 318 int mul::ldegree(const symbol & s) const
 319 {
 320     int deg_sum = 0;
 321     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 322         deg_sum+=(*cit).rest.ldegree(s) * ex_to_numeric((*cit).coeff).to_int();
 323     }
 324     return deg_sum;
 325 }
 326
 327 ex mul::coeff(const symbol & s, int n) const
 328 {
 329     exvector coeffseq;
 330     coeffseq.reserve(seq.size()+1);
 331
 332     if (n==0) {
 333         // product of individual coeffs
 334         // if a non-zero power of s is found, the resulting product will be 0
 335         epvector::const_iterator it=seq.begin();
 336         while (it!=seq.end()) {
 337             coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 338             ++it;
 339         }
 340         coeffseq.push_back(overall_coeff);
 341         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 342     }
 343
 344     epvector::const_iterator it=seq.begin();
 345     bool coeff_found=0;
 346     while (it!=seq.end()) {
 347         ex t=recombine_pair_to_ex(*it);
 348         ex c=t.coeff(s,n);
 349         if (!c.is_zero()) {
 350             coeffseq.push_back(c);
 351             coeff_found=1;
 352         } else {
 353             coeffseq.push_back(t);
 354         }
 355         ++it;
 356     }
 357     if (coeff_found) {
 358         coeffseq.push_back(overall_coeff);
 359         return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 360     }
 361
 362     return _ex0();
 363 }
 364
 365 ex mul::eval(int level) const
 366 {
 367     // simplifications  *(...,x;0) -> 0
 368     //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 369     //                  *(x;1) -> x
 370     //                  *(;c) -> c
 371
 372     debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 373
 374     epvector * evaled_seqp=evalchildren(level);
 375     if (evaled_seqp!=0) {
 376         // do more evaluation later
 377         return (new mul(evaled_seqp,overall_coeff))->
 378                    setflag(status_flags::dynallocated);
 379     }
 380
 381 #ifdef DO_GINAC_ASSERT
 382     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 383         GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 384                (!(ex_to_numeric((*cit).coeff).is_integer())));
 385         GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 386         if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 387             printtree(cerr,0);
 388         }
 389         GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 390         /* for paranoia */
 391         expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 392         GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 393         GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 394         /* end paranoia */
 395     }
 396 #endif // def DO_GINAC_ASSERT
 397
 398     if (flags & status_flags::evaluated) {
 399         GINAC_ASSERT(seq.size()>0);
 400         GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 401         return *this;
 402     }
 403
 404     int seq_size=seq.size();
 405     if (overall_coeff.is_equal(_ex0())) {
 406         // *(...,x;0) -> 0
 407         return _ex0();
 408     } else if (seq_size==0) {
 409         // *(;c) -> c
 410         return overall_coeff;
 411     } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 412         // *(x;1) -> x
 413         return recombine_pair_to_ex(*(seq.begin()));
 414     } else if ((seq_size==1) &&
 415                is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 416                ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 417         // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 418         const add & addref=ex_to_add((*seq.begin()).rest);
 419         epvector distrseq;
 420         distrseq.reserve(addref.seq.size());
 421         for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 422             distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit,
 423                                    overall_coeff));
 424         }
 425         return (new add(distrseq,
 426                         ex_to_numeric(addref.overall_coeff).
 427                         mul_dyn(ex_to_numeric(overall_coeff))))
 428             ->setflag(status_flags::dynallocated |
 429                       status_flags::evaluated);
 430     }
 431     return this->hold();
 432 }
 433
 434 ex mul::evalf(int level) const
 435 {
 436     if (level==1)
 437         return mul(seq,overall_coeff);
 438
 439     if (level==-max_recursion_level)
 440         throw(std::runtime_error("max recursion level reached"));
 441
 442     epvector s;
 443     s.reserve(seq.size());
 444
 445     --level;
 446     for (epvector::const_iterator it=seq.begin(); it!=seq.end(); ++it) {
 447         s.push_back(combine_ex_with_coeff_to_pair((*it).rest.evalf(level),
 448                                                   (*it).coeff));
 449     }
 450     return mul(s,overall_coeff.evalf(level));
 451 }
 452
 453 exvector mul::get_indices(void) const
 454 {
 455     // return union of indices of factors
 456     exvector iv;
 457     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 458         exvector subiv=(*cit).rest.get_indices();
 459         iv.reserve(iv.size()+subiv.size());
 460         for (exvector::const_iterator cit2=subiv.begin(); cit2!=subiv.end(); ++cit2) {
 461             iv.push_back(*cit2);
 462         }
 463     }
 464     return iv;
 465 }
 466
 467 ex mul::simplify_ncmul(const exvector & v) const
 468 {
 469     throw(std::logic_error("mul::simplify_ncmul() should never have been called!"));
 470 }
 471
 472 // protected
 473
 474 /** Implementation of ex::diff() for a product. It applies the product rule.
