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(false);
  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(true);
  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(std::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(std::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(std::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 std::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                 if (ex_to_numeric(cit->coeff).is_integer())
 314                         deg_sum+=cit->rest.degree(s) * ex_to_numeric(cit->coeff).to_int();
 315         }
 316         return deg_sum;
 317 }
 318
 319 int mul::ldegree(const symbol & s) const
 320 {
 321         int deg_sum = 0;
 322         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 323                 if (ex_to_numeric(cit->coeff).is_integer())
 324                         deg_sum+=cit->rest.ldegree(s) * ex_to_numeric(cit->coeff).to_int();
 325         }
 326         return deg_sum;
 327 }
 328
 329 ex mul::coeff(const symbol & s, int n) const
 330 {
 331         exvector coeffseq;
 332         coeffseq.reserve(seq.size()+1);
 333
 334         if (n==0) {
 335                 // product of individual coeffs
 336                 // if a non-zero power of s is found, the resulting product will be 0
 337                 epvector::const_iterator it=seq.begin();
 338                 while (it!=seq.end()) {
 339                         coeffseq.push_back(recombine_pair_to_ex(*it).coeff(s,n));
 340                         ++it;
 341                 }
 342                 coeffseq.push_back(overall_coeff);
 343                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 344         }
 345
 346         epvector::const_iterator it=seq.begin();
 347         bool coeff_found=0;
 348         while (it!=seq.end()) {
 349                 ex t=recombine_pair_to_ex(*it);
 350                 ex c=t.coeff(s,n);
 351                 if (!c.is_zero()) {
 352                         coeffseq.push_back(c);
 353                         coeff_found=1;
 354                 } else {
 355                         coeffseq.push_back(t);
 356                 }
 357                 ++it;
 358         }
 359         if (coeff_found) {
 360                 coeffseq.push_back(overall_coeff);
 361                 return (new mul(coeffseq))->setflag(status_flags::dynallocated);
 362         }
 363
 364         return _ex0();
 365 }
 366
 367 ex mul::eval(int level) const
 368 {
 369         // simplifications  *(...,x;0) -> 0
 370         //                  *(+(x,y,...);c) -> *(+(*(x,c),*(y,c),...)) (c numeric())
 371         //                  *(x;1) -> x
 372         //                  *(;c) -> c
 373
 374         debugmsg("mul eval",LOGLEVEL_MEMBER_FUNCTION);
 375
 376         epvector * evaled_seqp=evalchildren(level);
 377         if (evaled_seqp!=0) {
 378                 // do more evaluation later
 379                 return (new mul(evaled_seqp,overall_coeff))->
 380                                    setflag(status_flags::dynallocated);
 381         }
 382
 383 #ifdef DO_GINAC_ASSERT
 384         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 385                 GINAC_ASSERT((!is_ex_exactly_of_type((*cit).rest,mul))||
 386                            (!(ex_to_numeric((*cit).coeff).is_integer())));
 387                 GINAC_ASSERT(!((*cit).is_numeric_with_coeff_1()));
 388                 if (is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric)) {
 389                         printtree(cerr,0);
 390                 }
 391                 GINAC_ASSERT(!is_ex_exactly_of_type(recombine_pair_to_ex(*cit),numeric));
 392                 /* for paranoia */
 393                 expair p=split_ex_to_pair(recombine_pair_to_ex(*cit));
 394                 GINAC_ASSERT(p.rest.is_equal((*cit).rest));
 395                 GINAC_ASSERT(p.coeff.is_equal((*cit).coeff));
 396                 /* end paranoia */
 397         }
 398 #endif // def DO_GINAC_ASSERT
 399
 400         if (flags & status_flags::evaluated) {
 401                 GINAC_ASSERT(seq.size()>0);
 402                 GINAC_ASSERT((seq.size()>1)||!overall_coeff.is_equal(_ex1()));
 403                 return *this;
 404         }
 405
 406         int seq_size=seq.size();
 407         if (overall_coeff.is_equal(_ex0())) {
 408                 // *(...,x;0) -> 0
 409                 return _ex0();
 410         } else if (seq_size==0) {
 411                 // *(;c) -> c
 412                 return overall_coeff;
 413         } else if ((seq_size==1)&&overall_coeff.is_equal(_ex1())) {
 414                 // *(x;1) -> x
 415                 return recombine_pair_to_ex(*(seq.begin()));
 416         } else if ((seq_size==1) &&
 417                    is_ex_exactly_of_type((*seq.begin()).rest,add) &&
 418                    ex_to_numeric((*seq.begin()).coeff).is_equal(_num1())) {
 419                 // *(+(x,y,...);c) -> +(*(x,c),*(y,c),...) (c numeric(), no powers of +())
 420                 const add & addref=ex_to_add((*seq.begin()).rest);
 421                 epvector distrseq;
 422                 distrseq.reserve(addref.seq.size());
 423                 for (epvector::const_iterator cit=addref.seq.begin(); cit!=addref.seq.end(); ++cit) {
 424                         distrseq.push_back(addref.combine_pair_with_coeff_to_pair(*cit, overall_coeff));
 425                 }
 426                 return (new add(distrseq,
 427                                 ex_to_numeric(addref.overall_coeff).