 475  *  @see ex::diff */
 476 ex mul::derivative(const symbol & s) const
 477 {
 478     exvector new_seq;
 479     new_seq.reserve(seq.size());
 480
 481     // D(a*b*c)=D(a)*b*c+a*D(b)*c+a*b*D(c)
 482     for (unsigned i=0; i!=seq.size(); i++) {
 483         epvector sub_seq = seq;
 484         sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff*
 485                                       power(sub_seq[i].rest,sub_seq[i].coeff-1)*
 486                                       sub_seq[i].rest.diff(s));
 487         new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated));
 488     }
 489     return (new add(new_seq))->setflag(status_flags::dynallocated);
 490 }
 491
 492 int mul::compare_same_type(const basic & other) const
 493 {
 494     return inherited::compare_same_type(other);
 495 }
 496
 497 bool mul::is_equal_same_type(const basic & other) const
 498 {
 499     return inherited::is_equal_same_type(other);
 500 }
 501
 502 unsigned mul::return_type(void) const
 503 {
 504     if (seq.size()==0) {
 505         // mul without factors: should not happen, but commutes
 506         return return_types::commutative;
 507     }
 508
 509     bool all_commutative = 1;
 510     unsigned rt;
 511     epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 512
 513     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 514         rt=(*cit).rest.return_type();
 515         if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 516         if ((rt==return_types::noncommutative)&&(all_commutative)) {
 517             // first nc element found, remember position
 518             cit_noncommutative_element = cit;
 519             all_commutative = 0;
 520         }
 521         if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 522             // another nc element found, compare type_infos
 523             if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 524                 // diffent types -> mul is ncc
 525                 return return_types::noncommutative_composite;
 526             }
 527         }
 528     }
 529     // all factors checked
 530     return all_commutative ? return_types::commutative : return_types::noncommutative;
 531 }
 532
 533 unsigned mul::return_type_tinfo(void) const
 534 {
 535     if (seq.size()==0) {
 536         // mul without factors: should not happen
 537         return tinfo_key;
 538     }
 539     // return type_info of first noncommutative element
 540     for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 541         if ((*cit).rest.return_type()==return_types::noncommutative) {
 542             return (*cit).rest.return_type_tinfo();
 543         }
 544     }
 545     // no noncommutative element found, should not happen
 546     return tinfo_key;
 547 }
 548
 549 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 550 {
 551     return (new mul(v,oc))->setflag(status_flags::dynallocated);
 552 }
 553
 554 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 555 {
 556     return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 557 }
 558
 559 expair mul::split_ex_to_pair(const ex & e) const
 560 {
 561     if (is_ex_exactly_of_type(e,power)) {
 562         const power & powerref=ex_to_power(e);
 563         if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 564             return expair(powerref.basis,powerref.exponent);
 565         }
 566     }
 567     return expair(e,_ex1());
 568 }
 569
 570 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 571                                           const ex & c) const
 572 {
 573     // to avoid duplication of power simplification rules,
 574     // we create a temporary power object
 575     // otherwise it would be hard to correctly simplify
 576     // expression like (4^(1/3))^(3/2)
 577     if (are_ex_trivially_equal(c,_ex1())) {
 578         return split_ex_to_pair(e);
 579     }
 580     return split_ex_to_pair(power(e,c));
 581 }
 582
 583 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 584                                             const ex & c) const
 585 {
 586     // to avoid duplication of power simplification rules,
 587     // we create a temporary power object
 588     // otherwise it would be hard to correctly simplify
 589     // expression like (4^(1/3))^(3/2)
 590     if (are_ex_trivially_equal(c,_ex1())) {
 591         return p;
 592     }
 593     return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 594 }
 595
 596 ex mul::recombine_pair_to_ex(const expair & p) const
 597 {
 598     // if (p.coeff.compare(_ex1())==0) {
 599     // if (are_ex_trivially_equal(p.coeff,_ex1())) {
 600     if (ex_to_numeric(p.coeff).is_equal(_num1())) {
 601         return p.rest;
 602     } else {
 603         return power(p.rest,p.coeff);
 604     }
 605 }
 606
 607 bool mul::expair_needs_further_processing(epp it)
 608 {
 609     if (is_ex_exactly_of_type((*it).rest,mul) &&
 610         ex_to_numeric((*it).coeff).is_integer()) {
 611         // combined pair is product with integer power -> expand it
 612         *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 613         return true;
 614     }
 615     if (is_ex_exactly_of_type((*it).rest,numeric)) {
 616         expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 617         if (!ep.is_equal(*it)) {
 618             // combined pair is a numeric power which can be simplified
 619             *it=ep;
 620             return true;
 621         }
 622         if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 623             // combined pair has coeff 1 and must be moved to the end
 624             return true;
 625         }
 626     }
 627     return false;
 628 }
 629
 630 ex mul::default_overall_coeff(void) const
 631 {
 632     return _ex1();
 633 }
 634
 635 void mul::combine_overall_coeff(const ex & c)
 636 {
 637     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 638     GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 639     overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 640 }
 641
 642 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 643 {
 644     GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 645     GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 646     GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 647     overall_coeff = ex_to_numeric(overall_coeff).
 648                         mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 649 }
 650
 651 bool mul::can_make_flat(const expair & p) const
 652 {
 653     GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 654     // this assertion will probably fail somewhere
 655     // it would require a more careful make_flat, obeying the power laws
 656     // probably should return true only if p.coeff is integer
 657     return ex_to_numeric(p.coeff).is_equal(_num1());
 658 }
 659
 660 ex mul::expand(unsigned options) const
 661 {
 662     if (flags & status_flags::expanded)
 663         return *this;
 664
 665     exvector sub_expanded_seq;
 666     intvector positions_of_adds;
 667     intvector number_of_add_operands;
 668
 669     epvector * expanded_seqp = expandchildren(options);
 670
 671     const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 672
 673     positions_of_adds.resize(expanded_seq.size());
 674     number_of_add_operands.resize(expanded_seq.size());
 675
 676     int number_of_adds = 0;
 677     int number_of_expanded_terms = 1;
 678
 679     unsigned current_position = 0;
 680     epvector::const_iterator last = expanded_seq.end();
 681     for (epvector::const_iterator cit=expanded_seq.begin(); cit!=last; ++cit) {
 682         if (is_ex_exactly_of_type((*cit).rest,add)&&
 683             (ex_to_numeric((*cit).coeff).is_equal(_num1()))) {
 684             positions_of_adds[number_of_adds] = current_position;
 685             const add & expanded_addref = ex_to_add((*cit).rest);
 686             unsigned addref_nops = expanded_addref.nops();
 687             number_of_add_operands[number_of_adds] = addref_nops;
 688             number_of_expanded_terms *= addref_nops;
 689             number_of_adds++;
 690         }
 691         current_position++;
 692     }
 693
 694     if (number_of_adds==0) {
 695         if (expanded_seqp==0) {
 696             return this->setflag(status_flags::expanded);
 697         }
 698         return (new mul(expanded_seqp,overall_coeff))->
 699             setflag(status_flags::dynallocated |
 700                     status_flags::expanded);
 701     }
 702
 703     exvector distrseq;
 704     distrseq.reserve(number_of_expanded_terms);
 705
 706     intvector k;
 707     k.resize(number_of_adds);
 708
 709     int l;
 710     for (l=0; l<number_of_adds; l++) {
 711         k[l]=0;
 712     }
 713
 714     while (1) {
 715         epvector term;
 716         term = expanded_seq;
 717         for (l=0; l<number_of_adds; l++) {
 718             const add & addref=ex_to_add(expanded_seq[positions_of_adds[l]].rest);
 719             GINAC_ASSERT(term[positions_of_adds[l]].coeff.compare(_ex1())==0);
 720             term[positions_of_adds[l]]=split_ex_to_pair(addref.op(k[l]));
 721         }
 722         distrseq.push_back((new mul(term,overall_coeff))->
 723                            setflag(status_flags::dynallocated |
 724                                    status_flags::expanded));
 725
 726         // increment k[]
 727         l=number_of_adds-1;
 728         while ((l>=0) && ((++k[l])>=number_of_add_operands[l])) {
 729             k[l]=0;
 730             l--;
 731         }
 732         if (l<0) break;
 733     }
 734
 735     if (expanded_seqp!=0)
 736         delete expanded_seqp;
 737
 738     return (new add(distrseq))->setflag(status_flags::dynallocated |
 739                                         status_flags::expanded);
 740 }
 741
 742 //////////
 743 // new virtual functions which can be overridden by derived classes
 744 //////////
 745
 746 // none
 747
 748 //////////
 749 // non-virtual functions in this class
 750 //////////
 751
 752 epvector * mul::expandchildren(unsigned options) const
 753 {
 754     epvector::const_iterator last = seq.end();
 755     epvector::const_iterator cit = seq.begin();
 756     while (cit!=last) {
 757         const ex & factor = recombine_pair_to_ex(*cit);
 758         const ex & expanded_factor = factor.expand(options);
 759         if (!are_ex_trivially_equal(factor,expanded_factor)) {
 760
 761             // something changed, copy seq, eval and return it
 762             epvector *s=new epvector;
 763             s->reserve(seq.size());
 764
 765             // copy parts of seq which are known not to have changed
 766             epvector::const_iterator cit2 = seq.begin();
 767             while (cit2!=cit) {
 768                 s->push_back(*cit2);
 769                 ++cit2;
 770             }
 771             // copy first changed element
 772             s->push_back(split_ex_to_pair(expanded_factor));
 773             ++cit2;
 774             // copy rest
 775             while (cit2!=last) {
 776                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 777                 ++cit2;
 778             }
 779             return s;
 780         }
 781         ++cit;
 782     }
 783
 784     return 0; // nothing has changed
 785 }
 786
 787 //////////
 788 // static member variables
 789 //////////
 790
 791 // protected
 792
 793 unsigned mul::precedence = 50;
 794
 795
 796 //////////
 797 // global constants
 798 //////////
 799
 800 const mul some_mul;
 801 const type_info & typeid_mul = typeid(some_mul);
 802
 803 #ifndef NO_NAMESPACE_GINAC
 804 } // namespace GiNaC
 805 #endif // ndef NO_NAMESPACE_GINAC