 428                                 mul_dyn(ex_to_numeric(overall_coeff))))
 429                       ->setflag(status_flags::dynallocated | 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 addseq;
 479         addseq.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 mulseq = seq;
 484                 mulseq[i] = split_ex_to_pair(power(seq[i].rest,seq[i].coeff - _ex1()) *
 485                                              seq[i].rest.diff(s));
 486                 addseq.push_back((new mul(mulseq,overall_coeff*seq[i].coeff))->setflag(status_flags::dynallocated));
 487         }
 488         return (new add(addseq))->setflag(status_flags::dynallocated);
 489 }
 490
 491 int mul::compare_same_type(const basic & other) const
 492 {
 493         return inherited::compare_same_type(other);
 494 }
 495
 496 bool mul::is_equal_same_type(const basic & other) const
 497 {
 498         return inherited::is_equal_same_type(other);
 499 }
 500
 501 unsigned mul::return_type(void) const
 502 {
 503         if (seq.size()==0) {
 504                 // mul without factors: should not happen, but commutes
 505                 return return_types::commutative;
 506         }
 507
 508         bool all_commutative = 1;
 509         unsigned rt;
 510         epvector::const_iterator cit_noncommutative_element; // point to first found nc element
 511
 512         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 513                 rt=(*cit).rest.return_type();
 514                 if (rt==return_types::noncommutative_composite) return rt; // one ncc -> mul also ncc
 515                 if ((rt==return_types::noncommutative)&&(all_commutative)) {
 516                         // first nc element found, remember position
 517                         cit_noncommutative_element = cit;
 518                         all_commutative = 0;
 519                 }
 520                 if ((rt==return_types::noncommutative)&&(!all_commutative)) {
 521                         // another nc element found, compare type_infos
 522                         if ((*cit_noncommutative_element).rest.return_type_tinfo()!=(*cit).rest.return_type_tinfo()) {
 523                                 // diffent types -> mul is ncc
 524                                 return return_types::noncommutative_composite;
 525                         }
 526                 }
 527         }
 528         // all factors checked
 529         return all_commutative ? return_types::commutative : return_types::noncommutative;
 530 }
 531
 532 unsigned mul::return_type_tinfo(void) const
 533 {
 534         if (seq.size()==0) {
 535                 // mul without factors: should not happen
 536                 return tinfo_key;
 537         }
 538         // return type_info of first noncommutative element
 539         for (epvector::const_iterator cit=seq.begin(); cit!=seq.end(); ++cit) {
 540                 if ((*cit).rest.return_type()==return_types::noncommutative) {
 541                         return (*cit).rest.return_type_tinfo();
 542                 }
 543         }
 544         // no noncommutative element found, should not happen
 545         return tinfo_key;
 546 }
 547
 548 ex mul::thisexpairseq(const epvector & v, const ex & oc) const
 549 {
 550         return (new mul(v,oc))->setflag(status_flags::dynallocated);
 551 }
 552
 553 ex mul::thisexpairseq(epvector * vp, const ex & oc) const
 554 {
 555         return (new mul(vp,oc))->setflag(status_flags::dynallocated);
 556 }
 557
 558 expair mul::split_ex_to_pair(const ex & e) const
 559 {
 560         if (is_ex_exactly_of_type(e,power)) {
 561                 const power & powerref=ex_to_power(e);
 562                 if (is_ex_exactly_of_type(powerref.exponent,numeric)) {
 563                         return expair(powerref.basis,powerref.exponent);
 564                 }
 565         }
 566         return expair(e,_ex1());
 567 }
 568
 569 expair mul::combine_ex_with_coeff_to_pair(const ex & e,
 570                                           const ex & c) const
 571 {
 572         // to avoid duplication of power simplification rules,
 573         // we create a temporary power object
 574         // otherwise it would be hard to correctly simplify
 575         // expression like (4^(1/3))^(3/2)
 576         if (are_ex_trivially_equal(c,_ex1()))
 577                 return split_ex_to_pair(e);
 578
 579         return split_ex_to_pair(power(e,c));
 580 }
 581
 582 expair mul::combine_pair_with_coeff_to_pair(const expair & p,
 583                                             const ex & c) const
 584 {
 585         // to avoid duplication of power simplification rules,
 586         // we create a temporary power object
 587         // otherwise it would be hard to correctly simplify
 588         // expression like (4^(1/3))^(3/2)
 589         if (are_ex_trivially_equal(c,_ex1()))
 590                 return p;
 591
 592         return split_ex_to_pair(power(recombine_pair_to_ex(p),c));
 593 }
 594
 595 ex mul::recombine_pair_to_ex(const expair & p) const
 596 {
 597         if (ex_to_numeric(p.coeff).is_equal(_num1()))
 598                 return p.rest;
 599         else
 600                 return power(p.rest,p.coeff);
 601 }
 602
 603 bool mul::expair_needs_further_processing(epp it)
 604 {
 605         if (is_ex_exactly_of_type((*it).rest,mul) &&
 606                 ex_to_numeric((*it).coeff).is_integer()) {
 607                 // combined pair is product with integer power -> expand it
 608                 *it=split_ex_to_pair(recombine_pair_to_ex(*it));
 609                 return true;
 610         }
 611         if (is_ex_exactly_of_type((*it).rest,numeric)) {
 612                 expair ep=split_ex_to_pair(recombine_pair_to_ex(*it));
 613                 if (!ep.is_equal(*it)) {
 614                         // combined pair is a numeric power which can be simplified
 615                         *it=ep;
 616                         return true;
 617                 }
 618                 if (ex_to_numeric((*it).coeff).is_equal(_num1())) {
 619                         // combined pair has coeff 1 and must be moved to the end
 620                         return true;
 621                 }
 622         }
 623         return false;
 624 }
 625
 626 ex mul::default_overall_coeff(void) const
 627 {
 628         return _ex1();
 629 }
 630
 631 void mul::combine_overall_coeff(const ex & c)
 632 {
 633         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 634         GINAC_ASSERT(is_ex_exactly_of_type(c,numeric));
 635         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c));
 636 }
 637
 638 void mul::combine_overall_coeff(const ex & c1, const ex & c2)
 639 {
 640         GINAC_ASSERT(is_ex_exactly_of_type(overall_coeff,numeric));
 641         GINAC_ASSERT(is_ex_exactly_of_type(c1,numeric));
 642         GINAC_ASSERT(is_ex_exactly_of_type(c2,numeric));
 643         overall_coeff = ex_to_numeric(overall_coeff).mul_dyn(ex_to_numeric(c1).power(ex_to_numeric(c2)));
 644 }
 645
 646 bool mul::can_make_flat(const expair & p) const
 647 {
 648         GINAC_ASSERT(is_ex_exactly_of_type(p.coeff,numeric));
 649         // this assertion will probably fail somewhere
 650         // it would require a more careful make_flat, obeying the power laws
 651         // probably should return true only if p.coeff is integer
 652         return ex_to_numeric(p.coeff).is_equal(_num1());
 653 }
 654
 655 ex mul::expand(unsigned options) const
 656 {
 657         if (flags & status_flags::expanded)
 658                 return *this;
 659
 660         exvector sub_expanded_seq;
 661         intvector positions_of_adds;
 662
 663         epvector * expanded_seqp = expandchildren(options);
 664
 665         const epvector & expanded_seq = expanded_seqp==0 ? seq : *expanded_seqp;
 666
 667         int number_of_adds = 0;
 668         epvector non_adds;
 669         non_adds.reserve(expanded_seq.size());
 670         epvector::const_iterator cit = expanded_seq.begin();
 671         epvector::const_iterator last = expanded_seq.end();
 672         ex last_expanded=_ex1();
 673         while (cit!=last) {
 674                 if (is_ex_exactly_of_type((*cit).rest,add) &&
 675                         ((*cit).coeff.is_equal(_ex1()))) {
 676                         ++number_of_adds;
 677                         if (is_ex_exactly_of_type(last_expanded,add)) {
 678                                 // expand adds
 679                                 const add & add1 = ex_to_add(last_expanded);
 680                                 const add & add2 = ex_to_add((*cit).rest);
 681                                 int n1 = add1.nops();
 682                                 int n2 = add2.nops();
 683                                 exvector distrseq;
 684                                 distrseq.reserve(n1*n2);
 685                                 for (int i1=0; i1<n1; ++i1) {
 686                                         for (int i2=0; i2<n2; ++i2) {
 687                                                 distrseq.push_back(add1.op(i1)*add2.op(i2));
 688                                         }
 689                                 }
 690                                 last_expanded = (new add(distrseq))->setflag(status_flags::dynallocated | status_flags::expanded);
 691                         } else {
 692                                 non_adds.push_back(split_ex_to_pair(last_expanded));
 693                                 last_expanded = (*cit).rest;
 694                         }
 695                 } else {
 696                         non_adds.push_back(*cit);
 697                 }
 698                 ++cit;
 699         }
 700
 701         if (is_ex_exactly_of_type(last_expanded,add)) {
 702                 add const & finaladd = ex_to_add(last_expanded);
 703                 exvector distrseq;
 704                 int n = finaladd.nops();
 705                 distrseq.reserve(n);
 706                 for (int i=0; i<n; ++i) {
 707                         epvector factors = non_adds;
 708                         factors.push_back(split_ex_to_pair(finaladd.op(i)));
 709                         distrseq.push_back((new mul(factors,overall_coeff))->setflag(status_flags::dynallocated | status_flags::expanded));
 710                 }
 711                 return ((new add(distrseq))->
 712                         setflag(status_flags::dynallocated | status_flags::expanded));
 713         }
 714         non_adds.push_back(split_ex_to_pair(last_expanded));
 715         return (new mul(non_adds,overall_coeff))->
 716                 setflag(status_flags::dynallocated | status_flags::expanded);
 717 }
 718
 719
 720 //////////
 721 // new virtual functions which can be overridden by derived classes
 722 //////////
 723
 724 // none
 725
 726 //////////
 727 // non-virtual functions in this class
 728 //////////
 729
 730 epvector * mul::expandchildren(unsigned options) const
 731 {
 732         epvector::const_iterator last = seq.end();
 733         epvector::const_iterator cit = seq.begin();
 734         while (cit!=last) {
 735                 const ex & factor = recombine_pair_to_ex(*cit);
 736                 const ex & expanded_factor = factor.expand(options);
 737                 if (!are_ex_trivially_equal(factor,expanded_factor)) {
 738
 739                         // something changed, copy seq, eval and return it
 740                         epvector *s=new epvector;
 741                         s->reserve(seq.size());
 742
 743                         // copy parts of seq which are known not to have changed
 744                         epvector::const_iterator cit2 = seq.begin();
 745                         while (cit2!=cit) {
 746                                 s->push_back(*cit2);
 747                                 ++cit2;
 748                         }
 749                         // copy first changed element
 750                         s->push_back(split_ex_to_pair(expanded_factor));
 751                         ++cit2;
 752                         // copy rest
 753                         while (cit2!=last) {
 754                                 s->push_back(split_ex_to_pair(recombine_pair_to_ex(*cit2).expand(options)));
 755                                 ++cit2;
 756                         }
 757                         return s;
 758                 }
 759                 ++cit;
 760         }
 761
 762         return 0; // nothing has changed
 763 }
 764
 765 //////////
 766 // static member variables
 767 //////////
 768
 769 // protected
 770
 771 unsigned mul::precedence = 50;
 772
 773
 774 //////////
 775 // global constants
 776 //////////
 777
 778 const mul some_mul;
 779 const std::type_info & typeid_mul = typeid(some_mul);
 780
 781 #ifndef NO_NAMESPACE_GINAC
 782 } // namespace GiNaC
 783 #endif // ndef NO_NAMESPACE_GINAC